Critical scattering in A3B compounds at structural transitions

Abstract

A theory of critical scattering in A 3 B compounds having A 15 structure at structural transitions (martensitic phase transitions) is developed. The theory is based on the assumption that the critical scattering is due to density fluctuations. This primary variable is coupled to current density fluctuations considered as secondary variable. Zwanzig-Mori projection operator technique is used to derive equations of motion. The time dependence of thememory function describing the delayed response of the stress tensor due to a change of rate of shear is modeled and is assumed to decay exponentially. This description takes into account elastoviscous effects in solids, and leads, near the transition temperature, to a correct three-pole structure around ω = 0 and includes the central peak and the resonances of the conventional soft phonon mode. The central peak is predicted whenever elastoviscous effects are important. Our theory clarifies the phenomenological expressions for the dynamic structure factor proposed by Shirane and Axe. If order-parameter fluctuations were considered to be responsible for the dynamic structure factor, our results would correspond to theories proposed by Schwabl and Schneider for perovskites. Our paper thus helps clarify and unify the existing theories on critical dynamics at structural transitions in A 3 B compounds and ABO 3 perovskites.