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Item Open Access Ab initio machine-learning unveils strong anharmonicity in non-Arrhenius self-diffusion of tungsten(2025) Zhang, Xi; Divinski, Sergiy V.; Grabowski, BlazejThe knowledge of diffusion mechanisms in materials is crucial for predicting their high-temperature performance and stability, yet accurately capturing the underlying physics like thermal effects remains challenging. In particular, the origin of the experimentally observed non-Arrhenius diffusion behavior has remained elusive, largely due to the lack of effective computational tools. Here we propose an efficient ab initio framework to compute the Gibbs energy of the transition state in vacancy-mediated diffusion including the relevant thermal excitations at the density-functional-theory level. With the aid of a bespoke machine-learning interatomic potential, the temperature-dependent vacancy formation and migration Gibbs energies of the prototype system body-centered cubic (BCC) tungsten are shown to be strongly affected by anharmonicity. This finding explains the physical origin of the experimentally observed non-Arrhenius behavior of tungsten self-diffusion. A remarkable agreement between the calculated and experimental temperature-dependent self-diffusivity and, in particular, its curvature is revealed. The proposed computational framework is robust and broadly applicable, as evidenced by first tests for a hexagonal close-packed (HCP) multicomponent high-entropy alloy. The successful applications underscore the attainability of an accurate ab initio diffusion database.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 Finite-temperature interplay of structural stability, chemical complexity, and elastic properties of bcc multicomponent alloys from ab initio trained machine-learning potentials(2021) Gubaev, Konstantin; Ikeda, Yuji; Tasnádi, Ferenc; Neugebauer, Jörg; Shapeev, Alexander V.; Grabowski, Blazej; Körmann, FritzAn active learning approach to train machine-learning interatomic potentials (moment tensor potentials) for multicomponent alloys to ab initio data is presented. Employing this approach, the disordered body-centered cubic (bcc) TiZrHfTax system with varying Ta concentration is investigated via molecular dynamics simulations. Our results show a strong interplay between elastic properties and the structural ω phase stability, strongly affecting the mechanical properties. Based on these insights we systematically screen composition space for regimes where elastic constants show little or no temperature dependence (elinvar effect).Item Open Access Structural and magnetic properties of newly found BaFeO2.667 synthesized by oxidizing BaFeO2.5 obtained via nebulized spray pyrolysis(2021) Wollstadt, Stephan; Ikeda, Yuji; Sarkar, Abhishek; Vasala, Sami; Fasel, Claudia; Alff, Lambert; Kruk, Robert; Grabowski, Blazej; Clemens, OliverA new vacancy-ordered perovskite-type compound Ba3Fe3O8 (BaFeO2.667) was prepared by oxidizing BaFeO2.5 (P21/c) with the latter compound obtained by a spray-pyrolysis technique. The structure of Ba3Fe3O8 was found to be isotypic to Ba3Fe3O7F (P21/m) and can be written as Ba3Fe3+2Fe4+1O8. Mössbauer spectroscopy and ab initio calculations were used to confirm mixed iron oxidation states, showing allocation of the tetravalent iron species on the tetrahedral site and octahedral as well as square pyramidal coordination for the trivalent species within a G-type antiferromagnetic ordering. The uptake and release of oxygen was investigated over a broad temperature range from RT to 1100 °C under pure oxygen and ambient atmosphere via a combination of DTA/TG and variable temperature diffraction measurements. The compound exhibits a strong lattice enthalpy driven reduction to monoclinic and cubic BaFeO2.5 at elevated temperatures.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 Crystal structure and phase stability of Co2N: a combined first-principles and experimental study(2021) Ikeda, Yuji; Lehmann, Tanja S.; Widenmeyer, Marc; Coduri, Mauro; Grabowski, Blazej; Niewa, RainerThe crystal structure and phase stability of Co2N are revisited based on experiments and first-principles calculations. Powder X-ray diffraction (PXRD) measurements and Rietveld refinements clearly confirm that the stable crystal structure of Co2N is an isotype of η-Fe2C and Co2C with the space group Pnnm rather than the closely related ζ-Fe2N with the space group Pbcn. The refined lattice parameters of Co2N in the Pnnm structure are a = 4.6108(1) Å, b = 4.3498(1) Å, c = 2.85592(7) Å, obtained from X-ray diffraction using synchrotron radiation. Furthermore, differential scanning calorimetry (DSC) with subsequent diffraction experiments reveal an endothermal transition to an ε-type order at 398 °C followed by an exothermal decomposition at 446 °C. First-principles density-functional-theory (DFT) calculations including the Hubbard U correction (DFT+U) demonstrate that it is essential for transition metal nitrides to consider strong electron correlation to predict the correct experimental structure and magnetic state. In particular, an effective value of Ueff = 2.75 eV can be utilized to obtain an antiferromagnetic Pnnm phase of Co2N in agreement with experiments.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 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 Ab initio simulations of the surface free energy of TiN(001)(2021) Forslund, Axel; Zhang, Xi; Grabowski, Blazej; Shapeev, Alexander V.; Ruban, AndreiThe temperature dependence of the surface free energy of the industrially important TiN(001) system has been investigated by means of an extended two-stage upsampled thermodynamic integration using Langevin dynamics (TU-TILD) methodology, to include the fully anharmonic vibrational contribution, as obtained from ab initio molecular dynamics (AIMD). Inclusion of the fully anharmonic behavior is crucial, since the standard low-temperature quasiharmonic approximation exhibits a severe divergence in the surface free energy due to a high-temperature dynamical instability. The anharmonic vibrations compensate for the quasiharmonic divergence and lead to a modest overall temperature effect on the TiN(001) surface free energy, changing it from around 78 meV Å-2 at 0 K to 73 meV Å-2 at 3000 K. The statistical convergence of the molecular dynamics is facilitated by the use of machine-learning potentials, specifically moment tensor potentials, fitted for TiN(001) at finite temperature. The surface free energy obtained directly from the fitted machine-learning potentials is close to that obtained from the full AIMD simulations.