A microscopic model for the concentration dependence of the antiferrodistortive phase transition in mixed betaine phosphate/phosphite crystals

The concentration dependence of the high temperature antiferrodistortive (afd) phase transition temperature Te in single crystals of the mixed crystal system betaine phosphate and betaine phosphite (BP1-xBPIx) is studied. New experimental data obtained by H-2 nuclear magnetic resonance (NMR) spectroscopy on deuterated single crystals of this system confirm the nonlinear behaviour of T-C(x), in particular the maximum at intermediate concentrations. A microscopic model is proposed which in extension of the treatment of a small defect concentration makes use of the virtual crystal approximation (VCA) to be applicable to the mixed crystal system DBP1-xDBPIx with finite concentrations x. By this means the experimentally observed behaviour of the afd phase transition temperature as a function of x is elucidated and the nonlinear behaviour of T-C(x) is explained in agreement with the afd character of the transition.