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

Abstract

The concentration dependence of the high temperature antiferrodistortive (afd) phase transition temperature TC in single crystals of the mixed crystal system betaine phosphate and betaine phosphite (BP1-xBPIx) is studied. New experimental data obtained by 2H nuclear magnetic resonance (NMR) spectroscopy on deuterated single crystals of this system confirm the nonlinear behaviour of TC(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 TC(x) is explained in agreement with the afd character of the transition.

NMR relaxation study of disorder in condensed matter: solid solutions of betaine phosphate and phosphite

“…The crystal structure diagrams of DBP and DBPI (deuterated BP and BPI) were reported by Braeter et al [30], Freude et al [31] and Dvorak [32].…”

2H nuclear magnetic resonance studies on the deuteron dynamics in betaine phosphate/phosphite mixed crystals

“…C 11 where x is the concentration of component 1 (DBPI in our case). Details of the considerations used to obtain this equation, together with a different, more general, theoretical approach which allows the exact derivation of equation (2), are given in a forthcoming paper [18].…”