Second-order phase transitions and Ehrenfest equation for strained solids

Abstract

The equations describing the second-order phase transitions at the hydrostatic and non-hydrostatic pressures are considered. It is shown that the proportionality coefficient between an “effective” volume and the true one V^∗= AV is inversely proportional to the compressibility of the solid at a uniaxial pressure and has a jump at the second-order phase transition. In the case of the non-hydrostatic pressure the “effective” volume of the solid is not a continuous function of temperature and has a jump at the phase transition as well. The Ehrenfest equation is generalized to the solids with an arbitrary homogeneous elastic deformation accompanied by change of the solid volume, in particular, to the solid strained by the uniaxial, biaxial or triaxial pressure. It is shown that the sum of the derivatives of the phase transition temperature with respect to uniaxial pressures applied along axes a, b, c does not coincide with the derivative of the phase transition temperature with respect to the hydrostatic pressure.

Keywords:

• phase transitions
• ferroelectrics
• ferromagnetism
• strain
• superconducting materials
• uniaxial pressure