Coupling between non-convergent ordering and transition temperature in theC2/c↔P21/cphase transition in pigeonite

Abstract

A Landau potential with linear-quadratic coupling has been developed to describe interactions between a non-convergent order parameter, Q OD, for Fe/Mg ordering, and the order parameter, Q D, for the C 2/ c - P 21/ c phase transition in pigeonite. Spontaneous strain relationships, and expressions for the effect of ordering on the transition temperature derived from this expansion, have been tested by single crystal X-ray diffraction methods. Lattice parameters collected from a natural pigeonite crystal with composition En47Fs44Wo9, in situ at temperatures up to 1050 °C, reveal that increasing Q OD could act to suppress Q D by a mechanism which includes overlapping and opposing strain fields. In a second experiment, the intensities of superlattice reflections ( h + k = 2 n + 1) were followed in situ at temperatures up to 500 °C. The crystal was heated ex situ successively at 700, 750, 800, and 850 °C between repeated in situ measurements in order to produce changes in the degree of cation order. The resulting data sets, giving the temperature dependence of Q D2 for different fixed values of Q OD, are consistent with the initial Landau model. In particular, they show a strong and linear dependence of transition temperature on Q OD. The fourth order coefficient of the expansion describing the phase transition is perhaps also renormalized by changes in Q OD. It is suggested that the influence of Q OD on the phase transition could be greater than the influence of the phase transition on the equilibrium variation of Q OD.