Anomalous self-diffusion in tungsten and molybdenum: Exonerating the di-vacancy contribution and the key role of interatomic interaction
Phys. Rev. Materials 9, 093801 – Published 4 September, 2025
DOI: https://doi.org/10.1103/c612-psgt
Abstract
This study completes the long-standing effort to understand experimental measurements of self-diffusion in body-centered cubic (bcc) metals. Over the past decade, a growing consensus has emerged regarding the attribution of the anomalous non-Arrhenius behavior to the anharmonicity of atomic interactions. This work advances the understanding of two fundamental issues: (i) the free energy contributions from small vacancy clusters are quantitatively accounted for, leading to the conclusion that the di-vacancy contribution is negligible; and (ii) quantitative agreement between theory and experiment can only be achieved when employing interatomic interactions of a quality beyond standard exchange-correlation functionals, such as those provided by recent meta-generalized gradient approximations (meta-GGAs). The present conclusions are made possible thanks to an accurate characterization of the free energy landscape of metals that goes beyond the perfect bulk and simple defects, such as mono-vacancies. Moreover, the present treatment is able to provide the free energy landscape not only for the absolute minimum of defect configurations, but also for other local minima. These achievements make use of advanced Bayesian sampling techniques applied to the calculation of the formation free energy and the optimal solution through averaged force projection for migration free energy, utilizing high-precision, data-driven force fields at ab initio accuracy. We emphasize the importance of atomic interactions, as produced by the exchange-correlation functional underlying the data-driven force fields, by investigating two machine-learning potentials constructed using standard GGAs. Corrections to formation energies at zero temperature, arising from differences between the standard GGA and a recent meta-GGA functional, are shown to be the primary source of discrepancies between theoretical predictions and experimental values. The workflow developed in this study paves the way for the comprehensive study of diffusion in materials and enables automated, systematic investigations of complex energetic landscapes.
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Machine Learning for Materials Discovery and Understanding
The Editors of Physical Review Materials are pleased to present the Collection on Machine Learning for Materials Discovery and Understanding, highlighting cutting-edge advances in machine learning method development and applications for materials discovery and fundamental understanding of the structure-property-function relationship. The Collection is being guest-edited by Deyu Lu of Brookhaven National Laboratory (USA) and Jinlan Wang of Southeast University (China). Every article published in this collection underwent a rigorous peer review process, adhering to the same high standards applied to all papers. The Physical Review Materials editorial team managed the peer review and made all editorial decisions.
