Volume Effect in the Landau Theory of Martensitic Phase Transitions in Cubic Crystals

TL;DR

This paper investigates how volume changes influence martensitic phase transitions in cubic crystals, analyzing pressure effects on transition temperature and anomalies, with implications for phase transformations in alloys.

Contribution

It introduces a detailed analysis of volume effects in the Ginzburg-Landau framework for cubic-to-tetragonal transitions, linking theory with recent experimental data.

Findings

Pressure affects critical temperature and phase transition anomalies.

Non-linearity of thermal expansion relates shear strain to volume change.

Elastic energy minimization explains FCC to BCC transformations.

Abstract

An effect of the volume change upon proper ferroelastic (martensitic) phase transitions in cubic crystals is considered. Corresponding terms in the Ginzburg-Landau expansion of the Gibbs free energy are analyzed for the first- as well as second-order phase transitions from cubic to tetragonal lattice under the action of uniaxial and hydrostatic pressure. The pressure effect on the critical temperature as well as on the phase transition anomalies of isothermal compressibility and linear thermal expansion coefficient are studied and recent experimental data on thermal expansion anomalies in V$_3$Si, In-Tl and Ni-Al are discussed. The non-linearity of thermal expansion leads to the special relation between the shear strain and volume change as a result of the elastic energy minimization. This phenomenon can provide the transformation from FCC lattice to BCC one, observed in the iron alloys.