Max-Planck-Institut für Metallforschung Stuttgart Experimental and Computational Phase Studies of the ZrO2-based Systems for Thermal Barrier Coatings Chong Wang Dissertation an der Universität Stuttgart Bericht Nr. 189 September 2006 Experimental and Computational Phase Studies of the ZrO2- based Systems for Thermal Barrier Coatings Dissertation Von der Fakultät Chemie der Universität Stuttgart zur Erlangung der Würde eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Abhandlung Vorgelegt von Chong Wang Aus Jingmen, Hubei, China Hauptberichter : Prof. Dr. rer. nat. Fritz Aldinger Mitberichter : Prof. Dr. rer. nat. Dr. hc. mult. Günter Petzow Mitpruefer und Prüfungsvorsitzender : Prof. Dr. Eric. J. Mittemeijer Tag der mündlichen Prüfung : 19.09.2006 Institut für Nichtmetallische Anorganische Materialien der Universität Stuttgart Max-Planck-Institut für Metallforschung, Stuttgart Pulvermetallurgisches Laboratorium / Abteilung Aldinger Stuttgart 2006 -1- Acknowledgements I owe my current research to many contributors’ help and suggestion. Without their patience and intelligence, I undoubtedly cannot present this thesis. First of all, my sincere gratitude should go first and foremost to my supervisor, Prof. Dr. F. Aldinger, who has been giving me the most decisive and effective support and encouragement. His valuable instructions and constructive suggestions have always inspired me to carry on this study, so that I can finish my PhD thesis smoothly. He always brings people comfortable feeling during talking and discussion. I really learned a lot from him not only on the attitude of academic research, but also on the art of making good relationship with people. Deeply sincere gratitude is also delivered to my good group leader, Dr. M. Zinkevich, who gave me great contribution on the research work from very beginning. Without his guidance on both experimental work and computations in my thesis, I could not grow into an experienced person in my research field. Importantly, I learned from him on how to independently organize my research work. The financial support from the program of international research collaboration between Europe Commission (GRD2-200-30211) and the National Science Foundation (DMR-0099695), and the Max-Planck-Society are greatly acknowledged. I am much obliged to Prof. Dr. G. Petzow and Prof. Dr. E. J. Mittemeijer for agreeing to be the co-examiners of my PhD examination. My endless thanks would be presented to all those individuals who have assisted in the development of my present research. Among them special thanks go to Prof. Zhanpeng Jin in Central South University who is and will still be the most important person in my academic career. His active spirits in both life and scientific research always promote me to go ahead. All of his students make up of a large family, in which we always help each other without any hesitation. Especially, I am very grateful to Prof. Yong Du for his recommendation for my PhD position, and his diligence is really impressive to me. At the same time, I would like to acknowledge Dr. Xiaogang Lu for his help during my application of this position. It is my great pleasure to have extensive discussions with Dr. O. Fabrichnaya, and really benefit much and appreciate for her help on my work. Dr. B. Wu makes the opportunity for us to talk thermodynamics in Chinese, and I am happy to learn the knowledge of ab initio calculation from him. The other students in our group: N. Solak, V. Manga Rao, S. Geupel, M. Cancarevic and D. Djurovic also gave me much help, and made lots of discussions with me. -2- I would like to extend my great appreciation to Prof C. G. Levi who helped me much and gave me suggestion on the work of my thesis in University of California at Santa Barbara from Jan. to Mar. in 2004. It was also my pleasure to get known his postdocs and PhD students N. R. Rebollo Franco, A. S. Gandhi, R. Leckie et al. I thank them for their great help. Ms. Klink and Ms. Paulsen are appreciated for their great help on both my life and study since I was in Stuttgart. I thank those technicians for their important technical assistance on my experiments: Mr. Labizke and Ms. Predel for SEM, Ms. Haug for EPMA, Ms. Thomas for XRD, Ms. Shafer for ceramography, Mr. Kumer for DTA, Mr. Mager, Mr. Kaiser, Mr. Meyer, Mr. Werner for ICP−OES analysis, Mr. Schweizer, Ms. Hofer for Pt crucible and many other people who are not mentioned here. Dr. F. M. Morales in Prof. M. Ruhle department is also appreciated for his TEM analysis. Thank Dr. N. Dupin for sending her thesis so that I could write program to solve the equations for order-disorder modeling. I enjoyed my office time with Shijun Jia, Ravi Kumar, S. H. Lee, Y. Qiu and S. F. Du in past several years. Furthermore, I owe much gratitude to some Chinese who brought me much happiness in Stuttgart: Longjie Zhou and his wife, Hong Peng and her husband, Jianyun Shuai, Pengxiang Qian, Youping Huang, Hanlin Li, and some other Chinese who played table tennis with me. The memory from those people will stay forever in my life. I am also pleased to know Prof. Hui Gu and Prof. Wenqing Zhang in Shanghai Ceramic Institute, and grateful to them for interesting discussions and nice care when I was in Shanghai. A special word of gratitude also should be said to aunt Deng and uncle Wang who have been taking care of me since I was in Changsha. Last but not the least, my parents, my sister and her boyfriend always gave me great encouragement and understanding in past years. I would like to dedicate this thesis to my family and share my happiness with them at this moment. Chong Wang, June-2006, Stuttgart -I- Table of Contents Acknowledgements ---------------------------------------------------------------------------------------1 Abstract -----------------------------------------------------------------------------------------------------1 1. Introduction ---------------------------------------------------------------------------------------------4 1.1. TBC for high temperature gas turbine engines--------------------------------------------------4 1.2. Phase transformations in ZrO2-based systems and their implications on TBC -------------5 1.2.1. Phase transformation phenomena in doped zirconia ---------------------------------------5 1.2.2. Implications on TBC ---------------------------------------------------------------------------7 1.3. Scope of the present work -------------------------------------------------------------------------7 2. Experimental procedures and thermodynamic modeling -------------------------------------9 2.1. Sample preparation ---------------------------------------------------------------------------------9 2.2. Sample treatment and characterization-----------------------------------------------------------9 2.3. Thermodynamic modelling of phases ---------------------------------------------------------- 10 2.3.1. Introduction ----------------------------------------------------------------------------------- 10 2.3.1.1. The CALPHAD approach -------------------------------------------------------------- 10 2.3.1.2. Pure elements----------------------------------------------------------------------------- 12 2.3.1.3. Thermodynamic models for the solution phases ------------------------------------- 12 2.3.2. Pure components ----------------------------------------------------------------------------- 17 2.3.3. The gas phase -------------------------------------------------------------------------------- 17 2.3.4. The liquid phase ----------------------------------------------------------------------------- 17 2.3.4.1. The Hf − Zr − O system ---------------------------------------------------------------- 17 2.3.4.2. The ZrO2 − REO1.5 systems------------------------------------------------------------- 17 2.3.5. The bcc and hcp phase ----------------------------------------------------------------------- 18 2.3.6. The ZrO2 (HfO2)-based solid solution phases -------------------------------------------- 19 2.3.6.1. The Hf − Zr − O system ---------------------------------------------------------------- 19 2.3.6.2. The ZrO2 − REO1.5 systems------------------------------------------------------------- 20 2.3.7. The RE2O3-based phases -------------------------------------------------------------------- 21 2.3.8. The pyrochlore phase------------------------------------------------------------------------ 23 2.3.8.1. The model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1 ------------------- 25 2.3.8.2. The splitting model (Zr+4,RE+3)2(RE+3,Zr+4)2(O-2,Va)8 ----------------------------- 30 2.3.9. The RE4Zr3O12 (δ) phase -------------------------------------------------------------------- 32 -II- 3. Experimental study and thermodynamic modeling of the Zr − O, Hf − O and ZrO2 − HfO2 systems------------------------------------------------------------------------------------------- 35 3.1. Literature review ---------------------------------------------------------------------------------- 35 3.1.1. The Zr − O system---------------------------------------------------------------------------- 35 3.1.2. The Hf − O system --------------------------------------------------------------------------- 38 3.1.3. The ZrO2 − HfO2 system -------------------------------------------------------------------- 40 3.2. Experimental results and discussion------------------------------------------------------------ 41 3.3. Thermodynamic assessments and calculations------------------------------------------------ 44 3.3.1. Pure zirconia ---------------------------------------------------------------------------------- 44 3.3.2. The Zr − O system---------------------------------------------------------------------------- 46 3.3.3. Pure hafnia ------------------------------------------------------------------------------------ 50 3.3.4. The Hf − O system --------------------------------------------------------------------------- 52 3.3.5. The ZrO2 − HfO2 system -------------------------------------------------------------------- 55 4. Experimental study and thermodynamic modeling of the ZrO2 − LaO1.5 system------- 62 4.1. Literature review ---------------------------------------------------------------------------------- 62 4.1.1. Phase equilibria ------------------------------------------------------------------------------- 62 4.1.2. Thermodynamic data------------------------------------------------------------------------- 64 4.2. Experimental results and discussion------------------------------------------------------------ 65 4.3. Selected experimental data for optimization -------------------------------------------------- 66 4.3.1. Phase diagram data --------------------------------------------------------------------------- 66 4.3.2. Thermodynamic data------------------------------------------------------------------------- 67 4.4. Optimization procedure -------------------------------------------------------------------------- 67 4.5. Calculated results and discussion --------------------------------------------------------------- 68 5. Experimental study and thermodynamic modeling of the ZrO2 − NdO1.5 system ------ 73 5.1. Literature review ---------------------------------------------------------------------------------- 73 5.1.1. Phase equilibria ------------------------------------------------------------------------------- 73 5.1.2. Thermodynamic data------------------------------------------------------------------------- 74 5.2. Experimental results and discussion------------------------------------------------------------ 75 5.2.1. The as-pyrolysed state ----------------------------------------------------------------------- 75 5.2.2. The tetragonal + fluorite phase equilibrium----------------------------------------------- 76 5.2.3. The fluorite + pyrochlore phase equilibrium---------------------------------------------- 76 5.2.4. The fluorite + A-Nd2O3 and pyrochlore + A-Nd2O3 phase equilibria ----------------- 78 -III- 5.3. Selected experimental data for optimization -------------------------------------------------- 79 5.4. Optimization procedure -------------------------------------------------------------------------- 79 5.5. Calculated results and discussion --------------------------------------------------------------- 79 6. Experimental study and thermodynamic modeling of the ZrO2 − SmO1.5 system ------ 84 6.1. Literature review ---------------------------------------------------------------------------------- 84 6.1.1. Phase equilibria ------------------------------------------------------------------------------- 84 6.1.2. Thermodynamic data------------------------------------------------------------------------- 85 6.2. Experimental results and discussion------------------------------------------------------------ 85 6.2.1. The as-pyrolysed state ----------------------------------------------------------------------- 85 6.2.2. The tetragonal + fluorite phase equilibrium----------------------------------------------- 86 6.2.3. The fluorite + pyrochlore phase equilibrium---------------------------------------------- 86 6.2.4. The fluorite + B-Sm2O3 phase equilibrium ----------------------------------------------- 88 6.3. Selected experimental data for optimization ------------------------------------------------ 89 6.4. Optimization procedure ------------------------------------------------------------------------ 89 6.5. Calculated results and discussion------------------------------------------------------------- 90 7. Experimental study and thermodynamic modeling of the ZrO2 − GdO1.5 system ------ 94 7.1. Literature review ---------------------------------------------------------------------------------- 94 7.1.1. Phase equilibria ------------------------------------------------------------------------------- 94 7.1.2. Thermodynamic data------------------------------------------------------------------------- 96 7.2. Experimental results and discussion------------------------------------------------------------ 96 7.2.1. The as-pyrolysed state ----------------------------------------------------------------------- 96 7.2.2. The fluorite / pyrochlore phase transition ------------------------------------------------- 96 7.2.3. The fluorite + C-Gd2O3 and C-Gd2O3 + B-Gd2O3 phase equilibria-------------------102 7.2.4. The martensitic transformation temperatures of the tetragonal phase ----------------103 7.3. Selected experimental data for optimization -------------------------------------------------103 7.3.1. Phase diagram data --------------------------------------------------------------------------103 7.3.2. Thermodynamic data------------------------------------------------------------------------104 7.4. Optimization procedure -------------------------------------------------------------------------104 7.5. Calculated results and discussion --------------------------------------------------------------104 7.5.1. The phase diagram without pyrochlore ordering ----------------------------------------104 7.5.2. Calculated results by the pyrochlore model (Zr+4,Gd+3)2(Gd+3,Zr+4)2(O-2,Va)6(O-2)1 (Va,O-2)1 ---------------------------------------------------------------------------------------106 -IV- 7.5.3. Calculated results by the pyrochlore model (Zr+4,Gd+3)2(Gd+3,Zr+4)2(O-2,Va)8 -----107 7.5.4. Thermodynamic properties-----------------------------------------------------------------110 8. Experimental study and thermodynamic modeling of the ZrO2 − DyO1.5 system------114 8.1. Literature review ---------------------------------------------------------------------------------114 8.2. Experimental results and discussion-----------------------------------------------------------115 8.2.1. The as-pyrolysed state ----------------------------------------------------------------------115 8.2.2. The tetragonal + fluorite phase equilibrium----------------------------------------------115 8.2.3. The martensitic transformation temperatures of the tetragonal phase ----------------116 8.2.4. The fluorite + C-Dy2O3 phase equilibrium-----------------------------------------------117 8.3. Selected experimental data for optimization -------------------------------------------------118 8.4. Optimization procedure -------------------------------------------------------------------------118 8.5. Calculated results and discussion --------------------------------------------------------------118 9. Experimental study and thermodynamic modeling of the ZrO2 − YbO1.5 system -----123 9.1. Literature review ---------------------------------------------------------------------------------123 9.2. Experimental results and discussion-----------------------------------------------------------124 9.2.1. The as-pyrolysed state ----------------------------------------------------------------------124 9.2.2. The tetragonal + fluorite phase equilibrium----------------------------------------------125 9.2.3. The phase equilibria involving δ and C-Yb2O3------------------------------------------126 9.3. Selected experimental data for optimization -------------------------------------------------127 9.4. Optimization procedure -------------------------------------------------------------------------128 9.5. Calculated results and discussion --------------------------------------------------------------128 10. Experimental study and calculation of the ZrO2 − GdO1.5 − YO1.5 system ------------133 10.1. Calculations and experimental results -------------------------------------------------------133 10.2. Discussion ---------------------------------------------------------------------------------------135 11. Characteristic changes in the ZrO2 − REO1.5 systems--------------------------------------136 11.1. The evolutions of the phase relations in the ZrO2 − REO1.5 systems --------------------136 11.2. The evolutions of the thermodynamic properties in the ZrO2 − REO1.5 systems-------139 11.3. The mechanism of the pyrochlore ordering -------------------------------------------------141 Zusammenfassung -------------------------------------------------------------------------------------144 -V- Appendix: The thermodynamic parameters obtained in this work--------------------------147 References -----------------------------------------------------------------------------------------------154 Curriculum Vitae --------------------------------------------------------------------------------------170 List of symbols and abbreviations: TBC: Thermal Barrier Coatings XRD: X-ray diffraction HTXRD: high-temperature X-ray diffraction SEM: Scanning electron microscopy EDX: Energy dispersive X-ray TEM: Transmission electron microscopy DTA: Differential thermal analysis DSC: Differential scanning calorimetry ND: Neutron diffraction RS: Raman scattering M: Monoclinic T: Tetragonal F: Fluorite A: A-type RE2O3 B: B-type RE2O3 C: C-type RE2O3 H: H-type RE2O3 X: X-type RE2O3 L: Liquid P: Pyrochlore δ: RE4Zr3O12 -1- Abstract The ZrO2-based materials are practically important as the thermal barrier coatings (TBC) for high temperature gas turbines, due to their low thermal conductivity, high temperature thermal stability and excellent interfacial compatibility. Studies of the phase equilibira, phase transformation, and thermodynamics of the ZrO2-based systems can provide the necessary basic knowledge to develop the next generation TBC materials. In the thesis, the systems ZrO2 − HfO2, ZrO2 − LaO1.5, ZrO2 − NdO1.5, ZrO2 − SmO1.5, ZrO2 − GdO1.5, ZrO2 − DyO1.5, ZrO2 − YbO1.5 and ZrO2 − GdO1.5 − YO1.5 were experimentally studied. The samples were prepared by the chemical co-precipitation method, with aqueous solutions Zr(CH3COO)4, HfO(NO3)2, and RE(NO3)3⋅xH2O (RE=La, Nd, Sm, Gd, Dy, Yb) as starting materials. Various experimental techniques, X-ray diffraction (XRD), scanning electron microscopy (SEM), electron probe microanalysis (EPMA), transmission electron microscopy (TEM), differential thermal analysis (DTA), and high temperature calorimetry were employed to study the phase transformation, phase equilibria between 1400 and 1700°C, heat content and heat capacity of the materials. A lot of contradictions in the literature were resolved and the phase diagrams were reconstructed. Firstly, the thermodynamic transformation temperatures (T0, where the Gibbs energies of monoclinic and tetragonal phases are identical) were reviewed and extrapolated for pure ZrO2 (1367 ± 5 K) and HfO2 (2052 ± 5 K) from the DTA study of ZrO2 − HfO2 system. The temperatures (As, Af, Ms, Mf) on the martensitic transformation of the materials in ZrO2 − HfO2 system directly obtained by DTA measurements show well consistent behavior together with the calculated T0 temperatures. Based on the present DTA results and literature information on transformation temperatures of monoclinic ↔ tetragonal, tetragonal ↔ cubic and cubic ↔ liquid, as well as the thermodynamics of different structures, the thermodynamic parameters of the pure ZrO2 and HfO2 were assessed, and the ZrO2 − HfO2 phase diagram was calculated without any fitting parameter. Within the scope of the thesis, the tetragonal + fluorite (or the tetragonal + pyrochlore for RE=La) two-phase region, the phase equilibria between disordered fluorite and ordered pyrochlore (or the δ phase for RE=Yb), and the phase equilibria between fluorite and REO1.5 terminal solutions were well established for ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb) systems, and the enthalpy increments of the materials with 30 mol% REO1.5, and 50 mol% REO1.5 (57.14 mol% for RE=Yb) were determined in the temperature range 200-1400°C. -2- Furthermore, the isothermal sections of ZrO2 − GdO1.5 − YO1.5 system at 1200-1600°C were experimentally investigated by XRD measurements. Based on the experimental data obtained in this work and literature, the systems Zr − O, Hf − O, ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb) were thermodynamically optimized using the CALPHAD (CALculation of PHase Diagram) approach. Most of the experimental data were well reproduced, and the self-consistent thermodynamic parameters were derived for all the systems. Since the experimental isothermal sections on the ZrO2 − GdO1.5 − YO1.5 system could be reproduced well only by the extrapolation from binary systems, no any further optimization was done. Finally, based on the present experiments and calculations, some clear characteristic evolutions with the change of the ionic radius of doping element RE+3 can be concluded and applied also for those ZrO2 − REO1.5 systems which are not studied in this work: 1). The solubility of REO1.5 in the tetragonal phase increases almost linearly with decreasing the radius of RE+3. At the same time, the homogeneity range of fluorite phase enlarges towards ZrO2. Those changes result in a narrower tetragonal + fluorite two-phase region for the ZrO2 − REO1.5 system with smaller RE+3. 2). It is confirmed that the pyrochlore structure is only stable when the ionic radius of RE+3 is larger than that of Dy+3. The homogeneity range of the pyrochlore phase gradually increases from RE=La to Gd, while the fluorite ⇔ pyrochlore transformation temperature decreases. There is no any detectable ordered compound in the system ZrO2 − DyO1.5. For the ZrO2 − YbO1.5 system, the ordered structure of fluorite is δ (RE4Zr3O12) phase. It is reasonable to deduce that the δ phase is only stable when the ionic radius of RE+3 is smaller than that of Dy+3, and the δ ⇔ fluorite transformation temperature increases with reducing the ionic radius of RE+3. 3). The enthalpy of formation of the fluorite phase has more negative value for the system with smaller RE+3, while that of the ordered pyrochlore phase presents the opposite tendency. Those evolutions result in the smaller energetic differences between fluorite and pyrochlore for the system with smaller RE+3, and thus the narrower fluorite + pyrochlore two- phase region. 4). The complete ordering of the pyrochlore phase with ZrO2 excess may take very long time, especially for the systems with smaller RE+3, while the ordering of pyrochlore with REO1.5 excess is much more easily approached, because less oxygen atoms take part in the -3- process. The XRD results show that the samples in ZrO2-rich region of the ZrO2 − NdO1.5 system distinctly separate into fluorite + pyrochlore two-phase structure after the heat treatment of 1700°C for 36h, while samples heat treated at lower temperatures do not. No any separation of the XRD peaks of fluorite and pyrochlore was found for the samples with ZrO2 excess in the ZrO2 − SmO1.5 and ZrO2 − GdO1.5 systems. Those observations reveal that the fluorite ⇔ pyrochlore phase transformation in materials with ZrO2 excess is a long kinetic process, and may be initially of second-order, and then of first order only when a critical configurational state of the ordered structure is reached to offer enough driving force for the long distance diffusion. -4- Chapter 1 Introduction 1.1. TBC for high temperature gas turbine engines Nowadays, the development of the novel Thermal Barrier Coatings (TBC) for the new generation high temperature gas turbine engines is increasingly promoted. The crucial ZrO2- based TBC or ‘‘top coat’’ plays an important role for improving the performance and lifetime of gas turbine engines, by creating a large temperature gradient (100-300°C) from the surface of the layer of the TBC to the coated alloy components. Such benefit allows increasing the hot gas temperature around the engines, and improving the efficiency, without change of the Ni- based superalloy components. On the one hand, modern turbine engines can be operated at temperatures above the melting point (~1300°C) of the superalloys with the protection of the TBC. On the other hand, TBC can lower the temperature on the superalloy surface, to improve the durability and performance of the engines [2002Pad]. A thermal barrier system generally consists of four different layers as shown in Fig. 1- 1. The TBC is the top layer of the system, and directly contacts with the high temperature hot gas stream. The most widely adopted material for TBC is the yttria-stabilized zirconia (YSZ, ~8 mol % YO1.5), which is manufactured by air-plasma spraying (APS) or electron-beam physical vapour deposition (EB-PVD) technology. To prevent the oxidation of the alloy components, a thin layer of dense thermally grown oxide (TGO) is very critical between TBC and alloys. Generally, the main component of the TGO is Al2O3. To produce this TGO and modify the surface between TBC and the superalloy, a ‘‘bond coat’’ is essential for the thermal barrier system. The single β-(Ni, Pt)Al (B2) phase and overlay two phase (γ’ + β/γ) MCrAlY alloys are the two groups of bond coat materials which are practically used [2004Lev]. The superalloy is generally the Ni-based alloy. Worldwide, a lot of efforts have been put into the development of alternative ceramics for TBC other than state-of-the-art YSZ (yttria-stabilized zirconia), aiming to lower thermal conductivity and/or to improve high temperature performance and durability [2004Lev], so that larger temperature gradients can be established through the TBC without excessive augmentation of its thickness. Co-doping of YSZ by rare earths such as Gd is of interest in thermal barrier systems because of concomitant benefits to the thermal insulating efficiency [2002Nic, 2003Zhu]. Some rare earth zirconates have been proposed to reduce the thermal conductivity of TBC by as much as 30% of current levels without the change of the thermal stability [2000Vas, 2002Wu]. At the same time, the TBC/Al2O3 (TGO) interface can maintain -5- good thermochemical compatibility and stability at high temperatures without losing the reliability of TBC. Especially, the pyrochlore phases in some ZrO2-based systems containing rare earth oxides are paid much more attention in recent years because they combine lower thermal conductivity with enhanced microstructural stability upon high temperature exposure [2001Mal, 2002Wu, 2004Lev, 2005Lec]. Figure 1-1. The schematic of the thermal barrier system (with the permission from C. G. Levi at University of California, Santa Barbara). 1.2. Phase transformations in ZrO2-based systems and their implications on TBC 1.2.1. Phase transformation phenomena in doped zirconia It is well known that the phase transformation behaviour in doped ZrO2 presents large complexity. There are three structural modifications for the pure ZrO2 at ambient pressure [1986Abr]: the cubic structure with the fluorite type ( mFm3 ) at high temperatures, the tetragonal structure (P42/nmc) at intermediate temperatures, and the monoclinic structure (P21/c) at low temperatures. Many experimental studies confirmed that the monoclinic ↔ tetragonal phase transformation is of displacive martensitic type [1974Sub]. The transformation between cubic and tetragonal phases may be not the regular first order transition [1991Hil]. The solubility of rare earths in the monoclinic ZrO2 phase is negligible, while the tetragonal phase can dissolve considerable amounts of rare earth elements depending on the radius of cations. The tetragonal ZrO2 phase cannot be stabilized to low temperature due to the diffusionless martensitic transformation. Since about 8% volume change is associated with this transformation, cracks can form at the grain boundaries, what is detrimental to the materials. -6- The tetragonal ↔ monoclinic athermal phase transformation occurs martensitically with a temperature hysteresis loop near 1373 K [1995And] for pure ZrO2. The hysteresis loop extends about 200 K for ZrO2. Generally, the transformation temperatures on heating and cooling are referred as As (starting) and Af (finishing), and as Ms (starting) and Mf (finishing). For thermodynamic studies, the transformation temperature T0 (where the Gibbs energies of monoclinic and tetragonal phases are identical) is undoubtedly important. Due to the experimental difficulty in the direct measurement of the T0 temperature, it is customary to calculate it empirically by the equation [1995Yas] 20 ss MAT += (1-1) or 20 ff MAT += (1-2) In the literature [1995Yas] it was already confirmed that the results obtained by these two equations are quite similar. However, mostly equation (1-1) is preferred, because As and Ms can be determined more precisely from the results of DTA or dilatometry methods than Af and Mf. The high temperature cubic fluorite-type structure can be stabilized to lower temperatures by doping with certain amounts of rare earth elements, so that the destructive tetragonal ↔ monoclinic transition can be avoided. Nevertheless, in some composition range, even the cubic phase is not quenchable due to a diffusionless transformation from cubic to another kind of tetragonal phase T′ [1992She, 1996Yas]. Such diffusionless transformation occurs near the stable cubic + tetragonal two-phase region, within a certain temperature hysteresis during heating and cooling as the martensitic tetragonal ↔ monoclinic transformation. Unlike the equilibrium tetragonal phase, the T′ phase is kinetically non- transformable into the equilibrium phase assemblage at low temperatures due to its smaller axis ratio c/a than that of equilibrium tetragonal phase, although it is thermodynamically metastable. Another tetragonal phase T′′ was also found as the transformation product of the cubic phase, where the axis ratio c/a is nearly 1 [1996Yas]. 1.2.2. Implications on TBC (1). Due to the destructive tetragonal-to-monoclinic phase transition, the composition of the TBC must satisfy the demand to avoid this transformation. The TBC are often partially -7- stabilized zirconia, i.e. the metastable supersaturated T′ phase, which is the most preferred TBC material of practical interest because of its higher cyclic lives [2004Lev]. However, it can transform into the stable tetragonal and fluorite phases during the long-term thermal cycling, and thus brings the risk of failure due to the destructive martensitic transformation. To select the composition and thermal cycling temperature range (operating temperature limits), it is very important to understand the equilibrium phase diagrams, so that the formation of stable tetragonal phase can be avoided, and the appropriate operating temperature limits can be determined to prevent the destructive transformation. In recent study it was found that the 8YSZ TBC partly transforms into stable tetragonal phase at 1425°C [2005Lug]. It is reasonable to believe that the upper temperature limits are different for the materials with different compositions or doping elements according to the phase diagrams of different systems. (2). A possible failure of thermal barrier system occurs at the TBC/TGO interface, if the TGO is not thermodynamically stable and reacts with TBC. As an example, the pyrochlore phases of some ZrO2 − RE2O3 (RE=Rare Earth Element) systems are very promising TBC materials for their lower thermal conductivity and high temperature stability, however, they react with Al2O3. The phase diagram calculations can give the answer if TBC reacts with TGO. Furthermore, the limits of doping and the temperature range in which TBC can stably coexist with TGO can be determined [2004Fab]. For example, compositions with more than ~32 mol % GdO1.5 are not thermochemically compatible with the underlying alumina layer in the coating system [2005Lec, 2006Lak] and tend to form interphases at high temperature, with significantly active kinetics at ~1100°C and above [2005Lec]. An approach to circumvent the problem is to add an interlayer of YSZ between Gd2Zr2O7 and the underlying alumina [2004Lev]. It is undoubted that precise phase diagrams and thermodynamic data are very helpful tools to study the interfacial stabilities in thermal barrier system. 1.3. Scope of the present work Basic system ZrO2 − YO1.5 − AlO1.5 was already assessed by O. Fabrichnaya [2004Fab]. In order to evaluate the full potential of ZrO2 − REO1.5 − AlO1.5 (RE=Rare earth elements) and ZrO2 − YO1.5 − REO1.5 − AlO1.5 systems, it is the object of this work to study phase equilibria, phase transformation, and thermodynamics of some zirconia-based systems. Although there are numerous literature works on zirconia, most of them are concentrated on the materials properties. Phase equilibria or phase transformation studies mainly concern the -8- ZrO2 − Y2O3, ZrO2 − CeO2, ZrO2 − CaO, and ZrO2 − MgO systems. As for the ZrO2 − RE2O3 systems except RE=Y, only very limited phase equilibria and thermodynamic investigations are available in literature, despite the importance of such systems. Additionally, the martensitic transformation temperatures are affected by many factors such as particle size, impurities, stress and thermal history of materials, the literature data present large discrepancies, and no quantitative analysis has been done yet on how these factors can affect the transformation temperatures. Therefore, some critical experiments had to be done in this work to offer reliable results for thermodynamic calculations. In summary, present work covers the following issues related to phase equilibria and thermodynamics of ZrO2-based thermal barrier coating systems: (1). Careful literature reviews on the phase transformation temperatures and thermodynamic properties of ZrO2 and HfO2, on the phase equilibria and thermodynamic information for the systems ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb). (2). Experimental investigations on the phase relations, phase transformation, and thermodynamic properties of the ZrO2 − HfO2, ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb) and ZrO2 − GdO1.5 − YO1.5 systems by means of XRD, SEM, EPMA, TEM, DTA, and high temperature calorimetry. (3). Assessment of the thermodynamic parameters of pure ZrO2 and HfO2, and self- consistent thermodynamic modelling and calculations on Zr − O, Hf − O, ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb), and ZrO2 − GdO1.5 − YO1.5 systems based on the experimental results obtained in this work and those reported in literature. -9- Chapter 2 Experimental procedures and thermodynamic modeling 2.1. Sample preparation The zirconium acetate solution, Zr(CH3COO)4 (99.99 %, Sigma-Aldrich), rare earth nitrate hydrate, RE(NO3)3⋅xH2O [Dy(NO3)3⋅5H2O: 99.99 %, Alfa Aesar; Gd(NO3)3⋅6H2O: 99.99 %, Strem Chemicals; La(NO3)3⋅6H2O: 99.99 %, Alfa Aesar; Nd(NO3)3⋅6H2O: 99.9 %, Alfa Aesar; Sm(NO3)3⋅6H2O: 99.99 %, Sigma-Aldrich; Y(NO3)3⋅6H2O: 99.9 %, Alfa Aesar; Yb(NO3)3⋅5H2O: 99.9 %, Sigma-Aldrich] and the hafnium dinitrate oxide, HfO(NO3)2 (99.9%, 10% W/V aqueous solution, Alfa Aesar) were adopted as the starting chemicals. The RE(NO3)3⋅xH2O was dissolved in the water as the first step. After the determination of the oxide yield of different solutions, they were mixed according to the given ratios. Thus obtained precursor solution was dropped from the buret at a low speed (around 1 ml⋅min-1) into a big beaker containing about 500 ml of deionized water, while maintaining the pH value above 9.0 by adding ammonium hydrate. The precipitation occurred during dropping and stirring. The precipitate was then filtered and dried at 75°C. Finally, the white powder was obtained after pyrolysis of the dried precipitate at 700°C for 3h or 1000°C for 1h in air. 2.2. Sample treatment and characterization The pyrolysed powder was isostatically pressed into cylindrical pellets and sintered in air at temperatures ranging from 1400 to 1700 °C to obtain the equilibrium microstructure (Pt- crucible, heating and cooling rate of 10 K⋅min-1). The duration of heat treatments was 10 days at 1400 °C, 5 days at 1500 °C, 3 days at 1600 °C, and 36 h at 1700 °C. The samples were then analyzed by XRD, SEM, EPMA, TEM, DTA and high temperature calorimetry. The XRD patterns of powdered specimens were recorded on Siemens diffractometer D5000 (CuKα1 radiation, λ = 0.15406 nm, 2θ range 10-80°). Precise measurements of lattice parameters were carried out using silicon or alumina powder as internal standard. The microstructures of sintered samples were examined by SEM (Zeiss DSM 982 GEMINI operating at 20 kV and 10 nA) and the energy dispersive X-ray spectroscopy (EDX, Oxford-Instrument ISIS 300) was employed to obtain the compositions of phases (± 1 mol% REO1.5) in equilibrium state. Furthermore, the electronic probe microanalyser (EPMA, SX- 100, Cameca) was also employed for the precise composition analysis. -10- Specimens of the ZrO2 − GdO1.5 system for TEM studies were prepared using mechanical thinning and Ar+ ion milling in a Gatan Precision Ion Polishing System (PIPS). Conventional TEM was performed in JEOL 2000FX and JEOL 4000FX electron microscopes equipped with EDX detector (HPGe, Voyager, Noran Instruments), which allowed high spatial resolution (< 20 nm). Selected area electron diffraction (SAED) experiments were accomplished in both microscopes. The EDX spectra were carefully collected from electron- transparent thin areas of single grains and then analyzed by the software “Flame”. Standard- less quantitative analysis was carried out, and theoretical k-factors were used for converting intensity ratios into composition ratios [1996Wil]. Each grain was measured at least five times and the standard deviation was estimated as 2 mol% GdO1.5. The heat contents of the compositions ZrO2-30 mol% REO1.5 (RE=Nd, Sm, Gd, Dy), ZrO2-30 mol% REO1.5 (RE= Nd, Sm, Gd, Dy, Yb), and ZrO2-57.14 mol% YbO1.5, were determined by high temperature drop calorimetry (SETARAM, Pt crucible air atmosphere) in the temperature range 200°C-1400°C. Before measurement, the samples were heat treated at 1600°C for 72 h, and then ground into small pellets in the range 10-60mg. The heat capacity of the pyrochlore sample with the composition of 50 mol% GdO1.5 was measured in the temperature range 100-1400°C by using high-temperature DSC (SETARAM, heating and cooling rate 5 K/min; He + 20 vol.% O2; Pt crucible). The sample was heat treated at 1400°C for 240h, and then ground into fine powder. The samples in the ZrO2 − HfO2 system and those with ZrO2-rich in the ZrO2 − GdO1.5 and ZrO2 − DyO1.5 systems were studied by DTA up to 1700°C (Bähr, heating and cooling rate 5 K/min, Al2O3 crucible). The uncertainty of the measurements is estimated to be ± 5 K. 2.3. Thermodynamic modelling of phases 2.3.1. Introduction 2.3.1.1. The CALPHAD approach It is easy to accept that the combination of thermodynamics and visualized phase diagrams can be very efficient to describe and analyze the phase equilibira and phase transformation under both equilibium and non-equilibium conditions. The CALPHAD (CALculation of PHAse Diagram) approach is a method which was developed originally for the calculation of phase diagram and now as the powerful tool for materials design. It is an approach of coupling the phase diagram with thermochemistry. Fig. 2-1 schematically presents how the CALPHAD method works. There are three critical factors in the CALPHAD approach [1992Nis]: -11- 1). The input data. Because CALPHAD is an approach strongly based on the experimental data, it is very important that all possible input data are collected before the work is started. The experimental data include the crystal structure information, stable and metastable phase equilibria, thermodynamic properties such as enthalpy and Gibbs energy of phases and changes of these quantities during phase formation, structural transformations and change of temperatures, the absolute value of heat capacity and entropy, vapour pressure, various partial molar properties for multicomponent systems. Nowadays, with the development of the theoretical models and computer technology, the first principle calculations can offer very important data on the enthalpy of formation at ground state, which is comparable to the standard enthalpy of formation at 298.15K, when the experimental data are not available yet. All the original experimental and theoretical data should be carefully evaluated in order that the selected data are reasonable and consistent. 2). The model for phases. Appropriate thermodynamic model has to be adopted to describe the energetic behavior of phases. Reasonably, only the model based on the structural and physical realities can truly reproduce the thermodynamic behavior of different phases. The model is composed of a series of parameters, which are optimized from the input experimental data. Some thermodynamic models have already been constructed to reflect the real interactions between different atoms with good generalization. For example, the sublattice model can describe both the substitutional solid solution formed by the atoms with similar properties, and the interstitial solid solution formed by the atoms with largely different properties and the high temperature liquid phases. 3). The method of computation. Both the assessment of the model parameters and calculation of the phase diagram must be carried out by computer program. Since H. L. Lukas [1977Luk] developed the first software LUKAS, a lots of commercial software based on different mathematical methods and computer languages have been developed for scientific and industrial users, (e.g. Thermo-Calc, www.thermocalc.com; Pandat, www.computherm.com; MTDATA, www.npl.co.uk/mtdata; FactSage, www.factsage.com). All the optimizations and calculation in this thesis were carried out by the Thermo- calc software package [1985Sun]. To derive the thermodynamic parameters of different phases, appropriate thermodynamic models have to be selected based on their structures. -12- Figure 2-1. The schematic diagram for the CALPHAD approach. 2.3.1.2. Pure elements The Gibbs energy of an element or a stoichiometric substance at the ambient pressure can be expressed by: G = A + BT + CTLnT + DT2 + ET-1 + … (2-1) where A, B, C, D, E, … are the parameters which can be optimized from the experimental heat capacity, heat content and entropy data. The equation (2-1) actually is valid only in a certain temperature range, and generally phases have different Gibbs energy functions in different temperature ranges. At the interval limits, the Gibbs energies are continuous. Because only the thermodynamic properties above room temperature (298.15 K) are of practical interest, it is supposed that the enthalpy of stable structure of any element at 298.15 K and 1 bar is equal to zero, and this assumption is set to be the reference state of elements. This reference state has already been widely accepted, and SGTE (Scientific Group Thermodata Europe: www.sgte.com) has optimized the lattice stabilities of all elements with this principle. 2.3.1.3. Thermodynamic models for the solution phases (1). Substitutional solution -13- The solution formed by components which can substitute randomly is called substitutional solution. The thermodynamic properties of substitutional solution (gas, some liquid and solid solution phases) are referred to the ideal solution. The molar Gibbs energy of substitutional solution α phase is generally expressed by the following equation: ααα m M i i im GGxG +=∑ 0 (2-2) where xi means the mole fraction of component i. αiG 0 is the Gibbs energy of component i with the same structure of α, and αmM G is called the Gibbs energy of mixing which is composed of two parts: α m M G = αm Eideal m M GST +− (2-3) in which idealm MST− is the part from the contribution of ideal mixing, and αmEG is the excess Gibbs energy. For the ideal mixing, because no any heat effect is produced, and thus only the entropy makes contribution to the Gibbs energy of mixing. αm EG reflects how large the mixing behavior deviates from the ideal case, and how it varies with composition. For example, the Gibbs energy of a solution phase which is composed of two components A and B can be formulated by: αααα m E BBAABBAAm GxxxxRTGxGxG ++++= )lnln(00 (2-4) αα BBAA GxGx 00 + is the part of Gibbs energy of mechanical mixing, and )lnln( BBAA xxxxRT + is the part of Gibbs energy associated with the entropy of mixing. The sum of these two parts is the Gibbs energy function of ideal mixing. For the ideal case, the bond energies of A-A, A-B, and B-B are equal, and the atoms of A and B mix randomly without the production of heat. For the nonideal substitutional solution, αm EG can be expressed by some polynomials, for example the Redlich-Kister polynomial [1948Red]: j BA j jBAm E xxIxxG )( −= ∑α (2-5) in which xA and xB are the mole fraction of atoms A and B, respectively, and the Ij is called the interaction parameter in the order of j. In case of j=0, the equation (2-5) is simplified to be: 0IXXG BAm E =α (2-6) Such case is called regular solution. In regular solution, the bond energies of A-A, A-B and B-B are not equal. Suppose ν is the energy to form a A-B or B-A atom bond by destroying a A-A and a B-B bonds (2ν=2εA-B-εA-A-εB-B, ε means the bond energy), N is the number of atoms, and Z is the coordination numbers of A and B, then the numbers of A-B and B-A -14- bonds will be NZXAXB. Therefore, the excess Gibbs energy will be νNZXAXB, and the interaction parameter is: I0=νNZ (2-7) The I0 is related to the solution status after the mixing of A and B atoms, and thus explicitly its physical meanings are described as follows: (a). I0=0. This means εA-B=(εA-A+εB-B)/2, which corresponds to the ideal mixing. The atoms of A and B can substitute and arrange randomly. (b). I0>0. This means εA-B>(εA-A+εB-B)/2, which corresponds to less stable A-B and B- A bonds than A-A and B-B bonds. Different kinds of atoms are repulsive to each other, and the same atoms can form clusters or order in some short range. In case of large positive I0, the solution phase may separate into two isostructural compositions, which forms the miscibility gap. (c). I0<0. This means εA-B<(εA-A+εB-B)/2, which corresponds to more stable A-B and B-A bonds than A-A and B-B bonds. The formation of A-B and B-A bonds is a spontaneous process, by decreasing the Gibbs energy of the system after mixing. However, the regular solution model treats the solution by assuming the atoms always distribute randomly without the consideration of the influence of the different atoms surroundings. Actually, the atoms surroundings can make the thermodynamic properties of solution more complicated than those of regular mixing. To describe the more complicated cases, sometimes the sub-regular solution model (j=1) or the sub-sub-regular solution model (j=2) has to be used. (2). Compound energy formalism The compound energy formalism developed by M. Hillert et al. [2001Hil] can be applied to the most of solution phases, which have separate crystallographic sublattices. It is called formalism because it includes a large variety of thermodynamic models. Compound energy formalism was developed from the sublattice model for the reciprocal quaternary system [2001Hil]. It assumes that in crystals different atomic species occupy separate (the stoichiometric compounds) or same sublattices (the phases with composition range). A certain sublattice can be occupied by the intrinsic atoms, anti-site atoms, interstitial atoms, vacancies and electrons. The compound energy formalism can be thought as the substitutional model applied for the case of phase with two or more sublattices. This generalized formalism can be used to describe different solution phases with substitutional and intersititial species, charged species, ordering behavior, etc. The -15- construction of the sublattices should be exactly based on the structure information of phases, so that the model has a physical meaning. The compound energy formalism applied in different cases is shortly reviewed in the following paragraphs. (a). General case The model for a solution phase can be expressed with the formula (A,B,…)k (C,D,…)l(…)…, in which A, B, C, D,... are the constituents, and k, l, … are called stoichiometric coefficients. The division on sublattices is made according to the phase structures, and in principle there are no limitation on the numbers of sublattices. The Gibbs energy function of generalized model is given by: m ES J S J S end S Jm GyynRTGyG ++∏= ∑∑∑ )ln(0 (2-8) in which nS is stoichiometric coefficient of sublattice S, and SJy is the site fraction of constituent J in the sublattice S. endG 0 is the Gibbs energy of end members which are the stoichiometric compounds formed by the constituents when each sublattice is only occupied by only one species, e.g. AkCl…. The excess Gibbs energy m EG is expressed by: ......:,:,...::, +∏+∏= ∑∑∑ EDCBAuDtBSJDCBAtBSJmE LyyyLyyG (2-9) where the commas in the subscripts separate different constituents in the same sublattice, and the colons separate the species in different sublattices. In the first group of terms, the interaction parameter ...::, DCBAL describes the interactions in a certain sublattice while each of the other sublattices is only occupied by a single constituent. In the second group of terms, the interaction parameter ...:,:, EDCBAL describes the interactions occurred in two sublattices at a same time while each of the other sublattices is only occupied by a single constituent, and this interaction parameter is called ‘‘reciprocal parameter’’. All these interaction parameters can be expanded as the Redlich-Kister polynomials. (b). Ionic crystals For the ionic crystals, the constituents are charged ions, and the sublattices are distinguished by cation and anion sublattices. The model is given by the formula (A+m, B+n,…)a(C+i, D+j,…)b(E-k, F-l,…)c(…)…. Some of these end members could be not electroneutral, and thus the occupations of constituents in certain sublattice are not always independent on the occupations of constituents in other sublattices so that the model can -16- maintain the electroneutrality. The equation (2-8) can also be applied for the Gibbs energy function of ionic crystal phase, and the only difference is that the constraint on the electroneutrality can affect the site fractions of constituents in sublattices. (c). Ionic melts For the melted ionic crystals, its long range ordering disappears, and the atoms do not have their fixed lattice positions by reaching disordered state. However, due to the interactions between the atoms with opposite charges, it can still be assumed that there are one cation and one anion sublattices in a short distance range. To maintain the electroneutrality of the phase, the assumption is made that the numbers of the cation and anion sublattices are changeable, what is consistent with the real structure of ionic liquid. If we use the model APBQ, in which A, B are the cation and anion sublattices respectively, and P, Q are the stoichiometric coefficients, and can be calculated by: ∑ −= )( jjyP γ (2-10) ∑= iiyQ γ (2-11) where γ is the valence, and y is the site fraction of species in sublattices. Subscripts i and j represent the different components in sublattices. The Gibbs energy of two-sublattice ionic solution model is given by: ∑ ∑ ∑ +++= ij i j m E jjiijijim GyyQRTyyPRTGyyG )ln()ln(: 0 (2-12) jiG : 0 is the Gibbs energy of formation of the substance formed by cation species i and anion species j. ∑ i ii yyPRT )ln( is the entropy of mixing by the species in cation sublattice, and ∑ j jj yyQRT )ln( is the entropy of mixing by the species in anion sublattice. The excess Gibbs energy m EG can be expressed by equation (2-9). (d). The stoichiometric phases A limiting case of the model (A,B,…)k(C,D,…)l(…)… is that each sublattice is only occupied by different single species, which are also components of the system. This means that the different components have their own fixed crystal lattices, without the variation of the stoichiometry. Such phase is called stoichiometric compound. The Gibbs energy of such compound can be simply described by the format of equation (2-1) if there are enough thermodynamic data on heat capacity, enthalpy increment, or entropy. However, for the case -17- that such thermodynamic data are not available, the Gibbs energy function can be simply expressed by Neumann-Kopp rule [1998Hil]: BTAGxG i iim ++= ∑ 0 (2-13) where the xi and iG 0 are the mole fraction and Gibbs energy of component i, respectively. A and B are the parameters to be determined and can be thought as the enthalpy and entropy of formation of the compound from the components. In the case of lacking thermodynamic data, A and B can be optimized from phase equilibria data. 2.3.2. Pure components In this work, the lattice stability functions of the pure elements are taken from SGTE database [1991Din]. The Gibbs energy functions for stoichiometric ZrO2 and HfO2 are assessed in this thesis, while those for rare earth oxides are taken from the recent evaluation [2006Zin]. 2.3.3. The gas phase The gas phase in the Hf − Zr − O system (Zr − O and Hf − O systems in this work) is treated as ideal mixture of species O, O2, O3, ZrO, ZrO2, Zr, Zr2, Hf, HfO, and HfO2 according to the SGTE substance database [Version 1997, SGTE, Gernoble, France, 1997]. All the parameters for these species are also taken from SGTE database. The Gibbs energy function can be formulated by: )ln()ln( 0 0 P PRTxxRTGxG i iiiim ++= ∑ (2-14) in which xi is the mole fraction of constituent i, and iG 0 is Gibbs energy of substance i in gas state. P0 is the standard pressure of 1 bar (101325 Pa). 2.3.4. The liquid phase 2.3.4.1. The Hf − Zr − O system The two-sublattice model for partially ionic liquids within the compound formalism [2001Hil] is used to describe the liquid phase of the Hf − Zr − O system. For simplicity, the model (Hf+4, Zr+4)P(O-2, Va-4)Q without the O species in the anion sublattice is selected in this work. The stoichiometry coefficients P and Q can be represented as follows: P= 42 42 −− + VaO yy (2-15) -18- Q= 44 44 ++ + ZrHf yy (2-16) in which the yi is the site fraction of constituent in certain sublattice. Accordingly, the Gibbs energy function for the liquid phase can be given by: [ ]LyyLyy yyyyQRTyyyyPRT GyyGyy GyyGyyG VaOVaO VaVaOOZrZrHfHf L VaZrVaZr L OZrOZr L VaHfVaHf L OHfOHf L m 10 : 0 : 0 : 0 : 0 )( )lnln()lnln( 4242 44224444 44442424 44442424 −−−− −−−−++++ −+−+−+−+ −+−+−+−+ −++ ++++ + += (2-17) where L OHfG 24: 0 −+ , L VaHfG 44: 0 −+ , L OZrG 24: 0 −+ and L VaZrG 44: 0 −+ represent the Gibbs energies of end- members in the liquid state, respectively. L0 and L1 are the interaction parameters to be optimized. 2.3.4.2. The ZrO2 − REO1.5 systems The liquid phase of the ZrO2 − REO1.5 system is also described with the two-sublattice model for ionic liquids [2001Hil] (RE+3, Zr+4)P(O-2)Q but without vacancies in the anion sublattice. The stoichiometry coefficients P and Q are formulated by: P=2 (2-18) Q=3 3+REy + 4 4+Zry (2-19) where 3+REy and 4+Zry are the site fractions of the RE +3 and Zr+4 in cation sublattice, respectively. The Gibbs energy function for the liquid phase can be given by: [ ]LyyLyy yyyyPRT GyyGyyG ZrREZrRE ZrZrRERE L OZrOZr L OREORE L m 10 : 0 : 0 )( )lnln( 4343 4433 24242323 ++++ ++++ −+−+−+−+ −++ ++ += (2-20) where the L OREG 23: 0 −+ and L OZrG 24: 0 −+ are the Gibbs energies of end components ZrO2 and REO1.5 in liquid state, respectively. The L0 and L1 in equation (2-20) are the interaction parameters, which are lineally temperature dependent, and to be optimized in the work. 2.3.5. The bcc and hcp phase The bcc and hcp phases are Zr- or Hf-based solid solutions in the Zr − O and Hf − O systems. In this work, the model of hcp phase is selected to be (Hf, Zr)1(O, Va)0.5 according to the standard thermodynamic database of SGTE. The bcc phase however is described by a model (Hf, Zr)1(O, Va)1 suggested in a recent work of the Ce − O system [2006Zin1], rather than the traditional model (Hf, Zr)1(O, Va)3 due to the limited homogeneity range of bcc -19- phases in both Zr − O and Hf − O systems. The general expression of the Gibbs energies of bcc and hcp can be given by: α αα ααα m E VaVaOOHfHfZrZr VaHfVaHfOHfOHf VaZrVaZrOZrOZrm G yyyyxRTyyyyRT GyyGyy GyyGyyG + ++++ ++ += )lnln()lnln( : 0 : 0 : 0 : 0 (2-21) in which α denotes hcp or bcc solution, and yi is the site fraction of species i in different sublattices. x is 0.5 for hcp phase and 1 for bcc phase, and αm EG is the excess Gibbs energy, which can be formulated by the expression (2-9). 2.3.6. The ZrO2 (HfO2)-based solid solution phases 2.3.6.1. The Hf − Zr − O system The ZrO2 or HfO2-based solutions with structures of cubic fluorite, tetragonal and monoclinic in the Zr − O and Hf − O system are described by the model (Hf+2, Zr+2, Hf+4, Zr+4)1(O-2,Va)2 in this work according to [2004Wan]. The Gibbs energy is formulated by: SolutionZrO m EII Va II Va II O II O I Zr I Zr I Hf I Hf I Zr I Zr I Hf I Hf SolutionZrO VaZr II Va I Zr SolutionZrO VaHf II Va I Hf SolutionZrO OZr II O I Zr SolutionZrO OHf II O I Hf SolutionZrO VaZr II Va I Zr SolutionZrO VaHf II Va I Hf SolutionZrO OZr II O I Zr SolutionZrO OHf II O I Hf SolutionZrO m GyyyyRT yyyyyyyyRT GyyGyy GyyGyy GyyGyy GyyGyyG _ _ : 0_ : 0 _ : 0_ : 0 _ : 0_ : 0 _ : 0_ : 0_ 2 22 44442222 2 44 2 44 2 2424 2 2424 2 22 2 22 2 2222 2 2222 2 )lnln(4 )lnlnlnln(2 +++ ++++ ++ ++ ++ += −− ++++++++ ++++ −+−+−+−+ ++++ −+−+−+−+ (2-22) in which the SolutionZrObaG _ : 0 2 are the Gibbs energies of end-members, and I and II mean the different sublattice. The excess Gibbs energy in (2-22) can be expressed by: [ ] [ ][ ] [ ][ ] [ ][ ] [ ] VaZrZr I Zr I ZrVaZrZr II Va I Zr I Zr VaHfHf I Hf I HfVaHfHf II Va I Hf I Hf OZrZr I Zr I ZrOZrZr II O I Zr I Zr OHfHf I Hf I HfOHfHf II O I Hf I Hf VaOZr II Va II OVaOZr II Va II O I Zr VaOHf II Va II OVaOHf II Va II O I Hf VaOZr II Va II OVaOZr II Va II O I Zr VaOHf II Va II OVaOHf II Va II O I Hf SolutionZrO m E LyyLyyy LyyLyyy LyyLyyy LyyLyyy LyyLyyy LyyLyyy LyyLyyy LyyLyyyG :, 1 :, 0 :, 1 :, 0 :, 1 :, 0 :, 1 :, 0 ,: 1 ,: 0 ,: 1 ,: 0 ,: 1 ,: 0 ,: 1 ,: 0_ 42424242 42424242 24242242242 24242242242 2422424 2422424 2222222 2222222 2 )( )( )( )( )( )( )( )( ++++++++ ++++++++ −++++−++−++ −++++−++−++ −+−−+−+ −+−−+−+ −+−−+−+ −+−−+−+ −++ −++ −++ −++ −++ −++ −++ −+= (2-23) -20- where the interaction parameters L0 and L1 are to be optimized from the experimental data. 2.3.6.2. The ZrO2 − REO1.5 systems Three kinds of ZrO2-based solid solutions with cubic fluorite, tetragonal and monoclinic structures are treated with same model, (RE+3,Zr+4)2(O-2,Va)4 in this work. The Gibbs energies of these phases are given by: SolutionZrO m E II Va II Va II O II O I Zr I Zr I RE I RE SolutionZrO VaZr II Va I Zr SolutionZrO VaRE II Va I RE SolutionZrO OZr II O I Zr SolutionZrO ORE II O I RE SolutionZrO m G yyyyRTyyyyRT GyyGyy GyyGyyG _ _ : 0_ : 0 _ : 0_ : 0_ 2 224433 2 44 2 33 2 2424 2 2323 2 )lnln(4)lnln(2 + ++++ ++ += −−++++ ++++ −+−+−+−+ (2-24) where SolutionZrO ORE G _ : 0 2 23 −+ , SolutionZrO OZrG _ : 0 2 24 −+ , SolutionZrO VaREG _ : 0 2 3+ , and SolutionZrO VaZrG _ : 0 2 4+ are the Gibbs energies of the end members formed between species in different sublattices, and I and II represent the different sublattice. The composition square composed by these end members is shown in Fig. 2-2. RE2O3 in Fig. 2-2 represents the hypothetical compound of pure RE2O3 with the structure of zirconia. For the fluorite phase, the functions of the Gibbs energies of FZrO OZr G _ : 0 2 24 −+ and FZrO VaZrG _ : 0 2 4+ are given as follows: FZrO OZr G _ : 0 2 24 −+ =2·GZrO2F (2-25) FZrO VaZr G _ : 0 2 4+ = 2·GZrO2F – 4·GHSEROO (2-26) The Gibbs energy of compound RE2O3 with cubic fluorite-type structure is modified from that of the stable structure at low temperatures: GRE2O3F=GRE2O3C + A + BT + ClnT (2-27) where A, B and C are the parameters to be optimized. The parameter C is used to assess the experimental heat capacity data when it is necessary. According to the composition square, a relation is obtained: GRE2O3F= FZrO OREG _ : 0 2 234 3 −+ + FZrO VaREG _ : 0 2 34 1 + + 4RT( 4 1ln 4 1 4 3ln 4 3 + ) (2-28) By combining with the constraint of the reciprocal reaction: FZrO ORE G _ : 0 2 23 −+ + FZrO VaZrG _ : 0 2 4+ – FZrO VaREG _ : 0 2 3+ – FZrO OZrG _ : 0 2 24 −+ =0 (2-29) The following equations is obtained: FZrO ORE G _ : 0 2 23 −+ = GRE2O3F + GHSEROO + 18.702165T (2-30) FZrO VaRE G _ : 0 2 3+ = GRE2O3F – 3·GHSEROO + 18.702165T (2-31) -21- Likewise, very similar results can be obtained for the tetragonal phase, by only replacing the GZrO2F with GZrO2T, and replacing GRE2O3F with GRE2O3T which represents the Gibbs energy of the RE2O3 with tetragonal structure. The function of GRE2O3T is arbitrarily given by: GRE2O3T= GRE2O3F + 10000 (2-32) since there are no any available thermodynamic data concerning the tetragonal solid solution phase. The Gibbs energy of RE2O3 with the monoclinic structure is simply modified from the RE2O3 phase by adding a positive constant which will be determined from the experimental T0 data for tetragonal + monoclinic equilibrium. SolutionZrO m EG _2 in equation (2-24) is the excess Gibbs energy, which is expressed as follows: [ ] [ ] [ ][ ] VaZrRE I Zr I REVaZrRE II Va I Zr I RE OZrRE I Zr I REOZrRE II O I Zr I RE VaOZr II Va II OVaOZr II Va II O I Zr VaORE II Va II OVaORE II Va II O I RE SolutionZrO m E LyyLyyy LyyLyyy LyyLyyy LyyLyyyG :, 1 :, 0 :, 1 :, 0 ,: 1 ,: 0 ,: 1 ,: 0_ 43434343 24343243243 2422424 2322323 2 )( )( )( )( ++++++++ −++++−++−++ −+−−+−+ −+−−+−+ −++ −++ −++ −+= (2-33) in which the L0 and L1 are the interaction parameters to be optimized. In order to simplify the optimization, some assumptions are given to reduce the numbers of parameters: VaOREL ,: 0 23 −+ = VaOZrL ,: 0 24 −+ =0 (2-34) VaOREL ,: 1 23 −+ = VaOZrL ,: 1 24 −+ =0 (2-35) 243 :, 0 −++ OZrREL = VaZrREL :, 0 43 ++ = D + ET (2-36) 243 :, 1 −++ OZrREL = VaZrREL :, 1 43 ++ = F + GT (2-37) where D, E, F and G are the parameters to be optimized. For the fluorite phase, both L0 and L1 are used for optimization due to its existence in a wide composition and temperature range. Only one parameter without temperature dependence is adopted for the tetragonal phase. For simplicity, the interaction parameter is not given to the monoclinic phase, since its homogeneity range is negligible. 2.3.7. The RE2O3-based phases In the RE2O3-rich region, there are five polymorphic structures named A, B, C, H, and X in literature [2006Zin]. From La to Nd, the stable structure of RE2O3 at room temperature is -22- A-type, while from Sm to Yb, the stable structure of RE2O3 at room temperature is C-type. The phases with solubility range are described with the three-sublattice model (RE+3, Zr+4)2(O-2)3(O-2,Va)1 in this work according to the suggestion by O. Fabrichnaya et al. [2004Fab]. Thus, the Gibbs energy function can be expressed by: SolutionORE m E III Va III Va III O III O I Zr I Zr I RE I RE SolutionORE VaOZr III Va II O I Zr SolutionORE VaORE III Va II O I RE SolutionORE OOZr III O II O I Zr SolutionORE OORE III O II O I RE SolutionORE m G yyyyRTyyyyRT GyyyGyyy GyyyGyyyG _ _ :: 0_ :: 0 _ :: 0_ :: 0_ 32 224433 32 2424 32 2323 32 224224 32 223223 32 )lnln()lnln(2 + ++++ ++ += −−++++ −+−+−+−+ −−+−−+−−+−−+ (2-38) In above equation, the SolutionORE OORE G _ :: 0 32 223 −−+ , SolutionORE OOZrG _ :: 0 32 224 −−+ , SolutionORE VaOREG _ :: 0 32 23 −+ and SolutionORE VaOZrG _ :: 0 32 24 −+ are the Gibbs energies of the end members formed between species in different sublattices. The superscripts I, II and III denote the different sublattice, while IIOy 2− always equal to 1. The composition square is given in Fig. 2-3. The dashed line corresponds to all the available electroneutral combinations. The two terminals of the neutral line are RE2O3 and ZrO2 with the same structure. Figure 2-2. The composition square of the ZrO2-rich phases with the model (RE+3, Zr+4)2(O-2, Va)4. The dashed line means the combinations with electroneutrality. (R, Z, O, V represent the species RE+3, Zr+4, O-2, Va respectively. IZry 4+ and II Vay mean the Zr +4 species in first sublattice and vacancy in second sublattice, respectively). Figure 2-3. The composition square of the RE2O3-rich phases with the model (RE+3, Zr+4)2(O-2)3(O-2, Va)1. The dashed line means the combinations with electroneutrality. (R, Z, O, V denote the species RE+3, Zr+4, O-2, and Va. IZry 4+ and III Vay mean the Zr +4 species in first sublattice and vacancy in third sublattice, respectively). -23- As an example, for the C-RE2O3 phase, the Gibbs energies of the four end members are given as follows: 32 23 :: 0 OREC VaORE G − −+ = GRE2O3C (2-39) 32 223 :: 0 OREC OORE G − −−+ = GRE2O3C + GHSEROO (2-40) 32 224 :: 0 OREC OOZr G − −−+ = GZRO2F + 5000 (2-41) 32 24 :: 0 OREC VaOZr G − −+ = GZRO2F + 5000 – GHSEROO (2-42) The Gibbs energies of the four end members for other RE2O3 phases can be given by similar functions. The excess Gibbs energy SolutionOGdm EG _32 is given with following formula: [ ] [ ] [ ][ ] VaOZrRE I Zr I REVaOZrRE III Va I Zr I RE OOZrRE I Zr I REOOZrRE III O I Zr I RE VaOOZr III Va III OVaOOZr III Va III O I Zr VaOORE III Va III OVaOORE III Va III O I RE SolutionORE m E LyyLyyy LyyLyyy LyyLyyy LyyLyyyG ::, 1 ::, 0 ::, 1 ::, 0 ,:: 1 ,:: 0 ,:: 1 ,:: 0_ 2434324343 2243432243243 224222424 223222323 32 )( )( )( )( −++++−++++ −−++++−−++−++ −−+−−−+−+ −−+−−−+−+ −++ −++ −++ −+= (2-43) where L0 and L1 are the interaction parameters for optimization. Like the case of ZrO2-rich phases, some simplifications also made. Only the interaction parameters VaOZrREL ::, 0 243 −++ and VaOZrREL ::, 1 243 −++ are adopted in the optimization, and the other are simply fixed to be zero because of their lower significance for the phase diagram. For the other structures of RE2O3 except C-type phase, only one interaction parameter without temperature dependence is adopted, due to their limited composition or temperature range. 2.3.8. The pyrochlore phase The pyrochlore phase is the ordered structure of the fluorite phase at low temperatures. A detailed description of the pyrochlore structure has been given elsewhere [2000Min, 2002Sta]. The crystal structures of the fluorite and pyrochlore phases are shown in Fig. 2-4. The general formula of the pyrochlore structure can be written as A2B2O6O’. There are four crystallographically unique atom positions for the stoichiometric phase, and the space group is mFd3 . The pyrochlore structure of stoichiometric A2B2O7 can be derived from the fluorite structure by doubling the fluorite cell edge, placing the large A+3 ions at 16d site, the smaller B+4 ions at 16c, and the O-2 ions at 48f and 8b, leaving the fluorite position 8a vacant. The A+3 cations are eight-fold coordinated with six 48f oxygen atoms (O1) and two 8b oxygen atoms (O2), and the B+4 cations are coordinated with six 48f oxygen atoms, while the O1 anions in 48f site are coordinated with two A+3 and two B+4 cations, and O2 anions in 8b site are -24- coordinated with four A+3 cations. The substitution between A+3 and B+4 or introducing point defects into the pyrochlore-type structure (vacancies or interstitials) results in formation of the nonstoichiometric phases A2-xB2+xO7+0.5x. There is a lot of information on the occupancies of different lattice sites by oxygen and vacancies in nonstoichiometric pyrochlore. Generally, it is accepted that excess oxygen will enter into the 8a site, while the 16d sublattice site will be partially occupied by Zr+4 species. However, in the modeling work [1985Dij], the authors found that the oxygen interstitials would preferably occupy the 8a site, and a new 32e site. This 32e site occupation was also reported by [1999Tho] in their study of the oxygen excess pyrochlore, and additionally they reported that both 8b and 8a sites were not fully occupied in this case. The existence of oxygen interstitial in 32e site was later confirmed by Blundred et al. [2004Blu] even in the oxygen deficient pyrochlores. Furthermore, they also stated that preferential loss of oxygen anions occurs from 48f site rather than 8b site, because the B+4 species were not directly bound to the O2 in the 8b site. This is in agreement with most of investigations [1998Wil, 1999Wil, 2001Pir, 2001Wil, 2004Pan] that for the case of Zr+4 deficiency the oxygen vacancy for the pyrochlore forms more easily at the 48f site rather than 8b site. The nonstoichiometry in A2B2O7 pyrochlore was simulated by Stanek et al. [2002Sta]. They proposed two preferential ways for the BO2 excess: one is the cation vacancy mechanism in the A+3 sublattice, and another is the oxygen interstitials mechanism in the 8a site while additional B+4 species have to enter into 16d site to compensate the electroneutrality, and in the stable pyrochlores, the A+3 cation vacancy mechanism is predicted to be more favorable. For the A2O3 excess case, the predicted most favorable way is the formation of oxygen vacancies in 48f site. Taking all the literature information into account, it is not possible to find the general occupancy rules for the defect pyrochlore, because it seems that the case partly depends on the radius of A+3 and B+4 cations, and the samples in different experimental works with different ordering degree may also cause the discrepancies. In this work, based on the principle to adopt simplified model, the 32e site and the vacancy in cation sublattice are not considered, and only two general and simple cases for defect pyrochlore are accepted. For the oxygen excess case, additional oxygen species enter into the 8a sites, and excess B+4 species enter into 16d site. For oxygen deficiency case, vacancies are formed in 48f site, and additional A+3 species enter into 16c site. In both cases, the 8b site is fully occupied by oxygen. These two cases produce the nonstoichiometry of pyrochlore. At the stoichiometric composition, the 48f site is completely occupied by oxygen, and the 8a site is fully vacant. Thus, a model can be created to describe the pyrochlore phase with five sublattices (Zr+4, -25- RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1, in which the forth sublattice is fully occupied by oxygen. As it was already pointed out [2005Zin], the transition between fluorite and pyrochlore in the ZrO2 − GdO1.5 system shows a hybrid character, and it is not clear yet whether it is of first or second order. Thus, except the model proposed in above paragraph, further efforts are also put to model it as a second-order phase transition in this work. The thermodynamic model to describe the order-disorder transitions in metallic systems has been developed by Ansara et al. [1988Ans, 1997Ans], and makes it possible to describe the ordered and disordered phases within the single splitting sublattice model. By this way, the Gibbs energies of the ordered and disordered phases can be expressed by a continuous function, which is the sum of two terms, a disordered part and an ordered part. Examples could be found in literature for the fcc↔L12 first-order transition [1997Ans] and bcc_A2↔bcc_B2 second-order transition [1999Dup]. Generally, mathematical constraints are needed for parameters to ensure that the Gibbs energy always has an extremum at the disordered state. Currently, the applications of this model are mainly concerning the metal alloy systems. For the case of pyrochlore phase, what is different from the metallic system is that the ordering occurs independently at both cation sublattice and anion sublattice. According to the crystal structure information, the pyrochlore phase can be described with the model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2, Va)1(Va, O-2)1. The phase becomes completely disordered when 1iy = 2 iy (i=RE +3, Zr+4), and 3jy = 54 jj yy = (j=O-2, Va). However, the commercial softwares such as Thermo-Calc are not available to simultaneously treat the orderings in both cation and anion sublattices for this model yet. Very recently, Ohtani et al. [2005Oht] applied the model (Zr+4, Nd+3)0.5(Nd+3, Zr+4)0.5(O-2, Va)2 to study the order-disorder transition between fluorite and pyrochlore phase for ZrO2 − Nd2O3 system. The model proposed there is also accepted in this work with the formula (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)8 to describe the second-order transition in the ZrO2 − GdO1.5 system, without considering the ordering of the oxygen and vacancies. For the first model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1, it is impossible to give appropriate values for all end members without any constraints. The derivation of all the parameters for this model takes several steps. Fig. 2-5 gives the composition space of this model, where the dashed triangles and parallelogram represent the compositional possibilities of electroneutrality. 2.3.8.1. The model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1 -26- (1). The stoichiometric pyrochlore The homogeneity range of the pyrochlore phase is ignored in the first step, with the model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2)6(O-2)1(Va)1. In the ideally ordered stoichiometric pyrochlore structure, the first sublattice (16c site) is fully occupied by Zr+4, and the second sublattice (16d site) is completely occupied by RE+3. In Fig. 2-5, all the available stoichiometric compositions are on the electroneutral line which connects the end members Zr+4:RE+3:O-2:O-2:Va (ZROOV) and RE+3:Zr+4:O-2:O-2:Va (RZOOV) if only the substitution of cation species is taken into account. The Gibbs energy function of stoichiometric pyrochlore thus can be given by: )lnln(2)lnln(2 22221111 :::: 054321 :::: 054321 :::: 054321 :::: 054321 33444433 2244 2244 2234 2234 2243 2243 2233 2233 ++++++++ −−++−−++−−++−−++ −−++−−++−−++−−++ +++ +++ ++ = REREZrZrZrZrRERE VaOOZrZrVaOOREZr VaOOZrREVaOORERE yyyyRTyyyyRT GyyyyyGyyyyy GyyyyyGyyyyy G pyrochlore VaOOZrZr pyrochlore VaOOREZr pyrochlore VaOOZrRE pyrochlore VaOORERE pyrochlore m (2-44) where the superscripts 1 to 5 denote the different sublattices, respectively. The Gibbs energy function for the ideal stoichiometric pyrochlore Zr+4:RE+3:O-2:O-2:Va can be assessed from the experimental data of heat capacity, enthalpy increment, and enthalpy of formation, i.e., pyrochlore VaOOREZrG :::: 0 2234 −−++ = a + bT + cTlnT + dT-1 + eT2 (2-45) The Gibbs energy of inverse pyrochlore RE+3:Zr+4:O-2 :O-2:Va is expressed by adding an arbitrary large positive value to the pyrochlore VaOOREZrG :::: 0 2234 −−++ : pyrochlore VaOOZrREG :::: 0 2243 −−++ = pyrochlore VaOOREZrG :::: 0 2234 −−++ + V1 (2-46) in which V1 is the cationic anti-site energy. The end member Zr+4:Zr+4:O-2:O-2:Va (ZZOOV) can be treated as pyrochlore-type (ZrO2)4 with the deficiency of one oxygen species. Firstly, the Gibbs energy of the end member Zr+4:Zr+4:O-2:O-2:O-2 (ZZOOO) is assumed to be: pyrochlore OOOZrZrG 22244 :::: 0 −−−++ =4·GZRO2F + V2 + V3T (2-47) where the GZRO2F is the Gibbs energy of fluorite-type ZrO2, and V2 and V3 are the parameters to be optimized. Then the Gibbs energy of the Zr+4:Zr+4:O-2:O-2:Va is given by: pyrochlore VaOOZrZrG :::: 0 2244 −−++ = pyrochlore OOOZrZrG 22244 :::: 0 −−−++ – GHSEROO (2-48) where the GHSEROO is the Gibbs energy of 1/2 mole of oxygen gas. A constraint is then given for this reciprocal system to obtain the function of pyrochlore VaOOREREG :::: 0 2233 −−++ : pyrochlore VaOOZrZrG :::: 0 2244 −−++ + pyrochlore VaOOREREG :::: 0 2233 −−++ – pyrochlore VaOOZrREG :::: 0 2243 −−++ – pyrochlore VaOOREZrG :::: 0 2234 −−++ =∆G1 (2-49) in which the energy difference ∆G1 is set to zero to simplify the modeling. -27- (a) (b) Figure 2-4. The visualized crystal unit cells for the fluorite (a) and pyrochlore (b) phases. (2). The oxygen excess pyrochlore The excess of oxygen in the fifth sublattice is accompanied by the additional Zr+4 species in the second sublattice. This case can be expressed by the model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2)6(O-2)1(Va, O-2)1, which can be seen as the middle cube in Fig. 2-5. Totally the parameters of eight end members are to be determined according to this model. The available compositional combinations with electroneutrality are denoted by the dashed triangle ZROOV-RZOOV-ZZOOO. The Gibbs energies of five end members pyrochlore VaOOZrZrG :::: 0 2244 −−++ , pyrochlore VaOOREREG :::: 0 2233 −−++ , pyrochlore VaOOZrREG :::: 0 2243 −−++ , pyrochlore VaOOREZrG :::: 0 2234 −−++ and pyrochlore OOOZrZrG 22244 :::: 0 −−−++ are already determined in the first step, and the three others pyrochlore OOOREZrG 22234 :::: 0 −−−++ , pyrochlore OOOZrREG 22243 :::: 0 −−−++ and pyrochlore OOOREREG 22233 :::: 0 −−−++ can be determined by the equations: pyrochlore VaOOZrZrG :::: 0 2244 −−++ + pyrochlore OOOREZrG 22234 :::: 0 −−−++ – pyrochlore VaOOREZrG :::: 0 2234 −−++ – pyrochlore OOOZrZrG 22244 :::: 0 −−−++ =∆G2 (2-50) pyrochlore VaOOREZrG :::: 0 2234 −−++ + pyrochlore OOOREREG 22233 :::: 0 −−−++ – pyrochlore OOOREZrG 22234 :::: 0 −−−++ – pyrochlore VaOOREREG :::: 0 2233 −−++ =∆G3 (2-51) pyrochlore OOOZrREG 22243 :::: 0 −−−++ + pyrochlore VaOOREREG :::: 0 2233 −−++ – pyrochlore VaOOZrREG :::: 0 2243 −−++ – pyrochlore OOOREREG 22233 :::: 0 −−−++ =∆G4 (2-52) ∆G2, ∆G3, and ∆G4 are the reciprocal energies to be determined in this work. The ZrO2 excess can be approached if only 16/1 53 22 >+ −− OO yy is reached. It must be noted that this composition space cannot give all the available combinations for the ZrO2 excess. The description of all the available cases for the ZrO2 excess involves the substitution of species in the four sublattices, which cannot be visualized simply in a three dimensional space. -28- ZZO O O ZR O O O R R O O O ZZO O V R ZO O V ZG O O V G G O O V ZZV O O R ZV O O ZR V O O R R V O O ZZO O O R ZO O O ZR O O V R R O O V ZZV O V R ZVO V ZR V O V R R V O V P-RE O2 3 Figure 2-5. The composition space for the pyrochlore structure (R, Z, O, V denote the species RE+3, Zr+4, O-2, and Va.) (3). The oxygen deficient pyrochlore The oxygen deficiency in the third sublattice is accompanied by the additional RE+3 in the cation sublattice. This causes the Zr+4 deficiency in the pyrochlore structure, which can be seen in the bottom cube in Fig. 2-5, and it can be expressed by the model (Zr+4, RE+3)2(RE+3, Zr+4)2 (O-2, Va)6(O-2)1(Va)1. The electroneutrality triangle is shown by the dashed line. The -29- pyrochlore structure with the composition of pure RE2O3 is denoted by P-RE2O3, and its Gibbs energy function can be derived from the equation: G(P-RE2O3) =2·GRE2O3C + V4 + V5T = pyrochlore VaOOREREG :::: 0 2233 6 5 −−++ + pyrochlore VaOVaREREG :::: 0 233 6 1 −++ + 6RT[ 6 1ln 6 1 6 5ln 6 5 + ] (2-53) where GRE2O3C is the Gibbs energy function for the cubic RE2O3, and the V4, V5 are the parameters to be assessed. With this equation, pyrochlore VaOVaREREG :::: 0 233 −++ can be determined: pyrochlore VaOVaREREG :::: 0 233 −++ =6·G(P-RE2O3) – 5· pyrochlore VaOOREREG :::: 0 2233 −−++ – 36RT [ 6 1ln 6 1 6 5ln 6 5 + ] =12·GRE2O3C + 6V4 + 6V5T – 5· pyrochlore VaOOREREG :::: 0 2233 −−++ + 134.8548T (2-54) Subsequently, three constraints can be made for the end members on the bottom of the composition space: pyrochlore VaOVaREZrG :::: 0 234 −++ + pyrochlore VaOOREREG :::: 0 2233 −−++ – pyrochlore VaOVaREREG :::: 0 233 −++ – pyrochlore VaOOREZrG :::: 0 2234 −−++ =∆G5 (2-55) pyrochlore VaOVaZrZrG :::: 0 244 −++ + pyrochlore VaOOREZrG :::: 0 2234 −−++ – pyrochlore VaOVaREZrG :::: 0 234 −++ – pyrochlore VaOOZrZrG :::: 0 2244 −−++ =∆G6 (2-56) pyrochlore VaOVaZrREG :::: 0 243 −++ + pyrochlore VaOOREREG :::: 0 2233 −−++ – pyrochlore VaOVaREREG :::: 0 233 −++ – pyrochlore VaOOZrREG :::: 0 2243 −−++ =∆G7 (2-57) (4). The model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(O-2)1: The oxygen deficiency in the third sublattice with the fifth sublattice occupied by oxygen. Except the cases mentioned above, another case of electroneutrality can be reached when the vacancies enter into third sublattice partly while the fifth sublattice is fully occupied by oxygen species. This case is shown by the parallelogram which intercepts the top rectangle in the Fig. 2-5. According to the structural information, for both oxygen excess and oxygen deficiency in the pyrochlore phase, such case is not physically preferable. The following constraints are made to determine the parameters of the four end members ZRVOO, RZVOO, ZZVOO, and RRVOO: pyrochlore OOVaREZrG 2234 :::: 0 −−++ + pyrochlore VaOOREZrG :::: 0 2234 −−++ – pyrochlore OOOREZrG 22234 :::: 0 −−−++ – pyrochlore VaOVaREZrG :::: 0 234 −++ =∆G8 (2-58) pyrochlore OOOREZrG 22234 :::: 0 −−−++ + pyrochlore OOVaREREG 2233 :::: 0 −−++ – pyrochlore OOVaREZrG 2234 :::: 0 −−++ – pyrochlore OOOREREG 22233 :::: 0 −−−++ =∆G9 (2-59) pyrochlore OOVaZrZrG 2244 :::: 0 −−++ + pyrochlore OOOREZrG 22234 :::: 0 −−−++ – pyrochlore OOOZrZrG 22244 :::: 0 −−−++ – pyrochlore OOVaREZrG 2234 :::: 0 −−++ =∆G10 (2-60) pyrochlore OOVaZrREG 2243 :::: 0 −−++ + pyrochlore OOOZrZrG 22244 :::: 0 −−−++ – pyrochlore OOOZrREG 22243 :::: 0 −−−++ – pyrochlore OOVaZrZrG 2244 :::: 0 −−++ =∆G11 (2-61) -30- For the complete description (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1, the Gibbs energy of the pyrochlore phase is formulated by pyrochlore m E OOVaVaVaVaOO REREZrZrZrZrRERE pyrochlore VaOVaZrZrVaOVaZrZr pyrochlore OOVaZrZrOOVaZrZr pyrochlore VaOOZrZrVaOOZrZr pyrochlore OOOZrZrOOOZrZr pyrochlore VaOVaREZrVaOVaREZr pyrochlore OOVaREZrOOVaREZr pyrochlore VaOOREZrVaOOREZr pyrochlore OOOREZrOOOREZr pyrochlore VaOVaZrREVaOVaZrRE pyrochlore OOVaZrREOOVaZrRE pyrochlore VaOOZrREVaOOZrRE pyrochlore OOOZrREOOOZrRE pyrochlore VaOVaREREVaOVaRERE pyrochlore OOVaREREOOVaRERE pyrochlore VaOOREREVaOORERE pyrochlore OOOREREOOORERE pyrochlore m G yyyyRTyyyyRT yyyyRTyyyyRT GyyyyyGyyyyy GyyyyyGyyyyy GyyyyyGyyyyy GyyyyyGyyyyy GyyyyyGyyyyy GyyyyyGyyyyy GyyyyyGyyyyy GyyyyyGyyyyy G +++++ +++ ++ ++ ++ ++ ++ ++ ++ ++ = −−−− ++++++++ −++−++−−++−−++ −−++−−++−−−++−−−++ −++−++−−++−−++ −−++−−++−−−++−−−++ −++−++−−++−−++ −−++−−++−−−++−−−++ −++−++−−++−−++ −−++−−++−−−++−−−++ )lnln()lnln(6 )lnln(2)lnln(2 55553333 22221111 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 :::: 054321 2222 33444433 24424422442244 224422442224422244 23423422342234 223422342223422234 24324322432243 224322432224322243 23323322332233 223322332223322233 (2-62) where njy represents the site fraction of species j in the sublattice n, and pyrochlore edcbaG :::: 0 are the Gibbs energies of the end members of this model. Totally there are 16 combinations, which are determined so far in the previous steps. The excess Gibbs energy pyrochlorem EG is set to be zero in the present optimization, to avoid too many independent adjustable parameters for such a complicated model. 2.3.8.2. The splitting model (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)8 According to the suggestion by I. Ansara et al. [1988Ans], a splitting model can be applied for both disordered and ordered phases, by dividing the Gibbs energy into contributions of a disordered and an ordered states by the following equation: )()( si ord mimm yGxGG ∆+=Φ φ (2-63) in which )( im xG φ is the Gibbs energy of the disordered phase φ, and )( siordm yG∆ is the Gibbs energy part contributed by the ordering of sublattices, which is given by the equation: )( si ord m yG∆ = )()( isimsim xyGyG =− (2-64) where )( i s im xyG = represents the disordered part which is corresponding to the case that the site fraction of species i in sublattice s is equal to the mole fraction xi. As long as the i s i xy ≠ , the phase becomes ordered, and then its Gibbs energy is expressed by )( sim yG , so that the -31- Gibbs energy difference )( si ord m yG∆ in (2-64) is the Gibbs energy of ordering with respect to the disordered state. Finally, the Gibbs energy can be represented by the equation: pyrochlore m E VaVaOO REREZrZrZrZrRERE pyrochlore VaZrZrVaZrZr pyrochlore VaZrREVaZrRE pyrochlore VaREZrVaREZr pyrochlore VaREREVaRERE pyrochlore OZrZrOZrZr pyrochlore OZrREOZrRE pyrochlore OREZrOREZr pyrochlore OREREORERE pyrochlore m GyyyyRT yyyyRTyyyyRT GyyyGyyy GyyyGyyy GyyyGyyy GyyyGyyyG +++ ++++ +++ + +++ += −− ++++++++ ++++++++ ++++++++ −++−++−++−++ −++−++−++−++ )lnln(8 )lnln(2)lnln(2 22 33444433 44444343 34343333 244244243243 234234233233 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 :: 0 (2-65) where pyrochlorecbaG :: 0 denotes the Gibbs energy of end members, and y is the site fraction of constituent in a certain sublattice. pyrochlorem EG is the excess Gibbs energy, which can be given by the equation: VaREZrZrREVaREZrZrRE OREZrZrREOREZrZrRE VaOREZrVaOREZrVaOREREVaORERE VaOZrZrVaOZrZrVaOZrREVaOZrRE VaREZrZrVaREZrZrVaREZrREVaREZrRE OREZrZrOREZrZrOREZrREOREZrRE VaREZrREVaREZrREVaZrZrREVaZrZrRE OREZrREOREZrREOZrZrREOZrZrRE pyrochlore m E Lyyyyy Lyyyyy LyyyyLyyyy LyyyyLyyyy LyyyyLyyyy LyyyyLyyyy LyyyyLyyyy LyyyyLyyyy G :,:, 32211 :,:, 32211 ,:: 3321 ,:: 3321 ,:: 3321 ,:: 3321 :,: 3221 :,: 3221 :,: 3221 :,: 3221 ::, 3211 ::, 3211 ::, 3211 ::, 3211 34433443 2344323443 234234233233 244244243243 344344343343 2344234423432343 343343443443 2343234324432443 ++++++++ −++++−++++ −++−++−++−++ −++−++−++−++ ++++++++++++ −+++−+++−+++−+++ ++++++++++++ −+++−+++−+++−+++ + + ++ ++ ++ ++ ++ + = (2-66) in which njy means the site fraction of species j in the sublattice n, and L are the interaction parameters. When 1 4+Zry = 2 4+Zry = 4+Zrx , the pyrochlore phase is completely disordered into the fluorite structure, and its Gibbs energy can be expressed by the equation (2-24). It must be emphasized that the contribution by the disordering should be subtracted from the pyrochloremG and pyrochlorem EG in above equations. The model thus works with two splitting parts, in which one part describes the disordered state, and another part describes the ordered part. Because the disordering can always be stable before ordering occurs, a constraint must be made so that the Gibbs energy surface always has a minimum at the composition where 1 4+Zry = 2 4+Zry = 4+Zrx when the first and second sublattices merge into a single one. This constraint can be realized when the derivative of the pyrochloremG with respect to the 1 4+Zry or 2 4+Zry is zero: -32- [ 22 1 1 4 4 4 4 + + + + ∂ ∂+∂ ∂= Zr Zr Zr Zr dy y Gdy y GdG ] 4+Zrx =0 (2-67) By using suitable mathematical software and taking the relationship 4+Zrdx = 1 4+Zrdy + 2 4+Zrdy =0 into account, the above equation can be solved to find the relations of different parameters. Generally, there are many solutions which can fit this equation, thus some assumptions are necessary. In this work, the final constraints are given as follows: pyrochlore OREZrG 234 :: 0 −++ = u1 pyrochloreOZrREG 243 :: 0 −++ = u2 pyrochlore VaREZrG :: 0 34 ++ = u3 pyrochloreVaZrREG :: 0 43 ++ = u4 2344 :,: −+++ OREZrZrL = VaREZrZrL :,: 344 +++ = 2343 :,: −+++ OREZrREL = VaREZrREL :,: 343 +++ = u5 VaOZrREL ,:: 243 −++ = VaOZrZrL ,:: 244 −++ = VaOREREL ,:: 233 −++ = VaOREZrL ,:: 234 −++ = u6 24334 :,:, −++++ OZrREREZrL = VaZrREREZrL :,:, 4334 ++++ = u7 2434 ::, −+++ OZrREZrL = u5+ u1 – u2 VaZrREZrL ::, 434 +++ = u5 + (8u1 – 8u2 + u3 – u4) 2334 ::, −+++ OREREZrL = u5 + (–5u1 + 5u2 – u3 + u4)/2 VaREREZrL ::, 334 +++ = u5 + (9u1 – 9u2 + u3 – u4)/2 where u1-u7 are the parameters to be evaluated from experimental data. Further assumptions are u1= u2= u3= u4 to simplify the modeling in case of very limited experimental information, and u6 and u7 are set to be zero since they are not related to the other parameters. 2.3.9. The RE4Zr3O12 (δ) phase The δ phase is also a kind of ordered superstructures of fluorite at low temperatures when the ionic radius of the doping element RE+3 is smaller than that of Dy+3 [1991Red]. The crystal structure of this phase has been described in literature [1970Tho, 1976Ros, 1977Sco, 2002Lop]. It can be derived from the defective fluorite structure by the ordering of oxygen vacancies to produce a rhombohedral cell. There are two different cation positions: one is the single site at the origin which is octahedrally coordinated with anions, and another are the six equivalent sites which are coordinated by anions on seven of the eight vertices of a slightly distorted cube. For the ideally ordered δ phase, the position 3a is fully occupied by Zr+4, and the other cationic sites 18f are occupied by RE+3 ions and the residual Zr+4 ions, while the -33- oxygen ions occupy two anion 18f positions. The anion vacancies are on the position of 6c according to the references [1976Ros, 1991Red]. Based on crystal structure information, in this work the δ phase is described with the four-sublattice model (Zr+4)1(RE+3, Zr+4)6(O-2, Va)12(Va, O-2)2 and its Gibbs energy function of δ phase is given by: δ δδ δδ δδ δδ δ m E VaVaOO VaVaOOZrZrRERE VaVaZrZrVaVaZrZrVaVaREZrVaVaREZr OVaZrZrOVaZrZrOVaREZrOVaREZr VaOZrZrVaOZrZrVaOREZrVaOREZr OOZrZrOOZrZrOOREZrOOREZr m GyyyyRT yyyyRTyyyyRT GyyyyGyyyy GyyyyGyyyy GyyyyGyyyy GyyyyGyyyy G +++ ++++ ++ ++ ++ + = −− −−++++ ++++++++ −++−++−++−++ −++−++−++−++ −−++−−++−−++−−++ )lnln(2 )lnln(12)lnln(6 4444 33332222 ::: 04321 ::: 04321 ::: 04321 ::: 04321 ::: 04321 ::: 04321 ::: 04321 ::: 04321 22 224433 44443434 244244234234 244244234234 2244224422342234 (2-68) where njy means the site fraction of the species j in the sublattice n. δ dcbaG ::: 0 is the Gibbs energy of the end member. The excess Gibbs energy δm EG is simply set to zero in this work, because the available thermodynamic data are scarce. Figure 2-6. The composition space for the model of δ (Yb4Zr3O12). The dashed plane represents the compositional possibilities with the electroneutrality (Y, Z, O, V denote the species Yb+3, Zr+4, O-2, and Va.). Fig. 2-6 gives the composition space for the δ phase, and the combinations with the electroneutrality are shown by the dashed plane, where Yb4Zr3O12 is the stable phase, and ZrYb6O11Va2 and ZrYb6O9O2 are two compounds with oxygen deficiency. According to the -34- structural information, the oxygen species prefer the third sublattice, and ZrYb6O9O2 will be less stable than the compound ZrYb6O11Va2, thus the nonstoichiometry can be reached by changing the compositions along the lines ZZOO−Yb4Zr3O12 and Yb4Zr3O12−ZrYb6O11Va2. Totally there are eight end members in this model. The Gibbs energies of ZZOO, ZZOV and the compounds Yb4Zr3O12 and ZrYb6O11Va2 can be as: δ 2244 ::: 0 −−++ OOZrZrG = 7·GZRO2F + V6 + V7T (2-69) δ VaOZrZrG ::: 0 244 −++ =7·GZRO2F − 2·GHSEROO + V6 + V7T (2-70) G(Yb4Zr3O12)= 2·GYB2O3C + 3·GZRO2F + V8 + V9T (2-71) G(ZrYb6O11Va2)= 3·GYB2O3C + GZRO2F + V10 + V11T (2-72) where V6 to V11 are the parameters to be determined from the experimental data. Accordingly, the Gibbs energies of the end members δ VaOYbZrG ::: 0 234 −++ (ZYOV) and δ VaVaYbZrG ::: 0 34 ++ (ZYVV) are derived by the following equations: G(Yb4Zr3O12)= δ VaOYbZrG ::: 0 234 3 2 −++ + δ VaOZrZrG ::: 0 244 3 1 −++ + 6RT[ 3 1ln 3 1 3 2ln 3 2 + ] (2-73) G(ZrYb6O11Va2)= δ VaOYbZrG ::: 0 234 12 11 −++ + δ VaVaYbZrG ::: 0 34 12 1 ++ + 12RT[ 12 1ln 12 1 12 11ln 12 11 + ] (2-74) and the following relations are obtained: δ VaOYbZrG ::: 0 234 −++ = 1.5·G(Yb4Zr3O12) − 0.5· δ VaOZrZrG :::0 244 −++ + 47.6278T (2-75) δ VaVaYbZrG ::: 0 34 ++ = 12·G(ZrYb6O11Va2) − 11· δ VaOYbZrG :::0 234 −++ + 343.4046T (2-76) To determine the Gibbs energies of other four end members, four independent reciprocal reactions are given: δ 2244 ::: 0 −−++ OOZrZrG + δ VaOYbZrG ::: 0 234 −++ − δ VaOZrZrG :::0 244 −++ − δ 2234 :::0 −−++ OOYbZrG = ∆Ga (2-77) δ VaOZrZrG ::: 0 244 −++ + δ VaVaYbZrG ::: 0 34 ++ − δ VaOYbZrG :::0 234 −++ − δ VaVaZrZrG :::0 44 ++ = ∆Gb (2-78) δ 2244 ::: 0 −−++ OOZrZrG + δ VaVaZrZrG ::: 0 44 ++ − δ VaOZrZrG :::0 244 −++ − δ 244 :::0 −++ OVaZrZrG = ∆Gc (2-79) δ 244 ::: 0 −++ OVaZrZrG + δ 2234 ::: 0 −−++ OOYbZrG − δ 2244 :::0 −−++ OOZrZrG − δ 234 :::0 −++ OVaYbZrG = ∆Gd (2-80) in which ∆Ga, ∆Gb, ∆Gc and ∆Gd are the reciprocal energies of the independent reactions, which are determined by the phase equilibria data concerning the δ phase. Finally, the Gibbs energies of all end members can be solved from the above equations. -35- Chapter 3 Experimental study and thermodynamic modeling of the Zr − O, Hf − O and ZrO2 − HfO2 systems 3.1. Literature review 3.1.1. The Zr − O system A detailed review of the experimental phase equilibria and thermodynamic information for the Zr − O system was given by Abriata et al. [1986Abr]. According to the assessment [1986Abr], only one stable oxide i.e. zirconium dioxide (ZrO2) exists in this system. A compilation of the literature information on the polymorphic transformations of ZrO2 is given in Table 3-1. As indicated above, ZrO2 has a monoclinic (M) structure below 1478 K, where it transforms into the intermediate tetragonal (T) structure, and at its stoichiometric composition at about 2650 K into cubic fluorite-type (F) modification. At sub-stoichiometric compositions the cubic modification is stable down to 1798 K at its eutectoid decomposition into the hcp solution of O in Zr and the tetragonal modification. The cubic phase was reported to melt congruently at about 2983 K. There is a eutectic reaction liquid ⇔ hcp-Zr + F at about 2338 K, 40 at.% O. The homogeneity range of the hcp solid solution of Zr extends to 35 at.% O. It reveals a congruent melting point at 2583 K, 25 at.% O, and is stable down to room temperature. A lower oxygen content the bcc structure will be formed by a peritectic reaction (liquid + hcp-Zr ⇔ bcc-Zr) at about 2243 K and 10 at.% O. Furthermore, many experimental investigations indicate that several ordered phases can exist at low temperature in the hcp-Zr phase region [1973Cla, 1974Hir, 1995Tsu1]. After the assessment by Abriata et al. [1986Abr], very few experimental works about the phase equilibria were reported, and only some experimental determinations of thermodynamic properties were published [1990Nev, 1995Tsu2, 1999Toj, 2003Deg, 2005Nav1, 2006Mor]. The temperature of the M ↔ T structural transformation has extensively been studied in the literature. There are large discrepancies, due to the experimental difficulties from martensitic nature of the M ↔ T transformation, and some other factors such as impurities in samples, the particle size of the powder, the experimental techniques, and the errors in experiments. In Table 3-1, the literature data obtained by thermal analysis, high-temperature X-ray diffraction, dilatometry and some other methods are compiled. The enthalpy of M ↔ T transformation was studied by [1950Cou, 1965Tsa, 1966Kir, 1979Che, 1995Yas, 2001Jer, -36- 2003Sur, 2006Mor]. The value of 5941 J·mol-1, which was determined by [1950Cou], was accepted in the review work of Ackerman et al. [1975Ack]. Tsagareishvili and Gvelesiani [1965Tsa] reported a value of 5272 J·mol-1 at 1475 K. Subsequently, Kirillin et al. [1966Kir] and Chekhovskoi et al. [1979Che] reported the values of 7763 J·mol-1 and 8297 J·mol-1, respectively, which were higher than previous data. Yashima et al. [1995Yas] measured this enthalpy of transformation by DSC as 5640 J·mol-1 and evaluated the entropy of transformation as 4.07 J·mol-1·K-1at around 1395 K. By using DTA method, Jerebtsov et al. [2001Jer] determined the enthalpy of M ↔ T transformation in their experimental studies of phase diagram involving ZrO2 systems, and obtained the value of 5175.24 ± 616.1 J·mol-1 at about 1435 K. Suresh et al. [2003Sur] determined the enthalpy of M ↔ T transformation for the ZrO2 powder with different crystallite sizes, and obtained a plateau value of around 4313 J·mol-1 when the crystallite size was beyond 150 nm. This value was accepted in their work as the volumetric heat of transformation (∆Hvol) although the reported temperature of the transformation was only 1286 K. Very recently, [2006Mor] carried out the measurement between 1000-1700 K by DSC. The determined enthalpy and entropy of the M ↔ T transformation in their work were 5430 ± 310 J.mol-1 and 3.69 ± 0.21 J.mol-1.K-1, respectively, while the transformation occurred in the temperature range 1460~1480 K on heating, and in the temperature range 1325~1305 K on cooling. The enthalpies of formation of cubic yttria-stabilized zirconia with different compositions were measured by high temperature solution calorimetry and oxide melt solution calorimetry [1998Mol, 2003Lee]. The enthalpy of M ↔ F transformation was then extrapolated to be 13500 ± 2200 J·mol-1 at 1043 K and 9700 ± 1100 J·mol-1 at 973 K, respectively. However, Lee et al. [2003Lee] also got a modified result 9200 ± 1200 J·mol-1 at 1043 K by using the original experimental data of [1998Mol]. Since there are no other experimental data available, the reliability of their extrapolated results cannot be assessed. The literature data on the temperature of the T ↔ F transformation are also included in the Table 3-1. Ackermann et al. [1975Ack] evaluated a value of 5564 J·mol-1 for the enthalpy of transformation, and the entropy of transition as 2.09 J·mol-1·K-1. [2005Nav1] measured the temperature and enthalpy for the T ↔ F phase transformation by high temperature calorimeter in the temperature range 2000-2400°C, with the results of 2584 ± 15 K, and 3400 ± 3100 J·mol-1. The melting point was reported by many groups (Table 3-1). Owing to the experimental uncertainties at such high temperatures, the data show some disagreement. Most of the authors accepted the value 2983 K or 2950 K. No any experimental data exist on the -37- enthalpy of F ↔ L transformation. The assessed value given in JANAF compilation [1971JAN] is 87027 J·mol-1. Many works contributed to the determination of the heat content of zirconia in a wide temperature range [1950Cou, 1950Art, 1963Pea, 1965Tsa1, 1966Kir, 1979Che]. The heat capacities were studied by [1950Art, 1990Nev, 1999Toj, 2001Tan, 2003Deg, 2006Mor]. The data of enthalpy of formation, entropy, and heat capacity of monoclinic ZrO2 at 298 K reported in literature are compiled in Table 3-2. Several groups contributed to the thermodynamic modeling of the Zr − O system due to its practical significance in the past several years [1998Che, 2001Lia, 2002Arr, 2004Che, 2004Chen, 2004Sun]. In these studies, however, various thermodynamic models, especially for the cubic zirconia were adopted, and so were the parameters for stoichiometric zirconia. The Gibbs energy parameters of ZrO2 were reported in several papers [1992Du, 1998Che, 2001Lia, 2002Arr, 2004Chen]. Their data on the critical transformation temperatures, enthalpies, and entropies are also compiled in Table 3-1 and Table 3-2. The different models so far used for the Zr − O system are summarized in Table 3-3. Chevalier and Fischer [1998Che] adopted for the liquid an associate solution model (O, ZrO2, Zr), and for the cubic ZrO2 phase a two-sublattice model (Zr,Va)(O,Va)2 in their assessment of the Zr − O system. The calculated phase diagram shows poor agreement with the experimental data. Very recently, they published an improved assessment [2004Che]. A better agreement between the experimental and calculated phase diagram was obtained. A revised model (Zr)(O,Va)2(Va,O) was applied to the cubic zirconia. Liang and co-workers [2001Lia] described the high temperature cubic ZrO2 also with the two-sublattice model (Zr)(O,Va)2. For the liquid phase they used the partial ionic sublattice model (Zr+4)P(O-2,Va,O)Q, where P and Q are the site numbers of cation and anion sublattices, respectively. The oxygen and vacancy species can be neutrally substituted under the assumption of the model for cubic zirconia phase. The ordering of hcp-Zr phase at low temperature was taken into account in their description with the model Zr6(O,Va)2(Va,O)2 (Va,O)2. Arroyave and co-workers [2002Arr] treated the cubic ZrO2 as pure ionic compound with the sublattice model (Zr+4)(O-2,Va-2)2. However, this model is actually identical to that of reference [2001Lia], due to introducing the charged vacancy. The calculated bcc-Zr / bcc-Zr + hcp-Zr phase boundary shows large disagreement with the experimental data and the bcc phase is stable in the temperature range 4400-5000 K, and a broad gas + liquid two-phase region is presented compared with the result of Liang et al. [2001Lia]. -38- A very recent work on this system is done by Chen and co-workers [2004Chen]. The authors introduced a neutral Zr species into the cation sublattice to obtain the electroneutrality with the model (Zr,Zr+4)(O-2,Va)2. The phase diagram agrees well with most of the experimental data except small deviation between experimental and calculated F / F + hcp-Zr phase boundary at the temperatures near the eutectoid point of reaction F ⇔ hcp-Zr + T, and a higher congruent melting point obviously deviating from stoichiometric composition is obtained for the cubic ZrO2 in comparison with the results of [2001Lia] and [2002Arr]. Sundman [2004Sun] recently modified the description of [2001Lia] in his work on the Zr − U − O system, by keeping all the parameters of [2002Lia], except that the cubic ZrO2 was described with the model (Zr+2,Zr+4)(O-2,Va)2. The calculated phase diagram is very similar to that of [2001Lia]. 3.1.2. The Hf − O system The phase diagram of the Hf − O system was first established by Rudy and Stecher [1963Rud] by means of XRD, metallographic method and thermal analysis. Two eutectic reactions involving liquid phase were determined at high temperatures: liquid ⇔ bcc-Hf + hcp-Hf at 2000 ± 30°C, and liquid ⇔ hcp-Hf + F (cubic fluorite-type HfO2) at 2180 ± 40°C, while the hcp-Hf phase melted at 2300 ± 20°C congruently. The temperature of the transition between the monoclinic and tetragonal phase was measured at around 1700°C. The solubility of oxygen in hcp-Hf extends to around 20 at.%. [1965Dom] contributed to the phase equilibria study on this system later. They obtained 2500°C for the melting point of the hcp-Hf phase which was 200°C higher than the result of [1963Rud]. Moreover, the invariant reaction in the hafnium-rich part was reported as peritectic at 2250°C, while the temperature of 2200°C for the reaction liquid ⇔ hcp-Hf + F was quite consistent with the previous result. In the later work [1973Ruh], the reaction of cubic F ⇔ hcp-Hf + T (tetragonal HfO2) was carefully determined at 2125°C, which was very close to the temperature of the reaction liquid ⇔ hcp-Hf + F. The maximum oxygen deficiency was measured to be around 64 at.% in cubic HfO2. Subsequently, [1976Rud] studied phase relation in the Hf-rich region. The reported solubility of oxygen in hcp-Hf was 20 at.% up to 2000°C, and that in bcc-Hf was less than 5 at.%. The temperature for the reaction liquid ⇔ hcp-Hf + F is 2100 ± 20°C according to their work. -39- In the hafnium-rich part, there are some reports concerning the ordering of the hcp-Hf phase at low temperatures. [1972Hir, 1973Hir] found the order-disorder transformations near the compositions HfO1/6 by neutron diffraction, while [1995Kat1, 1997Kat] determined the temperatures of order-disorder transition by means of the low-temperature heat capacity measurements. HfO2 and ZrO2 are thought as twin oxides, for their similarities in structural modifications, lattice constants, chemical and physical properties. Because of the higher temperature of the martensitic transformation of HfO2 as compared to that of ZrO2, the literature data on the M ↔ T transition are more limited and show some inconsistency. The temperature measured by thermal analysis, high-temperature XRD and some other methods are compiled in Table 3-4. The [2001Fuj] studied the phase transition of pure hafnia by using in situ Ultraviolet Raman scattering up to 2085 K. The monoclinic-to-tetragonal phase transition finished at around 2080 K on heating, and started at 2018 K on cooling. Since the Af temperature is comparable to the temperature As, it can be seen in Table 3-4 that the result of [2001Fuj] is quite consistent with the works of [1965Sta, 1976Kuz, 1987She, 1991Gul]. For the start temperature of tetragonal-to-monoclinic transition, the result of [2001Fuj] also presents good agreement with those of [1965Sta, 1983Sen]. Stacy et al. [1972Sta] determined the variation of the lattice parameters of the monoclinic and tetragonal phase by using high- temperature XRD up to 2213 K, and derived an equilibrium temperature at 2023 ± 20 K. Coutures [1987Cou] obtained the same value with the same route, while Aldebert et al. [1975Ald] reported a value of 2038 K by measuring the lattice expansion with the neutron diffraction. All these results [1972Sta, 1975Ald, 1987Cou] are very close to the approximate T0 temperature calculated from the data of Fujimori et al. [2001Fuj]. The results [1963Wol, 1963Bau, 1975Sta] obtained by HTXRD are questionable, because they present higher Ms temperatures than the As temperatures, and the other results of HTXRD [1954Cur, 1965Bog, 1968Ruh, 1976Ruh] reveal considerable deviation from the DTA, dilatometry and Raman scattering results are considered as less reliable in that respect. The T ↔ F transformation of HfO2 was experimentally studied by only a few groups (Table 3-4). The existence of the cubic HfO2 was firstly confirmed by Boganov et al. [1965Bog] using the HTXRD, and the T ↔ F transformation was observed at around 2973 K. Other values obtained by thermal analysis and radiation pyrometry are between 2763 and 2873 K [1985She, 1987Cou, 1987She, 1988Sig, 1988Yam, 1997And] with a maximum discrepancy of 110 K. The works [1985She, 1987She, 1997And] were preformed by same -40- group based on DTA measurements. On cooling a value of 2803 K was reported [1985She, 1997And], whereas on heating 2793 K was obtained [1987She]. Many data are available on the melting point. Most of the results are in the temperature range 3073-3105 K [1975Sta, 1977Sch, 1985She, 1986Yam, 1987She, 1988Sig, 1988Yam, 1997And], whereas the result 3123 K of Coutures [1987Cou] is slightly higher. There is also good agreement between cooling and heating curves of DTA measurements (3073 K) [1985She, 1987She, 1997And]. Earlier measurements [1932Cla, 1954Cur, 1966Nog] seem to be less reliable. The literature data are collected in Table 3-4. [1963Sil] determined the partial molar Gibbs free energy of oxygen in hcp solid solution of Hf from 0 to 25 at.%O in the temperature range 968 to 1232 K by equilibrating samples with alkaline metal oxide-metal vapor combinations. The enthalpy of formation of the hcp-Hf phase was obtained by [1974Kor] from the measurements of the heats of combustion at four HfOx compositions. With the help of the Tian-Calvet microcalorimetric method, [1984Bou] measured the partial molar enthalpy of mixing of oxygen ( 2OH ) in hafnium at 1232 K. The standard enthalpy of formation of the monoclinic hafnia was experimentally determined by several groups [1932Rot, 1953Hum, 1968Hub, 1971Kor, 1974Pap, 1975Kor], ranging from –1144.74 kJ·mol-1 [1968Hub] to –1113.2 kJ·mol-1 [1953Hum]. Kornilov and Ushakova [1971Kor] first reported –1117.128 kJ·mol-1, and shortly offered a very consistent value –1117.630 kJ·mol-1 [1975Kor] in cooperation with Huber and Holley [1968Hum]. The result of this measurement [1975Kor] is thus thought to be the most reliable one. All of these data are summarized in Table 3-5. [1953Tod] measured the heat capacity of HfO2 at low temperatures (52.47-298.16 K) and determined the entropy of HfO2 at 298.16 K (Table 3-5). The heat content of hafnia was studied in the temperature ranges 382.7-1803.6 K [1953Orr], and 650.4-2883.7 K [1963Pea]. Lee and Navrotsky determined the enthalpy of formation of the cubic solid solution in the system HfO2 − YO1.5 by oxide melt solution calorimetry. The enthalpy of transition of monoclinic to cubic of pure hafnia was extrapolated to be 32.5 ± 1.7 kJ·mol-1 [2004Lee]. However, this value is three times larger than the related value of ZrO2 (9.7 ± 1.1 kJ·mol-1) [2003Lee] estimated by the same group. In view of the similarity of HfO2 and ZrO2, such difference seems to be too large. 3.1.3. The ZrO2 − HfO2 system -41- The difference of the lattice constants of both ZrO2 and HfO2 are very small, due to the equivalent valence and almost equivalent ionic radii of Zr+4 and Hf+4. For this reason, the ZrO2 − HfO2 system can form continuous solutions, and it is only possible to distinguish the X-ray diffraction patterns of ZrO2, HfO2, and solid solutions of them by using extremely high resolution. Stansfield [1965Sta] firstly studied the thermal expansion of five solid solutions in the ZrO2 − HfO2 system by dilatometry measurement in the temperature range between 1173 and 2773 K, but did not give quantitative values. Ruh et al. [1968Ruh] determined the transformation temperatures of As, Af, Ms, and Mf in the whole composition range by both the HTXRD and DTA. The results obtained by HTXRD showed a large disagreement with the DTA results, which however are consistent with the dilatometric study of Stansfield [1965Sta]. With the help of thermal analysis, the phase transformations M ↔ T and T ↔ F were studied in the temperature range 1373-3073 K by Shevchenko et al. [1987She]. But, in fact, only the As temperatures for the monoclinic-to-tetragonal transition were reported, and were misinterpreted as the monoclinic / tetragonal phase boundary data. [1993Yam] reported the temperatures of the T ↔ F transformation using radiation pyrometry, and their data are well consistent with those from reference [1987She]. An additional solid-solid transformation peak was found by Yamada et al. [1993Yam] at temperatures higher than that of the T ↔ F transformation, for which no explanation was given. Obolonchik et al. [1991Obo] reported two sets of tetragonal / monoclinic phase equilibiria data in their work on the ternary HfO2 − ZrO2 − Y2O3 system. Three groups [1968Ruh, 1987She, 1988Yam] measured the liquidus of the ZrO2 − HfO2 system. The two data sets [1987She, 1988Yam] are mutually consistent and lie almost on a straight line connecting the end members. The activities of ZrO2 and HfO2 in the ZrO2 − HfO2 system at 2773 K derived from the vapor pressure data obtained from high temperature mass spectrometry were reported in the literature [1985Bel] with large errors. Both of the reported activities of ZrO2 and HfO2 presented some deviation from the ideal behavior. 3.2. Experimental results and discussion The ZrO2 − HfO2 system was experimentally studied by DTA measurements. All the prepared compositions are given in Table 3-6. The XRD patterns of the sample No.8 before and after heat treatment are shown in Fig. 3-1. After the pyrolysis at 700°C for 3h, the structure is mainly monoclinic with a small amount of tetragonal phase. Since the particle size is quite small, the tetragonal phase is stabilized because of its lower surface energy than that -42- of the monoclinic phase [2005Pit]. There are no visible differences between the XRD patterns of different samples. After heat treatment at higher temperature, the XRD patterns show pure monoclinic structure. The DTA curves for each sample reveal one peak on heating and one on cooling according to the transition between monoclinic and tetragonal phases. Fig. 3-2 shows the DTA curve of the sample No.5 as an example, where the temperatures As, Af, Ms, and Mf are identified. All the transformation temperatures measured by DTA are included in Table 3-6, and plotted in Fig. 3-3 together with the data reported in references [1968Ruh, 1987She]. Compared with the literature data, the results of the present work are quite consistent. With the change of the composition, the present data of As, Af, Ms, and Mf show a linear behavior in the whole composition range. By applying the linear relations, the As, Af, Ms, and Mf temperatures can be fitted well against the composition (x(HfO2)=mole fraction). The functions obtained in this work are: As = 1429.71 + 6.36181*x(HfO2) (3-1) Af = 1473.93 + 6.60491*x(HfO2) (3-2) Ms = 1304.75 + 7.32675*x(HfO2) (3-3) Mf = 1263.66 + 7.19513*x(HfO2) (3-4) 20 30 40 50 60 70 In te ns ity (A rb .u ni ts ) 2θ (degree) after heat treatment as-pyrolysed 1000 1200 1400 -6 0 6 XX X D iff er en tia l t em pe ra tu re (K ) Temperature (K) As Af Ms Mf heating cooling X exo. endo. Figure 3-1. The XRD patterns of the sample No.8 in ZrO2 − HfO2 system after pyrolysis (700°C, 3h) and after heat treatment (1400°C, 48h). Figure 3-2. The DTA curve of the sample No.5 in ZrO2 − HfO2 system (The As, Af, Ms, and Mf represent the starting and finishing temperatures on heating and cooling, respectively). -43- With increasing HfO2 content, the temperature difference between As and Af as well as between Ms and Mf do not change evidently. However, due to the higher slope of function (3- 3) and (3-4), it can be seen that the difference between As and Ms for pure hafnia is much smaller that that for pure zirconia. In this work, the difference between As and Ms is 125 K for ZrO2 and 28 K for HfO2 which is quite consistent with the value reported by [1963Wol] (30 K). The As (1430 K), Af (1474 K), Ms (1305 K), Mf (1264 K) of pure ZrO2 obtained in this work show striking agreement with the results of Ruh et al. [1968Ruh] (As: 1433 K, Af: 1488 K, Ms: 1311 K, Mf: 1266 K). Additionally, the current As of ZrO2 is consistent with the literature data [1966Kir, 1968Ruh, 1973Mit, 1977Ruh, 1979Che, 1984Ruh, 1985Per, 1987She, 1990Fre, 1995And, 2001Jer] within the maximum deviation of 20 K, and the Ms obtained in this work for ZrO2 presents maximum 32 K deviation with the data from references [1968Ruh, 1984Ruh, 1985Ada, 1985Per, 1987She, 1990Dur, 1995And, 1995Yas, 1997Kas, 1999Hay, 2003Sur, 2006Mor,]. For the HfO2, though the literature data are scarce, present work still provides considerable consistency with the reported As temperatures [1976Kuz, 1975Sta, 1991Gul, 2001Fuj] and Ms temperatures reported by Senft and Stubican [1983Sen] and Fujimori et al. [2001Fuj]. The calculated T0 temperatures for different compositions are also given in Table 3-6. They are calculated by two different ways which agree within a maximum discrepancy of 6 K. Fig. 3-4 shows the T0 temperatures calculated using equation (1-1), together with the linear fit function and the literature data [1968Ruh]. The data of of Ruh et al. [1968Ruh] agree well with the fitted function in both the ZrO2 and HfO2-rich region, but deviate in the composition range 20-50 mol% HfO2. According to the fitted function: T(T0) = 1367.23 + 6.84428*x(HfO2) (3-5) for the two end members, T0 are 1367 K and 2052 K, respectively. The uncertainties introduced by linear fit are estimated to be 5 K. The value of 1367 K for ZrO2 is only 20 K lower than the value 1387 K suggested in the work of Yashima et al. [1996Yas] by extrapolating the T0 data of the ZrO2 − YO1.5 system, and agree well with most of literature data obtained by DTA or dilatometry, while the value of 2052 K for HfO2 is also consistent with the experimental data of [1965Sta, 1972Sta, 1987Cou, 2001Fuj] within the limits of uncertainty. -44- 0 10 20 30 40 50 60 70 80 90 100 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 Te m pe ra tu re (K ) mol% HfO2 As,this work Af, this work Ms, this work Mf, this work As,1968Ruh Af, 1968Ruh Ms, 1968Ruh Mf, 1968Ruh As,1987She Figure 3-3. The measured As, Af, Ms, and Mf temperatures in the ZrO2 − HfO2 system together with the fitting linear functions. 0 10 20 30 40 50 60 70 80 90 100 1300 1400 1500 1600 1700 1800 1900 2000 2100 T0 HfO2=2052 T0,this work T0, 1968Ruh linear fit, this work mol% HfO2 Te m pe ra tu re (K ) T0 ZrO2=1367 Figure 3-4. The calculated T0 data for the ZrO2 − HfO2 system together with linear fit and literature data. 3.3. Thermodynamic assessments and calculations 3.3.1. Pure zirconia The experimental data on the heat capacity [1950Art, 1990Nev, 1999Toj, 2001Tan, 2003Deg, 2006Mor] and heat content [1950Art, 1950Cou, 1965Tsa1, 1966Kir, 1979Che] are accepted for the optimization. The standard values at 298.15 K are taken for the enthalpy of formation from the references [1964Hub, 1967Kor], for the heat capacity and entropy from the reference [1999Toj]. -45- For the M ↔ T transition, the value obtained in this work (1367 K) is taken. The most reliable data [1950Cou, 1965Tsa, 1995Yas, 2001Jer, 2006Mor] on the enthalpy of transformation (Table 3-1) are in the range of 5000-6000 J·mol-1. All of the data were obtained at the As temperature on heating, and they could have slight differences compared with the results measured on cooling [1995Yas]. In this work, it is assumed that both enthalpy and entropy of transformation are independent on temperature. The entropy of transformation is selected as 4 J·mol-1·K-1, and the enthalpy of transformation as 5648 J·mol-1, which both fall well among those literature data. There is only one experimental report on the enthalpy of the T ↔ F phase transformation [2005Nav1]. Their data on the transformation temperature (2584 K) is accepted in this work, but the enthalpy value (3400 ± 3100 J·mol-1) is not taken for present optimization, partly due to the large experimental error. Moreover, it has been clear from several thermodynamic assessments [2004Jac, 2004Che, 2005Fab] that by accepting a low enthalpy of T ↔ F transformation, the F + T two-phase equilibrium boundaries in ZrO2-based binary systems cannot be well reproduced. The lower the value which has been used, the worse was the F + T phase equilibrium of the phase diagram presented [2004Jac]. Actually, the T ↔ F transition may be of second-order type at high temperature, and the F + T two- phase region in ZrO2-based binary systems could be a miscibility gap [1991Hil]. In this work, because it is modeled as a first-order transition, a relatively large value is selected. Compared with the M ↔ T transition, assuming the same entropy of transformation (4 J·mol-1·K-1) for the T ↔ F transition, the enthalpy of transformation 10336 J·mol-1 is well consistent with the enthalpy of monoclinic-to-cubic transformation extrapolated from calorimetric experiments [2003Lee]. The temperature and enthalpy of transformation for F ↔ L transition are selected to be 2983 K, and 87027 J·mol-1, as recommended in reference [1971JAN]. The calculated heat capacity and enthalpy increment (HT-H298) are shown in Fig. 3-5 and Fig. 3-6, together with experimental data. The calculated heat capacity, entropy, and enthalpy of formation of monoclinic ZrO2 at 298.15 K are 56.26 J·mol-1·K-1, 49.76 J·mol-1·K-1 and −1100.56 kJ·mol-1, respectively. All the experimental data are well reproduced. The assessed Gibbs energy parameters are given in Appendix. -46- Figure 3-5. The calculated heat capacity of ZrO2 together with experimental data. Figure 3-6. The calculated heat content (HT-H298) of ZrO2 together with experimental data. 3.3.2. The Zr − O system The phase equilibria in the Zr − O system were studied by [1954Dom, 1961Geb, 1961Hol, 1977Ack, 1978Ack, 1980Rau]. Most of the phase boundary data in these works are adopted for the optimization. The thermodynamic data reported by [1962Kom, 1974Bou, 1974Vas, 1979Ack, 1984Bou] are accepted as well for the assessment in this work. The data of invariant reactions reviewed by [1986Abr] are input in the optimization as the start values. -47- The phase diagram calculated in this work is shown in Fig. 3-7 together with the experimental data. The calculated invariant reactions are presented in Table 3-7 together with the assessed data [1986Abr]. It can be seen in Fig. 3-7 that the existing experimental data are reproduced very well within the experimental errors. The optimized parameters are listed in Appendix. The congruent melting point of the hcp-Zr phase (2404 K) is calculated at 29 at.% O, which has to be compared with 25 at.% O given by [1986Abr]. However, the calculated value is rather consistent with the results of previous assessments [2001Lia, 2002Arr, 2004Che, 2004Chen]. Since many thermodynamic and phase boundary data for the hcp-Zr phase region are employed in the optimization, the calculated values seems to be more reasonable than the assessed one [1986Abr]. The calculated congruent melting point of cubic zirconia is at 65.78 at.% O and 3055 K, which is very similar to the result of [2004Chen]. Chevalier et al. [2004Che] and Liang et al. [2001Lia] obtained the results of 66.3 at.% O at 2993 K and 66 at.% O at 2983 K, respectively, and reproduced the L + F / F phase boundary very well. Both the results [2001Lia, 2004Che] present their efforts to obtain a stoichiometric congruent melting point. Compared to the results of this work and [2004Chen], the models with substitutional species adopted by [2001Lia] and [2004Che] are more workable to deal with the L + F phase equilibrium. However, the associated model in the work of [2004Che] produces a discontinuity in the slope of the liquidus. The phase diagram calculated by [2002Arr] presents a congruent melting point very close to the stoichiometric composition at 2950 K, but lacks the consistency with the experimental data for the phase boundary L + F / F at high temperatures. Because there is no any experimental data concerning the composition of the congruent melting point, it is impossible to judge which result is more valid. Since the experimental data can be reproduced well, the present results are thought to be acceptable. The present thermodynamic dataset also gives reasonable predictions at high temperatures (Fig. 3-8) and a very similar result to that of [2002Arr] is obtained for the gas + liquid phase region. The calculated partial molar Gibbs energy of O in the hcp phase region at 1100 K is shown in Fig. 3-9, together with the experimental data in the temperature range 1073-1273K [1962Kom]. Fig. 3-10 presents the experimental and calculated partial molar enthalpy of oxygen ( 2OH ) in the whole composition range. Fig. 3-11 shows the calculated partial pressure of the species Zr, ZrO, ZrO2 and O over the saturated Zr + ZrO2 two-phase region. In view of -48- the less reliability of such thermodynamic data, the agreements in Fig. 3-9, Fig. 3-10 and Fig. 3-11 are reasonable. Figure 3-7. The calculated Zr − O phase diagram in this work together with experimental data. Figure 3-8. The Zr − O phase diagram calculated in this work at high temperatures. -49- Figure 3-9. Calculated and experimental partial Gibbs energy of oxygen in the Zr − O system at 1100K, referred to pure O2 at 1 bar. Figure 3-10. Calculated partial pressures of ZrO2(g), ZrO(g), Zr(g) and O(g) over the saturated Zr + ZrO2 two-phase region, together with experimental data. -50- Figure 3-11. Calculated partial molar enthalpy as a function of the oxygen content in the Zr − O system together with experimental data. 3.3.3. Pure hafnia The heat capacity and heat content data given in the literature [1953Tod, 1953Orr] are taken for the optimization. Since the heat content data of Pears and Osment [1963Pea] have been already confirmed to be incorrect for ZrO2, they are not used for optimization but only for comparison in this work. The standard enthalpy of formation data of Kornilov et al. [1975Kor] is accepted, while the heat capacity and entropy at 298.15 K reported by Todd [1953Tod] are selected as starting values. Due to the lack of the high temperature heat capacity data, the heat capacity of the solid phase at the melting point is taken as that of ZrO2. There are not any experimental data on the enthalpy of transformation for the monoclinic ↔ tetragonal, tetragonal ↔ cubic, and cubic ↔ liquid transitions of HfO2. Owing to the similarity of HfO2 and ZrO2, the same entropies of transformation as for ZrO2 are adopted for HfO2. The present result of 2052 K is accepted for the temperature of monoclinic ↔ tetragonal transformation. For the temperature of the tetragonal ↔ cubic transformation, the result 2803 K obtained in the literature [1985She, 1997And] from the cooling curve of the DTA measurements is consistent with the results [1987She, 1988Sig] within a maximum discrepancy of 22 K, and is selected in this work. For the melting point, the reported temperatures 3073 K [1985She, 1987She, 1997And], 3076 K [1986Yam], and 3074 K [1988Yam] are in very good agreement, and the deviations with the most of other results -51- [1932Cla, 1975Sta, 1988Sig, 1977Sch] are within 30 K. Therefore, the value of 3073 K is accepted in this work. Thus, the enthalpies for the monoclinic ↔ tetragonal, tetragonal ↔ cubic, and cubic ↔ liquid transformation are 8208 J·mol-1, 11212 J·mol-1, and 89653 J·mol-1, respectively. Figure 3-12. The calculated heat capacity of HfO2 together with experimental data. Figure 3-13. The calculated heat content (HT-H298) of HfO2 together with experimental data. The calculated heat capacity and heat content (HT-H298) are shown in Fig. 3-12 and Fig. 3-13, together with experimental data. The optimized parameters for the HfO2 are included in Appendix. -52- 3.3.4. The Hf − O system Though [1963Rud] investigated the system in a wide composition range, their results present large deviation with those obtained by [1965Dom] in Hf-rich region. Compared to the Zr − O and Ti − O systems, a eutectic reaction liquid ⇔ bcc-Hf + hcp-Hf reported by [1963Rud] is probably less reasonable, because the reaction types involving these three phases are both peritectic for the Zr − O and Ti − O systems. Thus, the reaction liquid + hcp- Hf ⇔ bcc-Hf proposed by [1965Dom] is accepted together with the phase equilibria data for solid phases. However, with increasing the O content, the liquidus temperatures determined by [1965Dom] change very sharply, while the results of [1963Rud, 1976Rud] are well consistent. Therefore, the congruent melting temperature and the liquidus temperatures beyond 18 at.% O are taken from [1963Rud, 1976Rud], as well as the invariant reaction liquid ⇔ hcp-Hf + F. The results of the reaction F ⇔ hcp-Hf + T obtained by [1973Ruh] are also accepted as the starting values for optimization. The thermodynamic data reported by [1963Sil, 1974Kor, 1984Bou] are all adopted for the assessment. Figure 3-14. The Hf − O phase diagram calculated in this work together with experimental data. -53- Figure 3-15. The Hf − O phase diagram calculated in this work at high temperatures. A calculated Hf − O phase diagram together with experimental data is shown in Fig. 3- 14. The calculated invariant reactions are presented in Table 3-8 together with the experimental data. At higher temperatures, a similar gas + liquid two-phase region to that of the Zr-O system is obtained, and shown in Fig. 3-15. In the Hf-rich region, the calculated liquidus temperatures are between the results of [1963Rud] and [1965Dom], but agree well with that of [1976Rud]. The calculated invariant reaction involving liquid, hcp-Hf and bcc-Hf phases occurs at 2522 K, which is consistent with the value 2523 K reported by [1965Dom]. However, present calculation gives a eutectic type for this reaction rather than peritectic type, while the compositions of liquid and bcc-Hf are very close. In view of the large uncertainties in this region, the calculation is thought to be acceptable, but further experimental investigations are necessary. The congruent melting point of hcp-Hf phase calculated in this work is 2583 K, which is close to the results reported by [1963Rud] (2573 K). At the same time, like in the Zr − O system, the calculated composition (13.7 at.% O) for this congruent melting shifts to Hf-rich region, comparing to the experimental data (18 at.% O) of [1963Rud]. This is reasonable because it is optimized from both the liquidus data and the phase boundary data of the hcp-Hf phase. The experimental liquidus data beyond 18 at.% O are considerably well reproduced by the calculations. The calculated invariant reaction liquid ⇔ hcp-Hf + F is 2512 K, 30.4 at.% -54- Figure 3-16. Calculated and experimental partial Gibbs energy of oxygen in the Hf − O system at 1100K, referred to pure O2 at 1 bar. Figure 3-17. Calculated partial molar enthalpy of oxygen (O2) in the Hf − O system together with experimental data. -55- O, and agrees with the composition reported by [1963Rud]. To obtain good agreement with the liquidus data, the calculated temperature for this reaction is slightly higher than the literature data [1963Rud, 1965Dom]. The temperature of 2398 K determined by [1973Ruh] for the reaction F ⇔ hcp-Hf + T is difficult to be well reproduced, but the present result 2379 K, is accepted within the limits of experimental uncertainties. The calculated congruent melting point of HfO2 deviates from the stoichiometric composition, and is highly elevated compared with the melting temperature of stoichiometric composition. This is similar to the case of the Zr − O system. Fig. 3-16 and Fig. 3-17 give the calculated partial Gibbs energy as a function of the oxygen content at 1100 K, and the partial molar enthalpy of oxygen ( 2OH ) compared with the experimental data. Reasonable agreement is obtained in both cases. Figure 3-18. The calculated ZrO2 − HfO2 phase diagram compared with experimental data. 3.3.5. The ZrO2 − HfO2 system All the phases in the ZrO2 − HfO2 system are modeled as ideal solutions. The calculated phase diagram is presented in Fig. 3-18. It shows a narrow monoclinic + tetragonal two-phase region, as a result of the similar thermodynamic properties of ZrO2 and HfO2. The DTA data [1968Ruh, 1987She] and the phase boundary data [1991Obo] are in reasonable agreement with the calculation. The calculated high temperature T / F and F / L phase -56- equilibria are almost straight lines without visible two-phase regions, and consistent with the phase diagrams proposed by references [1968Ruh, 1987She, 1988Yam]. The liquidus shows some deviation with that of Ruh et al. [1968Ruh], because the melting point of HfO2 which was taken in this work is based on the data of Shevchenko et al. [1987She] and Yamada et al. [1988Yam]. Table 3-1. Literature information on phase transition data of ZrO2. Temperature (K) Transition Reference As Ms T0 Enthalpy of transformation (J.mol-1) Entropy of transformation (J.mol-1. K-1) Experimental method [1950Cou] 1478 5941 4.0 drop calorimetry [1963Bau] 1273 1243 1258 HTXRD [1963Wol] 1328 1183 1255.5 HTXRD [1965Tsa] 1475 5272 ± 544 3.56 calorimetry [1966Kir] 1420 7763 mixing method [1970Pat] 1373 1303 1338 HTXRD [1973Mit] 1433 ~1463 1343 ~1373 1388 ~1418 DTA [1974Sri] 1443 DTA [1977Ruh] 1429 1036 1232.5 DTA [1979Che] 1423 8297 5.836 mixing method [1984Ruh] 1425 1318 1371.5 DTA [1985Ada] 1452 1447 1321 1319 1386.5 1383 dilatometry [1985Per] 1343 1273 1308 RS [1986Ban] 1473 1213 1343 DTA [1986Yos] 1373 ± 100 dilatometry [1987She] 1423 1283 1353 DTA [1990Fre] 1450 ND [1990Dur] 1473 1273 1373 DTA [1991Boy] 1373 ND [1995And] 1446 1284 1365 DTA [1995Yas] 1477 1323 1400 5710 ± 290 4.07 DSC [1997Kas] 1469 1317 1393 dilatometry [1999Hay] 1454 1320 1387 dilatometry [2001Jer] 1438±7 5175 DTA [2003Sim] ~1380 ~1390 ~1385 ND [2003Sur] 1286 4312.80 DSC M ↔ T [2006Mor] 1461 1326 1393.5 5430 ± 310 3.69 ± 0.21 DSC -57- [1975Ack] 1478 5941 assessed [1981Sub] 1443 assessed [1986Abr] ~1478 assessed [1992Du] 1454 6024 optimization [1998Che] [2004Che] 1478 8075 optimization [2001Lia] 1476 6441 optimization [2002Arr] 1478 5941 optimization [2004Chen] 1387 6000 optimization This work 1430 1305 1367 5468 DTA, extrapolated; optimization [1962Smi] 2558 ± 15 HTXRD [1963Wol] 2566 HTXRD [1965Vie] 2645 ± 50 HTXRD [1965Bog] 2573 HTXRD [1987She] 2603 ± 30 DTA [1993Yam] 2641 ± 25 pyrometer [2001Sch] 1450 molecular dynamics [2005Nav1] 2584 ± 15 3400 ± 3100 DTA [1975Ack] 2650 5564 2.09 assessed [1981Sub] 2643 assessed [1986Abr] ~2650 assessed [1992Du] 2642 5968 optimization [1998Che] [2004Che] 2650 13000 optimization [2001Lia] 2627 21699 optimization [2002Arr] 2641 6045 optimization [2004Chen] 2647 7500 optimization T ↔ F This work 2584 10336 optimization [1925Hen] 2960 not reported [1932Cla] 2950 ± 20 not reported [1965Lam] 2983 not reported [1965Nog] 2979 ± 20 Solar furnace [1966Nog1] 2995 ± 20 Solar furnace [1966Nog2] 2972 ± 20 Solar furnace [1970Lat] 2953 ± 15 DTA [1977Ack] 2983 ± 15 pyrometry [1987She] 2973 DTA [1993Yam] 2980 ± 25 pyrometer [1971JAN] 87027 assessed [1981Sub] 2953 assessed [1992Du] 2983 87986.62 optimization [1998Che] [2004Che] 2985 87027 optimization [2001Lia] 2961 86313 optimization [2002Arr] 2950 87027 optimization [2004Chen] 2984 68600 optimization F ↔ L * This work 2983 87027 optimization M ↔ F [1998Mol] 1043 13500±2200 9200±1200 (modified) solution calorimetry -58- [2003Lee] 973 9700±1100 solution calorimetry *(at the stoichiometric composition for the optimized results) Table 3-2. Experimental and optimized heat capacity, entropy and enthalpy of formation of monoclinic ZrO2 at 298.15 K. Reference Heat capacity J·mol-1·K-1 Entropy J·mol-1·K-1 Enthalpy of formation kJ·mol-1 [1944Kel] 50.33 ± 0.33 [1961Kel] 50.71 [1964Hub] −1100.919 [1967Kor] −1100.559 [1990Nev] 56.50 [1999Toj] 56.14 49.79 [1992Du] 56.12 50.35 −1100.568 [2001Lia] 63.43 50.73 −1100.970 [2002Arr] 55.90 50.36 −1100.308 [2004Chen] 57.21 49.8 −1100.686 [1998Che] [2004Che] 56.04 50.35 −1100.568 This work 56.26 49.76 −1100.56 Table 3-3. List of models of the Zr − O system adopted in previous works. Model Reference Liquid Cubic ZrO2 [2004Che] (O, ZrO2,Zr) (Zr)(O,Va)2(Va,O) [2001Lia] (Zr+4)P(O-2,Va-4,O)Q (Zr)(O,Va)2 [2002Arr] (Zr+4)P(O-2,Va-4)Q (Zr+4)(O-2,Va-2)2 [2004Chen] (Zr+4)P(O-2,Va-4)Q (Zr,Zr+4)(O-2,Va)2 [2004Sun] (Zr+4)P(O-2,Va-4,O)Q (Zr+2,Zr+4)(O-2,Va)2 This work (Zr+4)P(O-2,Va-4)Q (Zr+2,Zr+4)(O-2,Va)2 Table 3-4. Literature information on the phase transition data of HfO2. Temperature (K) Transition Reference As Ms T0 Enthalpy of transformation (J·mol-1) Entropy of transformation (J·mol-1·K-1) Experimental method [1954Cur] 1973 HTXRD [1963Wol] 1883 2013 1948 HTXRD [1963Bau] 1773 1823 1798 HTXRD [1965Sta] 2113 2063 2088 dilatometry [1965Bog] 2173 HTXRD M ↔ T [1968Ruh] 1893 HTXRD -59- [1972Sta] 2023 ±20 HTXRD [1975Ald] 2038 ND [1975Sta] 2023 2073 2048 HTXRD [1976Ruh] 1863 HTXRD [1976Kuz] 2073 DTA [1983Sen] 2066 ±40 HTXRD [1987Cou] 2023 ±20 HTXRD [1987She] 2103 2083 2093 DTA [1991Gul] 2073 HTXRD [2001Fuj] 2080 (Af) 2018 RS This work 2066 2038 2052 8208 DTA, extrapolated, optimization [1965Bog] 2973 HTXRD [1987Cou] 2873 DTA [1985She] 2803 DTA [1987She] 2793 DTA [1988Sig] 2825 DTA [1988Yam] 2763 ± 25 pyrometry [1997And] 2803 DTA T ↔ F This work 2803 11212 optimization [1932Cla] 3047 ± 25 pyrometry [1954Cur] 3173 optical pyrometry [1966Nog1 ] 3026 ± 20 pyrometry [1975Sta] 3098 pyrometry [1977Sch] 3093 ± 40 microoptical pyrometry [1986Yam] 3076 ± 15 pyrometry [1985She] 3073 DTA [1987She] 3073 DTA [1987Cou] 3123 DTA [1988Sig] 3105 DTA [1988Yam] 3074 ± 25 pyrometry [1997And] 3073 DTA F ↔ L * This work 3073 89653 optimization *(at the stoichiometric composition for the optimized results) -60- Table 3-5. Experimental heat capacity, entropy and enthalpy of formation of monoclinic HfO2 at 298.15 K. Reference Heat capacity (J·mol-1·K-1) Entropy (J·mol-1·K-1) Enthalpy of formation (kJ·mol-1) [1932Rot] −1135.956 [1953Hum] −1113.195 ± 1.172 [1953Tod] 60.2496 59.33 ± 0.48 [1968Hub] −1144.742 ± 1.255 [1974Pap] −1133.864 ± 6.276 [1975Kor] −1117.630 ± 1.63 This work 61.76 59.43 −1117.628 Table 3-6. Sample compositions and the DTA results of the ZrO2 − HfO2 system. On heating On cooling Sample No. Composition (mol%)HfO2 As (K) Af (K) Ms (K) Mf (K) T0, (As+Ms)/2 (K) T0’, (Af+Mf)/2 (K) 1 6.7 1466 1515 1358 1313 1412 1414 2 8.2 1480 1526 1361 1321 1420.5 1423.5 3 10.3 1491 1536 1377 1340 1434 1438 4 12.0 1509 1555 1392 1349 1450.5 1452 5 13.8 1522 1566 1412 1369 1467 1467.5 6 18.2 1548 1599 1436 1391 1492 1495 7 33.1 1647 1701 1547 1497 1597 1599 8 67.3 1854 1914 1798 1750 1826 1832 Table 3-7. Comparison of the invariant reactions in the Zr − O system. Reaction Reference Temperature (K) Composition of phases (at.% O) [1986Abr] 2243 ± 10 10.0 ± 0.5 19.5 ± 2 10.5 ± 0.5L + hcp-Zr ⇔ bcc-Zr This work 2242 10.05 19.1 10.95 [1986Abr] 2338 ± 5 40 ± 2 35 ± 1 62 ± 1 L ⇔ hcp-Zr + F This work 2337 40.7 31.1 62.15 [1986Abr] 1798 63.6 ± 0.4 31.2 ± 0.5 66.5 ± 0.1F ⇔ hcp-Zr + T This work 1798 64.05 30.98 66.667 [1986Abr] 2983 66.6 66.6 − L ⇔ F This work 3055 65.78 65.78 − [1986Abr] 2403 ± 10 25 ± 1 25 ± 1 − L ⇔ hcp-Zr This work 2404 29.05 29.05 − -61- Table 3-8. Comparison of the invariant reactions in the Hf − O system. Reaction Reference Temperature (K) Composition of phases (at.% O) [1965Dom] 2523 1 3 8 [1963Rud] 2273 8 5 12 L + hcp-Hf ⇔ bcc-Hf This work 2522 3.34 2.9 6.9 [1965Dom] 2473 37 22 − [1963Rud] 2453 29 21 62 L ⇔ hcp-Hf + F This work 2512 30.4 19 61.5 [1973Ruh] 2398 63.6 22 − F ⇔ hcp-Hf + T This work 2379 65.2 19.4 66.3 L ⇔ F This work 3222 64.7 64.7 − [1965Dom] 2773 − − − [1963Rud] 2573 18 18 − L ⇔ hcp-Hf This work 2583 13.7 13.7 − -62- Chapter 4 Experimental study and thermodynamic modeling of the ZrO2 − LaO1.5 system 4.1. Literature review 4.1.1. Phase equilibria Many groups [1937War, 1955Bro, 1959Lef, 1962Per, 1963Lef, 1964Lin, 1968Rou3, 1971Rou, 1972Cab, 1973Pal, 1978Zoz, 1988Bas, 1990Zhe, 1995And, 1999Tab1, 2005Lak] contributed to the investigation of the phase equilibria of the ZrO2 − La2O3 system. [1937War] reported the liquidus temperature of six compositions with possible large experimental error. [1955Bro] firstly reported the phase relations for the ZrO2 − La2O3 system. However, no any intermediate compound was found, and wrong structural modifications on both ZrO2 and La2O3 were given. The reaction T ⇔ M + F was measured at 930°C, and the reported solubility of both tetragonal and monoclinic phases were around 4 mol% La2O3. Additionally, a wrong fluorite phase region was shown, which was actually the pyrochlore phase region according to the latter experimental reports of [1959Lef]. [1962Per] proposed that a compound with cubic CaF2-type structure existed in the La2O3 rich, and [1963Lef] presented a similar phase diagram with that of [1955Bro]. Lin and Yu [1964Lin] determined the phase relations above 1600°C, but didn’t give quantitative results for the liquidus. The structural information on both ZrO2 and La2O3 were wrong, and only the monoclinic ZrO2 and hexagonal La2O3 were shown in their reported phase diagram. The ZrO2-based CaF2-type solid solution was reported to be only stable in a limited temperature and composition range. In their work, the existence of a very wide pyrochlore La2Zr2O7 field was confirmed, but the compound reported by [1962Per] was not detected. The congruent melting point of La2Zr2O7 (P) was measured at 2250°C. Four invariant reactions were determined in their study: Liquid ⇔ P + H-La2O3 at 1925 ± 25°C, 82.5 ± 2.5 wt.% La2O3; M + Liquid ⇔ F, at 2325 ± 25°C; F ⇔ P + M, at 1775 ± 25°C, 30 wt.% La2O3; Liquid ⇔ F + P, at 2125 ± 25°C, 42.5 ± 2.5 wt.% La2O3. Rouanet [1968Rou3, 1971Rou] studied this system and reported a detailed phase diagram above 1800°C over the whole composition range. The correct stabilization region of the fluorite phase was given for the first time in their work. The solidus for the F / F + L and X-La2O3 / X-La2O3 + L were estimated according to the well-determined liquidus data by optical pyrometry. The solid-state phase transitions were determined by the HTXRD using a -63- Re ribbon under reducing conditions (He + ≈10% H2). The pyrochlore La2Zr2O7 was observed to melt congruently at 2280°C, and the eutectic reaction Liquid ⇔ F + P was determined to be at 2220°C and 25 mol% La2O3, which was very consistent with the result 2224 ± 10°C measured by [1972Cab]. The determined reaction F ⇔ P + T was at 1950°C and 7 mol% La2O3. At the La2O3-rich, a eutectic reaction occurred at 2030°C and 62.5 mol% La2O3, where the liquid phase transformed into X-La2O3 and a cubic Tl2O3-type C2 phase. However, due to the vaporization at high temperatures, the X phase could not be well studied, and its maximum solubility of ZrO2 was around 30 mol% ZrO2 at 1900°C. The temperature of the peritectic reaction Liquid + P ⇔ C2 was not reported in their papers. The C2 phase, which is stable in a very limited temperature and composition range, decomposes into La2Zr2O7 and X- La2O3 phase at the temperature 1950°C, 52 mol% La2O3. With decreasing the temperature, the eutectoid reaction X-La2O3 ⇔ P + H-La2O3 occurs at 1900°C. A possible invariant reaction for H-La2O3, P and the A-La2O3 phases was not reported in Rouanet’s work [1968Rou3, 1971Rou]. [1978Zoz] studied the solid phase formation at 1000-1900°C and in the composition range of 1-50 mol% La2O3 using XRD, IR spectroscopy, X-ray dilatometry, and crystal optics. The melting point of La2Zr2O7 was also measured at 2230 ± 20°C by high temperature thermal analysis. They determined the homogeneity range of the pyrochlore phase at different temperatures by lattice constant measurements. With the rise of the temperature, the reported width of the nonstoichiometry was more than 10 mol% La2O3 which were comparable to the data determined by [1962Per, 1973Pal, 1990Zhe], but was argued by very recent work [1999Tab1] that the pyrochlore phase region should be considerably narrower and less than 2 mol% LaO1.5 in width. The solubility of La2O3 in tetragonal ZrO2 proposed by [1978Zoz] was less than 1 mol%. [1988Bas] investigated the range of 0-15 mol% La2O3 using X-ray diffraction and thermal analysis. The eutectoid decomposition T ⇔ M + P was determined to occur at 1100°C, 0.75 mol% La2O3. [1995And] studied the T ⇔ M transformation in the same composition range, the same reaction was determined at 1110°C, 0.75 mol% La2O3, which was in good agreement with that of [1988Bas]. [2005Lak] reinvestigated some critical reactions involving the liquid phase by DTA: L ⇔ P (2340°C), L ⇔ P + F (2315°C), and L ⇔ P + X-La2O3 (1980°C). However, the same compositions of liquid phases for those reactions as the results of [1971Rou] were reported, and there were no more details on how many samples were studied. -64- Some general conclusions on the phase relation of the ZrO2 − LaO1.5 system can be made from review of the literature review outlined above: (1). The high temperature fluorite phase cannot be stabilized to low temperature by the doping of La, and the solubility of La in the tetragonal phase is not clear. (2). The pyrochlore phase melts congruently, but the homogeneity range is not clear yet due to the scattered experimental data. (3). The high temperature invariant reactions are well determined. The existence of the C2 phase reported by [1968Rou3, 1971Rou] was not confirmed by other works, and could be the fluorite phase, by taking account of the similarities of the many ZrO2 − REO1.5 systems. The compilation of all the invariant reactions in literature is given in Table 4-1. 4.1.2. Thermodynamic data [1971Kor] determined the enthalpy of formation of the stoichiometric pyrochlore phase by combustion in a bomb calorimeter. Du et al. [1995Du] carried out a thermodynamic assessment on the ZrO2 − La2O3 system based on all available phase diagram and thermodynamic data. They treated the fluorite phase and X-La2O3 phase as a miscibility gap, and adopted the substitutional solution models for all phases. [1995Bol] measured the enthalpy of formation of the stoichiometric pyrochlore phase at 974K by using high-temperature solution calorimetry in molten lead borate, and then derived the standard enthalpy of formation at 298.15 K. The heat capacity of La2Zr2O7 was measured by [1997Bol] from 4 to 400 K by adiabatic calorimetry. By using drop calorimetry, they also measured the enthalpy increment relative to 298.15 K from 500 to 900 K. Some thermodynamic data are derived and smoothed from 4 to 1000 K. [1998Jac] determined the Gibbs energy of formation of La2Zr2O7 (with respect to monoclinic ZrO2 and A-type LaO1.5) by a solid-state galvanic cell involving composition- graded electrolyte (xLaF3+(1-x)CaF2), in the temperature range of 870-1240 K. They reported a function of − 133800 − 10.32T for Gibbs energy of formation of the pyrochlore phase. The calculated enthalpy of formation from oxides was − 133.8 ± 5 kJ.mol-1 (per mole of compound). The standard entropy of formation from oxides was derived at 10.32 J.mol-1.K-1 (per mole of compound). [2002Rog] also determined the standard molar Gibbs energy of formation of La2Zr2O7 (with respect to monoclinic ZrO2 and A-type LaO1.5) by the e.m.f measurements in the -65- temperature range 1073-1273 K. The calculated enthalpy of formation was − 134.3 ± 0.8 kJ.mol-1 (per mole of compound), and the calculated standard entropy of formation was 10.54 ± 0.48 J.mol-1.K-1 (per mole of compound). The enthalpy increment (HT-H298) for the pyrochlore phase La2Zr2O7 was measured using drop calorimetry in a recent work of Sedmidubsky et al. [2005Sed] in the temperature range 888-1567 K. Combining the heat capacity data reported by [1995Bol], Sedmidubsky et al. derived the heat capacity function of the La2Zr2O7 in the temperature range 298-1550 K. In a more recent paper, [2005Nav] reported a less negative value (− 22585 J.mol-1, per mole of cations) for the enthalpy of formation of pyrochlore, without giving the detailed experimental method. The literature data on the enthalpy of formation of the pyrochlore phase are compiled in Table 4-2. 4.2. Experimental results and discussion Only two compositions in the ZrO2 − LaO1.5 system with 25 mol% and 75 mol% LaO1.5 were prepared, to determine the phase equilibria of tetragonal + pyrochlore, and pyrochlore + A-La2O3. However, the A-La2O3 phase at 75 mol% LaO1.5 reacts with moisture in air in very short time so that it is difficult to obtain dense samples for SEM or EPMA analyses. Therefore, only the tetragonal + pyrochlore phase equilibrium data at 1400°C, 1600°C, and 1700°C were finally determined from the composition 25 mol% LaO1.5. The XRD results of the samples containing 25 mol% and 75 mol% LaO1.5 after the pyrolysis at 700°C for 3h are shown in Fig. 4-1, which indicates that the pyrolyzed powder is poorly crystallized with very fine particle. Fig. 4-2 gives the XRD results for the samples heat treated at 1600°C. The sample with 25 mol% LaO1.5 presents the pyrochlore + monoclinic structure, where the monoclinic phase formed from the tetragonal phase by cooling. The sample with 75 mol% LaO1.5 presents the pyrochlore + La(OH)3 structure, in which La(OH)3 formed from A-La2O3 and water. The SEM back scattered electron image (×1000) of the sample with 25 mol% LaO1.5 heat treated at 1600°C for 72h is shown in Fig. 4-3, where the grey areas are the monoclinic phase, and the white areas are pyrochlore. It can be seen that the sample is quite homogeneous, and many cracks in the sample are caused by the volume change of the martensitic tetragonal-to-monoclinic transformation during cooling. The measured content of LaO1.5 in both the tetragonal and pyrochlore phases at different temperatures are given in Table 4-3. The composition range of the pyrochlore phase is very narrow in the studied temperature range. At 1400°C it is almost a stoichiometric compound. -66- This is consistent with the conclusion of [1999Tab1] that the width of the pyrochlore field is less than 2 mol%. Due to the temperature limitation of the current experiments, it was not possible to confirm the composition range of the fluorite phase in ZrO2-rich region, and its possible existence in the LaO1.5-rich region. 10 20 30 40 50 60 70 80 25 mol% LaO1.5 2θ(degree) In te ns ity (A rb .u ni ts ) 75 mol% LaO1.5 Figure 4-1. The XRD patterns of the as-pyrolysed ZrO2 − LaO1.5 samples at 700°C for 3h. 20 30 40 50 60 70 La(OH)3 La(OH)3 P M P P P P MM M M M M M La(OH)3 La(OH)3 La(OH)3 MM M M M P P P P PPP 25 mol% LaO1.5 P + M 75 mol% LaO1.5 P + La(OH)3 In te ns ity (A rb .u ni ts ) 2θ(degree) M Figure 4-2. The XRD peaks of the samples after heat treatments at 1700°C (The sample with 25 mol% LaO1.5 presents the P + M structure. The sample with 75 mol% LaO1.5 presents the P + La(OH)3 structure). 4.3. Selected experimental data for optimization 4.3.1. Phase diagram data The liquidus and high temperature phase equilibria data and invariant reactions reported by [1968Rou3, 1971Rou, 1972Cab, 2005Lak] are taken for the current assessment, together with the experimental data on the tetragonal + pyrochlore phase equilibrium obtained in this work. However, the C2 phase reported by [1968Rou3, 1971Rou] is considered as the fluorite phase according to the experience from other systems. For the temperature of the -67- reaction H-La2O3 ⇔ A-La2O3 + P, a start value of 2073 K is arbitrarily given, due to the lack of experimental data. The solubility of ZrO2 in the A-La2O3 phase is taken to be lower than 2 mol%, which is comparable to the result for the A-Nd2O3 phase. The homogeneity range of the pyrochlore phase is thought to be symmetric on both sides of the stoichiometric composition. Figure 4-3. The SEM back scattered electron image (×1000) of the ZrO2-25 mol% LaO1.5 sample heat treated at 1600°C for 72h (the grey areas are the monoclinic phase, and the white ones are pyrochlore). 4.3.2. Thermodynamic data The data of the enthalpy of formation of the pyrochlore phase reported by [1971Kor, 1995Bol, 1998Jac, 2002Rog] show good agreement. They are more negative than the value reported by [2005Nav]. All of these data are considered, but not given a high weight for the assessment. The assessed result of the thermodynamic property (CTlnT + ET-1 + FT2 part of the Gibbs energy) of the pyrochlore phase given by [2005Sed] is accepted in this work. 4.4. Optimization procedure The Gibbs energy parameters of the pyrochlore phase were preliminarily determined from the literature data on thermodynamic properties. Treating the pyrochlore phase as a stoichiometric compound, the phase diagram was roughly calculated by using the solid phase boundary and liquidus data, with only very limited number of parameters. Finally, a full optimization was carried out by taking the homogeneity range of pyrochlore into account. The parameters were adjusted simultaneously to fit all the selected experimental phase equilibria -68- and thermodynamic data. The thermodynamic parameters for all phases are summarized in Appendix. 4.5. Calculated results and discussion The calculated ZrO2 − LaO1.5 phase diagram is shown in Fig. 4-4. Most of the selected experimental data are reasonably reproduced within the limits of experimental uncertainties. The optimized invariant reactions are included in Table 4-1. The eutectic points for the reactions L ⇔ F + P and L ⇔ F + X-La2O3 calculated in this work are 2529 K (39.6 mol% LaO1.5) and 2288 K (77.5 mol% LaO1.5) respectively, which fall well among the results of [1968Rou3, 1971Rou, 2005Lak]. The calculated liquidus presents some deviation from the experimental data of [1971Rou], because the work of [2005Lak] was considered in the optimization. Moreover, the sharp liquidus reported by [1971Rou] was also questioned by the previous review on this system [1998Ond]. For the melting point of the pyrochlore phase, the result of the present work (2556 K) is closer to the data of [1971Rou] than that of [2005Lak]. The results of [2005Lak] are not given a higher weight for assessment because no detailed information on the measurements is given. However, in a parallel work on the ZrO2 − LaO1.5 − AlO1.5 system, it has been proved that the optimized phase diagram without taking account of the data of [2005Lak] will has a worse agreement with the liquidus projection of the ternary phase diagram. In fact, because the experimental uncertainty of 100 K at such temperatures is normal for many systems, the present calculations are thought to be reasonable. In the LaO1.5-rich region, the calculated data of the reactions L + P ⇔ F (2309 K, 75.6 mol% LaO1.5), F ⇔ P + X-La2O3 (2199 K, 69.1 mol% LaO1.5) and X-La2O3 ⇔ P + H-La2O3 (2165 K, 86 mol% LaO1.5) show reasonable agreements with the experimental results obtained by Rouanet [1971Rou], while the compositions of the solid phases could not be well fitted, because it was already accepted that the homogeneity range of the pyrochlore phase is not so wide, and the composition of X-La2O3 phase reported by [1971Rou] is also less reliable for their experimental difficulties at high temperatures. For the reaction H-La2O3 ⇔ P + A- La2O3, the present calculation reveals a value of 1994 K. -69- Figure 4-4. The calculated ZrO2 − LaO1.5 phase diagram together with experimental data. At the ZrO2-rich side of the diagram, the experimental data on the P + T equilibrium obtained in this work are well reproduced. However, the calculated temperature of the invariant reaction F ⇔ P + T cannot be fitted to value as high as 2223 K reported by [1971Rou], unless a very positive enthalpy of formation of the fluorite phase is used. Fig. 4-5 shows the calculated metastable ZrO2 − LaO1.5 phase diagram without the pyrochlore phase. In this work, the enthalpy of formation of the fluorite phase at 50 mol% LaO1.5 with respect to the monoclinic ZrO2 and A-type LaO1.5 is – 939 J.mol-1 at 298.15 K. A much more positive enthalpy of formation will make the fluorite phase only stable at high temperatures. Owing to the similarities of the ZrO2 − REO1.5 systems, it is reasonable to assume that before ordering occurs, the fluorite phase is always stable at room temperature. Additionally, the calculated phase diagram in Fig. 4-5 presents a wide tetragonal + fluorite two-phase region, which is also consistent with the tendency that with increasing the ionic radius of RE+3, the tetragonal + fluorite two-phase region enlarges gradually. The calculated temperature of the reaction T ⇔ P + M is 1363 K, which is only 4 K lower than the T0 temperature for pure ZrO2. Moreover, the calculated composition of the tetragonal phase for this reaction is only 0.13 mol% LaO1.5 which is consistent with present experimental result. The higher value 1.5 mol% LaO1.5 reported by [1988Bas, 1995And] is thought to be the composition at a nonequilibrium state. -70- Figure 4-5. The calculated ZrO2 − LaO1.5 phase diagram without the pyrochlore phase together with experimental data. Figure 4-6. Calculated and experimental heat capacity of the stoichiometric pyrochlore phase (per mole of cations) in the ZrO2 − LaO1.5 system. Figure 4-7. Calculated enthalpy increment (HT-H298) of the stoichiometric pyrochlore phase (per mole of cations) in the ZrO2 − LaO1.5 system together with experimental data. Figure 4-8. The calculated Gibbs energy of formation of the stoichiometric pyrochlore phase (per mole of cations) in the ZrO2 − LaO1.5 system together with experimental data. Though the enthalpy of formation of the pyrochlore phase was experimentally measured by several groups [1971Kor, 1995Bol, 1998Jac, 2002Rog, 2005Nav], the result obtained in this work doesn’t fit well any of them. A parallel work on the modeling of the ZrO2 − LaO1.5 − AlO1.5 system by Fabrichnaya et al. reveals that the values reported by -71- [1971Kor, 1995Bol, 1998Jac, 2002Rog] are too negative to reproduce the experimental tie- lines [2005Lak]. Finally, a value of – 27516 J.mol-1 was obtained for the enthalpy of formation of pyrochlore in this work, which is slightly less stable than the data of [1971Kor, 1995Bol, 1998Jac, 2002Rog], but more negative than the value around – 22585 J.mol-1 included in [2005Nav]. The calculated heat capacity and enthalpy increment (HT-H298) are plotted in Fig. 4-6 and Fig. 4-7 respectively, showing good agreement with the experimental data. In Fig. 4-8, owing to the more negative enthalpy of formation of the pyrochlore phase of the data [1998Jac, 2002Rog], some deviation also exists between the present calculated and their experimental Gibbs energies of formation of the pyrochlore phase. Table 4-1. The invariant reactions in the ZrO2 − LaO1.5 system. Reaction Type Reference Temperature (K) Composition of phases (mol% LaO1.5) [1971Rou] 2493 40 − − [1972Cab] 2497 ± 10 − − − [2005Lak] 2588 40 − − L ⇔ F + P eutectic This work 2529 39.6 31.4 48.2 [1971Rou] 2223 13.1 − − F ⇔ T + P eutectoid This work 2155 13.2 1.7 48.4 [1988Bas] 1373 1.5 − − [1995And] 1383 1.5 − − T ⇔ M + P eutectoid This work 1363 0.13 0.04 49.8 [1964Lin] 2523 − 50 − [1971Rou] 2553 − 50 − [1972Por] 2433 ± 50 − 50 − [1978Zoz] 2503 ± 20 − 50 − [2005Lak] 2613 − 50 − L ⇔ P congruent This work 2556 49.4 49.4 − [1971Rou] 2318 75.6 55 67 L + P ⇔ F peritectic This work 2309 75.6 51.4 67.4 [1971Rou] 2303 76.9 71 82.4 [2005Lak] 2253 76.9 − − L ⇔ F + X eutectic This work 2288 77.5 68.7 83.9 [1971Rou] 2223 68.4 55 83.7 F ⇔ P + X eutectoid This work 2199 69.1 51.5 85.2 -72- [1971Rou] 2173 83.7 55 87.3 X⇔ P + H eutectoid This work 2165 86 51.5 87.2 H ⇔ P + A eutectoid This work 1994 90.4 51.4 98.2 Table 4-2. The reported enthalpy of formation of the pyrochlore phase (ZrO2-50 mol% LaO1.5, for one mole of cations, from the monoclinic ZrO2 and A-type LaO1.5). Reference Value (J.mol-1) Temperature (K) [1971Kor] −31470 ± 1020 298.15 [1995Bol] −33950 ± 1600 −34025 ± 1600 974 298.15 [1998Jac] −33450 ± 1250 298.15 [2002Rog] −33575 ± 200 298.15 [2005Nav] −22585 298.15 This work −27515.6 298.15 Table 4-3. The measured phase composition data (mol% LaO1.5) for the tetragonal + pyrochlore phase equilibria in the ZrO2 − LaO1.5 system at different temperatures. Temperature (K) T P 1673 0.7 ± 0.3 49.9 ± 0.5 1873 0.6 ± 0.3 48.7 ± 0.5 1973 0.6 ± 0.3 48.4 ± 0.5 -73- Chapter 5 Experimental study and thermodynamic modeling of the ZrO2 – NdO1.5 system 5.1. Literature review 5.1.1. Phase equilibria The phase equilibria of the ZrO2 – Nd2O3 system were experimentally studied by many groups [1955Bro, 1956Rot, 1965Dav, 1965Glu, 1970Rou, 1971Rou, 1981Gav1, 1982Gav, 1995And, 1995Kat]. [1955Bro] firstly constructed a phase diagram for the ZrO2 – Nd2O3 system using X- ray diffraction. However, wrong structural modifications on both ZrO2 and Nd2O3 sides were given. The compound Nd2Zr2O7 was not reported, and a miscibility gap of the cubic phase was plotted in combination with an invariant reaction with the Nd2O3-based solid solution at around 1100°C. This phase diagram was slightly modified by [1956Rot] by including pyrochlore Nd2Zr2O7 (P). Later, [1962Per] reported a similar phase diagram to that of [1955Bro] by indicating the pyrochlore phase and a higher temperature for the invariant reaction F ⇔ P + A-Nd2O3. [1965Dav, 1965Glu] studied the phase relations in the complete composition range up to 1700°C by using XRD measurements. In the ZrO2-rich region, the F + T two-phase region was determined, and the fluorite phase could be stabilized to very low temperature according to [1965Dav]. The minimum solubility of Nd2O3 in the fluorite phase was reported for different temperatures. According to both work, the tetragonal and monoclinic phases can dissolve as much as 2-4 mol% Nd2O3. At the Nd2O3-rich side, the low temperature hexagonal structure of the Nd2O3 solid solution coexists with the pyrochlore phase. Above 1500° C, a phase with Mn2O3 structure (C-type) forms between the Nd2O3-rich hexagonal (H-type) and pyrochlore phases by a eutectoid reaction C2 ⇔ X-Nd2O3 + P. The maximum solubility of Nd2O3 in pyrochlore is 40 mol% at 1500-1700°C. The maximum solubility of ZrO2 in the H- type Nd2O3 was determined as 5 mol%. [1970Rou, 1971Rou] measured the ZrO2 – Nd2O3 phase diagram above 1400° C. The liquidus was determined by the cooling curve of the thermal analysis in the whole composition range, and the solidus was accordingly estimated. The solid-state phase transitions above 1800°C were observed by HTXRD using a Re ribbon under reducing conditions (He + ~10% H2). The pyrochlore phase was estimated to transform into fluorite at -74- around 2300° C, what is consistent with 2220°C reported by [1982Zoz], but does not agree with 2000°C reported by [1974Mic]. At high temperatures, Rouanet [1970Rou, 1971Rou] revealed two invariant reactions: L ⇔ C2 + X-Nd2O3 (2100°C, L: 70 mol% Nd2O3, C2: 60 mol% Nd2O3) and X-Nd2O3 ⇔ H-Nd2O3 + C2 (2060°C, H-Nd2O3: 87 mol% Nd2O3; X-Nd2O3: 80 mol% Nd2O3; C2: 59 mol% Nd2O3). The X-type Nd2O3-based solid solution was not well studied because of its high volatility, and a possible invariant reaction involving H-Nd2O3, A- Nd2O3, and the so-called Mn2O3 structured C2 phase was not detected in their work. At 1440° C, the C2 phase was found to decompose into pyrochlore and A-Nd2O3 using the X-ray diffraction, which is consistent with the work of [1965Glu]. [1972Por] measured the melting point of the composition Nd2Zr2O7 to be 2320°C. The respective result of [1982Zoz] was 2280 ± 20°C. Both studies revealed that the melting point was probably very close to the pyrochlore ⇔ fluorite transition temperature. Gavrish et al. [1981Gav1, 1982Gav] studied the phase formation of the ZrO2 – Nd2O3 system in the whole composition range between 1300 and 1900° C by X-ray diffraction and crystal-optical methods. However, some metastable phases were reported in their paper probably because the heat treatment was only done for a short time and not efficient to form the stable phases. They obtained same results on the phase relations as [1970Rou, 1971Rou] at high temperatures. The homogeneity range of the pyrochlore phase was found to be 30-33.3 mol% Nd2O3 at 1500°C, and increased to 20-55 mol% Nd2O3 at 1900°C. For the A-type Nd2O3 phase, the reported maximum solubility of ZrO2 was around 10 mol%. [1991Wit] studied the ZrO2 – NdO1.5 system using electron and XRD at 1600°C. The pyrochlore phase field was found to occur from 38 to 55 mol% NdO1.5. In a study of the influence of the composition on the T ⇒ M transformation, [1995And] derived the eutectoid point of the reaction T ⇔ M + P at 880° C and 1.0 mol% Nd2O3 using DTA and dilatometry. The F + T phase equilibrium was experimentally examined by [1995Kat], and the phase boundary data of both the fluorite and the tetragonal phase were determined at 1600, 1700, and 1800° C. The invariant reactions reported in literature are collected in Table 5-1. 5.1.2. Thermodynamic data [1971Kor] determined the enthalpy of formation of the stoichiometric pyrochlore phase (from oxides) by combustion in a bomb calorimeter and reported a value of –27719 J.mol-1 (per mole of cations). However, [2005Nav] reported a less negative value of around – 16200 J.mol-1 (per mole of cations) recently. -75- Lutique et al. [2003Lut1, 2003Lut2] measured the heat capacity of stoichiometric Nd2Zr2O7 from 300 K to 1600 K by differential scanning calorimetry and from 0.45 K to 400 K by adiabatic calorimetry and the hybrid adiabatic relaxation method. The heat content (HT-H298) for the pyrochlore phase Nd2Zr2O7 was measured using drop calorimetry in a recent work of Sedmidubsky et al. [2005Sed] in the temperature range 484-1487 K. Very recently, [2005Oht] modeled the fluorite ⇔ pyrochlore order-disorder transition in this system with a model (Zr+4,Nd+3)0.5(Nd+3,Zr+4)0.5(O-2,Va)2. Two miscibility gaps of fluorite were shown in their work, but poorly reasonable phase relationships were presented. 5.2. Experimental results and discussion 5.2.1. The as-pyrolysed state Totally sixteen compositions were prepared for the study of the ZrO2 – NdO1.5 system. The XRD patterns of selected samples after the pyrolysis at 1000°C for 1h are shown in Fig. 5-1. Very clear peaks in all samples reveal that well-crystallized powders already can be obtained under these conditions compared with the poor crystallized samples after pyrolysis at 700°C for the other systems. For the samples less than 70 mol% NdO1.5, the XRD patterns present mostly peaks of the tetragonal or fluorite phase, and above 70 mol% NdO1.5, the existence of the A-Nd2O3 phase can be identified from the XRD peaks. The phase identified together with the compositions of the samples are listed in Table 5-2. 20 30 40 50 60 70 80 80 mol% NdO1.5 70 mol% NdO1.5 50 mol% NdO1.5 30 mol% NdO1.5 10 mol% NdO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) 20 30 40 50 60 70 80 M M M M M M M M M MM F F F F M In te ns ity (A rb .u ni ts ) 2θ (degree) M Figure 5-1. The XRD patterns of the as- pyrolysed ZrO2 – NdO1.5 samples at 1000°C for 1h. Figure 5-2. The XRD patterns for the ZrO2-10 mol% NdO1.5 sample heat treated at 1600°C for 72h. -76- 5.2.2. The tetragonal + fluorite phase equilibrium The heat treated sample containing 10 mol% NdO1.5 presents well-distributed monoclinic + fluorite structure according to the XRD patterns in Fig. 5-2. Fig. 5-3 shows the SEM back scattered electron image (×1000) of the same sample. The grey areas in Fig. 5-3 are the monoclinic phase formed from the tetragonal phase during cooling, and the white ones are the fluorite phase. Table 5-3 gives the determined compositions for the tetragonal and fluorite phases. A wide tetragonal + fluorite two-phase region can be derived according to the present experimental data, which are consistent with the data reported by [1995Kat]. The solubility of NdO1.5 in the tetragonal phase is only around 2 mol% NdO1.5 in the studied temperature range. Figure 5-3. The SEM back scattered electron image (×1000) of the sample containing 10 mol% NdO1.5 heat treated at 1600°C for 72h (the grey areas are the monoclinic phase formed from the tetragonal phase during cooling, and the white ones are the fluorite phase). 5.2.3. The fluorite + pyrochlore phase equilibrium The order-disorder transition between the fluorite and pyrochlore phases presents complex characters according to the present experimental work. In the ZrO2-rich region, 10 samples with compositions from 30 to 40 mol% NdO1.5 (without 31 mol%) with the step of each 1 mol% were prepared, and heat treated at different temperatures. Clear superstructure peaks of pyrochlore with different intensities can be found for all the compositions. Up to 1600°C, the XRD peaks of all those samples do not show visibly separated peaks for the fluorite and pyrochlore phases. Probably the samples are not completely ordered at those temperatures. The XRD results of the samples heat treated at 1700°C confirm this point. At this temperature separated peaks of fluorite and pyrochlore can be found for the compositions -77- from 32 to 34 mol% NdO1.5. Fig. 5-4 shows the lattice parameters determined in this work by XRD using Si and Al2O3 powder as internal standard and those data collected from literature. The fluorite + pyrochlore two-phase region obtained from the difference of the lattice parameters is very narrow (around 30 to 36 mol% NdO1.5). 0 10 20 30 40 50 60 70 80 90 100 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 F+P Vegard's Slope F+A F 1997Kho 1997Cha 1991Wit 1959Col 1973Str 1980Dij 1962Per 1959Lef 2005Har Vegard's Slope This work, 1873 K This work, 1973 K NdO1.5 (Mol% ) La tti ce p ar am et er (Å ) T+F F P P+F 25 30 35 40 45 50 55 70 mol% 65 mol% 60 mol% 50 mol% 40 mol% 38 mol% 36 mol% 34 mol% 32 mol% 30 mol% In te ns ity (A rb .u ni ts ) 2θ (degree) P P P Figure 5-4. The lattice parameters of fluorite and pyrochlore in the ZrO2 – NdO1.5 system determined by this work and those data collected from literature. Figure 5-5. The XRD patterns for the ZrO2 – NdO1.5 samples (30-70 mol% NdO1.5) heat treated at 1600°C. Some selected XRD patterns for the samples heat treated at 1600°C are shown in Fig. 5-5. The intensities of the superstructure peaks of pyrochlore phases gradually enhance with increasing the NdO1.5 content up to 50 mol%, and then reduce at higher NdO1.5 contents due to the increase of the amount of the fluorite phase. The sample containing 70 mol% NdO1.5 consists of almost pure fluorite. In the NdO1.5-rich region, the XRD peaks of the fluorite and pyrochlore phases are easily separated after the heat treatment at 1600°C even for a short time (Fig. 5-5). Combining the XRD measurements with EDX analysis, the determined compositions for the fluorite + pyrochlore equilibrium at NdO1.5-rich side are given in Table 5-3, and also marked in Fig. 5-4 by the lattice parameter measurement. However, the homogeneity range of pyrochlore at the ZrO2-rich side is much larger than that at the NdO1.5- rich side according to present experimental data. Considering the difference of the ordering kinetics of the pyrochlore phase in different regions, it is reasonable to conclude that the ordering of pyrochlore at the ZrO2-rich side should be a long-time process, and it is even difficult to reach complete thermodynamic equilibrium at 1700°C after 36 h, while it is much easier for the samples in the NdO1.5-rich region. Thus, the data on the two-phase region in ZrO2-rich obtained from XRD measurements are thought to be still in metastable state. -78- Finally, different phase regions are divided according to the change of lattice parameters in Fig. 5-4, assuming that the pyrochlore phase has the symmetric homogeneity range. The Vegard’s slope is constructed based on the lattice parameter of pure zirconia in literature [1992Yas], which assessed this value from abundant ZrO2-based systems. However, it seems that the lattice parameter of completely ordered pyrochlore at 50 mol% NdO1.5 doesn’t fit onto this slope. 5.2.4. The fluorite + A-Nd2O3 and pyrochlore + A-Nd2O3 phase equilibria Fig. 5-6 is the SEM photograph for the fluorite + A-type Nd2O3 microstructure of the sample 80 mol% NdO1.5 heat treated at 1873 K for 72h, where the grey areas are the fluorite phase, and the white ones are the A-Nd2O3 phase with lathy morphology. According to the XRD measurements, the samples with the compositions 60-80 mol% NdO1.5 heat treated at 1673 K presents the pyrochlore and A-Nd2O3 structure. This result is consistent with the invariant reaction F ⇔ P + A-Nd2O3 which occurs at 1713 K reported by [1971Rou]. The measured compositions of the fluorite phase and the A-Nd2O3 phase are given in Table 5-3. The composition of the fluorite phase of fluorite + A-Nd2O3 phase equilibrium at 1873 K is rather close to that of fluorite + pyrochlore phase equilibrium, and indicates that the fluorite phase will decompose at some lower temperature in this region. Figure 5-6. The SEM back scattered electron image (×3000) of the sample with 80 mol% NdO1.5 heat treated at 1600°C for 72h (the grey areas are the fluorite phase, and the white ones are the A-type Nd2O3). -79- 5.3. Selected experimental data for optimization The liquidus data and the invariant reactions at the NdO1.5-rich side reported by [1971Rou], the phase boundary data of tetragonal + fluorite, fluorite + pyrochlore, and fluorite + A-Nd2O3 phase equilibria obtained in this work and those of [1995Kat, 1999Tab] are accepted as phase diagram data. The heat content data for pyrochlore determined by [1997Bol, 2005Sed] and in this work are consistent and are taken for the optimization of thermodynamic properties, as well as those data for 30 mol% NdO1.5 obtained in this work. Furthermore, the heat capacity data for the 50 mol% NdO1.5 pyrochlore measured by [2003Lut1, 2003Lut2] are also considered for the optimization. The enthalpy of formation of pyrochlore reported by [1971Kor] is considered, but not given much weight in the assessment, due to the proved uncertainty in the ZrO2 – LaO1.5 system. 5.4. Optimization procedure As the first step, the phase equilibria without the ordered pyrochlore phase were roughly optimized by adopting the liquidus, tetragonal + fluorite phase boundary data and the heat content data for the ZrO2-30 mol% NdO1.5 sample, with limited number of parameters. Then, by treating the pyrochlore phase as the stoichiometric compound, a further assessment was done by adding the heat content and enthalpy of formation data of the pyrochlore phase. Finally, a full assessment is carried out by simultaneously using all selected data. For the fluorite phase, a TlnT contribution to zeroth order interaction parameter was applied to fit the experimental enthalpy increment data. For the tetragonal, X-, H- and A-type phases, only one interaction parameter was adopted because they are only stable at a limited range of composition and temperature. No any interaction parameter was used for the monoclinic phase because of its negligible homogeneity range. The optimized thermodynamic parameters for all phases are given in Appendix. 5.5. Calculated results and discussion The calculated ZrO2 – NdO1.5 phase diagram is presented in Fig. 5-7, compared with the experimental data. The invariant reactions obtained in the calculation are listed in Table 5- 1 together with the experimental results. Due to a wide tetragonal + fluorite two-phase region, the fluorite phase can not be completely stabilized to low temperature. It decomposes into the tetragonal and pyrochlore phases at 1487 K and 23.4 mol% NdO1.5 according to the present calculation. The calculated -80- invariant reaction T ⇔ M + P occurs at 1326 K and 1.0 mol% NdO1.5, which is consistent with the composition reported by [1995And]. However, the temperature (1153 K) suggested for the reaction by [1995And] is much lower, and is actually the temperature of the martensitic transformation, which is not corresponding to this invariant reaction. The calculated T0 line for the monoclinic and tetragonal phases in Fig. 5-8 reproduces well the data of [1995And, 1993Yas]. For the diffusionless fluorite to tetragonal transition, the present calculation gives the prediction that the T′ phase can be only obtained for the compositions less than 12 mol% NdO1.5. Figure 5-7. The calculated ZrO2 – NdO1.5 phase diagram compared with the experimental data. The experimental data on the fluorite + pyrochlore phase equilibrium are reproduced well within the experimental limits. To fit the phase boundary of the fluorite phase at the NdO1.5-rich side, the congruent transition temperature has to be elevated by 11 K with respect to 2573 K estimated by [1971Rou]. Compared to the ZrO2 – LaO1.5 system, the homogeneity range of the pyrochlore phase in the ZrO2 – NdO1.5 system is considerably larger. The temperature of the invariant reaction F ⇔ P + A-Nd2O3 is calculated to be 1763 K, which is 50 K higher than the result reported in [1971Rou], while the calculated compositions of the fluorite and pyrochlore phases show deviation with the experimental data [1971Rou] within 5 mol% NdO1.5. The present results are thought to be more reasonable than the data obtained by XRD measurements in [1971Rou], because they are optimized from the more reliable phase -81- boundary data obtained in this work. The calculated invariant reactions L ⇔ F + X-Nd2O3 and X-Nd2O3 ⇔ H-Nd2O3 + F show reasonable agreement with the experimental data of [1971Rou] except some deviations on the compositions of the terminal solutions. Considering the large experimental error in this region, the present calculations are reasonably acceptable. At high temperatures, the calculated invariant reactions L ⇔ F + X-Nd2O3 (2393 K, L: 84.1 mol% NdO1.5) and X-Nd2O3 ⇔ F + H-Nd2O3 (2330 K, X: 92.1 mol% NdO1.5) are considerably consistent with those data reported by Rouanet [1971Rou] within the limits of uncertainties. The reaction H-Nd2O3 ⇔ F + A-Nd2O3 is predicted at 2169 K in this work. The enthalpies of formation of fluorite and pyrochlore (per mole of cations) of ZrO2- 50 mol% NdO1.5 at 298 K calculated in this work are – 8029 J.mol-1 and – 18169 J.mol-1, respectively, which are comparable to those data of the ZrO2 – LaO1.5 system. Fig. 5-9 and Fig. 5-10 present the experimental and calculated heat content for the composition 30 mol% NdO1.5 and 50 mol% NdO1.5, respectively. For the 30 mol% NdO1.5 sample with fluorite structure, the calculation shows some deviation with the experimental data at high temperatures. A better fit can be reached if a larger value for the TlnT part of the interaction parameter is used. However, finally this value is selected to be – 32 by taking the other ZrO2 – Figure 5-8. The calculated ZrO2 – NdO1.5 partial phase diagram, and T0 lines for monoclinic + tetragonal and tetragonal + fluorite equilibria together with experimental data. Figure 5-9. The calculated heat content (HT- H298) of the sample ZrO2-30 mol% NdO1.5 together with experimental data. -82- Figure 5-10. The calculated enthalpy increment (HT-H298) of the ZrO2-50 mol% NdO1.5 sample together with experimental data. Figure 5-11. The calculated heat capacity of stoichiometric pyrochlore in ZrO2 – NdO1.5 system together with the experimental data. REO1.5 system into account, and also because a coefficient with larger value for this TlnT part can question the reasonability of thermodynamic properties. For the pyrochlore at 50 mol% NdO1.5, good consistency is found between present experimental data and those of [2005Sed, 1997Bol], and the calculation reproduces experimental well except slight discrepancy at high temperatures. This is caused by the effort to obtain the agreement with the experimental heat capacity data, which is shown in Fig. 5-11. In view of the experimental uncertainties, the present calculations on both heat content and heat capacity are reasonably acceptable. Table 5-1. The invariant reactions in the ZrO2 – NdO1.5 system. Reaction Type Reference Temperature (K) Composition of phases (mol% NdO1.5) [1971Rou] 2388 82.3 75 89 L ⇔ F+ X eutectic This work 2393 84.1 76.7 91.8 [1971Rou] 2333 89 93.1 74.2 X ⇔ H + F eutectoid This work 2330 92.1 93 76.7 H ⇔ F + A eutectoid This work 2169 93.5 76 98.3 [1971Rou] 1713 66.7 51.9 97.4 F ⇔ P + A eutectoid This work 1763 70.3 55.3 98.6 [1971Rou] 2573 50 50 − F ⇔ P congruent This work 2584 50 50 − -83- F ⇔ T + P eutectoid This work 1487 23.4 1.6 47.1 [1995And] 1153 1.0 − − T ⇔ M + P eutectoid This work 1326 1.0 0.03 48.1 Table 5-2. The composition of the samples investigated in the ZrO2 – NdO1.5 system and observed phases. No. NdO1.5 (mol%) Observed phases 1400 °C 1600 °C 1700 °C 1 10 F + M F + M F + M 2 30 P F F 3 32 P P F + P 4 33 P P F + P 5 34 P P F + P 6 35 P P P 7 36 P P P 8 37 P P P 9 38 P P P 10 39 P P P 11 40 P P P 12 50 P P P 13 60 P + A P + F P + F 14 65 P + A P + F P + F 15 70 P + A F F 16 80 P + A F + A F + A Table 5-3. Measured phase composition data (mol% NdO1.5) for different phase equilibria in the ZrO2 – NdO1.5 system at different temperatures. Temperature (K) T + F P + F F (P) + A T F P F F (P) A 1673 2.3 ± 0.5 21 ± 1 − − 54 ± 1.5 98 ± 1 1873 2.0 ± 0.5 17.9 ± 1 55 ± 1 69.5 ± 1 71.5 ± 1 98 ± 1 1973 − − 54.5 ± 1 68.5 ± 1 98 ± 1 -84- Chapter 6 Experimental study and thermodynamic modeling of the ZrO2 − SmO1.5 system 6.1. Literature review 6.1.1. Phase equilibria The phase equilibria of the ZrO2 − Sm2O3 system were experimentally investigated by [1962Per, 1968Rou2, 1971Rou, 1981Gav, 1982Zoz, 1995And, 1999Tab]. [1962Per] firstly studied the phase relations of the ZrO2 − Sm2O3 system in the temperature range 1000-2500°C. However, most of the phase boundaries and reactions were given by dashed lines, which were thought to be less precise. A detailed determination was done by [1968Rou2, 1971Rou] above 1800°C using HTXRD measurements. The liquidus curve was well determined and the solidus was accordingly estimated. A continuous transition C1 ⇔ C2 was reported like in some other systems they studied. However, this was shown to be not correct according to the recent experimental work on the ZrO2 − GdO1.5 system [2005Zin]. The invariant reaction L ⇔ F + X-Sm2O3 was shown occurring at 2190°C and 75 mol% Sm2O3. Three other reactions X-Sm2O3 ⇔ F + H-Sm2O3, H-Sm2O3 ⇔ F + A-Sm2O3, and A-Sm2O3 + F ⇔ B-Sm2O3 were only estimated in the work of [1968Rou2, 1971Rou]. In the ZrO2-rich region of the system, the phase boundary of F / F + T was determined by HTXRD. A fluorite + pyrochlore two-phase region was proposed by dashed lines. [1999Tab] confirmed this two-phase region beyond 55 mol% SmO1.5 by XRD measurements, but, in the ZrO2-rich region, no two-phase region could be detected. The stoichiometric pyrochlore ⇔ fluorite transition was determined at 1920°C by [1982Zoz] using DTA. The melting point for this composition was found to be at 2497 ± 10°C. The pyrochlore ⇔ fluorite transformation temperature was measured to be about 100 K lower than the value reported by [1971Rou] (2025°C). The composition range of the pyrochlore phase reported by [1965Col] extended from 37.4 to 60.1 mol% SmO1.5 at 1450°C, which was very similar to the range shown by [1962Per]. [1981Gav] reported the fluorite / fluorite + pyrochlore phase boundary in ZrO2-rich region to be at 25 mol% Sm2O3. [1999Tab] determined the extent of the pyrochlore solid solution in the range from 38.5 to 55 mol% SmO1.5 at 1500°C by XRD method. At the ZrO2-rich side, the eutectoid point of the invariant reaction T ⇔ M + F was determined at 865°C and 1.5 mol% Sm2O3 by [1995And], together with a tentative phase -85- diagram for the ZrO2-rich region. However, the samples investigated were far from equilibrium condition according to the heat treatment route, resulting in rather large solubility of Sm2O3 (3-6 mol%) in the tetragonal phase at 1170°C. With the help of lattice parameter measurements, [1981Gav] found the minimum amount of Sm2O3 to stabilize the zirconia in the cubic fluorite structure to be 6 mol% at 2170 K and 9.5 mol% at 2020 K. The phase boundaries of the tetragonal + fluorite equilibrium were experimentally examined by [1995Kat] in the temperature range 1600-1800°C. All the experimental data on the invariant reactions are listed in Table 6-1. 6.1.2. Thermodynamic data [1971Kor] determined the enthalpy of formation (from oxides) of the stoichiometric pyrochlore phase by combustion in a bomb calorimeter. The measured value was – 26673 J.mol-1 (per mole of cations) at 298.15 K. Recently [2005Nav] reported a less negative value (– 14629 J.mol-1, per mole of cations). The entropy of the pyrochlore phase Sm2Zr2O7 (65.1 J.mol-1.K-1, 298.15 K, per mole of cations) was estimated by the method of ground-state degeneracy in the work of [2004Lut]. 6.2. Experimental results and discussion 20 30 40 50 60 70 80 95 mol% SmO1.5 70 mol% SmO1.5 58 mol% SmO1.5 50 mol% SmO1.5 30 mol% SmO1.5 10 mol% SmO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) 20 30 40 50 60 70 80 M M M MM M M M M F F F M 2θ (degree) In te ns ity (A rb .u ni ts ) F M Figure 6-1. The XRD patterns of the as- pyrolysed ZrO2 − SmO1.5 samples at 700°C for 3h. Figure 6-2. The XRD patterns of the ZrO2- 10 mol% SmO1.5 sample heat treated at 1400°C for 168h. 6.2.1. The as-pyrolysed state Totally thirteen samples with different compositions were prepared in this work. The prepared compositions together with the observed microstructures at different temperatures -86- are listed in Table 6-2. The XRD patterns of several pyrolysed samples are given in Fig. 6-1. It is clear that the compositions of 50 and 58 mol% SmO1.5 have wider fluorite peaks which correspond to finer powder particles. Samples in the ZrO2-rich region show peaks of the tetragonal phase, while in SmO1.5-rich samples some weak peaks of the B-type Sm2O3 are present. 6.2.2. The tetragonal + fluorite phase equilibrium The XRD patterns (Fig. 6-2) of the sample containing 10 mol% SmO1.5 heat treated in the temperature range 1400-1700°C show well developed monoclinic and fluorite structures. The SEM back scattered electron image (×1000) of the ZrO2-10 mol% SmO1.5 sample heat treated at 1600°C for 72h is shown in Fig. 6-3, where the light areas are the fluorite phase, and the dark areas are the monoclinic phase which formed from the tetragonal phase during cooling. The obvious cracks at the grain boundaries are caused by the considerable volume change during the tetragonal-to-monoclinic martensitic transformation. Table 6-3 gives the determined tetragonal + fluorite phase boundary data at different temperatures. Present measured data agree with those of [1995Kat] very well within small experimental uncertainties. Figure 6-3. The SEM back scattered electron image (×1000) of the ZrO2-10 mol% SmO1.5 sample heat treated at 1600°C for 72h (the light areas are the fluorite phase, and the dark ones are the monoclinic phase). 6.2.3. The fluorite + pyrochlore phase equilibrium It has been already inferred from the work on the ZrO2 − NdO1.5 system that the samples in the fluorite + pyrochlore two-phase region at the ZrO2-rich side could not reach -87- equilibrium even after 36h at 1700°C. For the ZrO2 − SmO1.5 system, the samples with 36, 37, 38, 39 and 40 mol% SmO1.5 heat treated at both 1600°C for 72h and 1700°C for 36h do not show any visible separate peaks of fluorite and pyrochlore. In the SmO1.5-rich region, the strong separated peaks of fluorite and pyrochlore can be found on the XRD patterns for the sample with 58 mol% SmO1.5, though there is only a small difference on the 2θ angles. The XRD patterns of the samples 36, 37, 38, 39, 40, 50 and 58 mol% SmO1.5 heat treated at 1600°C for 72h are shown in Fig. 6-4. With increasing the SmO1.5 content, the intensities of the superstructure peaks become stronger gradually up to 50 mol%, and then decrease until the composition 58 mol% SmO1.5. The same compositions heat treated at 1700°C for 36h do not show any difference on the XRD patterns. According to the intensities of the superstructure peaks, it is inferred in this work that the composition of the fluorite / fluorite + pyrochlore phase boundary is around 35 mol% SmO1.5 in the temperature range studied. The lattice parameters of the fluorite and pyrochlore phases were determined by using the Si powder as the internal standard, and are plotted in Fig. 6-5, together with literature data. The lattice parameter of the 50 mol% SmO1.5 sample does not seem to fit into the Vegard’s slope constructed from the data of the fluorite phase. Based on the XRD and EDX results of the ZrO2-58 mol% SmO1.5 sample, the fluorite + pyrochlore phase boundaries are around 55 and 69 mol% SmO1.5, respectively, at 1600°C, which can be seen in Table 6-3. 20 30 40 50 60 58 mol% SmO1.5 50 mol% SmO1.5 40 mol% SmO1.5 39 mol% SmO1.5 38 mol% SmO1.5 37 mol% SmO1.5 36 mol% SmO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) P P P Figure 6-4. The XRD patterns of the ZrO2 − SmO1.5 samples with the pyrochlore peaks (1600°C, 72h). -88- 0 10 20 30 40 50 60 70 80 90 100 5.1 5.2 5.3 5.4 5.5 La tti ce p ar am et er (Å ) F+P F 1999Tab 1997Cha 1981Shi 1962Per this work Vegard's Slope SmO1.5 (Mol% ) F+T F P Vegard's Slope B+F Figure 6-5. The lattice parameters of the fluorite and pyrochlore phases in the ZrO2 − SmO1.5 system determined in this work and in the literature. 20 30 40 50 60 70 80 BBB B B B BB B B B F F F F In te ns ity (A rb .u ni ts ) 2θ (degree) Figure 6-6. The XRD patterns of the ZrO2-80 mol% SmO1.5 sample after heat treatment at 1400°C. 6.2.4. The fluorite + B-Sm2O3 phase equilibrium According to XRD measurements, the sample ZrO2-80 mol% SmO1.5 heat treated between 1400°C-1700°C presents the fluorite and the B-Sm2O3 structure (Fig. 6-6). The measured phase boundary data for the fluorite + B-Sm2O3 phase equilibrium are listed in Table 6-3. With increasing temperature, the solubility range of the fluorite phase extends to higher SmO1.5 contents, and the solubility of ZrO2 in B-Sm2O3 also increases. Fig. 6-7 is the SEM back scattered electron image (×3000) of the sample ZrO2-80 mol% SmO1.5 heat treated at 1700°C for 36h, showing a very homogeneous microstructure. The grey areas are the fluorite phase, and the white areas with the lathy morphology are the B-Sm2O3 phase. -89- Figure 6-7. The SEM back scattered electron image (×3000) of the sample ZrO2-80 mol% SmO1.5 heat treated at 1700°C for 36h (the grey areas are the fluorite phase, and the white ones are the B-type Sm2O3 phase). 6.3. Selected experimental data for optimization The phase boundary data obtained in this work on the tetragonal + fluorite, fluorite + pyrochlore, and the fluorite + B-Sm2O3 phase equilibria together with those of [1995Kat], the temperatures of the P ⇔ F transformation, the liquidus and the invariant reactions measured by [1968Rou2, 1971Rou] as well as the homogeneity range data of the pyrochlore phase reported by [1999Tab] are accepted for the optimization. The enthalpy of formation of the pyrochlore phase reported by [2005Nav] is taken as a start value, while the data from [1971Kor] on the enthalpy of formation of the fluorite phase are rejected due to a too negative value. The average values of the heat capacities of Nd2Zr2O7 and Eu2Zr2O7 [2004Lut] are accepted as reference data for Sm2Zr2O7. The heat content data of ZrO2-30 mol% SmO1.5 and ZrO2-50 mol% SmO1.5 samples determined in this work are adopted for assessment of the thermodynamic properties. 6.4. Optimization procedure As a first step, a preliminary phase diagram without the ordered pyrochlore phase was roughly assessed based on the liquidus, tetragonal + fluorite, fluorite + B-Sm2O3 phase boundary data and the heat content data for the ZrO2-30 mol% SmO1.5 sample, by using a limited number of parameters. Secondly, further optimization was done by treating the pyrochlore phase as a stoichiometric compound, using the heat content and enthalpy of formation data. Finally, a full assessment was carried out by simultaneously taking all selected data into account. -90- For the fluorite phase, a TlnT contribution into the zeroth order interaction parameter was applied to fit the experimental heat content data. For the phases T, X, H, A and B, only one interaction parameter was adopted due to their limited composition and or temperature range. No any interaction parameter was applied for the monoclinic phase and the low- temperature C-type phase because of their negligible or unknown homogeneity ranges. The optimized thermodynamic parameters are summarized in Appendix. 6.5. Calculated results and discussion The calculated ZrO2 − SmO1.5 phase diagram is shown in Fig. 6-8, together with the experimental data. The phase equilibria data obtained in this work and those of [1971Rou, 1995Kat, 1999Tab] are well reproduced. The calculated invariant reactions are given in Table 6-1. It can be seen in Fig. 6-8 that the calculated tetragonal + fluorite two-phase region is well consistent with the experimental data of this work and of [1995Kat]. Compared with the ZrO2 − NdO1.5 system, this two-phase region of the ZrO2 − SmO1.5 system is a little bit narrower. The calculated invariant reaction T ⇔ M + F is 1315 K, at which the solubility of SmO1.5 in the tetragonal phase is only 1.3 mol%, and the homogeneity range of the monoclinic phase is negligible. Fig. 6-9 is the calculated ZrO2-rich partial phase diagram including the calculated T0 lines for the monoclinic + tetragonal and tetragonal + fluorite phase equilibria and experimental data. The results of [1993Yas, 1995And] on the T0 line of the former one are well reproduced. The calculated pyrochlore + fluorite equilibrium fit the phase boundary data obtained in this work and by [1999Tab], as well as the transformation temperature reported by [1971Rou]. Two invariant reactions involving the pyrochlore phase are calculated at 1115 K (F ⇔ M + P) and 1520 K (F ⇔ P + B-Sm2O3), respectively. At the SmO1.5-rich side, the phases pyrochlore, B-Sm2O3 and C-Sm2O3 are in equilibrium at low temperatures. Since it is not possible to equilibrate samples at such conditions, there is no experimental evidence for this, where the solubility range of the C-Sm2O3 phase is neglected. The experimental data obtained in this work are taken into account to optimize the phase boundaries of the fluorite + B-Sm2O3 phase equilibrium. A good agreement with the calculation is obtained. This agreement makes the calculations get less consistency with the experimental compositions of the fluorite phase for invariant reactions reported by [1971Rou] at higher temperatures. However, owing to the large uncertainties of the HTXRD data of [1971Rou], present calculations are thought to be more reasonable by fitting the reliable phase -91- boundary data. The reported temperatures of the invariant reactions L ⇔ F+ X and X ⇔ H + F by [1971Rou] are reproduced well. The temperatures of the reactions H ⇔ A + F and A + F ⇔ B were calculated as 2252 K and 2181 K, respectively. Figure 6-8. The calculated ZrO2 − SmO1.5 phase diagram together with experimental data. Figure 6-9. The calculated ZrO2 − SmO1.5 partial phase diagram together with the calculated T0 lines for the monoclinic + tetragonal and tetragonal + fluorite phase equilibria and experimental data. Figure 6-10. The calculated heat content (HT-H298) of the ZrO2-50 mol% SmO1.5 sample together with experimental data. -92- Figure 6-11. The calculated heat content (HT- H298) of the ZrO2-30 mol% SmO1.5 sample together with experimental data. Figure 6-12. The calculated heat capacity of the ZrO2-50 mol% SmO1.5 pyrochlore phase. The enthalpies of formation of the fluorite and the pyrochlore phases finally obtained in this work are – 9023 J.mol-1 and – 16049 J.mol-1 (per mole of cations), respectively, which are comparable to those data for the ZrO2 − NdO1.5 system. Fig. 6-10 and Fig. 6-11 show the experimental and calculated heat contents of the samples containing 50 mol% SmO1.5 and 30 mol% SmO1.5, respectively. Good agreements are obtained. The calculated heat capacity of the stoichiometric pyrochlore phase is shown in Fig. 6-12. The value at 298.15 K is 60.51 J.mol-1.K-1. Table 6-1 The invariant reactions in the ZrO2 − SmO1.5 system. Reaction Type Reference Temperature (K) Composition of phases (mol% SmO1.5) [1971Rou] 2463 85.7 71 93 L ⇔ F+ X eutectic This work 2463 85.8 75.4 91.8 [1971Rou] 2373 92.5 94.7 73.4 X ⇔ H + F eutectoid This work 2365 92.7 93.8 75.8 H ⇔ A + F eutectoid This work 2252 94.4 98 75.9 [1971Rou] 2173 − − − A + F ⇔ B eutectoid This work 2181 98.1 75.2 98.06 F ⇔ P + B eutectoid This work 1520 68.3 56.2 98.9 [1995And] 1138 1.5 − − T ⇔ M + F eutectoid This work 1315 1.3 0.02 21.7 -93- F ⇔ M + P eutectoid This work 1115 25.8 ~0 46.3 [1971Rou] 2298 50 50 − [1982Zoz] 2193 50 50 − F ⇔ P congruent This work 2299 50 50 − Table 6-2. The compositions of the samples investigated in the ZrO2 − SmO1.5 system and observed phases. No. SmO1.5 (mol%) Observed phases 1400 °C 1600 °C 1700 °C 1 10 F + M F + M F + M 2 25 F F F 3 30 F F F 4 36 P P P 5 37 P P P 6 38 P P P 7 39 P P P 8 40 P P P 9 50 P P P 10 58 P + F P + F P + F 11 75 F + B F F 12 80 F + B F + B F + B 13 95 F + B F + B F + B Table 6-3. Measured phase compositions data (mol% SmO1.5) for different phase equilibria in the ZrO2 − SmO1.5 system at different temperatures. Temperature (K) T + F F + P F + B T F F P F B 1673 2.2 ± 0.5 18.1 ± 1 67.2 ± 1 56.5 ± 1 69.5 ± 1 99.2 ± 0.5 1873 2.5 ± 0.5 14.5 ± 0.5 64.5 ± 1 56.2 ± 1 71.5 ± 1 98.6 ± 0.5 1973 2.7 ± 0.5 12.5 ± 0.5 − − 74.2 ± 1 98.4 ± 0.5 -94- Chapter 7 Experimental study and thermodynamic modeling of the ZrO2 − GdO1.5 system 7.1. Literature review 7.1.1. Phase equilibria Phase diagram studies of the system ZrO2 − GdO1.5 have been performed by [1962Per, 1963Lef, 1964Lin1, 1968Rou2, 1971Rou, 1972Neg, 1978Sco, 1987Ueh] by using X-Ray diffraction and thermal analysis. In addition, some particular phase equilibria have been investigated in limited temperature and/or composition ranges using XRD, Raman and Mössbauer spectroscopy, pertrographic analysis as well as EPMA [1980Dij, 1990Mor, 1991Leu, 1994Li, 1995Bha, 1995Kat, 1996Kar, 1999Kar, 2001Fei, 2003Wan, 2003Dut, 2004Nak]. The monoclinic structure of ZrO2 was found to dissolve negligible amounts of gadolinia. The tetragonal phase is known to dissolve up to 3 mol% GdO1.5 [1991Leu, 1995Kat]. The eutectoid decomposition of the tetragonal phase T ⇔ M + F was found to occur at 1140 - 1145 °C [1972Neg]. The cubic fluorite-type phase is stabilized in a wide range of compositions and temperatures [1962Per, 1963Lef, 1971Rou, 1978Sco, 1991Leu, 1995Kat]. It coexists with the solid solution based on C-type modification of Gd2O3 at the gadolinia-rich side [1978Sco, 2001Fei]. The minimum amount of gadolinia needed to stabilize the single fluorite phase increases with decreasing temperature. The GdO1.5-rich phase boundary shifts from 69.9 to 76.5 mol% GdO1.5 with increasing temperature (1450 to 1800 °C). The solubility of ZrO2 in the monoclinic B-type modification of GdO1.5 does not exceed 2 mol% [1962Per, 1971Rou, 2001Fei]. The literature data on the phase boundaries T / T + F, T + F / F, F / F + C- Gd2O3, and C-Gd2O3 + B-Gd2O3 / B-Gd2O3 are in good agreement. Rouanet and Foex studied the phase diagram of the ZrO2 − GdO1.5 system from 1800 °C up to the liquidus temperatures [1968Rou2, 1971Rou]. The hexagonal ordered polymorph of Gd2O3 (H) dissolves up to 7 mol% ZrO2. It forms through the peritectic reaction at about 2350 °C and decomposes eutectoidally at 2050 °C. The liquidus temperatures are gradually decreasing down to the eutectic point at 2260 °C and 86.7 mol% GdO1.5, where the liquid solidifies into the F and H-Gd2O3 phases. A lower temperature (2175°C) was reported for this eutectic reaction by [1964Lin1] with a similar eutectic composition (87.3 mol% GdO1.5). The high temperature X-phase exists only in the vicinity of pure gadolinia. Karaulov and Zoz detected the melting point of the cubic solid solution Zr0.5Gd0.5O1.75 at 2570 ± 14 °C -95- [1999Kar], which is consistent with the liquidus proposed by Rouanet [1971Rou], considering the possible large experimental error at high temperatures. Serious disagreement exists in the literature with respect to the homogeneity range of the pyrochlore phase. The smallest one (45-55 mol% GdO1.5) has been reported in Refs. [1962Per, 1980Dij, 2003Wan]. [1999Kar] determined the F / P phase boundary at 38 mol% GdO1.5. It is worth noting that the majority of works [1962Per, 1976Mic, 1980Dij, 1999Kar] are mutually consistent with respect to the P / F phase boundary and the temperature of the order-disorder transition (1530 - 1550 °C), while [1987Ueh] suggested a considerably larger homogeneity range of the pyrochlore phase (31 - 61 mol% GdO1.5) and a higher disordering temperature (> 1600 °C), while indicating two types of pyrochlore phase with sharp and broad superstructure reflections, respectively. A microdomain structure with antiphase boundaries was found in the composition ranges 33 - 43 and 57 - 60 mol% GdO1.5 at 1500 °C and 46 - 54 mol% GdO1.5 or wider at 1600 °C resulting in broad superstructure peaks of the pyrochlore phase accompanying sharp fundamental peaks of the fluorite structure [1987Ueh]. Also, phase equilibria involving C-type Gd2O3 phase are not well established. [1962Per] stated that a phase transition F ⇔ C-Gd2O3 is of first and second order at low and high temperatures, respectively and indicated the existence of the miscibility gap within the C-type phase domain from 71 to 87 mol% GdO1.5 at 1500 °C, which closes above 1800 °C. [1968Rou2, 1971Rou] stated that the F ⇔ C-Gd2O3 transition appears to be continuous with a theoretical boundary at the composition of 50 mol% GdO1.5. In contrast, [1978Sco] found in XRD study that samples with 80 mol% GdO1.5 annealed at 1450 - 1850 °C contain F and C- Gd2O3 phases. However, the samples equilibrated at 1850 °C did show, in addition to the sharp fluorite and C-type reflections, some weak, diffuse reflections corresponding to a second C-type phase, and also contained a trace of B-Gd2O3 phase. Two hexagonal intermediate phases H2 and H3, which do not form two-phase fields had been observed between 1450 and 1800 °C by [1962Per]. From the large values of the lattice parameters it can be inferred that they are probably ordered superstructures of the Mn2O3-type cubic solid solution (C-type phase). However, none of the subsequent studies of the ZrO2 − GdO1.5 system confirmed the existence of H2- or H3-phase. On the one hand, they are probably metastable phases. On the other hand, a very long heat treatment is typically necessary, e.g., 1 months at 1400 °C for the pyrochlore-type phase [1976Mic] to allow the ordered structure to form. All the reported invariant reactions are compiled in Table 7-1. -96- 7.1.2. Thermodynamic data [1971Kor] determined the enthalpies of formation of the fluorite phase at 50 mol% GdO1.5 by combustion of a mixture of Zr and Gd2O3 in a bomb calorimeter under an oxygen pressure of 25 atm. By using high temperature oxide melt solution calorimetry, [2001Hel] measured the enthalpies of formation of three compositions in this binary system: 50 mol% GdO1.5 (pyrochlore), 45.6 mol.% GdO1.5 (pyrochlore), and 53.5 mol.% GdO1.5 (fluorite). These results are compiled in Table 7-2. [2003Lut] determined the heat capacity of stoichiometric pyrochlore in the temperature range from 20 K to 1400 K by using adiabatic calorimetry and differential scanning calorimetry, while [2003Lec] measured the heat capacity of the sample with 20.4 mol% GdO1.5. 7.2. Experimental results and discussion 7.2.1. The as-pyrolysed state Totally samples with twenty eight different compositions were prepared for the ZrO2 − GdO1.5 system. Fig. 7-1 shows the XRD patterns of some as-pyrolysed samples after 450°C for 3h. The sample with 10 mol% GdO1.5 shows clear patterns of the tetragonal phase, while the other samples are poorly crystallized. For the sample with 98 mol% GdO1.5, the XRD patterns present probably the peaks of both the B- and C-type Gd2O3 phases. The prepared compositions together with the observed microstructures at different temperatures are listed in Table 7-3. 20 30 40 50 60 70 80 98 mol% GdO1.5 70 mol% GdO1.5 50 mol% GdO1.5 30 mol% GdO1.5 10 mol% GdO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) Fig. 7-1. The XRD patterns for the as-pyrolysed ZrO2 − GdO1.5 samples after 450°C for 3h. 7.2.2. The fluorite / pyrochlore phase transition -97- XRD patterns of the samples containing 41 to 59 mol% GdO1.5 are presented in Fig. 7- 2. It can be seen that at the composition of 44 mol% GdO1.5 fluorite transforms into pyrochlore, which has the superstructure reflections denoted by "P". With increasing GdO1.5 content the superstructure peaks grow until the stoichiometric composition (50 mol% GdO1.5) is reached and then decrease. At the composition of 55 mol% GdO1.5, the pyrochlore superstructure disappears and the fluorite phase is stable again. The homogeneity range of the pyrochlore phase at 1400 °C obtained in this work by XRD is thus around 44-54 mol% GdO1.5 and it is well consistent with the literature data (45-55 mol% GdO1.5) [1962Per, 1980Dij, 2003Wan]. It is, however, not possible to judge from the XRD patterns, whether two-phase regions between F and P exist, because the strongest peaks of fluorite and pyrochlore phases overlap. The lattice parameters of fluorite and pyrochlore determined by using the Si-standard powder as well as those from the literature are shown in Fig. 7-3. The majority of reports present mutually consistent values and results of the present study are in line with the general trend. According to the composition dependence of lattice parameters, the phase boundaries T + F / F and F / F + C-Gd2O3 are clearly seen. The values obtained in this study (16 and 68 mol% GdO1.5, respectively) are in good agreement with the available literature data for the temperature of 1400°C. At the same time, there is no any plateau in between indicating the absence of two-phase regions, where the structures of fluorite and pyrochlore coexist. An interesting observation is the marked deviation from Vegard's slope. It is evident that the lattice parameter is smaller than predicted one in the composition range from 25 to 45 mol% GdO1.5 (Fig. 7-3). Furthermore, results obtained in this work indicate (see inset) that the lattice parameter slightly exceeds theoretical value between 45 and 62 mol% GdO1.5. Similar observations were reported by two groups of authors [1980Dij, 1987Ueh], who mentioned the existence of a bend on the curve representing the composition dependence of the lattice parameter of Zr1-xGdxO2-0.5x solid solutions at x = 0.33 - 0.35. Around the same composition, the maximum activation enthalpy for ionic conductivity was found [1980Dij]. The observed discontinuity was interpreted as the onset of the ordering of oxygen vacancies [1980Dij] or even F / P phase boundary [1987Ueh]. In addition, an abrupt change of the relative absorption area and line width in Mössbauer spectra was detected between x = 0.30 and 0.35 [2004Nak]. However, more extensive compilation of the literature data as well as the results obtained in this work (Fig. 7-3) indicate that not just a bend, but a smooth S-shaped curve characterizes the composition dependence of the lattice parameter in the ZrO2 − GdO1.5 system. Such sigmoidal curve can be understood as the intermediate case between random -98- solution and phase separation, i.e., the ordering of the fluorite phase, which occurs in a wide composition range, from 25 to 62 mol% GdO1.5. In fact, the existence of ordering in the sample with 25 mol% GdO1.5, which has been quenched from 1600 °C was confirmed by electron diffraction [1991Wit]. Note that the unit cell parameter in the range of 18 - 25 mol% GdO1.5 does obey Vegard’s law (Fig. 7-3). 10 15 20 25 30 35 40 45 50 55 m ol% G dO 1.5 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 P FF in te ns ity (a rb . u ni ts ) FP P P P 41 42 43 2θ (degree) Fig. 7-2. XRD patterns of ZrO2 − GdO1.5 samples in the composition range from 41 to 59 mol% GdO1.5. The letters P and F show the positions of superstructure reflections of the pyrochlore phase and fundamental reflections of the fluorite subcell, respectively. 45 50 55 60 0.522 0.524 0.526 0.528 0.530 0 20 40 60 80 100 0.51 0.52 0.53 0.54 [1992Kan] [1990Mor] [1989Mor] [1978Sco] [2001Fei] [1991Leu] [1963Lef] [1962Col] [1980Dij] [1987Ueh] [2003Wan] [1985Dij] [1972Neg] [1959Col] [1973Str] [1994Li ] This work F F+C P La tti ce p ar am et er (n m ) mol% GdO1.5 T+F F Vegard's slope Fig. 7-3. Lattice parameters of the fluorite and pyrochlore phases of the ZrO2 − GdO1.5 system determined in this work and in literature. -99- Fig. 7-4 shows a bright field TEM micrograph of the typical microstructure found among the samples studied. The compositions of about 150 individual grains were analysed. The major quantity of these grains indicates a Zr:Gd ratio close to the nominal composition. However, partitioning at the nanometer level was detected and some of the grains exhibited very different GdO1.5 contents. Selected examples of SAED patterns from all the samples are shown in Fig. 7-5. Fig. 7-4. Bright field TEM micrograph showing the typical polycrystalline microstructure found among the ZrO2 − GdO1.5 samples studied. Fig. 7-5(a) presents a SAED pattern registered in the [101] zone axis of a monoclinic grain with a composition close to pure ZrO2. Fig. 7-5(b) shows the diffraction pattern associated with one of the tetragonal grains in the [110] zone axis. Note that the more intense reflections can also be indexed as cubic (fluorite-type) structure and there is a possibility that both the F and T phases contributed to the formation of this pattern. In fact, this kind of SAED patterns was observed in the grains with an average composition of 10-15 mol% GdO1.5. In this range of trivalent cations doping, either grains with low solute tetragonal domains oriented into a cubic matrix (colony structure) or supersaturated tetragonal grains (T´) could create patterns with the shown features [1988Heu]. Figs. 7-5 (c-e) show the SAED patterns registered along the [110] zone axis for the stoichiometric pyrochlore (50 mol% GdO1.5), fluorite and GdO1.5-rich pyrochlore grains, respectively. Fig. 7-5(f) shows the [110] SAED pattern taken from one of the grains with a composition close to pure gadolinia, where reflections associated with the cubic network are labeled. Note that as in the case of pyrochlore, some superstructure reflections appear. In Figs. 7-5(e) and (f), these are diffuse elongated reflections at half distances between the (111) reflections of the reciprocal cubic network. -100- Figs. 7-6(a-h) show a series of SAED patterns registered from different grains among all the samples studied, where the content of GdO1.5 measured by EDX increase from (a) to (h). In order to distinguish the fluorite and pyrochlore phase, [110] zone axis was used since (111) and (002) satellite reflections of the pyrochlore structure clearly appear in this orientation. Furthermore, this orientation is most suitable for investigating of transitional structures, since the shape of diffuse scattering in these patterns changes most sensitively with composition [1985Suz]. This scattering is caused by vacancies on the oxygen sublattice (or oxygen vacancy clusters), acting as scattering centers of the incoming electron beam [1988Rüh]. Fig. 7-5. SAED patterns of the monoclinic phase (a), tetragonal phase (b), stoichiometric pyrochlore (c), fluorite (d), GdO1.5-rich pyrochlore (e) and C-Gd2O3 (f) of the ZrO2 − GdO1.5 system. Starting from the sample containing around 43 mol% GdO1.5 the brightness of the superstructure reflections continuously increases as the composition approaches 50 mol% GdO1.5 and then gradually decreases upon further increasing of the GdO1.5 content. It is evident that a continuous transformation of the fluorite structure into pyrochlore one and then -101- again into fluorite (without any phase separation) takes place. Note that satellite spots are hardly visible in Fig. 7-6(a), while the SAED pattern shown in Fig. 7-6(h) corresponds to disordered fluorite phase. Thus, with respect to the homogeneity range of the pyrochlore phase, TEM observations are consistent with XRD measurements (Fig. 7-2). Also the sharpness and shape of the superstructure reflections change in a systematic way. Cubic grains in the ZrO2-rich region, presented sharp satellite spots Figs. 7-6(a-c). In the GdO1.5-rich grains, typical diffraction features of cubic (fluorite-type) structures, plus a subnetwork of diffuse and elongated (111) superstructure reflections are observed, Figs. 7-6(e-g). The extra diffuse scattered reflections are the proof of the existence of a partial pyrochlore character in these grains. They are largely perpendicular to the local <111> reciprocal space direction and seem to smear out as grains contain more GdO1.5, since the same trend towards the appearance of single fluorite reflections is observed (Fig. 7-6(h)). Fig. 7-6. Series of [110] SAED patterns from grains with compositions (mol% GdO1.5): 43 - 45 (a), 45 - 47 (b), 47 - 49 (c), 50 (d), 51-53 (e), 53-55 (f), 55-57 (g), 60-66 (h) in the ZrO2 − GdO1.5 system. In general, results obtained in the present work by TEM are consistent with the observations of Withers and co-workers [1991Wit] for a number of the ZrO2 − REO1.5 systems, where different superstructure patterns and/or diffuse scattering were found within the fluorite solid solution field depending on composition. From Figs. 7-6(a, b) it is evident that for ZrO2-rich grains the expected (002) satellite reflections of the pyrochlore structure are very weak. This is a characteristic feature of the "honeycomb pattern" [1991Wit], which was identified at 25 mol% LnO1.5. At the same time, the SAED pattern of the sample containing -102- 50 mol% GdO1.5, which has been annealed at 1600 °C [1991Wit] looks very similar to Fig. 7- 6(e). Such kind of ordering of the fluorite phase has been classified as "pyrochlore-like" [1991Wit]. Finally, the transition from "pyrochlore-like" to "C-type-related" ordering appears to be smooth [1991Wit], what is also evident from Figs. 7-5(e, f). 20 30 40 50 0 2000 4000 6000 8000 10000 12000 14000 F F F F C C CCC C CCC C C co un ts 2θ (degree) C Fig. 7-7. XRD pattern of the sample ZrO2-80 mol% GdO1.5 heat treated at 1400 °C for 240 h. The letters C and F denote the reflections, which belong to C-Gd2O3 and fluorite, respectively. Fig 7-8. SEM micrograph of the sample containing ZrO2-80 mol% GdO1.5 heat treated at 1700 °C for 36 h (the grey areas are the fluorite phase, and the white ones are C- Gd2O3). Fig. 7-9. SEM micrograph of the sample containing 95 mol% GdO1.5 heat treated at 1600 °C for 72 h (the matrix is C-Gd2O3, and the white areas are B-Gd2O3). 7.2.3. The fluorite + C-Gd2O3 and C-Gd2O3 + B-Gd2O3 phase equilibria As an example, Fig. 7-7 shows the XRD pattern of the specimen containing 80 mol% GdO1.5, which was heat treated at 1400 °C. Only the phases F and C-Gd2O3 are -103- observed. Fig. 7-8 shows the SEM micrograph of this sample, which was heat treated at 1700 °C. A very homogenous phase distribution can be seen, where the white areas correspond to C-Gd2O3 solid solution and the grey areas correspond to the fluorite phase. Very similar XRD and SEM results were obtained for the whole temperature range (1400 - 1700 °C). Also, the sample containing 70 mol% GdO1.5 was found to consist of two phases (F + C-Gd2O3) after annealing at 1400 - 1600 °C, although it becomes single-phase fluorite at 1700 °C. Fig. 7-9 shows a C-Gd2O3 + B-Gd2O3 two-phase microstructure in the sample containing 95 mol% GdO1.5, where the matrix is C-Gd2O3. The lighter area corresponds to the monoclinic B-GdO1.5. The measured phase boundary data for the F + C-Gd2O3 and C-Gd2O3 + B-Gd2O3 equilibria are compiled in Table 7-4. The values for F + C-Gd2O3 phase region are consistent with the data of [1978Sco]. The solubility of ZrO2 in B-Gd2O3 was found to be around 1 mol%, in agreement with the literature data [1962Per, 1971Rou]. The composition of the C-Gd2O3 phase in equilibrium with B-Gd2O3 was established for the first time. Thus, the present work shows that the phase transition F ⇔ C is of first order and a wide two-phase region exists. Neither the hexagonal phases H2 and H3 nor the miscibility gap within C-Gd2O3 reported elsewhere [1962Per] can be confirmed. 7.2.4. The martensitic transformation temperatures of the tetragonal phase The martensitic transformation temperatures of the ZrO2 − GdO1.5 samples with 1 and 2 mol% GdO1.5 were determined by DTA up to the temperature of 1400°C. The detailed data on the temperatures of As, Af, Ms and Mf are compiled in Table 7-5, together with the calculated T0 temperatures. 7.3. Selected experimental data for optimization 7.3.1. Phase diagram data The tetragonal + fluorite phase equilibrium data measured by [1991Leu, 1995Kat] are accepted because the samples were equilibrated for a long time and their compositions were supposed to be highly precise. For the order-disorder phase boundary between fluorite and pyrochlore, the results determined in this work and those of [2005Lec] are considered for optimization. Since at the GdO1.5-rich side the results obtained in this work are quite consistent with those of [1978Sco, 2001Fei], all these data are included in the assessment of the fluorite + C-Gd2O3 phase boundaries. At high temperatures, the only available data from [1971Rou] are accepted for the optimization. -104- 7.3.2. Thermodynamic data Among the data on the enthalpy of formation of pyrochlore, the results obtained by [1971Kor] are much more negative than those of [2001Hel]. In view of the comparability of the data of the ZrO2 − GdO1.5 and ZrO2 − YO1.5 systems [2003Lee], the data of [2001Hel] are accepted to optimize the stability of the pyrochlore and fluorite phases. The heat capacity data measured by [2003Lut] and in this work for pyrochlore, and by [2003Lec] for fluorite (20.4 mol% GdO1.5), as well as heat content data determined in this work for samples with 30 and 50 mol% GdO1.5 are taken for the optimization of thermodynamic properties. 7.4. Optimization procedure In the first step, the phase diagram was roughly assessed by using phase equilibria and thermodynamic data without regarding the pyrochlore phase. In a second step, the pyrochlore phase was added to the assessment. The enthalpy of formation and heat capacity data were employed to obtain a preliminary Gibbs energy function for the stoichiometric composition of pyrochlore. Finally, a set of self-consistent thermodynamic parameters is determined to fit most of the experimental data. By keeping all the parameters of other phases obtained in above steps, the system was assessed using the order-disorder model for pyrochlore phase. Only two more parameters describing the ordered pyrochlore were finally introduced to reproduce the second-order phase transition boundary. The optimized thermodynamic parameters are given in Appendix. 7.5. Calculated results and discussion 7.5.1. The phase diagram without pyrochlore ordering The calculated ZrO2 − GdO1.5 phase diagram without considering the pyrochlore phase is shown in Fig. 7-10. Most of the experimental data are well consistent with the calculated phase diagram. The calculated invariant reactions are given in Table 7-1. The experimentally derived temperatures of [1971Rou] on the liquidus, and the reactions L ⇔ F+ H-Gd2O3 and H-Gd2O3 ⇔ F + B-Gd2O3 are well reproduced, except the calculated solubility of GdO1.5 in the fluorite phase for the reaction L ⇔ F+ H-Gd2O3, which is about 4 mol% larger and that for the reaction H-Gd2O3 ⇔ F + B-Gd2O3, which is about 4 mol% less than the experimental data. The calculated phase compositions of the fluorite + C- -105- Figure 7-10. The calculated ZrO2 − GdO1.5 phase diagram without the pyrochlore phase compared with experimental data. Figure 7-11. The calculated partial ZrO2 − GdO1.5 phase diagram and T0 lines for the monoclinic + tetragonal and tetragonal + fluorite phase equilibria, together with the experimental data. -106- Gd2O3 phase equilibrium shows good agreement with the experimental data of [1978Sco, 2001Fei] and this work. The reaction F + B-Gd2O3 ⇔ C-Gd2O3 is extrapolated to occur at 2275 K, which is thought to be reasonable. The solubility of ZrO2 in C-type Gd2O3 reaches a maximum value near 1873 K, and decreases at higher temperatures. The compositions of the fluorite phase of the invariant reactions reported by [1971Rou] were not fitted well because these data obtained by HTXRD could be less precise. The enthalpy of formation of the fluorite phase has to be increased in order to make a better fit for the phase compositions of the invariant reactions, while the agreement with the experimental data of the present work on both fluorite + C-Gd2O3 and fluorite + tetragonal phase equilibria would become worse. The calculated decomposition of the tetragonal phase into the monoclinic phase and fluorite occurs at 1309 K and 1.4 mol% GdO1.5. The calculated phase boundaries for the fluorite + tetragonal equilibrium agree well with the experimental data of [1995Kat]. An enlarged phase diagram of the ZrO2-rich side of the system together with the experimental data of the T0 lines are shown in Fig. 7-11. The calculated T0 temperatures against compositions are given by dashed lines. There is a difference of about 3 mol% GdO1.5 between the T0 data for tetragonal + fluorite equilibrium evaluated by [1991Leu] and the current calculation. A better fit would badly influence the phase diagram in other areas. The T0 data obtained in this work by DTA measurements for the composition 1 and 2 mol% GdO1.5 are plotted in Fig. 7-11, and the present calculation reproduces them well within the experimental uncertainty. 7.5.2. Calculated results by the pyrochlore model (Zr+4, Gd+3)2(Gd+3, Zr+4)2(O-2, Va)6 (O-2)1(Va, O-2)1 The phase diagram with the pyrochlore phase is shown in Fig. 7-12, where the pyrochlore is modeled as an independent compound resulting in a fluorite + pyrochlore two- phase region. The calculated phase boundaries are in good agreement with the experimental data of [2005Lec] and of this work. The data of [1999Kar, 1962Per] on the pyrochlore / pyrochlore + fluorite phase boundary are questionable because it will be almost impossible to determine this boundary at such low temperatures. The calculated eutectoid point of the invariant reaction F ⇔ C-Gd2O3 + P is at 1145 K and 63 mol% GdO1.5. This is reasonable, because according to [2005Lec], there is considerable single fluorite phase region at 1200°C in the GdO1.5-rich region. In the ZrO2-rich region, according to the present calculation, the fluorite phase extends to room temperature. -107- Figure 7-12. The calculated ZrO2 − GdO1.5 phase diagram with the pyrochlore / fluorite modeled as a first order phase transition. 7.5.3. Calculated results by the pyrochlore model (Zr+4, Gd+3)2(Gd+3, Zr+4)2(O-2, Va)8 The calculated phase diagram using the order-disorder model for the pyrochlore phase is shown in Fig. 7-13. The second order pyrochlore / fluorite phase transition boundary is denoted by a dashed line. The experimental data of [2005Lec] and this work are well reproduced. The data [1962Per, 1999Kar] are not considered due to their less reliability. In accordance with experimental data, a phase transition boundary symmetric to 50 mol% GdO1.5 is obtained. At lower temperatures, the pyrochlore / fluorite phase boundary extends into the two-phase regions in both the ZrO2 and GdO1.5-rich region. It means at low temperatures the pyrochlore phase will be in equilibrium with both terminal solid solutions instead of the fluorite phase. The phase diagram modified in accordance with thermodynamic rules is shown in Fig. 7-14. At low temperatures, the phase boundaries of M + P and P + C- Gd2O3 two-phase equilibria are only slightly shifted, due to the small difference between the Gibbs energies of ordered pyrochlore and fluorite. It has to be mentioned that this phase diagram only gives the phase relations at the thermodynamically equilibrium state, and it doesn’t mean that such two-phase regions can really occur under the condition of sluggish diffusion and the low driving force. -108- Figure 7-13. The calculated ZrO2 − GdO1.5 phase diagram including a second order pyrochlore-fluorite transition boundary. Figure 7-14. The calculated ZrO2 − GdO1.5 phase diagram modeled with a second order pyrochlore-fluorite phase transition. The related phase boundaries are shown by dashed lines. -109- Figure 7-15. The calculated site fractions of the Zr+4 and Gd+3 species in the sublattice 1 and 2 for the composition ZrO2-50 mol% GdO1.5 at different temperatures. With increasing temperature, the degree of order decreases. Figure 7-16. The calculated molar Gibbs energy curves of the fluorite and pyrochlore phases in the ZrO2 − GdO1.5 system at 500 K using two different models for the pyrochlore phase. (Reference state: monoclinic ZrO2 and C-type GdO1.5). The site fractions of the Zr+4 and Gd+3 species in the sublattice 1 and 2 for the composition 50 mol% GdO1.5 at different temperatures are calculated (Fig. 7-15). It can be seen that the completely ideal ordering only occurs at very low temperatures. With increasing the temperature, the ordering degree decreases gradually, and all the species fractions become identical at the temperature where the pyrochlore transforms into fluorite phase. -110- 7.4.4. Thermodynamic properties The experimental and calculated enthalpies of formation of pyrochlore and fluorite with different compositions are given in Table 7-2. Present calculations reproduce the data of [2001Hel] very well, whereas the result of [1971Kor] is too negative compared with this work. The enthalpy of formation of the pyrochlore phase calculated by the first order phase model is about 2000 J.mol-1 more negative than that calculated by the second order phase model. Fig. 7-16 presents the calculated molar Gibbs energy curves for both models of pyrochlore and that of the fluorite at 500 K (Reference state: monoclinic ZrO2 and C-type GdO1.5). At 50 mol% GdO1.5 the energy difference between the fluorite and pyrochlore described by the first order phase model is more than 3000 J.mol-1, while the difference is greatly decreased by using the second order phase model. Beyond the compositions of second order phase transition, the Gibbs energy curves of the disordered fluorite and ordered pyrochlore will merge into a single curve. Figure 7-17. The calculated heat capacity for the sample ZrO2-20.4 mol% GdO1.5 together with the experimental data [2003Lec]. Figure 7-18. The calculated heat content for the sample ZrO2-30 mol% GdO1.5 together with the experimental data. Fig. 7-17 and Fig. 7-18 present the calculated and experimental heat capacity (20.4 mol% GdO1.5) and heat content (30 mol% GdO1.5) of fluorite. To fit the enthalpy increment and the heat capacity data, a TlnT contribution was used for zeroth order interaction parameter of the fluorite phase. The reasonable agreement of present calculations also demonstrates the consistency of the heat capacity and heat content data. The calculated and experimental heat capacity and heat content for the pyrochlore phase at 50 mol% GdO1.5 are shown in Fig. 7-19 -111- and Fig. 7-20, respectively, using two different pyrochlore models. The calculation by the first order phase model fits the heat capacity data well, while the result calculated by the second order phase model shows some deviation within the limits of experimental uncertainty. At the temperature of the pyrochlore-to-fluorite transition, the heat capacity calculated by the second order phase model indicates a discontinuity, since the pyrochlore phase becomes completely disordered. For the calculated heat content, however, a better fit with the experimental data is obtained using the order-disorder model. For the experimental heat capacity and heat content data, it can be seen that a good fit with one set of data will always cause a worse fit with other sets of data by using both models. This discrepancy originates from the uncertainties of the experimental data. Figure 7-19. The calculated heat capacity for the sample ZrO2-50 mol% GdO1.5 together with the experimental data with the two pyrochlore models used for assessments. Figure 7-20. The calculated heat content for the sample ZrO2-50 mol% GdO1.5 together with the experimental data with the two pyrochlore models used for assessments. Table 7-1. The invariant reactions in the ZrO2 − GdO1.5 system. Reaction Type Reference Temperature (K) Composition of phases (mol% GdO1.5) [1964Lin1] 2448 87.3 − − L ⇔ F+ H eutectic [1971Rou] 2533 86.7 ± 1 71 93 -112- This work 2518 85.7 75.4 91 [1971Rou] 2323 94.7 80.2 98.5 H ⇔ F + B eutectoid This work 2335 93.2 76.6 97.1 [1971Rou] 2623 96 99 97 L + X ⇔ H peritectic This work 2687 99.6 100 99.7 F + B ⇔ C peritectoid This work 2275 75.8 97.1 90.2 F ⇔ C + P eutectoid This work 1145 63 94.3 53.6 [1962Per] 1813 ± 10 50 50 − [1974Mic] 1803 50 50 − [1982Zoz] 1816 50 50 − [1989Mor] 1823 50 50 − P ⇔ F congruent This work 1823 50 50 − [1972Neg] 1415 − − − T ⇔ M + F eutectoid This work 1309 1.4 0.02 18.9 Table 7-2. Experimental and calculated enthalpies of formation in the ZrO2 − GdO1.5 system. Compositions Experimental data (J.mol-1)* Calculated results (J.mol-1)* 50 mol.% GdO1.5, P −13050 ± 1200 [2001Hel] −14752 (first order phase model) −12790 (second order phase model) 50 mol.% GdO1.5, F −18925 ± 2000 [1971Kor] −11731 45.6 mol.% GdO1.5, P −12725 ± 825 [2001Hel] −14849 (first order phase model) −12273 (second order phase model) 53.5 mol.% GdO1.5, F −11600 ± 850 [2001Hel] −11292 *per mole of cations Table 7-3. The compositions of the samples investigated in the ZrO2 − GdO1.5 system and observed phases. No. GdO1.5 (mol%) Observed phases 1400 °C 1600 °C 1700 °C 1 1 M 2 2 M 3 7.6 M + F 4 10 M + F M + F M + F 5 20 F F 6 30 F F 7 41 F 8 42 F 9 43 F 10 44 P -113- 11 45 P 12 46 P 13 47 P 14 48 P 15 49 P 16 50 P F F 17 51 P 18 52 P 19 53 P 20 54 P 21 55 F 22 56 F 23 57 F 24 58 F 25 59 F 26 70 F + C F + C F 27 80 F + C F + C F + C 28 95 C + B C + B C + B Table 7-4. Measured phase compositions data (mol% GdO1.5) for different phase equilibria in the ZrO2 − GdO1.5 system at different temperatures. F + C C + B Temperature (K) F C C B 1673 68.0 ± 1 89.0 ± 1 95.0 ± 1 99.1 ± 1 1773 69.0 ± 1 88.7 ± 1 1873 69.6 ± 1 88.3 ± 1 94.0 ± 1 98.8 ± 1 1973 71.2 ± 1 88.9 ± 1 Table 7-5. The DTA results of the martensitic transformation in the ZrO2 − GdO1.5 system. On heating On cooling Composition (mol% GdO1.5) As (K) Af (K) Ms (K) Mf (K) T0, (As+Ms)/2 (K) T0’, (Af+Mf)/2 (K) 1 1251 1324 1142 1108 1197 1216 2 1075 1155 1003 928 1039 1042 -114- Chapter 8 Experimental study and thermodynamic modeling of the ZrO2 − DyO1.5 system 8.1. Literature review The phase equilibria of the ZrO2 − Dy2O3 system were experimentally investigated by several groups [1962Per, 1970Tho, 1971Rou, 1980Pas, 1981Gav]. Perez [1962Per] firstly studied the phase relations in the temperature range 1000- 2500°C. A C1 ⇔ C2 continuous phase transition was found in the Dy2O3-rich region, and two metastable compounds H2 and H3 were reported. Furthermore, the C2 phase based on the C- type Dy2O3 could form a miscibility gap in the composition range around 55-65 mol% Dy2O3 according to their paper. However, most of the phase boundaries and reactions were given by dashed lines, which were thought to be less precise. [1970Tho] reported three intermediate phases in the ZrO2 − DyO1.5 system called α1, α2 and σ in the temperature range 1000-1350°C. After heat treatment at 1050°C for 20 days, α1 was considered to be stable in the composition range 21-29 mol% DyO1.5, and corresponded to the fluorite phase because it could coexist with the monoclinic phase. With increasing the DyO1.5 content, α2 was stable in the composition range 53-59 mol% DyO1.5. After heat treatment at 1350°C for 5 days, the σ phase was found beyond the composition of 85 mol% DyO1.5, and was probably the C-type terminal solution. However, no more detailed information on the structures of these phases was given in this paper. A detailed determination of the system above 1800°C was done by [1971Rou] using HTXRD measurements. The liquidus curve was well determined and the solidus was accordingly estimated. A continuous transition C1 ⇔ C2 was also reported like in the work of [1962Per]. This seems to be unreasonable according to the present experimental work on the ZrO2 − GdO1.5 system. The eutectic point of the invariant reaction L ⇔ F + H-Dy2O3 was determined at 2270°C and 80 mol% Dy2O3. At 2150°C, the H-Dy2O3 phase (95 mol% Dy2O3) was found to decompose into C2 and B-Dy2O3 phase by a eutectoid reaction. [1980Pas] studied the ZrO2 − Dy2O3 phase diagram over the whole composition range from 1150 to 2000°C. From 0 to 10 mol% Dy2O3, the HTXRD measurement was conducted between room temperature and 1500°C, and a high-temperature dilatometry was employed to obtain the thermal expansion data from room temperature to 1300°C. By determining the lattice parameter, the minimum solubility of Dy2O3 in the fluorite phase was found to be ∼8.5 -115- mol% at 500°C, 7 mol% at 1200°C, 6.3 mol% at 1450°C, 5 mol% at 1765°C and ∼2 mol% at ∼2000°C. The maximum solubility of Dy2O3 in fluorite was found to be 53 mol% at 1765°C and 59 mol% at 2000°C. The eutectoid point of the invariant reaction T ⇔ M + F was reported to occur at around 500°C and 4 mol% Dy2O3 based on the results of HTXRD and dilatometry measurements. The C1 ⇔ C2 continuous transition reported by [1962Per, 1971Rou] was not confirmed in their work, because the phase separation into fluorite and the C-type phases could be detected after the samples in the composition range 50 to 70 mol% Dy2O3 were annealed at ∼1800°C. A F + C-Dy2O3 two-phase region was found by [1980Pas] in the composition ranges 53-67 mol% Dy2O3 at 1765°C and 59-73 mol% Dy2O3 at ∼2000°C. Below 1765°C, two ordered hexagonal phases were detected in the Dy2O3-rich region. The M7O11.5-type H2 phase was found to exist at the temperatures below 1700°C at a composition of 55 mol% Dy2O3. In the composition range from 65 to 90 mol% Dy2O3, another hexagonal M7O11-type H3 phase was found. Both H2 and H3 were also reported previously by [1962Per] giving the same structure information. Neither the pyrochlore phase Dy2Zr2O7 nor δ- Dy4Zr3O12 was found in the work of [1980Pas]. Some invariant reactions involving fluorite, H2, H3, and C-type phases are not clear yet according to the experimental work of [1980Pas]. In the work of [1981Gav], the authors found the composition range of fluorite from 7 to 50 mol% Dy2O3 at 2020 K. All the experimental data on the invariant reactions are listed in Table 8-1. No any thermodynamic information concerning the ZrO2 − DyO1.5 system is available in literature. 8.2. Experimental results and discussion 8.2.1. The as-pyrolysed state Totally ten samples with different compositions were prepared in this work. The XRD patterns of the pyrolysed samples are given in Fig. 8-1. At the ZrO2-rich side, a sample presents clear tetragonal peaks, while the XRD patterns of samples in DyO1.5-rich region already show weak peaks of the C-type structure. For the sample containing 50 mol% DyO1.5, wide XRD peaks indicate that it is poorly crystallized at this temperature. The compositions of all the samples and information about the observed structure after heat treatment at different temperatures are given in Table 8-2. 8.2.2. The tetragonal + fluorite phase equilibrium -116- The XRD patterns in Fig. 8-2 show clear a fluorite + monoclinic two-phase structure for the sample with 7 mol% DyO1.5 after heat treatment. Fig. 8-3 is a SEM image of the sample containing 7 mol% DyO1.5 heat treated at 1700°C for 36h. The grey areas are the monoclinic phase transformed from the tetragonal phase during cooling, and the light ones are the fluorite phase. Compared with the ZrO2 − GdO1.5 system, in the ZrO2 − DyO1.5 system the tetragonal + fluorite two-phase region is narrower, and the solubility range of the tetragonal phase is larger (Table 8-3). 20 30 40 50 60 70 80 80 mol% DyO1.5 70 mol% DyO1.5 30 mol% DyO1.5 10 mol% DyO1.5 50 mol% DyO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) 20 30 40 50 60 70 80 MM M MM MM M F F F F M M F M 2θ (degree) In te ns ity (A rb .u ni ts ) In te ns ity (A rb .u ni ts ) Figure 8-1. The XRD patterns of the as- pyrolysed ZrO2 − DyO1.5 samples at 700°C for 3h. Figure 8-2. The XRD patterns of the sample ZrO2-7 mol% DyO1.5 heat treated at 1400°C for 240h. Figure 8-3. The SEM back scattered electron image (×3000) of the sample ZrO2-7 mol% DyO1.5 heat treated at 1700°C for 36h (the grey areas are the monoclinic phase transformed from the tetragonal phase, and the light ones are fluorite). 8.2.3. The martensitic transformation temperatures of the tetragonal phase -117- The martensitic transformation temperatures of the samples containing 1 and 2 mol% DyO1.5 were measured by DTA up to 1400°C. The detailed temperature data of As, Af, Ms and Mf are compiled in Table 8-4, together with the calculated T0 temperatures. 8.2.4. The fluorite + C-Dy2O3 phase equilibrium 20 30 40 50 60 70 80 F F F CC CC CCC CCC C C F F F 80 mol% DyO1.5 75 mol% DyO1.5 70 mol% DyO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) F Figure 8-4. The XRD patterns of the ZrO2 − DyO1.5 samples with 70, 75, and 80 mol% DyO1.5 heat treated at 1600°C for 72h. Figure 8-5. The SEM back scattered electron image (×3000) of the sample ZrO2-75 mol% DyO1.5 heat treated at 1700°C for 36h (the grey areas are fluorite, and the light ones are C- type Dy2O3). Neither pyrochlore nor the δ-type phase is found according to the XRD results in the investigated temperature range. This is consistent with the literature reports. Thus, the fluorite phase is only in equilibrium with the C-Dy2O3 phase beyond the composition of 50 mol% -118- DyO1.5. Fig. 8-4 includes the XRD patterns of the samples with 70, 75 and 80 mol% DyO1.5 after heat treatment at 1600°C, 72h. The sample with 70 mol% DyO1.5 only shows fluorite peaks, and both the samples with 75 and 80 mol% DyO1.5 present the superstructure peaks of C-type phase. SEM-EDX analysis reveals that a narrow fluorite + C-Dy2O3 two-phase region exists in this region. The two-phase region is not easy to be identified by using the XRD measurements due to the overlapping of the strong peaks of fluorite and the C-type phases. Fig. 8-5 is a SEM image of the sample with 75 mol% DyO1.5 after heat treatment at 1700°C for 36h. The width of this two-phase region is only around 10 mol% according to the EDX data (Table 8-3). With increasing the temperature, the solubility of ZrO2 in C-type phase reduces. 8.3. Selected experimental data for optimization The experimental data on the tetragonal + fluorite and fluorite + C-Dy2O3 phase equilibria obtained in this work are adopted in the optimization, together with the high temperature liquidus data and invariant reactions reported by [1971Rou]. The heat content data of the samples with 30 and 50 mol% DyO1.5 in the range 473- 1673 K measured in this work are accepted to assess the thermodynamic properties of the fluorite phase. For the enthalpy of formation of the fluorite phase, since there are no any experimental data, it is assumed that it should be slightly more negative than the value in the ZrO2 − GdO1.5 system. 8.4. Optimization procedure By using a limited number of parameters, in a first step the phase diagram was roughly assessed from the experimental phase equilibria data. In a second step, the optimization of the fluorite phase was improved by taking also the thermodynamic data of heat content into account. Finally, a full adjustment of the parameters of all phases was carried out in order that all the reliable experimental data could be well reproduced. To optimize the experimental heat content data, a TlnT contribution was added to the zeroth order interaction parameter of the fluorite phase. The optimized parameters are given in Appendix. 8.5. Calculated results and discussion The calculated ZrO2 − DyO1.5 phase diagram is shown in Fig. 8-6, together with the experimental data. The experimental phase boundary data obtained in this work and the -119- liquidus data of [1971Rou] are well reproduced. The calculated invariant reactions by this work are compiled in Table 8-1. A reasonable tetragonal + fluorite two-phase region is calculated based on the present experimental data. The XRD results of [1980Pas, 1981Gav] show some deviation with this work, due to their less accuracy. The calculated eutectoid point of the invariant reaction T ⇔ F + M occurs at 1233 K and 3.2 mol% DyO1.5. This temperature is much higher than the value 773 K reported by [1980Pas]. The present result is thought to be more reasonable, because the temperature of [1980Pas] obtained by dilatometry measurement is actually corresponding to the martensitic transformation temperature, rather than to the invariant reaction. Fig. 8-7 presents the calculated T0 lines for the monoclinic + tetragonal and tetragonal + fluorite equilibria, agreeing well with the experimental data obtained in this work. Figure 8-6. The calculated ZrO2 − DyO1.5 phase diagram together with experimental data. The data on the fluorite + C-Dy2O3 phase equilibrium reported by [1980Pas, 1981Gav] are not consistent with but close to present calculations. With elevating the temperature, the solubility of ZrO2 in C-type phase reduces in the temperature range studied. Two invariant reactions involving the C-type phase are calculated: H-Dy2O3 + F ⇔ C-Dy2O3 at 2543 K and H-Dy2O3 ⇔ B-Dy2O3 + C-Dy2O3 at 2445 K, for which the temperature is consistent with the experimental value 2423 K for this reaction reported by [1971Rou]. The temperature of the eutectic reaction L ⇔ F + H-Dy2O3 calculated in this work is 2569 K, -120- which is close to the experimental data 2543 K of [1971Rou], while the calculated composition of each phase shows large discrepancies with those reported by [1971Rou]. However, the temperature of the reaction H-Dy2O3 + F ⇔ C-Dy2O3 predicted by the present calculation well reproduces the value of 2543 K for L ⇔ F + H-Dy2O3 reported by [1971Rou]. In view of the large experimental uncertainties and the reliable fluorite + C-Dy2O3 phase equilibrium data obtained in this work, the results of the present calculations are accepted as more reasonable. Figure 8-7. The calculated T0 lines for the monoclinic + tetragonal and tetragonal + fluorite equilibria of the ZrO2 − DyO1.5 system, together with experimental data. Figure 8-8. The experimental and calculated heat content (HT-H298) for the composition ZrO2-30 mol% DyO1.5. Figure 8-9. The experimental and calculated heat content (HT-H298) for the composition ZrO2-50 mol% DyO1.5. -121- The experimental heat content data determined in this work for the samples containing 30 and 50 mol% DyO1.5 are given in Fig. 8-8 and Fig. 8-9 together with the calculated results. Though some data are scattered at high temperatures, the agreements are quite well after a TlnT contribution is adopted for the interaction parameter of the fluorite phase. Table 8-1. The invariant reactions in the ZrO2 − DyO1.5 system. Reaction Type Reference Temperature (K) Compositions of phases (mol% DyO1.5) [1971Rou] 2543 88.3 76.5 94.7 L ⇔ F+ H eutectic This work 2569 91.3 85 96.7 [1971Rou] 2423 − − − H ⇔ C + B eutectoid This work 2445 99.2 98.4 99.6 H + F ⇔ C peritectoid This work 2543 96.7 84.9 93.1 [1980Pas] 773 4.0 − − T ⇔ M + F eutectoid This work 1233 3.2 0.06 17.9 Table 8-2. The compositions of the samples investigated in the ZrO2 − DyO1.5 system and observed phases. No. DyO1.5 (mol%) Observed phases 1400 °C 1600 °C 1700 °C 1 1 M − − 2 2 M − − 3 7 F + M F + M F + M 4 10 F + M F + M F + M 5 30 F F F 6 50 F F F 7 60 F F F 8 70 F F F 9 75 F + C F + C F + C 10 80 C C C -122- Table 8-3. Measured phase compositions data (mol% DyO1.5) for different phase equilibria in the ZrO2 − DyO1.5 system at different temperatures. Temperature (K) T + F F + C T F F C 1673 3.95 ± 0.5 14.5 ± 1 67 ± 1 79.4 ± 1 1873 4.1 ± 0.5 12.3 ± 1 70.6 ± 1 82.6 ± 1 1973 4.3 ± 0.5 10.9 ± 1 74.4 ± 1 84.5 ± 1 Table 8-4. The DTA results of martensitic transformation in the ZrO2 − DyO1.5 system. On heating On cooling Composition (mol% DyO1.5) As (K) Af (K) Ms (K) Mf (K) T0, (As+Ms)/2 (K) T0’, (Af+Mf)/2 (K) 1 1272 1318 1153 1117 1212.5 1217.5 2 1123 1186 1018 975 1073 1080.5 -123- Chapter 9 Experimental study and thermodynamic modeling of the ZrO2 − YbO1.5 system 9.1. Literature review The phase equilibria of the ZrO2 − YbO1.5 system were experimentally investigated by the several groups [1968Rou1, 1970Tho, 1971Rou, 1982Zoz, 1984Stu, 1987Ste, 1993Gon, 1999Kar]. [1968Rou1, 1971Rou] studied the phase relations above 1800°C by thermal analysis and HTXRD measurements. A congruent melting point of the fluorite phase was determined at 2825°C and 25 mol% Yb2O3. The liquidus curve was well defined and the solidus was estimated according to the liquidus data. An invariant eutectic reaction in the Yb2O3-rich region was detected to occur at around 2420°C. At lower temperatures, a continuous second- order transition from the fluorite phase to a cubic Tl2O3-type phase was reported, and actually not correct according to the present experimental results on the ZrO2 − GdO1.5 and ZrO2 − DyO1.5 systems. The ordered compound Yb4Zr3O12 (δ) was reported by Thornber et al. [1970Tho]. By plotting the unit-cell volumes of fluorite and C-type Yb2O3 at 1600°C, they found that the fluorite phase extends up to 50 mol% YbO1.5. Beyond this composition, it was in equilibrium with the δ phase which formed near the composition of 57.14 mol% YbO1.5. At the YbO1.5- rich side, there was a two-phase region between δ and the C-type Yb2O3 solid solution phases up to the composition of 70 mol% YbO1.5. The phase relations below 2150°C were proposed by [1984Stu] based on the experiments in the composition range 0-60 mol% Yb2O3 using XRD measurements. The tetragonal + fluorite two-phase region was established and the invariant reaction T ⇔ F + M was determined at around 520°C with low reliability, while the temperature of the phase transition between fluorite and the δ phase was measured as 1637 ± 12°C. In the Yb2O3-rich region, three hexagonal phases H1, H2, and H3 reported by [1962Per] were not confirmed by the phase relations determined by [1984Stu], and thus were thought as metastable phases. A sharp boundary between the ordered δ phase and fluorite was shown in their work, together with a similar result on the ZrO2 − Y2O3 system. In the Yb2O3-rich region, the reaction F ⇔ δ + C-Yb2O3 occurs at 1612°C where the eutectoid composition of fluorite is very close to the composition of δ phase. [1987Ste] studied the phase formation in the ZrO2 − Yb2O3 system by -124- using XRD measurements. Samples in the composition range of 2 to 90 wt.% Yb2O3 were heat treated at 1400°C-1600°C for both 96h and 192h. Similar results to [1984Stu] were obtained on the phase evolution with increasing the Yb2O3 content. However, no any quantitative result was given on the phase boundaries. The tetragonal + fluorite two-phase region was studied by [1993Gon] in the range of 0-10 mol% Yb2O3 with 0.5 mol% composition increments using dilatometry and XRD measurements. The samples were heat treated at four temperatures: 1700°C for 4h, 1640°C for 24h, 1290°C for 336h, and 840°C for 1000h. Compared with the result of [1984Stu], Gonzalez et al. [1993Gon] presented a narrower tetragonal + fluorite two-phase region. The tetragonal zirconia solution can dissolve up to 3 mol% Yb2O3. The lower limit of the fluorite phase was established to be 7 mol% Yb2O3 at 840°C, 6 mol% Yb2O3 at 1290°C, 5 mol% Yb2O3 at 1640°C, and 4.8 mol% Yb2O3 at ∼1700°C. The eutectoid point of the invariant reaction T ⇔ F + M was determined at 400 ± 20°C and 2.3 mol% Yb2O3 by high-temperature dilatometry. However, this result is highly questionable and may be incorrect because the dilatometry actually only gives the T ⇔ M martensitic transformation temperature. The compound Yb4Zr3O12 was confirmed in their work, and the determined disordering temperature 1630 ± 10°C was well consistent with the result of [1984Stu]. The same result, 1630°C was also reported by [1999Kar]. The melting point of the sample ZrO2-50 mol% YbO1.5 was measured at 2697 ± 14°C by [1982Zoz], and was consistent with the liquidus data determined by [1968Rou1]. Karaulov and Zoz [1999Kar] determined the homogeneity range of the compound Yb4Zr3O12 in the temperature range 1200-1900°C. However, its composition range of 37-45 mol% Yb2O3 was given without an exact temperature. A thermodynamic assessment of the ZrO2 − YbO1.5 system was done by Jacobson et al. [2002Jac] only based on the experimental data of [1968Rou1, 1984Stu] and a phase diagram with a less reliable fluorite + tetragonal two-phase region was presented. No any experimental thermodynamic data are available in literature for the ZrO2 − YbO1.5 system. All the experimental data on the invariant reactions are listed in Table 9-1. 9.2. Experimental results and discussion 9.2.1. The as-pyrolysed state Totally seven samples with different compositions were prepared for the ZrO2 − YbO1.5 system: 6.5, 10, 30, 50, 57.14, 65 and 75 mol% YbO1.5. The XRD patterns of the -125- samples after pyrolysis at 700°C for 3h are shown in Fig. 9-1. With increasing the content of YbO1.5, the peaks become wider, and their number decreases, while revealing poorly crystallized microstructures. The observed phases of all samples after heat treatments by XRD measurement are summarized in Table 9-2. 10 20 30 40 50 60 70 80 75 mol% YbO1.5 65 mol% YbO1.5 57.1 mol% YbO1.5 50 mol% YbO1.5 30 mol% YbO1.5 10 mol% YbO1.5 In te ns ity (A rb .u ni ts ) 2θ (degree) 6.5 mol% YbO1.5 20 40 60 80 F+M, 6.5 mol% YbO1.5, 1673 K, 168h T'+M, 10 mol% YbO1.5, 1673 K, 48h T', 10 mol% YbO1.5, 1473 K, 15h In te ns ity (A rb .u ni ts ) 2θ (degree) Figure 9-1. The XRD patterns of the ZrO2 − YbO1.5 samples as-pyrolysed at 700°C for 3h. Figure 9-2. The XRD patterns of ZrO2 − YbO1.5 samples with 6.5 mol% and 10 mol% YbO1.5 after different heat treatments. 9.2.2. The tetragonal + fluorite phase equilibrium The tetragonal + fluorite phase equilibrium was determined by heat treating a sample with 6.5 mol% YbO1.5, while the sample with 10 mol% YbO1.5 heat treated at 1400°C has only a small amount of the monoclinic phase, and is not appropriate for composition analysis. The XRD patterns for these two samples heat treated at 1200°C and 1400°C are given in Fig. 9-2. The patterns of the sample containing 10 mol% YbO1.5 present mainly the T′ phase, which diffusionlessly transforms from fluorite during cooling, while those of the sample containing 6.5 mol% YbO1.5 indicate clear the monoclinic and fluorite structure. Fig. 9-3 is the SEM back-scattered electron image (×3000) of the sample with 6.5 mol% YbO1.5 heat treated at 1700°C for 36h. It shows a very homogeneous microstructure, in which the grey areas are the monoclinic phase transformed from the tetragonal phase during cooling, and the white areas are the fluorite phase. The measured data on the phase boundaries are listed in the Table 9-3. Present results agree better with the data of [1993Gon] than with those of [1984Stu]. The solubility of YbO1.5 in the tetragonal phase exceeds 4 mol%, and increases at elevated temperatures. This is consistent with the results of [1995Kat] on some other systems. The solubility limit of the fluorite phase in the ZrO2-rich region reaches a low value compared with the other ZrO2 − REO1.5 system, and accordingly the fluorite + tetragonal two-phase -126- region is very narrow with a width of only around 6 mol% YbO1.5 in the studied temperature range. Figure 9-3. The SEM back scattered electron image (×3000) of the sample ZrO2-6.5 mol% YbO1.5 heat treated at 1700°C for 36h (the grey areas are the monoclinic phase transformed from the tetragonal phase, and the white ones are fluorite). 20 30 40 50 60 δ, 57.14 mol%YbO1.5 1673K In te ns ity (A rb .u ni ts ) 2θ (degree) C-Yb2O3, 75 mol%YbO1.5 1873K Figure 9-4. The XRD patterns of the δ phase and C-type Yb2O3 in the ZrO2 − YbO1.5 system. 9.2.3. The phase equilibria involving δ and C-Yb2O3 As the ordered structure of the fluorite phase, the δ phase is the only compound found in this work. The phase relations involving δ phase reported by [1984Stu, 1987Ste] are confirmed by the XRD measurements. Fig. 9-4 includes the XRD patterns of δ and C-Yb2O3 . Because δ and C-Yb2O3 are both ordered structures of the fluorite phase, the strong peaks of δ -127- always overlap with the peaks of fluorite. As a result, the δ + C-Yb2O3 and F + C-Yb2O3 two- phase regions are hardly to be identified by the XRD measurements. Fig. 9-5 is the SEM image of the microstructure of the sample containing 65 mol% YbO1.5 consisting of δ and C-Yb2O3. The average grain size of the δ phase is less than 5 µm even after the heat treatment at 1600°C for 72h. The measured compositions of δ, C-Yb2O3 and fluorite of the δ + C-Yb2O3 and F + C-Yb2O3 two-phase equilibria are summarized in Table 9-3. Present XRD and SEM results are consistent with those of the δ ⇔ F transformation and the reaction F ⇔ δ + C reported by [1984Stu]. However, narrower δ + C-Yb2O3 and F + C-Yb2O3 two-phase regions are obtained in this work by precise determination of the phase boundary data. Figure 9-5. The SEM back scattered electron image (×5000) of the sample ZrO2-65 mol% YbO1.5 heat treated at 1600°C for 72h (the grey areas are the fluorite phase, and the light ones are C-Yb2O3). 9.3. Selected experimental data for optimization Due to the limited literature data on the phase diagram, the phase boundary data obtained in this work on the tetragonal + fluorite, δ + C-Yb2O3, and fluorite + C-Yb2O3 phase equilibria, the temperatures for the δ ⇔ F transformation and the reaction F ⇔ δ + C found by [1984Stu, 1999Kar], the homogeneity range data of the δ phase reported by [1999Kar], and the liquidus data determined by [1968Rou1] together with the temperature of the invariant reaction involving liquid, C-Yb2O3, and H-Yb2O3 are adopted for the optimization of the phase diagram. -128- The heat content data of the samples with 30 mol% YbO1.5 and 57.14 mol % YbO1.5 in the temperature range 473-1673 K measured in this work are adopted for modeling. The enthalpy of formation of the fluorite phase in the ZrO2 − YO1.5 system [2003Lee] is adopted as a start value, in view of the similarities of these two systems. 9.4. Optimization procedure In a first step, the phase diagram was roughly assessed by using liquidus and tetragonal + fluorite phase boundary data, without taking account of the ordered δ phase. Then, further optimization was done by treating the δ phase as a stoichiometric compound, and using the experimental heat content data. Finally, a full assessment is carried out by using all selected data simultaneously and introducing homogeneity range for the δ phase. For the fluorite phase, a TlnT contribution to zeroth order interaction parameter was applied to fit the experimental heat content data. The Neumann-Kopp rule was adopted for the δ phase since it reproduces the experimental heat content data well, and the entropy of formation of the δ phase with respect to monoclinic ZrO2 and C-type Yb2O3 was arbitrarily given 0.5 J.mol-1.K-1 in this work. The optimized thermodynamic parameters for all phases are given in Appendix. 9.5. Calculated results and discussion The calculated ZrO2 − YbO1.5 phase diagram is shown in Fig. 9-6, together with the experimental data, while the calculated invariant reactions are given in Table 9-1. The assessed tetragonal + fluorite two-phase region shows good agreement with the phase equilibria data obtained in this work and those data on the composition limits of the tetragonal phase by [1984Stu, 1993Gon]. As for the fluorite phase, the data reported by [1993Gon] agree with current results well at high temperatures, and indicates discrepancy at low temperatures due to the experimental uncertainties. The phase boundary data of fluorite phase obtained in the work of [1984Stu] are less accurate, partly because the phase transformation character in this region is complicated and XRD cannot correctly record the phase transformation temperatures. Likewise, the temperatures of decomposition of the tetragonal phase into fluorite and the monoclinic phase [1984Stu, 1993Gon] seem to be too low compared to that of the equilibrium state. Presently calculated eutectoid point of the invariant reaction T ⇔ M + F is at 1215 K and 3.6 mol% YbO1.5, while the related composition of the fluorite phase is 15.6 mol% YbO1.5, and the solubility of YbO1.5 in monoclinic phase is only around 0.1 mol%. -129- Figure 9-6. The calculated ZrO2 − YbO1.5 phase diagram together with experimental data. The calculated liquidus show reasonable agreement with the experimental data considering their large uncertainties at such high temperatures. The congruent melting point of the fluorite phase calculated in this work is at 3085 K and 33.6 mol% YbO1.5, which temperature is close to 3093 K reported by [1971Rou], but shows some discrepancy with respect to the composition (40 mol% YbO1.5). Considering the smooth liquidus temperatures in a wide composition range and the large experimental uncertainties, the present calculated result is acceptable. At low temperatures, the calculated temperature 1908 K for the invariant reaction F ⇔ δ + C agrees well with the experimental data, while the temperature for the F ⇔ δ transition is only 1 K lower. The experimental results of [1999Kar] on the homogeneity range of the δ phase as well as those obtained in the present work are reproduced well by the calculation. However, the phase boundaries of the δ phase at both sides are not symmetrical to the composition 57.14 mol% YbO1.5, and the calculated congruent composition for the F ⇔ δ transition is at 59.7 mol% YbO1.5. These are thought to be reasonable by taking account of the possible larger solubility of YbO1.5 in the δ phase in view of the difference of the Zr4+ and Yb3+. The solubility of ZrO2 in C-type Yb2O3 reaches its maximum value at this invariant reaction, and decreases at elevated temperatures. The F / F + C-Yb2O3 phase boundary data of [1984Stu] show large discrepancy with the calculations and present experimental data. The literature data are less reliable because it is very difficult to study the F + C-Yb2O3 two-phase region only by XRD according to the experience gathered in the present work due to the -130- overlapping of the XRD peaks of F and C-Yb2O3. In the Yb2O3-rich region, two calculated invariant reactions involving liquid phase are L ⇔ C-Yb2O3+ H-Yb2O3 at 2717 K, and L +F ⇔ C-Yb2O3 at 2754 K. In view of the large experimental uncertainties in this region, the present calculations provide at least a topologically reasonable phase diagram. Figure 9-7. The calculated partial ZrO2 − YbO1.5 phase diagram and the T0 lines for the monoclinic + tetragonal and tetragonal + fluorite phase equilibria, together with the experimental data. Fig. 9-7 presents the calculated T0 lines for the monoclinic + tetragonal and tetragonal + fluorite phase equilibria, in which the experimental T0 data are well reproduced. However, the estimated T0 data [1998Vor] for the transition between fluorite and T′, do not agree well with the present calculation. Since the calculation based on the equilibrium thermodynamics only gives the T0 for the fluorite and tetragonal phase, and it is not clear yet if the Gibbs energy of metastable T′ phase has exact the same behavior as the stable tetragonal phase. Thus, a better fit with the experimental data is not necessary and will make the phase diagram worse. The enthalpy of formation (per mole of cations) of fluorite at 50 mol% YbO1.5 calculated in this work (− 16094 J.mol-1) is more negative than the value (− 6700 J.mol-1) reported by [2003Lee] for the ZrO2 − YO1.5 system, however agrees with those data optimized by the CALPHAD method in the references [2004Chen, 2004Fab]. This is consistent with the results obtained for the other ZrO2 − REO1.5 systems and that there is a tendency that with decreasing the ionic radius of RE+3, the stability of fluorite will increase. The calculated heat -131- contents of samples with 30 mol% YbO1.5 and 57.14 mol% YbO1.5 are plotted in Fig. 9-8 and Fig. 9-9, respectively, together with the experimental data obtained in this work. Though the experimental data show scattering due to the experimental uncertainties, the agreements with the calculations are still good enough. It can be seen from these two figures that the heat content of the fluorite phase changes faster than that of the δ phase, and a higher heat capacity can be deduced for the fluorite phase. Figure 9-8. The experimental and calculated heat content (HT-H298) of fluorite with 30 mol% YbO1.5 . Figure 9-9. The experimental and calculated heat content (HT-H298) of δ with 57.14 mol% YbO1.5 . Table 9-1. The invariant reactions in the ZrO2 − YbO1.5 system. Reaction Type Reference Temperature (K) Compositions of phases (mol% YbO1.5) [1971Rou] 2693 92 − − L ⇔ C+ H eutectic This work 2717 98.1 97.3 98.3 L +F ⇔ C peritectic This work 2754 88.1 78.8 85.6 [1984Stu] 1885 − − − F ⇔ δ + C eutectoid This work 1907 60.8 60.6 72.5 [1984Stu] 1910 57.14 57.14 − [1993Gon] 1903 − − − [1999Kar] 1903 − − − δ ⇔ F congruent This work 1908 59.7 59.7 − -132- [1993Gon] 673 4.5 3.1 15.6 [1984Stu] 793 − − − T ⇔ M + F eutectoid This work 1215 3.6 0.1 15 [1971Rou] 3098 40 40 − F ⇔ L congruent This work 3085 33.6 33.6 − Table 9-2. The compositions of the samples investigated in the ZrO2 − YbO1.5 system and observed phases. No. YbO1.5 (mol%) Observed phases 1400 °C 1600 °C 1700 °C 1 6.5 F + M F + M F + M 2 10 T′ + M T′ + M T′ + M 3 30 F F F 4 50 F + δ F F 5 57.14 δ δ F 6 65 δ + C δ + C F + C 7 75 δ + C C C Table 9-3. Measured phase compositions data (mol% YbO1.5) for different phase equilibria in the ZrO2 − YbO1.5 system at different temperatures. Temperature (K) T + F δ + C F + C T F δ C F C 1673 4.2 ± 0.5 11.7 ± 1 62.0 ± 1 79.5 ± 1.5 − − 1873 4.3 ± 0.5 11.3 ± 1 59.2 ± 1 72.1 ± 1.5 − − 1973 4.7 ± 0.5 10.5 ± 1 − − 62.8 ± 1 72.8 ± 1 -133- Chapter 10 Experimental study and calculation of the ZrO2 − GdO1.5 − YO1.5 system 10.1. Calculations and experimental results The parameters for the ZrO2 − YO1.5 and GdO1.5 − YO1.5 systems are taken from a recent assessment [2005Fab] for present calculations. No any further assessment is done for the ZrO2 − GdO1.5 − YO1.5 system. The calculated ternary isothermal sections at 1200, 1400 and 1600°C are presented in Fig. 10-1 (a-c). Te projection of the liquidus surface is shown in Fig. 10-2. There is only one invariant reaction in this system C + L ⇔ H + F at a temperature of 2316°C and a liquid composition of 8.6 mol% ZrO2 and 61.3 mol% GdO1.5. The univariant reaction L ⇔ H + X is practically degenerated and proceeds in the GdO1.5 − YO1.5 system from 70 to 99.9 mol% GdO1.5. Figure 10-1 (a). Isothermal section at 1200°C Figure 10-1 (b). Isothermal section at 1400°C Selected XRD analysis of the samples annealed at 1400°C are presented in Fig. 10-3 and a summary of the phases identified in Table 10-1. No ternary compounds or three-phase regions were detected, as originally anticipated. In the ZrO2-rich region, the XRD analysis showed mainly the peaks of the fluorite and monoclinic phases. The monoclinic phase is not stable at 1400°C but results from martensitic transformation of the tetragonal phase during cooling. Fluorite is stable as a single phase in a wide composition range. At 1400° C, at least 5 mol% GdO1.5 can be substituted by YO1.5 in the pyrochlore structure. However, the XRD analysis could not conclusively ascertain if there is only pyrochlore or a pyrochlore + fluorite -134- phase assemblage in the region nominally denoted as a two-phase equilibrium in the thermodynamic model. The C-type phase is continuous along the GdO1.5-YO1.5 binary for the temperature range of interest. With increasing ZrO2 content a two-phase assemblage fluorite + C becomes stable across the entire range. The maximum concentration of ZrO2 in the C-type phase does not exceed 10 mol%. In the temperature range 1200-1600°C, the phase boundaries F / F + C and C / F + C appear not to change very much with temperature. Figure 10-1 (c). Isothermal section at 1600°C Figure 10-2. Calculated liquidus projection 20 30 40 50 60 70 80 In te ns ity (a rb .u ni ts ) Z20G20Y60 F+C Z33.3G33.3Y33.3 F Z50G45Y05 F+ P Z81G7.6Y11.4 F+M 2 Z88.6G7.6Y3.8 F+M θ (degree) Figure 10-3. XRD patterns for the samples in the ZrO2 − GdO1.5 − YO1.5 system heat treated at 1400°C (Z, G, Y represent mol% of ZrO2, GdO1.5 and YO1.5 respectively). -135- 10.2. Discussions The experimental results show good agreement with the calculated sections in Figs. 10-1(a-c) indicating that the reassessment of the thermodynamic parameters for the ternary is not necessary and the database derived from the binaries properly represents the behavior of the system in this temperature range. The similar behavior of the ZrO2 − YO1.5 and ZrO2 − GdO1.5 systems is reflected in the extension of the common fields across the entire ternary diagram, with the stability range of the ordered phases limited to the near vicinity of the corresponding binaries. It is well established that the ionic radius of Y+3 is too small to form a pyrochlore phase with ZrO2, so the de-stabilization of the pyrochlore with Y substitution for Gd is anticipated. A similar behavior is observed when Zr is substituted for Ti in the Y2Ti2O7 pyrochlore. At the same time, substitution of the larger Gd cation for Y is also bound to readily de-stabilize the δ structure. The isothermal section at 1473 K in Fig. 10-1(a) gives confidence to the approach of using an intermediate layer of 7YSZ to control the interaction between Gd2Zr2O7 and the protective Al2O3 in a TBC system, as discussed earlier. Incorporation of Y into Gd2Zr2O7 induces disorder but it is not expected to change significantly the thermal isolation benefits of the latter [2002Wu]. Table 10-1. Summary of the XRD analysis of the samples in the ZrO2 − GdO1.5 − YO1.5 system heat treated at 1200-1600° C. No. Composition (mol%) Observed phases ZrO2 GdO1.5 YO1.5 1200° C 1400° C 1600° C 1 88.6 7.6 3.8 − F + M − 2 88.6 3.8 7.6 − F + M − 3 84.8 7.6 7.6 − F + M − 4 81.0 7.6 11.4 − F − 5 50.0 45.0 5.0 − P − 6 45.0 45.0 10.0 F F F 7 45 10 45 F F F 8 33 33 33 F + C F F 9 30 35 35 F + C F + C F 10 20 20 60 C + F C + F C + F 11 20 60 20 − C + F − 12 20 40 40 C + F C + F C + F 13 10 10 80 C + F C + F C + F 14 10 45 45 C + F C + F C + F -136- Chapter 11 Characteristic changes in the ZrO2 − REO1.5 systems 11.1. The evolutions of the phase relations in the ZrO2 − REO1.5 systems The rare earth oxides present similar physical and chemical properties, and show some trends with changing the ionic radius and molecular weight of the rare earth elements. As a matter of course, the phase relations in all the ZrO2 − REO1.5 systems also reveal similar characteristics and evolve with the change of the ionic radius or molecular weight. For each ZrO2 − REO1.5 system except those with Dy and Sc, there is only one intermediate compound which is the ordered structure of the ZrO2-based cubic fluorite-type phase. From La to Gd, the pyrochlore phase at stoichiometric composition (50 mol% REO1.5) is the stable compound, and from Ho to Yb, the ordered structure is the δ phase with the stoichiometry of 57.14 mol% REO1.5. In the case of Dy, no any compound was found in this work. In the case of Sc, besides the δ phase, two other ordered compounds were also reported in literature [1970Spi, 1970Tho, 1977Ruh]. Fig. 11-1 collects the phase transition temperatures of the ordered phases in those systems. It is clear that the pyrochlore phase is preferably stable for the larger ionic radius of RE+3, while the δ phase is preferably stable for the smaller ionic radius of RE+3. With decreasing the ionic radius from La+3 to Dy+3 or increasing the ionic radius from Yb+3 to Dy+3, both the pyrochlore and δ are less stable, and that is why no any ordered compound is found in the ZrO2 − DyO1.5 system. This is consistent with the fact that the pyrochlore is only stable when the ++ 43 / BA rr ratio is between 1.46 and 1.80 [1983Sub]. On the other hand, even if the ordered structure can be thermodynamically stable, it will be kinetically very difficult to form at such low temperature. As can be seen in Fig. 11-2, the solubility of REO1.5 in tetragonal ZrO2 at 1600°C increases when the ionic radius of RE reduces, and an approximate linear relation can be found for the solubility against ionic radius. At the same time, the fluorite phase field also extends towards lower solubility limits in the ZrO2-rich region when the RE+3 has a smaller ionic radius. As a result, the width of the tetragonal + fluorite two-phase region becomes narrower with decreasing the ionic radius. Furthermore, the decomposition temperature of the tetragonal phase (i.e. T ⇔ F + M or T ⇔ P + M) is strongly influenced by the solubility limits of the tetragonal phase. Fig. 11-3 shows the calculated ZrO2-rich partial phase diagrams of the systems studied in this work without the pyrochlore phase. The clear trends for the change can be seen. Although some neighboring boundaries intersect each other in some temperature -137- ranges, reasonable characteristic changes are given by the present calculations within the limits of uncertainties. 100 102 104 106 108 110 112 114 116 118 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 2600 2700 δ Te m pe ra tu re (K ) Ionic radius (pm) [1971Rou],pyrochlore [1982Zoz] [1984Stu] [2004Fab],[2004Che] [2004Rus],pyrochlore,predicted [1981Pas] Yb Y Dy Tb Gd Eu Sm Nd LaPyrochlore Er Fig. 11-1. The phase transformation temperatures of the ordered phases in the ZrO2 − REO1.5 systems. 85 90 95 100 105 110 115 120 0 1 2 3 4 5 6 7 8 9 Literature data This work linear fit M ol e pe rc en t o f R EO 1. 5 Ionic radius (pm) La Nd Sm Gd Dy Y Er Yb Sc Figure 11-2. The average solubility of REO1.5 in tetragonal ZrO2. The linear functions of the lattice parameters of the fluorite phase constructed by Vegard’s law for different systems are compiled in Fig. 11-4, in which the stable fluorite phase region at 1700°C is lined out. With decreasing the lattice parameter of REO1.5, some fluctuations are present on the width of the fluorite phase region due to the influence of the structural evolution of REO1.5. The solubility of ZrO2 in C-type REO1.5 phase becomes larger when the radius of RE+3 decreases. -138- The phase equilibria are also related to the degree of lattice mismatch between different phases. According to the measured lattice parameters of the fluorite and pyrochlore phases in the ZrO2 − NdO1.5, ZrO2 − SmO1.5 and ZrO2 − GdO1.5 systems, the interface between the disordered and ordered phases should be more coherent and have less lattice mismatch with decreasing the radius of RE+3. This trend can be also applied to the equilibria between fluorite and the REO1.5 terminal solution phase. The two phases in equilibrium form a narrower two-phase region when they are more coherent at interface. This is consistent with the XRD observations on the overlapping of the strong peaks of the fluorite and C-type phase in the ZrO2-DyO1.5 and ZrO2-YbO1.5 systems. The large difference in SEM morphology between the two equilibrium phases (F + A equilibrium in the ZrO2 − NdO1.5 system and F + B equilibrium in the ZrO2 − SmO1.5 system) is also caused by the larger lattice mismatch for the case of larger RE+3, while for the systems with F + C equilibrium and smaller RE+3, the morphologies of fluorite and C-type phases do not show evident difference due to the more coherent interface. At high temperatures, as it has been investigated by [1971Rou], the ZrO2 − REO1.5 system with smaller ionic radius of RE+3 has higher temperatures of liquidus. At the same time, the temperatures for the invariant reactions involving liquid and fluorite phases in REO1.5-rich side are also elevated. Figure 11-3. The calculated ZrO2-rich partial phase diagrams of different doping RE elements. -139- 0 10 20 30 40 50 60 70 80 90 100 5.00 5.05 5.10 5.15 5.20 5.25 5.30 5.35 5.40 5.45 5.50 5.55 5.60 La tti ce p ar am et er (Å ) REO1.5 (Mol% ) Gd Dy Sm Nd Fluorite phase region Yb La Figure 11-4. The lattice parameters of fluorite phases in all ZrO2 − REO1.5 systems constructed by Vegard’s law (the solid lines give the stable fluorite phase region at 1700°C). 11.2. The evolutions of the thermodynamic properties in the ZrO2 − REO1.5 systems The phase relations are essentially determined by the thermodynamic properties of phases. With the change of the ionic radius of RE+3, it is found and confirmed in this work that some thermodynamic properties of different phases change towards a single trend. Fig. 11-5 presents the enthalpy of formation of the fluorite and pyrochlore phases, which are the most important thermodynamic data for the ZrO2 − REO1.5 systems. The experimental data of [1971Kor] indicate that both fluorite and pyrochlore phases are more stable with decreasing the ionic radius of RE+3. The experimental data reported by [2001Hel, 2003Lee, 2005Nav] are shown together with the fitted blue line, and it is interesting that all the data hold a single linear function, and the fluorite phase in the system with smaller RE+3 ionic radius is less stable. Present calculated results are given by the red symbols, in which the values for the pyrochlore phases are consistent with those of [2005Nav] within the experimental limits. However, present calculations on the enthalpies of formation of fluorite show complete different trends from those of [1971Kor, 2001Hel, 2003Lee]. With decreasing the RE+3 ionic radius, the enthalpy of formation of the fluorite phase becomes more negative. This is consistent with the phase relations that the tetragonal + fluorite two-phase region becomes gradually narrower with decreasing the radius of RE+3. Moreover, it can be seen from Fig. 11-5 that the difference between the enthalpies of fluorite and pyrochlore becomes gradually larger with increasing the radius of RE+3, and this tendency also agrees with the phase diagram that in case of a larger ionic radius of RE+3 there is a wider fluorite + -140- pyrochlore two-phase field, which is corresponding to larger difference between the Gibbs energies of fluorite and pyrochlore. Therefore, in view of those agreements with the evolution of phase relations, the present calculations on the enthalpies of formation of fluorite and pyrochlore are undoubtedly more reasonable than those experimental data. From La to Yb, the stable structure of rare earth oxides at ambient temperature changes from A-type to C-type. With the change of the ionic radius of RE+3, the enthalpies of transformation between those stable structures at ambient temperature to metastable fluorite structure are plotted in Fig. 11-6 together with the experimental and extrapolated data on the ZrO2-YO1.5 system. Following the energetic trends established for the structural transformations among the A, B, C, H and X-type structures [2006Zin], present calculations show the increasing values on the enthalpy of the A ⇒ F or C ⇒ F transformation towards the larger ionic radius of RE+3, and the linear functions can be constructed accordingly. So far, there is no reliable reference data on the enthalpy or entropy of those transformations for any system. Because such data cannot be obtained directly from experiments, some assumptions had to be made in the present work. 1.00 1.05 1.10 1.15 1.20 1.25 -140 -120 -100 -80 -60 -40 -20 0 20 YYb Dy Gd Sm Nd Ionic radius (Å) E nt ha lp y of fo rm at io n (k J. m ol -1 ) pyrochlore: [1971Kor] [1997Bol] [2005Nav] [1998Jac] [2002Rog] This work fluorite: [1971Kor] [2001Hel] [2003Lee] This work La Figure 11-5. The experimental and calculated enthalpies of formation of pyrochlore and fluorite (per four moles of cations, reference state: the monoclinic ZrO2 and the stable structure of REO1.5 at room temperature, for the composition at 50 mol% REO1.5). -141- 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 1.16 1.18 20000 40000 60000 80000 100000 This work 2003Lee 2005Che 2004Lee En th al py o f t ra ns fo rm at io n (J .m ol -1 ) Ionic radius (Å) LaNdSmGdDyYYb C F A F 0.95 1.00 1.05 1.10 1.15 1.20 0 5 10 15 20 25 30 35 40 Yb La This work Dy E nt ro py o f t ra ns fo rm at io n (J .m ol -1 .K -1 ) Ionic radius (Å) NdSmGd Figure 11-6. The calculated enthalpies of the A ⇒ F (RE=La, Nd) and C ⇒ F (RE=Sm, Gd, Dy, Y, Yb) transformations in RE2O3 compounds. Figure 11-7. The calculated entropies of the A ⇒ F (RE=La, Nd) and C ⇒ F (RE=Sm, Gd, Dy, Yb) transformations in RE2O3 compounds. For the corresponding entropies of transformation, it was assumed that those of C ⇒ F for RE=Sm, Gd, Dy are identical, and so do those of A ⇒ F for RE=La, Nd. However, for the transformation C ⇒ F, when RE=Yb, a lower entropy was selected during optimization. Fig. 11-7 shows an approximate increasing trend of the entropies against the ionic radius. Further experimental investigations are necessary to confirm the trends found in present calculations. 11.3. The mechanism of the pyrochlore ordering The pyrochlore-type ordering occurs in the systems ZrO2 − REO1.5 when RE=La−Gd. As mentioned above, the changes of the thermodynamic properties of the fluorite and pyrochlore phases result in the different characters of phase diagrams. Taking the nature of the structural relation between pyrochlore and fluorite phases into account, the Gibbs energies of these two phases are also related, and can be separated into the disordered part and ordered part, in which the former can be stable before the ordering occurs. In this section, the mechanism for the pyrochlore ordering will be proposed from thermodynamic point of view to explain some experimental results obtained in this work for different systems. Fig. 11-8 qualitatively shows the Gibbs energy curves at different states, in which the black and blue curves represent the completely disordered and ordered phases, respectively, while a given nonequilibrium state during the ordering is shown by the red dashed line. Since the ordering is a kinetically long process, it is reasonable to assume that there are many different intermediate configurational states which correspond to their own Gibbs energy curves. After a heat treatment for a certain time, the Gibbs energy curve of the ordered phase -142- may correspond to the red dashed line in Fig. 11-8. At the same time, the ordering kinetics may be different in different composition ranges. For example, the experimental results in the ZrO2 − NdO1.5 system already showed that the sample with 65 mol% NdO1.5 is much easier to separate into well ordered pyrochlore phase, while for the samples in ZrO2-rich region they are much more difficult to reach a complete ordered state. The sluggish ordering kinetics in ZrO2-rich materials is mainly caused by the fact that more oxygen atoms are taking part in the process. However, those problems do not contradict the present assumption, because for a given composition, the Gibbs energy will actually undergo such a process from the curve F to the curve P in Fig. 11-8. 0 20 40 60 80 100 G ib bs e ne rg y (J .m ol -1 ) REO1.5 (mol%) P F a given nonequilibrium state during ordering xF xF1 xP1 xP Figure 11-8. The Gibbs energy curves of fluorite and pyrochlore, together with that of a given non-equilibrium state during ordering. Since the ordering in REO1.5-rich region can be approached more easily, it will be more interesting to discuss the ordering at the ZrO2 excess side. Two common tangents are constructed based on the three Gibbs energy curves in Fig. 11-8. The blue one which connects the curve F and curve P determines the xF and xP, which represent the compositions of the fluorite and pyrochlore phases at equilibrium state, and the red one which connects the Gibbs energy curves of fluorite and the given state determines the xF1 and xP1, which represent the -143- compositions of the fluorite and pyrochlore phases at a given nonequilibrium state. Suppose a sample, which will finally be fluorite + pyrochlore mixture after complete ordering, is now under the state given by the red dashed line. It can be seen that the two-phase region under this non-equilibrium state is smaller than that of the equilibrium case. This can elucidate the apparent large homogeneity range of the pyrochlore phase and the narrow two-phase region obtained from XRD measurements in the ZrO2-rich region of the ZrO2 − NdO1.5 system. For the systems such as ZrO2 − SmO1.5 and ZrO2 − GdO1.5, due to the smaller difference of the Gibbs energies of fluorite and completely ordered pyrochlore, the ordering will take longer time because of lower driving force and ordering kinetics. In fact, the heat treatment of the samples of the ZrO2 − SmO1.5 system at 1700°C does not present separate XRD peaks for fluorite and pyrochlore like in the ZrO2 − NdO1.5 system. At the same time, for the ZrO2 − NdO1.5 system, the XRD results of the samples heat treated at 1600°C do not show separate fluorite and pyrochlore peaks, although the samples heat treated at 1700°C do. It reveals that the phase partition only occurs when the ordering process approaches a certain configurational state. Based on the available experimental data in this work, it is not easy to judge the fluorite-to-pyrochlore ordering is of first- or second-order. The second-order transition may firstly occur in the ZrO2-rich region due to the limited driving force for the long distance diffusion, and then the transition becomes first-order type only when a certain configurational state has been reached to offer the necessary driving force for the long- distance diffusion. For the system such as ZrO2 − GdO1.5 which has very small difference between the Gibbs energies of fluorite and completely ordered pyrochlore, it will probably never turn into first-order transition. Furthermore, as it has been experimentally found and modeled in this work, even in the REO1.5-rich region for RE=Gd, the transition can also be possibly of second-order type when the Gibbs energies of fluorite and pyrochlore are very close. As a conclusion, from a thermodynamic point of view, it may be not possible to distinguish if the fluorite to pyrochlore transition is first- or second-order for some systems, and the classification of this transition probably depends on the kinetic process. -144- Zusammenfassung ZrO2-basierte Materialien sind wegen ihrer niedrigen Wärmeleitfähigkeit, ihrer hohen Hochtemperaturbeständigkeit und ausgezeichneten Grenzflächenkompatibilität als Wärmedämmschichten (WDS) für Hochtemperaturgasturbinen praktisch wichtig. Forschungen an Phasengleichgewichten, Phasenumwandlungen und der Thermodynamik von ZrO2-basierten Systemen können die notwendigen grundlegenden Kenntnisse zur Verfügung stellen, um die nächste Generation von WDS Materialien zu entwickeln. In dieser Dissertation werden die Systeme ZrO2 − HfO2, Zr − O, Hf − O, ZrO2 − LaO1.5, ZrO2 − NdO1.5, ZrO2 − SmO1.5, ZrO2 − GdO1.5, ZrO2 − DyO1.5, ZrO2 − YbO1.5 und ZrO2 − GdO1.5 − YO1.5 experimentell und rechnerisch untersucht. Probenpräparation und experimentelle Methoden Die Proben werden durch chemische Fällung aus wässrigen Lösungen von Zr(CH3COO)4, HfO(NO3)2, und RE(NO3)3⋅xH2O (RE=La, Nd, Sm, Gd, Dy, Yb) hergestellt. Unterschiedliche experimentelle Methoden wie Röntgendiffraktometrie (XRD), Rasterelektronenmikroskopie (SEM), Elektronenstrahlmikroanalyse (EPMA: electron probe microanalysis), Transmissionselektronenmikroskopie (TEM), Differentialthermoanalyse (DTA) und Hochtemperaturkalorimetrie werden benutzt, um die Phasenumwandlungen und Phasengleichgewichte zwischen 1400 und 1700°C sowie die Enthalpie und Wärmekapazität der Materialien zu untersuchen. Experimentelle Resultate Erstens wurden die thermodynamischen Gleichgewichtstemperaturen (T0, bei denen die freien Enthalpien der monoklinen und tetragonalen Phase identisch sind) für reines ZrO2 (1367 ± 5 K) und HfO2 (2052 ± 5 K) durch die DTA Untersuchung des Systems ZrO2 − HfO2 überprüft und extrapoliert. Die direkt durch die DTA-Messungen erhaltenen Temperaturen (As, Af, Ms, Mf) bei der Martensitumwandlung der Materialien des Systems ZrO2 − HfO2 stimmen mit den berechneten Temperaturen T0 sehr gut überein. In dieser Dissertation werden das Tetragonal + Fluorit (oder das Tetragonal + Pyrochlor für RE=La) Zweiphasengebiet, das Phasengleichgewicht zwischen der ungeordneten Fluorit- und der geordneten Pyrochlorphase (oder δ Phase für RE=Yb) und das Phasengleichgewicht zwischen Fluorit und REO1.5 Phasen für ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb) Systeme gut etabliert und die Enthalpie von Materialien mit 30 mol% -145- REO1.5 und 50 mol% REO1.5 (57.14 mol% für RE=Yb) werden im Temperaturbereich von 200-1400°C bestimmt. Außerdem werden die isothermen Schnitte von ZrO2 − GdO1.5 − YO1.5 System bei der Temperatur 1200-1600°C durch XRD-Messungen experimentell untersucht. Thermodynamisches Modellieren Auf der Basis von erzielten DTA-Ergebnissen und Literaturdaten von Umwandlungstemperaturen von Monoklin ⇔ Tetragonal, Tetragonal ⇔ Kubisch and Kubisch ⇔ Flüssig, und der Thermodynamik von unterschiedlichen Strukturen werden die thermodynamischen Parameter von reinem ZrO2 und HfO2 eingeschätzt und das ZrO2 − HfO2 Phasediagram wird ohne Anpassungsparameter berechnet. Auf der Basis von in dieser Arbeit und in der Literatur erhaltenen experimentellen Daten werden die Systeme Zr − O, Hf − O, ZrO2 − REO1.5 (RE=La, Nd, Sm, Gd, Dy, Yb) mit der CALPHAD (CALculation of PHase Diagram) Methode thermodynamisch optimiert. Die Lösungphasen werden durch Untergitter-Modell beschrieben. Das Modell (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1 für Pyrochlorphase und das (Zr+4)1(RE+3, Zr+4)6(O-2, Va)12(Va, O-2)2 für δ-Phase werden in der ZrO2 − REO1.5 Systemen erfolgreich verwendet. Darüberhinaus wird das Modell (Zr+4,RE+3)2(RE+3,Zr+4)2(O-2,Va)8 auch für die mögliche Umwandlung zweiter Ordnung zwischen Fluorit- und Pyrochlorphase im ZrO2 − GdO1.5 System eingesetzt. Die meisten experimentellen Daten sind gut reproduzierbar und die selbstkonsistenten thermodynamischen Parameter sind für alle Systeme abgeleitet. Weil die experimentellen isothermen Schnitte des ZrO2 − GdO1.5 − YO1.5 Systems nur durch Extrapolation von binären Systemen gut reproduzierbar sind, wird keine weitere Optimierung durchgeführt. Charakteristische Änderung der Systeme ZrO2 − REO1.5 Schließlich, basierend auf Untersuchungen und Berechnungen dieser Arbeit lassen sich charakteristische Änderungen in der ZrO2 − REO1.5 Systemen als Funktion des Ionenradius des dotierten Element RE+3. 1). Die Löslichkeit von REO1.5 in tetragonaler Phase steigt fast linear mit abnehmendem RE+3 Radius, gleichzeitig erweitert sich der Homogenitätsbereich der Fluoritphase in die Richtung ZrO2. Diese Änderungen haben einen schmalen Tetragonal + Fluorit zweiphasigen Bereich für das ZrO2 − REO1.5 System mit kleinem RE+3 zur Folge. 2). Es wurde bestätigt, dass die Pyrochlorstruktur nur dann stabil ist, wenn RE+3 Radius größer als der von Dy+3 ist. Der Homogenitätsbereich der Pyrochlorphase nimmt -146- allmählich von RE=La auf Gd zu, während die Umwandlungstemperatur von Fluorit ⇔ Pyrochlor abnimmt. Im ZrO2 − DyO1.5 system findet man keine geordnete Verbindung, während die δ Phase im ZrO2 − YbO1.5 System geordnete Fluoritstruktur hat. Davon wird abgeleitet, dass die δ Phase nur dann stabil ist, wenn RE+3 Radius kleiner als der von Dy+3 ist, und die Umwandlungstemperatur von δ ⇔ Fluorit mit sinkendem Ionradius RE+3 steigt. 3). Die Bildungsenthalpie der Fluoritphase hat negativere Werte bei kleineren RE+3, während die geordnete Pyrochlorphase die umgekehrte Tendenz zeigt. Dies hat zur Folge, dass die Energiedifferenz zwischen Fluorit- und Pyrochlorphase bei kleinerem RE+3 kleiner wird, und deshalb das Fluorit + Pyrochlor Zweiphasengebiet schmaler wird. 4). Die komplette Ordnungseinstellung der Pyrochlor-phase mit ZrO2-Überschuß braucht sehr lange, besonders für Systeme mit kleinem RE+3. Die Ordnung von Pyrochlor mit REO1.5 -Überschuß geschieht viel schneller, weil wenige Sauerstoffatome an dem Prozess teilnehmen. Nach den XRD-Ergebnissen teilen sich die Proben im ZrO2-reichen Bereich nach 36 Stunden Wärmebehandlung bei 1700°C deutlich in eine 2-Phasen struktur auf, wohingegen die Probe nach Wärmebehandlung bei niedrigerer Temperatur dieses Verhalten nicht zeigt. Ähnliches Verhalten wird auch bei Proben mit ZrO2 Überschuß im ZrO2 − SmO1.5 und ZrO2 − GdO1.5 System beobachtet. Diese Beobachtungen zeigen, dass die Fluorit ⇔ Pyrochlor Phasenumwandlung in Materialien mit ZrO2 Überschuß ein kinetisch langsamer Prozess ist. Er kann zuerst von zweiter Ordnung sein und dann von erster Ordnung, wenn eine bestimmte Konfiguration der geordneten Struktur erreicht wird und damit genügend Triebkraft für die langreichweitige Diffusion angeboten werden kann. -147- Appendix: The thermodynamic parameters obtained in this work Ionic liquid: (Hf+4, Zr+4)P(O-2, Va)Q (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)P(O-2, Va)Q liq OHfG 24: 0 −+ = 2·GHFO2L liq OZrG 24: 0 −+ = 2·GZRO2L liq ODyG 23: 0 −+ = GDY2O3L liq OLaG 23: 0 −+ = GLA2O3L liq OSmG 23: 0 −+ = GSM2O3L liq VaOHfL 424 ,: 0 −−+ = 368630.5 – 115.0386T liq VaOZrL 424 ,: 0 −−+ = 75166 – 55.2382T liq OZrDyL 243 :, 0 −++ = –160886 liq OZrGdL 243 :, 0 −++ = – 76968 liq OZrLaL 243 :, 0 −++ = – 171356 liq OZrNdL 243 :, 0 −++ = – 173257 liq OZrSmL 243 :, 0 −++ = – 122143 liq OZrYbL 243 :, 0 −++ = – 85702 liq VaHfG 44: 0 −+ = GHFLIQ liq VaZrG 44: 0 −+ = GZRLIQ liq OGdG 23: 0 −+ = GGD2O3L liq ONdG 23: 0 −+ = GND2O3L liq OYbG 23: 0 −+ = GYB2O3L liq VaOHfL 424 ,: 1 −−+ = 55969 liq VaOZrL 424 ,: 1 −−+ = 39057.5 liq OZrDyL 243 :, 1 −++ = – 40724.6 liq OZrGdL 243 :, 1 −++ = – 248789.5 + 80T liq OZrLaL 243 :, 1 −++ = – 34723 liq OZrNdL 243 :, 1 −++ = – 33251 liq OZrSmL 243 :, 1 −++ = – 51808 liq OZrYbL 243 :, 1 −++ = – 28822 Bcc: (Hf, Zr)1(O, Va)1 bcc OHfG : 0 = GHSEROO + GHSERHF – 5000 bcc OZrG : 0 = GHSEROO + GHSERZR – 513959.73 + 100T bcc VaHfG : 0 = GHFBCC bcc VaOHfL ,: 0 = – 336506.062 bcc VaZrG : 0 = GZRBCC bcc VaOZrL ,: 0 = – 79547.224 Hcp: (Hf, Zr)(O, Va)0.5 hcp OHfG : 0 = 0.5·GHSEROO + GHSERHF – 273475.246 + 43.223T hcp OZrG : 0 = 0.5·GHSEROO + GHSERZR – 286427.91 + 43.223T hcp VaHfG : 0 = GHSERHF hcpVaZrG : 0 = GHSERZR hcp VaOHfL ,: 0 = – 30160.306 + 3.303T hcp VaOZrL ,: 0 = – 37876.66 + 17.2915T hcp VaOHfL ,: 1 = – 2820.874 hcp VaOZrL ,: 1 = – 4471.39 Monoclinic: (Hf+4, Zr+4)2(O-2, Va)4 (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2, Va)4 M OHfG 24: 0 −+ = 2·GHFO2M m OZrG 24: 0 −+ = 2·GZRO2M m VaZrG : 0 4+ =2·GZRO2M – 4·GHSEROO m ODyG 23: 0 −+ =GDY2O3C + GHSEROO + 18.702165T + 65000 m VaDyG : 0 3+ = GDY2O3C – 3·GHSEROO + 18.702165T + 65000 m OGdG 23: 0 −+ =GGD2O3B + GHSEROO + 18.702165T + 150000 -148- m VaGdG : 0 3+ =GGD2O3B – 3·GHSEROO + 18.702165T + 150000 m OLaG 23: 0 −+ =GLA2O3A + GHSEROO + 18.702165T + 130000 m VaLaG : 0 3+ = GLA2O3A – 3·GHSEROO + 18.702165T + 130000 m ONdG 23: 0 −+ =GND2O3A + GHSEROO + 18.702165T + 160000 m VaNdG : 0 3+ = GND2O3A – 3·GHSEROO + 18.702165T + 160000 m OSmG 23: 0 −+ =GSM2O3B + GHSEROO + 18.702165T + 150000 m VaSmG : 0 3+ = GSM2O3B – 3·GHSEROO + 18.702165T + 150000 m OYbG 23: 0 −+ =GYB2O3C + GHSEROO + 18.702165T + 30000 m VaYbG : 0 3+ =GYB2O3C – 3·GHSEROO + 18.702165T + 30000 Tetragonal: (Hf+4, Zr+4)2(O-2, Va)4 (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2, Va)4 T OHfG 24: 0 −+ = 2·GHFO2T t OZrG 24: 0 −+ = 2·GZRO2T t VaZrG : 0 4+ = 2·GZRO2T – 4·GHSEROO t OREG 23: 0 −+ = GRE2O3T + GHSEROO + 18.702165T t VaREG : 0 3+ = GRE2O3T – 3·GHSEROO + 18.702165T VaZrDyOZrDy LL :, 0 :, 0 43243 ++−++ = = – 103339.5 VaZrGdOZrGd LL :, 0 :, 0 43243 ++−++ = = – 29296 VaZrLaOZrLa LL :, 0 :, 0 43243 ++−++ = = + 20000 VaZrNdOZrNd LL :, 0 :, 0 43243 ++−++ = = –16304 VaZrSmOZrSm LL :, 0 :, 0 43243 ++−++ = = – 25000 VaZrYbOZrYb LL :, 0 :, 0 43243 ++−++ = = – 171196 + 40T Fluorite: (Hf+2, Hf+4, Zr+2, Zr+4)2(O-2, Va)4 (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2, Va)4 f OHfG 24: 0 −+ = 2·GHFO2F f VaHfG : 0 4+ =2·GHFO2F – 4·GHSEROO f OZrG 24: 0 −+ = 2·GZRO2F f VaZrG : 0 4+ = 2·GZRO2F – 4·GHSEROO f OHfG 22: 0 −+ = 2·GHSERHF + 4·GHSEROO – 875527.46 + 106.942T f OZrG 22: 0 −+ = 2·GHSERZR + 4·GHSEROO – 817859.56 + 106.942T f VaHfG : 0 2+ = 2·GHSERHF – 875527.46 + 106.942T f VaZrG : 0 2+ = 2·GHSERZR – 817859.56 + 106.942T f OHfHfL 242 :, 0 −++ = –11487.45 + 25T f VaHfHfL :, 0 42 ++ = –11487.45 + 25T f OZrZrL 242 :, 0 −++ = – 211148.18 + 76.2T f VaZrZrL :, 0 42 ++ = – 211148.18 + 76.2T f OHfHfL 242 :, 1 −++ = – 80000 + 20T f VaHfHfL :, 1 42 ++ = – 80000 + 20T f OZrZrL 242 :, 1 −++ = – 99968.54 + 23.58T f VaZrZrL :, 1 42 ++ = – 99968.54 + 23.58T f OREG 23: 0 −+ = GRE2O3F + GHSEROO + 18.702165T f VaREG : 0 3+ = GRE2O3F – 3·GHSEROO + 18.702165T -149- VaZrLaOZrLa LL :, 0 :, 0 43243 ++−++ = = – 259855 + 39.811T VaZrLaOZrLa LL :, 1 :, 1 43243 ++−++ = = – 143201 VaZrNdOZrNd LL :, 0 :, 0 43243 ++−++ = = – 269134.9 + 299.193T – 32TlnT VaZrNdOZrNd LL :, 1 :, 1 43243 ++−++ = = – 54416 VaZrNdOZrNd LL :, 2 :, 2 43243 ++−++ = = + 35213 VaZrSmOZrSm LL :, 0 :, 0 43243 ++−++ = = – 268887 + 246.6T – 25TlnT VaZrSmOZrSm LL :, 1 :, 1 43243 ++−++ = = – 23987.7 – 25.33T VaZrGdOZrGd LL :, 0 :, 0 43243 ++−++ = = – 280478.5 + 271.7T – 25TlnT VaZrGdOZrGd LL :, 1 :, 1 43243 ++−++ = = – 21424 VaZrDyOZrDy LL :, 0 :, 0 43243 ++−++ = = – 280272.6 + 200.08T – 20TlnT VaZrDyOZrDy LL :, 1 :, 1 43243 ++−++ = = 20890 – 25T VaZrYbOZrYb LL :, 0 :, 0 43243 ++−++ = = – 301096 + 267574T – 25TlnT VaZrYbOZrYb LL :, 1 :, 1 43243 ++−++ = = 103435 –50T A-RE2O3: (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2)3(O-2, Va)1 A VaOREG :: 0 23 −+ = GRE2O3A A VaOZrG :: 0 24 −+ = 2·GZRO2F – GHSEROO + 50000 A OOREG 223 :: 0 −−+ = GRE2O3A + GHSEROO A OOZrG 224 :: 0 −−+ = 2GZRO2F + 50000 VaOZrLaOOZrLa LL ::, 0 ::, 0 2432243 −++−−++ = = + 20000 VaOZrNdOOZrNd LL ::, 0 ::, 0 2432243 −++−−++ = = + 10000 VaOZrSmOOZrSm LL ::, 0 ::, 0 2432243 −++−−++ = = + 15000 B-RE2O3: (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2)3(O-2, Va)1 B VaOREG :: 0 23 −+ = GRE2O3B B VaOZrG :: 0 24 −+ = 2·GZRO2M – GHSEROO + 20000 B OOREG 223 :: 0 −−+ = GRE2O3B + GHSEROO B OOZrG 224 :: 0 −−+ = 2·GZRO2M + 20000 VaOZrSmOOZrSm LL ::, 0 ::, 0 2432243 −++−−++ = = + 45000 VaOZrGdOOZrGd LL ::, 0 ::, 0 2432243 −++−−++ = = + 51000 VaOZrDyOOZrDy LL ::, 0 ::, 0 2432243 −++−−++ = = + 5000 C-RE2O3: (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2)3(O-2, Va)1 C VaOREG :: 0 23 −+ = GRE2O3C C VaOZrG :: 0 24 −+ = 2·GZRO2F – GHSEROO + 5000 C OOREG 223 :: 0 −−+ = GRE2O3C + GHSEROO C OOZrG 224 :: 0 −−+ = 2·GZRO2F + 5000 VaOZrGdOOZrGd LL ::, 0 ::, 0 2432243 −++−−++ = = – 78798 + 21.2367T VaOZrGdOOZrGd LL ::, 1 ::, 1 2432243 −++−−++ = = + 30000 VaOZrGdOOZrGd LL ::, 2 ::, 2 2432243 −++−−++ = = + 30000 VaOZrDyOOZrDy LL ::, 0 ::, 0 2432243 −++−−++ = = – 109928 VaOZrDyOOZrDy LL ::, 1 ::, 1 2432243 −++−−++ = = + 30000 -150- VaOZrDyOOZrDy LL ::, 2 ::, 2 2432243 −++−−++ = = + 12910 VaOZrYbOOZrYb LL ::, 0 ::, 0 2432243 −++−−++ = = – 124356 + 20.914T VaOZrYbOOZrYb LL ::, 1 ::, 1 2432243 −++−−++ = = 32000 H-RE2O3: (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Yb+3, Zr+4)2(O-2)3(O-2, Va)1 H VaOREG :: 0 23 −+ = GRE2O3H H VaOZrG :: 0 24 −+ = 2·GZRO2F – GHSEROO + 10000 H OOREG 223 :: 0 −−+ = GRE2O3H + GHSEROO H OOZrG 224 :: 0 −−+ = 2·GZRO2F + 10000 VaOZrLaOOZrLa LL ::, 0 ::, 0 2432243 −++−−++ = = – 31179 VaOZrNdOOZrNd LL ::, 0 ::, 0 2432243 −++−−++ = = – 27000 VaOZrSmOOZrSm LL ::, 0 ::, 0 2432243 −++−−++ = = – 4188 VaOZrGdOOZrGd LL ::, 0 ::, 0 2432243 −++−−++ = = 17367 VaOZrDyOOZrDy LL ::, 0 ::, 0 2432243 −++−−++ = = – 30828 VaOZrYbOOZrYb LL ::, 0 ::, 0 2432243 −++−−++ = = – 8253 X-RE2O3: (Dy+3, Gd+3, La+3, Nd+3, Sm+3, Y+3, Yb+3, Zr+4)2(O-2)3(O-2, Va)1 X VaOREG :: 0 23 −+ = GRE2O3X X VaOZrG :: 0 24 −+ = 2·GZRO2F – GHSEROO + 10000 X OOREG 223 :: 0 −−+ = GRE2O3X + GHSEROO X OOZrG 224 :: 0 −−+ = 2·GZRO2F + 10000 VaOZrLaOOZrLa LL ::, 0 ::, 0 2432243 −++−−++ = = – 38254 VaOZrNdOOZrNd LL ::, 0 ::, 0 2432243 −++−−++ = = – 35763 VaOZrSmOOZrSm LL ::, 0 ::, 0 2432243 −++−−++ = = – 14857 Pyrochlore: (Zr+4, RE+3)2(RE+3, Zr+4)2(O-2, Va)6(O-2)1(Va, O-2)1. The suffixes RE define the corresponding functions (see below). P OOOREREG 22233 :::: 0 −−−++ = 2·GPYRORE + 2·GHSEROO – GPYROZR + GANCARE + GREC1 + GREC2 + GREC3 P OOOREZrG 22234 :::: 0 −−−++ = GPYRORE + GHSEROO + GREC2 P OOOZrREG 22243 :::: 0 −−−++ = GPYRORE + GHSEROO + GANCARE –GREC1 + GREC2 + GREC3 + GREC4 P OOOZrZrG 22244 :::: 0 −−−++ = GPYROZR P OOVaREREG 2233 :::: 0 −−++ =5·GPYROZR – 10·GPYRORE + 6·GPYRORE2O3 – 4·GHSEROO –5·GANCARE + 134.8548T – 5·GREC1 + GREC2 + GREC3 + GREC5 + GREC8 + GREC9 P OOVaREZrG 2234 :::: 0 −−++ = 6·GPYROZR – 11·GPYRORE + 6·GPYRORE2O3 – 5·GHSEROO – 6·GANCARE + 134.8548T – 6·GREC1 + GREC2 + GREC5 + GREC8 P OOVaZrREG 2243 :::: 0 −−++ = 6·GPYROZR – 11·GPYRORE + 6·GPYRORE2O3 – 5·GHSEROO – 5·GANCARE + 134.8548T – 6·GREC1 + GREC5 + GREC8 + GREC10 P OOVaZrZrG 2244 :::: 0 −−++ = 7·GPYROZR – 12·GPYRORE + 6·GPYRORE2O3 – 6·GHSEROO – 6·GANCARE + 134.8548T – 6·GREC1 + GREC5 + GREC8 + GREC10 P VaOOREREG :::: 0 2233 −−++ = 2·GPYRORE – GPYROZR + GHSEROO + GANCARE + GREC1 -151- P VaOOREZrG :::: 0 2234 −−++ = GPYRORE P VaOOZrREG :::: 0 2243 −−++ = GPYRORE + GANCARE P VaOOZrZrG :::: 0 2244 −−++ = GPYROZR – GHSEROO P VaOVaREREG :::: 0 233 −++ = 6·GPYRORE2O3 – 10·GPYRORE + 5·GPYROZR – 5·GHSEROO – 5·GANCARE + 134.8548T – 5·GREC1 P VaOVaREZrG :::: 0 234 −++ = 6·GPYRORE2O3 – 11·GPYRORE + 6·GPYROZR– 6·GHSEROO – 6·GANCARE + 134.8548T – 6·GREC1 + GREC5 + GREC6 P VaOVaZrREG :::: 0 243 −++ = 6·GPYRORE2O3 – 11·GPYRORE + 6·GPYROZR– 6·GHSEROO – 6·GANCARE + 134.8548T – 6·GREC1 + GREC7 P VaOVaZrZrG :::: 0 244 −++ = 6·GPYRORE2O3 – 12·GPYRORE + 7·GPYROZR – 7·GHSEROO – 6·GANCARE + 134.8548T – 6·GREC1 + GREC5 + GREC6 Pyrochlore: (Zr+4, Gd+3)2(Gd+3, Zr+4)2(O-2, Va)8 (has the disordered contribution from fluorite). P VaGdZrG :: 0 34 ++ = P VaZrGdG :: 0 43 ++ = P OGdZrG 234 :: 0 −++ = P OZrGdG 243 :: 0 −++ = –13.962T 2334 ::, 0 −+++ OGdGdZrL = 2434 ::, 0 −+++ OZrGdZrL = + 4844.5 VaGdGdZrL ::, 0 334 +++ = VaZrGdZrL ::, 0 434 +++ = + 4844.5 2434 :,: 0 −+++ OZrGdZrL = 2433 :,: 0 −+++ OZrGdGdL = + 4844.5 VaZrGdZrL :,: 0 434 +++ = VaZrGdGdL :,: 0 433 +++ = + 4844.5 δ (RE4Zr3O12): (Zr+4)1(RE+3, Zr+4)6(O-2, Va)12(Va, O-2)2 δ 2244 ::: 0 −−++ OOZrZrG (GZZOO) = 7·GZRO2F + 175000 δ VaOZrZrG ::: 0 244 −++ = 7·GZRO2F − 2GHSEROO + 175000 δ VaOYbZrG ::: 0 234 −++ = 1.5·GDELTA − 0.5·GZZOO + GHSEROO + 47.6278T δ VaVaYbZrG ::: 0 34 ++ = 12·GDELTA1 − 16.5·GDELTA + 5.5·GZZOO − 11·GHSEROO − 180.5012T δ 2234 ::: 0 −−++ OOYbZrG = 1.5·GDELTA − 0.5·GZZOO + 3·GHSEROO + 47.6278T − REC1 δ VaVaZrZrG ::: 0 44 ++ = 7·GZZOO − 14·GHSEROO − 18·GDELTA + 12·GDELTA1 − 228.129T − REC2 δ VaOZrZrG ::: 0 244 −++ = 7·GZZOO − 12·GHSEROO − 18·GDELTA + 12·GDELTA1 − 228.129T − REC2 − REC3 δ 234 ::: 0 −++ OVaYbZrG = 12·GDELTA1 − 16.5·GDELTA + 5.5·GZZOO − 9·GHSEROO − 180.5012T − REC1 − REC2 − REC3 − REC4 Functions: GZRLIQ, GHSERZR, GZRBCC, and GHSEROO are the lattice stabilities for liquid, hcp-Zr, bcc-Zr and 1/2 O2 gas from SGTE pure elements database [1991Din]. GHFO2M: – 1144228.5 + 446.1053T – 74.15647TLnT – 0.00297849T2 + 630000T-1; GHFO2T: 8208 – 4T + GHFO2M; GHFO2F: 19420 – 8T + GHFO2M; GHFO2L: 109073 – 37.1743T + GHFO2M; GZRO2M: – 1126163.5 + 424.8908T – 69.38751TlnT– 0.0037588T2 + 683000T-1; GZRO2T: 5468 – 4T + GZRO2M; -152- GZRO2F: 15804 – 8T + GZRO2M; GZRO2L: 102831 – 37.1743T + GZRO2M; GPYROZR: 4·GZRO2F +10000 + 16T ZrO2 – LaO1.5 system: GLA2O3A: –1833257 + 692.9664T – 120.629Tln(T) – 0.006854T2 + 808000T–1 – 1.0E+07T-2 GLA2O3C: GLA2O3A + 8337 + 7.788T GLA2O3B: GLA2O3A + 4139 + 2.215T GLA2O3H: GLA2O3A + 32350 – 13.986T GLA2O3X: GLA2O3A + 43192 – 18.555T GLA2O3L: GLA2O3A + 141329 – 56.622T GLA2O3F: GLA2O3A + 73630.5 – 11T GLA2O3T: GLA2O3F + 10000 GPYROLA: – 4194070 + 1531.07053T – 260.811Tln(T) – 0.00891455T2 + 1898400T–1 GPYROLA2O3: 2GLA2O3A + 160000 GREC2= 140000 GANCALA= 400000 ZrO2 – NdO1.5 system: GND2O3A: – 1847329 + 637.4243T – 116.358Tln(T) – 0.014677T2 + 711000T–1 – 10000000T-2 GND2O3C: GND2O3A – 1311 + 6.550T GND2O3B: GND2O3A – 399 + 1.684T GND2O3H: GND2O3A + 33189 – 13.986T GND2O3X: GND2O3A + 44489 – 18.555T GND2O3L: GND2O3A + 143621 – 56.785T GND2O3F: GND2O3A + 63285.47 – 19.33T GND2O3T: GND2O3F + 10000 GPYROND: – 4175068 + 1561.884T – 270.0852Tln(T) + 1894137.6T–1 – 0.01561361T2 GPYROND2O3: 2·GND2O3A + 98491.2 – 10T GREC2= 160000 GANCAND= 300000 ZrO2 – SmO1.5 system: GSM2O3C: – 1875835 + 780.6356T – 135.618Tln(T) – 0.006896T2 + 1191000T–1 GSM2O3B: – 1871213 + 751.7711T – 132.137Tln(T) – 0. 008367T2 + 1405000T–1 – 40000000T-2 GSM2O3A: GSM2O3B + 3324 –1.5295T GSM2O3H: GSM2O3B + 36932 – 15.515T GSM2O3X: GSM2O3B + 48460 – 20.084T GSM2O3L: GSM2O3B + 154133 – 60.603T GSM2O3F: GSM2O3C + 63018.408 – 18.7T GSM2O3T: GSM2O3F + 10000 GPYROSM: – 4186073 + 1590.2918T – 273.4902TlnT + 1700000T–1 – 0.01142041T2 GPYROSM2O3: 2·GSM2O3C + 158810 – 39T GREC2= 20000 GREC6= – 250000 GANCASM= 250000 ZrO2 – GdO1.5 system: -153- GGD2O3C: – 1868812 + 660.0623T – 119.1688Tln(T) – 0.006438T2 + 772000T–1 GGD2O3B: – 1858111 + 620.0992T – 114.534Tln(T) – 0.007203T2 + 540000T–1 GGD2O3A: GGD2O3B + 6300 – 2.579T GGD2O3H: GGD2O3B + 41000 – 16.565T GGD2O3X: GGD2O3B + 53031 – 21.134T GGD2O3L: GGD2O3B + 124733 – 47.759T GGD2O3F: GGD2O3C + 57983.8 – 18.7T GGD2O3T: GGD2O3F + 10000 GPYROGD: – 4186033 + 1593.9449T – 271.805TlnT + 2454000T–1 – 0.0098325T2 GPYROGD2O3: 2·GGD2O3C + 100000 GREC6= – 250000 GANCAGD= 200000 ZrO2 – DyO1.5 system: GDY2O3C: – 1902316 + 679.1313T – 122.593Tln(T) – 0. 006971T2 + 59000T–1 + 40000000T-2 GDY2O3B: GDY2O3C + 9255 – 4.09T GDY2O3A: GDY2O3C + 15637 – 5.546T GDY2O3H: GDY2O3C + 43703 – 18.076T GDY2O3X: GDY2O3B + 55825 – 22.645T GDY2O3L: GDY2O3B + 134876 – 52.131T GDY2O3F: GDY2O3C + 56553.6 – 18.7T GDY2O3T: GDY2O3F + 10000 ZrO2 – YbO1.5 system: GYB2O3C: – 1853511 + 702.7502T – 123.821Tln(T) – 0.004567T2 + 50000000T-2 GYB2O3B: GYB2O3C + 15345 – 3.725T GYB2O3A: GYB2O3C + 25165 – 5.293T GYB2O3H: GYB2O3C + 25612 – 9.654T GYB2O3X: GYB2O3B + 38391 – 14.223T GYB2O3L: GYB2O3B + 107451 – 39.875T GYB2O3F: GYB2O3C + 50837.64 – 15T GYB2O3T: GYB2O3F + 10000 GDELTA: 2·GYB2O3C + 3·GZRO2C – 183993 + 3.5T GDELTA1: 3·GYB2O3C + GZRO2C – 21000 – 14T GREC1= 400000 -154- References: [1925Hen] F. 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