Ab initio machine-learning unveils strong anharmonicity in non-Arrhenius self-diffusion of tungsten

Aug 5, 2026

An efficient ab initio framework is proposed to compute the Gibbs energy of a vacancy-mediated transition state while explicitly accounting for relevant thermal excitations at density-functional-theory accuracy. Using a dedicated machine-learning interatomic potential, temperature-dependent vacancy formation and migration Gibbs energies for BCC tungsten are shown to be strongly anharmonic, explaining experimentally observed non-Arrhenius self-diffusion. Calculations reproduce temperature-dependent self-diffusivity behavior and its curvature, and initial tests on an HCP multicomponent high-entropy alloy demonstrate robust applicability.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages22

Reading Time55 min

AccessFree to download

Introduction

Arrhenius behavior and deviations near melting

Vacancy formation energies and anharmonic vibrations

Limitations of existing (quasi)harmonic approaches

Thermodynamic integration and dynamical stability

Results and discussion

Transition state thermodynamic integration

arXiv :2311 .00633v2 [ cond-mat .mtrl-sci ] 7 Oct 2024 Ab initio machine-learning unveils strong anharmonicity in non-Arrhenius self-diffusion of tungsten Xi Zhang 1,* , Sergiy V. Divinski2 , and Blazej Grabowski 1 1 Institute for Materials Science, University of Stuttgart, D-70569 Stuttgart, Germany 2 Institute of Materials Physics, University of Mnster, 48149 Mnster, Germany *[xi.zhang@imw.uni-stuttgart.de](xi.zhang@imw.uni-stuttgart.de) ABSTRACT 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 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. Introduction Understanding atomic diffusion is of fundamental importance in developing materials with controlled mechanical and functional properties. For the majority of metals, the temperature dependence of thermally activated, vacancy-mediated diffusion is well assessed from countless studies. The common knowledge expects a linear Arrhenius behavior, especially when phase transformations do not interfere.1 The logarithm of the diffusion rate, D, scales linearly with the inverse temperature, T −1 , lnD = −(Q/kB )T −1 +lnD0 , (1) with the slope, −Q/kB , and the intercept, lnD0, controlled by the activation energy Q and the prefactor D0 (kB: Boltzmann constant) . Both Q and D0 are generally assumed to be independent or very weakly dependent on temperature6. The universality of this widespread assumption is, however, limited, especially close to the melting point6. Diffusion measurements covering wide temperature intervals revealed deviations from linearity7–12. Textbook knowledge explains this“anomaly” of substitutional diffusion with di-vacancies in addition to mono-vacancies6, 13, 14. Various measurements 15–17 were interpreted as supporting the di-vacancy explanation, which grew into an undisputed paradigm. Nevertheless, some researchers proposed an alternative explanation in terms of temperature-dependent activation energies 18–22 indicating problems with the mono-/di-vacancy interpretation even in simple metals. Temperature-dependent vacancy formation energies driven by anharmonic vibrations were indeed uncovered by recent ab initio simulations23, 24. Temperature-dependent vacancy energies were also found for self-diffusion in Mo25. These theoretical findings call for a conceptual revision of the long-standing paradigm. However, a paradigm shift requires strong support. Therefore, not only further ab initio simulations of defect energetics are required, but in particular methodological advances to enable access to reliable predictions at high temperatures. While efficient high-accuracy ab initio techniques are available for vacancy formation23, 26 , state-of-the-art ab initio approaches approximate migration Gibbs energies by (quasi)harmonic transition state theory (hTST)27 , utilizing either the full quasiharmonic free energy28 or a simplified Vineyard formula27 with explicit phonon calculations29. It will be shown below that hTST is unrealistic at elevated temperatures and causes significant errors. The most accurate approach to exploring the full vibrational space i

FAQs

What new ab initio method is proposed for vacancy-mediated diffusion?

An efficient framework computes the Gibbs energy of the vacancy-mediated transition state using DFT-level accuracy, including relevant thermal excitations supported by a machine-learning interatomic potential and stabilization within a thermodynamic-integration scheme.

How does the approach explain tungsten’s non-Arrhenius self-diffusion?

The temperature-dependent vacancy formation and migration Gibbs energies in BCC tungsten are found to be strongly affected by anharmonicity, providing a physical origin for the experimentally observed non-Arrhenius behavior.

How do the computed results compare with experiments?

The calculated and experimental temperature-dependent self-diffusivity match closely, especially capturing the curvature of the temperature dependence.

Aug 5, 2026

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