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Ab initio relaxation volumes of transition metal solutes in iron and tungsten

Andrew R. Warwick*, Jacob B. J. Chapman†, Duc Nguyen-Manh‡, Pui-Wai Ma§, and Sergei L. Dudarev∥

  • *Contact author: Andrew.Warwick@ukaea.uk
  • †Contact author: jbjchapman@gmail.com
  • ‡Contact author: Duc.Nguyen@ukaea.uk
  • §Contact author: leo_ma55@hotmail.com
  • ∥Contact author: Sergei.Dudarev@ukaea.uk
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Phys. Rev. Materials 10, 045402 – Published 13 April, 2026

DOI: https://doi.org/10.1103/2zkp-g15b

Abstract

Atomic volume differences determine the structure and phase stability of alloys. To assess the size mismatch, atomic volumes of pure elements, derived from their elemental crystalline states, are normally used as a reference. Using ab initio calculations, we show that substitutional transition metal solute atoms in bcc iron or tungsten exhibit sizes substantially different from their elemental volumes. Analysis of electronic structure suggests that the significant oversizing of substitutional solutes in bcc α-iron is caused by the asymmetric filling of electronic states of solute atoms. This produces a strong local magnetovolume effect where, for example, the apparent sizes of platinum and palladium solute atoms are from 35% to 40% larger than their elemental volumes. The analysis of nonlocal variation of electronic structure in the neighborhood of a solute atom shows that in bcc tungsten, the atoms near a substitutional 3d transition metal solute atom shrink, whereas in bcc iron, atoms next to a substitutional site swell, further increasing the apparent relaxation volume of the solute atom. Constrained magnetic DFT calculations show that manganese, iron, and cobalt solute impurity atoms in tungsten retain their magnetic moments, with collinear spin-flip barriers of 0.20, 0.52, and 0.17 eV, respectively. In other instances, elements like Cr in α-Fe are nominally undersized if the elemental volumes are compared, but in a solute form the relaxation volume of Cr is positive (+20% of its atomic volume), stemming from the electron transfer effect and variation of the effective volume of neighboring host Fe atoms. Simulations suggest that application of strong magnetic field might also affect the relaxation volume of transition metal solutes and their solubility.

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Phys. Rev. Materials 10, 045402– Published 13 April, 2026
  • Received 13 February 2026
  • Accepted 24 February 2026
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