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Coupling between non-convergent ordering and transition temperature in the C2/c P2₁/c phase transition in pigeonite

¹ CNR-Istituto di Geoscienze e Georisorse, sezione di Pavia, via Ferrata 1, I-27100 Pavia, Italy
² Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, U.K.
³ Dipartimento Scienze della Terra, Università di Pavia, Via Ferrata 1, I-27100 Pavia, Italy

Correspondence: ^* E-mail: camara{at}crystal.unipv.it

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-P2₁/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 = 2n + 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.

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