Monoclinic phase in PZT: order parameter and phase transition from Tetragonal Phase

A solution of the Lagrange-Euler equations for the order parameter-the electric polarisation vector P-which describes the monoclinic phase in PZT is found exactly in this article for the Gibbs free energy expansion done for the cubic phase up to the sixth-order in the order parameter. The phase transition from the tetragonal phase to the monoclinic phase in materials of the PZT type may be described within the Landau theory of phase transitions used by Haun and co-workers. The phase transition is found to be of the first order in general. The order parameter in the parameter space is two dimensional: the amplitude A and the angle. The PZT material has values of expansion coefficients in the Gibbs free energy such that the exact solution for description of the monoclinic phase is a metastable state. We may conclude then that the monoclinic phase exists in PZT due to higher than sixth-order terms in the Gibbs free energy expansion which are present due to high anharmonicity present in this material.