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Item Open Access Strong impact of spin fluctuations on the antiphase boundaries of weak itinerant ferromagnetic Ni3Al(2023) Xu, Xiang; Zhang, Xi; Ruban, Andrei; Schmauder, Siegfried; Grabowski, BlazejAntiphase boundaries (APBs) are crucial to understand the anomalous temperature dependence of the yield stress of Ni3Al. However, the required, accurate prediction of temperature-dependent APB energies has been missing. In particular, the impact of magnetism at elevated temperatures has been mostly neglected, based on the argument that Ni3Al is a weak ferromagnet. Here, we show that this is an inappropriate assumption and that - in addition to anharmonic and electronic excitations - thermally-induced magnetic spin fluctuations strongly affect the APB energies, especially for the (100)APB with an increase of nearly up to 40% over the nonmagnetic data. We utilize an ab initio framework that incorporates explicit lattice vibrations, electronic excitations, and the impact of magnetic excitations up to the melting temperature. Our results prompt to take full account of thermally-induced spin fluctuations even for weak itinerant ferromagnetic materials. Consequences for large-scale modeling in Ni-based superalloys, e.g., of dislocations or the elastic-plastic behavior, can be expected.Item Open Access Interstitials in compositionally complex alloys(2023) Baker, Ian; Grabowski, Blazej; Divinski, Sergiy V.; Zhang, Xi; Ikeda, YujiThe effects of interstitial alloying on the mechanical and diffusive properties of compositionally complex alloys (CCAs), including high-entropy alloys (HEAs), are reviewed. The solubility of interstitial elements in CCAs can be extraordinarily high, a feature corroborated by ab initio density functional theory simulations. The yield stresses, work-hardening rates, and Hall-Petch slopes of CCAs are normally reported to increase due to interstitial alloying. In some CCAs, interstitial alloying has been found to enhance both strength and ductility, thus circumventing the traditional tradeoff between these properties. Self-diffusivities of the HEA CoCrFeMnNi are found to show complex dependences on interstitial C concentration as well as on temperature. Some CCAs with Laves phase or body-centered cubic crystal structures show potential as hydrogen-storage materials, with both experimental and computational research in this area steadily increasing. Based on the insights obtained, possible directions for further studies on the impacts of interstitial alloying in CCAs are suggested.Item Open Access Dynamically stabilized phases with full ab initio accuracy : thermodynamics of Ti, Zr, Hf with a focus on the hcp-bcc transition(2023) Jung, Jong Hyun; Forslund, Axel; Srinivasan, Prashanth; Grabowski, BlazejCertain systems feature phases that are dynamically unstable at 0 K but are stabilized by vibrations at higher temperatures. Treatment of these phases by conventional 0-K methods is not feasible and effective harmonic models introduce approximations. Here, we significantly advance the direct upsampling methodology [npj Comput. Mater. 9, 3 (2023)] to obtain free energies including the anharmonic contribution to full ab initio accuracy also for such dynamically stabilized phases. The centerpiece behind the procedure is accurate machine-learning potentials (moment tensor potentials) which are used to efficiently scan the volume-temperature space to uncover the stability regime and to perform thermodynamic integration on a dense grid within the stable window. We apply the methodology to the prototype systems Ti, Zr, and Hf and calculate hcp-bcc transition properties and thermodynamic properties of both phases. We find a very good agreement for the heat capacities with existing experimental/CALPHAD data, and an overall best agreement for Ti. The transition properties agree well on a relative temperature axis, where the temperature is scaled with respect to the transition temperature. Anharmonic free energies increase the transition temperature by up to one thousand kelvin. Electronic effects are smaller and bring down the transition temperature by as much as 172 K. We establish a new definition of the 0-K energy-volume curve for the dynamically stabilized bcc phase. Instead of using static lattice ab initio values, an extrapolation of the high-temperature high-accuracy free-energy surface to 0 K provides a physically more meaningful description. With this effective 0-K definition, discrepancies existing in the literature between CALPHAD and ab initio values are addressed.Item Open Access Microstructure stability and self-diffusion in the equiatomic HfScTiZr HCP multi-principal element alloy(2023) Muralikrishna, G. Mohan; Sen, Sandipan; Ayyappan, Sai Kumaran; Sankaran, Shanmugam; Guruvidyathri, K.; Schell, Juliana; Rogal, Lukasz; Zhang, Xi; Mayer, Joachim; Grabowski, Blazej; Wilde, Gerhard; Divinski, Sergiy V.Tracer diffusion of 44Ti, 46Sc and 89Zr in the hexagonal close-packed (HCP) HfScTiZr multicomponent alloy is investigated using the radiotracer technique. The microstructure stability is thoroughly examined by conducting prolonged heat treatments between 873 K and 1373 K to mimic the diffusion conditions. Electron microscopy analysis reveals that the alloy contains a mixture of two HCP phases with similar lattice constants, among which the major phase is enriched in Sc, whereas the minor phase is strongly enriched in Ti. The thermal stability is assessed by ab initio-informed calculations which support the existence of the two HCP phases. The Sc diffusion coefficients differ markedly between the HCP phases, while only marginal influence is found for the diffusion of Zr and Ti. The Arrhenius parameters are determined, i.e., the activation energy and the pre-factor. The diffusion properties are analyzed in correlation with the microstructure stability and the ab initio-informed thermodynamic results. The DFT-calculated mean squared atomic displacements, which represent the lattice distortions, are found to provide an appropriate parameter for predicting the diffusion trends of the individual elements. The phase analysis is further compared with existing CALPHAD-type predictions, and the discrepancies between the theoretical assessments and experimental observations are examined and discussed.Item Open Access Thermodynamic properties on the homologous temperature scale from direct upsampling : understanding electron-vibration coupling and thermal vacancies in bcc refractory metals(2023) Forslund, Axel; Jung, Jong Hyun; Srinivasan, Prashanth; Grabowski, BlazejWe have calculated thermodynamic properties of four bcc refractory elements - V, Ta, Mo, and W - up to the melting point with full density-functional-theory accuracy, using the recently developed direct-upsampling method [J. H. Jung et al., npj Comput. Mater. 9, 3 (2023)]. The direct-upsampling methodology takes full account of explicit anharmonic vibrations and electron-vibration coupling very efficiently using machine-learning potentials. We have thus been able to compute highly converged free-energy surfaces for the PBE exchange-correlation functional, from which accurate temperature dependencies of various thermodynamic properties such as the heat capacity, thermal expansion coefficient, and bulk modulus are accessible. For all four elements, the electronic contribution is large, including a strong coupling with the thermal vibrations. The atomic forces in W are even affected by the temperature-consistent Fermi broadening, which alters the free energy by around 3 meV/atom at the melting point. Trends within group V and group VI refractory elements are observed and explained by qualitative differences in the electronic density of states. We also provide an estimate of the Gibbs energies of vacancy formation and the vacancy contribution to the thermodynamics. Lastly and most importantly, our results are analyzed in terms of the homologous temperature scale relative to theoretically predicted melting points (for the PBE functional). The homologous temperature dependencies show a remarkable agreement with experiments and reveal the predictive power of self-consistently determined ab initio thermodynamic properties.Item Open Access Performance of two complementary machine-learned potentials in modelling chemically complex systems(2023) Gubaev, Konstantin; Zaverkin, Viktor; Srinivasan, Prashanth; Duff, Andrew Ian; Kästner, Johannes; Grabowski, BlazejChemically complex multicomponent alloys possess exceptional properties derived from an inexhaustible compositional space. The complexity however makes interatomic potential development challenging. We explore two complementary machine-learned potentials - the moment tensor potential (MTP) and the Gaussian moment neural network (GM-NN) - in simultaneously describing configurational and vibrational degrees of freedom in the Ta-V-Cr-W alloy family. Both models are equally accurate with excellent performance evaluated against density-functional-theory. They achieve root-mean-square-errors (RMSEs) in energies of less than a few meV/atom across 0 K ordered and high-temperature disordered configurations included in the training. Even for compositions not in training, relative energy RMSEs at high temperatures are within a few meV/atom. High-temperature molecular dynamics forces have similarly small RMSEs of about 0.15 eV/Å for the disordered quaternary included in, and ternaries not part of training. MTPs achieve faster convergence with training size; GM-NNs are faster in execution. Active learning is partially beneficial and should be complemented with conventional human-based training set generation.Item Open Access Anharmonicity in bcc refractory elements : a detailed ab initio analysis(2023) Srinivasan, Prashanth; Shapeev, Alexander; Neugebauer, Jörg; Körmann, Fritz; Grabowski, BlazejExplicit anharmonicity, defined as the vibrational contribution beyond the quasiharmonic approximation, is qualitatively different between the group V and group VI bcc refractory elements. Group V elements show a small and mostly negative anharmonic entropy, whereas group VI elements have a large positive anharmonic entropy, strongly increasing with temperature. Here, we explain this difference utilizing highly accurate anharmonic free energies and entropies from ab initio calculations for Nb and Ta (group V), and Mo and W (group VI). The numerically calculated entropies are in agreement with prior experimental data. The difference in behavior between the two sets of elements arises not from their high-temperature behavior but rather from the 0K quasiharmonic reference state. We understand this by analyzing the 0K and the high-temperature phonon density of states and the electronic density of states. The qualitative difference disappears when the anharmonicity is instead referenced with a high-temperature effective harmonic potential. However, even for an optimized effective harmonic reference, the remaining effective anharmonicity is significant. The reason is that the anharmonicity in the bcc systems - carried by asymmetric distributions in the nearest neighbors - can never be accounted for by a harmonically restricted potential.Item Open Access Atom probe study on CuNi thin films : miscibility gap and grain boundary segregation(2023) Duran, Rüya; Schmitz, Guido (Prof. Dr. Dr. h. c.)In dieser Arbeit wurde die Lage der Mischungslücke, und die Korngrenzsegregation im Legierungssystem, Kupfer-Nickel, per Atomsondentomographie (APT) analysiert. Zur Untersuchung der Mischungslücke eines binären Systems mit langsamer Diffusion wurde ein neues Verfahren verwendet. Multilagen aus Cu- und Ni- Dünnschichten wurden mittels Ionenstrahlbeschichtung (IBS) auf Wolframpfosten beschichtet und durch fokussierte Ionenstrahlung (FIB) geformt. Bei drei unterschiedlichen Temperaturen, zwischen 573 und 673 K, wurden isotherme Auslagerungssequenzen an einem Ultrahochvakuumofen (UHV) durchgeführt und der Mischungsprozess analysiert. Ein Modell des Diffusionsprozesses wurde mittels mathematischer Überlegungen erstellt. Durch das Fitten der experimentellen Kompositionsprofile mittels dieses Modells konnten die Gleichgewichtskonzentrationen der Schichten auch mit relativ kurzen Auslagerungszeiten ermittelt werden. Darüber hinaus konnten aus den diffusionskontrollierten Zeit- und Temperaturdaten physikalische Eigenschaften wie der effektive Diffusionskoeffizient (Gitterdiffusion einschließlich Defektdiffusion) bestimmt werden. Dieser betrug Deff = 1.86 ∙ 10-10 m2/s ∙ exp(-164 kJ mol-1/RT). Während dem Vermischen wurde die Änderung der multilagigen Mikrostruktur bis zur vollständigen Mischung bei 623 und 673 K beobachtet, wobei Korngrenzen als schneller Diffusionsweg eine wichtige Rolle spielen. Bei 573 K wurde Nichtmischbarkeit experimentell deutlich nachgewiesen, wobei die Phasengrenzen bei cNi=26 at.% und cNi=66 at.% liegen. Mit diesen Phasengrenzen wurde die Mischungslücke über eine Redlich-Kister-Parametrisierung der Gibbs‘schen freien Energie über den gesamten Konzentrationsbereich rekonstruiert. Hierin wurde für die kritische Temperatur, TC, 608 K bei einer Konzentration von 45 at% Ni gefunden. Im zweiten Teil wurde die Korngrenzsegregation durch die FIB/tEBSD- (Transmissions-Elektronen-Rückstreubeugung) Technik, in Korrelation zu APT-Messung charakterisiert. Vier Legierungen mit einem Ni-Anteil zwischen 25 und 85 at.% wurden auf Wolframpfosten per IBS beschichtet, und bei 700 K für 24 h wärmebehandelt. Die Segregation von Cu in die Korngrenzen wurde beobachtet. Durch die Verwendung eines theoretischen Models wurde die Exzess-Kurve über den gesamten Konzentrationsbereich, und die Korngrenz-Formationsenergie auf Basis der experimentellen Daten berechnet. Die tEBSD-Analyse während der FIB-Präparation erlaubt die Identifikation der Körner und deren Orientierung. Ein neues Verfahren wurde entwickelt, um mithilfe der Orientierung benachbarter Körner, Berechnungen zur Ermittlung der Korngrenzorientierung durchzuführen und somit die Orientierung natürlicher Korngrenzen zu bestimmen. Mit diesem Verfahren konnte der zeitliche Aufwand dieser anspruchsvollen Auswertung (verglichen zur herkömmlichen Methode mittels TEM-Untersuchung) stark reduziert werden, so dass eine quantitative Analyse vieler Korngrenzen möglich wurde. Aus den einzelnen Korngrenzorientierungen wurde die Korngrenzrotation, und die jeweiligen Anteile an Kippung und Drehung berechnet. Eine Abhängigkeit der Feststoffsegregation vom Kipp- und Drehanteil der Korngrenze wurde beobachtet, die am kleinsten für die reine Kipp- und Drehrotation war. Die ermittelten Segregationsweiten sind signifikant größer als die strukturellen Korngrenzweiten und bewegen sich zwischen 12 und 85 Å. Dieses Verhalten wurde durch eine künstliche Verbreiterung der Korngrenze erklärt, die durch eine Flugbahnabweichung der Korngrenzatome während der Verdampfung verursacht wurde. Eine Korngrenzweite von w0 = (10.1 ± 1.5) Å wurde für eine unverfälschte Korngrenze gefunden.Item Open Access High-accuracy thermodynamic properties to the melting point from ab initio calculations aided by machine-learning potentials(2023) Jung, Jong Hyun; Srinivasan, Prashanth; Forslund, Axel; Grabowski, BlazejAccurate prediction of thermodynamic properties requires an extremely accurate representation of the free-energy surface. Requirements are twofold - first, the inclusion of the relevant finite-temperature mechanisms, and second, a dense volume–temperature grid on which the calculations are performed. A systematic workflow for such calculations requires computational efficiency and reliability, and has not been available within an ab initio framework so far. Here, we elucidate such a framework involving direct upsampling, thermodynamic integration and machine-learning potentials, allowing us to incorporate, in particular, the full effect of anharmonic vibrations. The improved methodology has a five-times speed-up compared to state-of-the-art methods. We calculate equilibrium thermodynamic properties up to the melting point for bcc Nb, magnetic fcc Ni, fcc Al, and hcp Mg, and find remarkable agreement with experimental data. A strong impact of anharmonicity is observed specifically for Nb. The introduced procedure paves the way for the development of ab initio thermodynamic databases.Item Open Access Temperature dependence of (111) and (110) ceria surface energy(2023) Kholtobina, Anastasiia S.; Forslund, Axel; Ruban, Andrei; Johansson, Börje; Skorodumova, Natalia V.High-temperature properties of ceria surfaces are important for many applications. Here, we report the temperature dependencies of surface energy for (111) and (110) CeO2 obtained in the framework of the extended two-stage up-sampled thermodynamic integration using Langevin dynamics. The method was used together with machine-learning potentials called moment tensor potentials (MTPs), which were fitted to the results of the ab initio molecular dynamics calculations for (111) and (110) CeO2 at different temperatures. The parameters of MTP training and fitting were tested, and the optimal algorithm for the ceria systems was proposed. We found that the temperature increases from 0 to 2100 K led to the decrease of the Helmholtz free energy of (111) CeO2 from 0.78 to 0.64 J/m2. The energy of (110) CeO2 dropped from 1.19 J/m2 at 0 K to 0.92 J/m2 at 1800 K. We show that it is important to consider anharmonicity, as simple consideration of volume expansion gives the wrong temperature dependencies of the surface energies.