Influence of Coherent Elastic Strain on Phase Separation in BCC Nb-V Alloys

TL;DR

This paper introduces a thermodynamic framework that incorporates coherent elastic strain into phase diagram calculations, revealing its significant impact on phase separation behavior in BCC Nb-V alloys.

Contribution

The authors develop a novel approach integrating coherent elastic compatibility into phase diagrams, advancing understanding of lattice-mismatched alloy systems.

Findings

Coherent elasticity suppresses phase separation in Nb-V alloys.

It narrows the miscibility gap and lowers the critical temperature.

The two-phase boundary depends on both temperature and overall composition.

Abstract

Coherent elastic strain is an important but often neglected contribution to phase-separation thermodynamics in alloy systems where decomposed phases have appreciable lattice mismatch. We develop a thermodynamic framework that incorporates coherent elastic compatibility directly into phase-diagram calculations alongside conventional CALPHAD chemical free energies. Applied to the BCC Nb-V system, the framework shows that coherent elasticity substantially suppresses phase separation, narrows the miscibility gap, and lowers the critical temperature toward experimentally observed values. Beyond these quantitative effects, the coherent constraint qualitatively alters the interpretation of phase equilibria: the equilibrium decomposition compositions become functions of both temperature and overall alloy composition, so the two-phase boundary no longer represents unique coexistence compositions. These results establish coherent elasticity as a key thermodynamic factor in lattice-mismatched systems and provide a general framework for coherent phase-diagram modeling.