Role of Alloying-Atom Size Factor and System Shape Factor in Energetics of bcc Fe under Macroscopic Deformation

TL;DR

This study reveals a universal linear relation linking alloying atom size, system shape, and volume in bcc Fe under deformation, providing a predictive framework for alloy energetics.

Contribution

It introduces a new linear relation involving system shape and atom size factors to describe alloying energetics under deformation.

Findings

The volume dependence of substitutional energy is linearly related to system shape and atom size factors.

The size factor captures effects of alloying atom size and chemical interactions.

The relation is validated with data from GaP doping studies.

Abstract

We present an \emph{ab initio} study of the effect of macroscopic deformation on energetics of twelve alloying elements in bcc Fe under three specially designed strain modes. We find that there exists a universal linear relation of describing the volume dependence of substitutional energy of alloying elements via introducing two factors --- the system shape factor ($f_{\scriptsize{ss}}$) and the size factor of alloying element $M$ ($\Omega^{M}_{\scriptsize{sf}}$): $E_{\scriptsize{sub}} \sim f_{\scriptsize{ss}}\Omega^{M}_{\scriptsize{sf}}V$. $\Omega^{M}_{\scriptsize{sf}}$ well describes the effect of intrinsic alloying-atom size and the influence of chemical interaction with matrix atom, and $f_{\scriptsize{ss}}$ characterizes the degree of system lattice distortion under deformation. This relation is further validated using the published data of stained-modulated doping in GaP