Elastic energy of multi-component solid solutions and strain origins of phase stability in high-entropy alloys

The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model. By surveying the dependence of the elastic energy on the chemical composition and lattice misfit, we derive a lattice strain coefficient lambda*. Studying several high-entropy alloys and super alloys, we propose that most solid solution multi-component alloys are stable when lambda* < 0 . 16 , generalizing the Hume-Rothery atomic-size rule for binary alloys. We also reveal that the polydispersity index delta , frequently used for describing strain in multi-component alloys, directly represents the elastic energy (e ) with e = q delta(2) , q being an elastic constant. Furthermore, the effects of (i) the number and (ii) the atomic size distribution of constituting elements on the phase stability of high-entropy alloys were quantified. The present derivations and discussions open for richer considerations of elastic effects in high-entropy alloys, offering immediate support for quantitative assessments of their thermodynamic properties and studying related strengthening mechanisms. (C) 2021 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Automated summary

The study derives the elastic energy of mixing for multi-component solid solutions by generalizing Eshelby's model and proposes that most solid solution multi-component alloys are stable when lambda* < 0.16. It also reveals that the polydispersity index delta can directly represent the elastic energy, providing support for quantitative assessments of the thermodynamic properties of high-entropy alloys.