Peculiarities of Ehrenfest equation for solids strained by uniaxial or hydrostatic pressure

TL;DR

This paper rigorously derives and generalizes the Ehrenfest equation for strained solids, highlighting how uniaxial and hydrostatic pressures influence phase transition temperatures through effective volume and thermal expansion coefficients.

Contribution

It provides a rigorous derivation and generalization of the Ehrenfest equation for strained solids considering effective volume and temperature dependence.

Findings

Ehrenfest equation for strained solids depends on the effective volume's temperature expansion.

For Rochelle salt, the coefficient A dominates the pressure dependence at room temperature.

Hydrostatic pressure effects can be expressed as a sum of contributions from thermal expansion along different axes.

Abstract

The Ehrenfest equation is derived rigorously for the case when an 'effective' volume V* = AV of the strained solids is a continuous function of the temperature. The Ehrenfest equation for strained solids is generalized to an arbitrary temperature. Far from 0 K (in contrast to the situation near 0 K) the phase transition temperature derivative with respect to uniaxial pressure depends on the temperature expansion coefficient of an ' effective' volume. For Rochelle salt strained by a uniaxial pressure at room temperature the predominant contribution into this dependence is made by the coefficient A. At the second order phase transition under uniaxial pressure the 'effective' (but not true) volume is the continuous function of the temperature. The Ehrenfest equation for solids strained by hydrostatic pressure can be presented as a sum of three linear parts proportional to the crystal linear thermal expansion coefficients along the axes a, b, c. These parts are equal to the second order transition temperature derivative with respect to hydrostatic (but not uniaxial) pressure,