‘Second’ Ehrenfest equation for second order phase transition under hydrostatic pressure

Abstract

It is shown that the fundamental conditions for the second-order phase transitions and , from which the two Ehrenfest equations follow (the ‘usual’ and the ‘second’ ones), are realised only at zero hydrostatic pressure (). At the volume jump ΔV at the transition is proportional to the pressure and to the jump of the compressibility Δζ_V, whereas the entropy jump ΔS is proportional to the pressure and to the jump of the thermal expansion coefficient Δα_V. This means that at non-zero hydrostatic pressure the phase transition is of the first order and is described by the Clausius–Clapeyron equation. At small pressure this equation coincides with the ‘second’ Ehrenfest equation . At high P, the Clausius–Clapeyron equation describes qualitatively the caused by the crystal compression positive curvature of the dependence.

Keywords:

• Phase transitions
• superconductors
• ferroelectrics
• theoretical
• elasticity
• ferroelectric composites
• Ehrenfest equation
• hydrostatic pressure
• Clausius–Clapeyron equation