Coupling between non-convergent ordering and transition temperature in the C2/c <-> P2(1)/c phase transition in pigeonite

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 C2/c-P2(1)/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 En(47)Fs(44)Wo(9), in situ at temperatures up to 1050 degreesC, 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 = 2n + 1) were followed in situ at temperatures up to 500 degreesC. The crystal was heated ex situ successively at 700, 750, 800, and 850 degreesC 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(D)(2) 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)