Phenomenological Equations Relating Various Critical Anomalies above a Cubic-to-Tetragonal Phase Transition Point

Abstract

Phenomenological equations are derived which interrelate the anomalies in various thermodynamic quantities above the transition point of a cubic-to-tetragonal phase transition caused by an instability of a triply degenerate soft mode. The anomalous part of the Gibbs free energy is assumed to be a simple sum of the three parts which represent the contributions from the three fluctuation components. A cylindrical approximation is adopted to each of the three contributions by taking into account the symmetry of the fluctuations. The theory predicts that the adiabatic elastic compliances, s₁₁^s, s₁₂^s, and also s₁₁^s−s₁₂^s should exhibit anomalies proportional to the anomaly in the specific heat at constant pressure. This is in marked contrast with the result of the generalized Pippard equations derived by Garland, and by Janovec. The new equations are successfully tested for KMnF₃, CsPbCl₃, and CsPbBr₃. The β-γ transition of NH₄Br is also discussed.