The thermodynamics of the I $ overline{1} $ –P $ overline{1} $ phase transition in Ca-rich plagioclase from an assessment of the spontaneous strain

摘要

In-situ powder diffraction measurements between 90 and 935 K on four anorthite-rich plagioclase samples (An100, An96Ab4, An89Ab11 and An78Ab22) were used to determine the detailed evolution of these samples through the $I overline{1} $ – $P overline{1} $ phase transition. The c-type reflections indicative of $P overline{1} $ symmetry were detected only in An100, An96Ab4, whereas deviations in the evolution of the unit-cell parameters with temperature were observed in all samples, most prominently in the β unit-cell angle. The c-type reflections disappear at ~510 and ~425 K in An100 and An96Ab4 respectively, and their intensity decreases according to a tricritical trend $ I^{2} propto left( {T - T_{text{c}} } right) $ . The cell parameter changes were used to determine the spontaneous strains arising from the transition which were modelled with Landau theory, allowing for low-temperature quantum saturation, in order to determine the thermodynamic behaviour. In An100 tricritical behaviour was observed [T c = 512.7(4) K; θs = 394(4)] in good agreement with previous studies, and the c-type superlattice reflections indicative of $P overline{1} $ symmetry persist up to the T c determined from the spontaneous strain, and then disappear. The evolution of the spontaneous strain in An96Ab4 is tricritical at low temperatures [T c = 459(1) K, θs = 396(5)] up to the temperature of disappearance of c-type reflections, but becomes second order beyond ~440 K. In An89Ab11 the strain displays second-order behaviour throughout [T c = 500(1) and θs = 212(5)], and the c-type reflections are not detected in the powder diffraction patterns at any temperature. The apparent discrepancy between the absence of c-type reflections in temperature ranges where the cell parameters display significant spontaneous strain is resolved through consideration of the sizes of the anti-phase domains within the crystals. It is deduced that the tricritical phase transition occurs in well-ordered crystals with large domains in which the behavior of individual domains is dominant (i.e. in pure anorthite) or where the $P overline{1} $ distortions within the domains are large enough to dominate the structural coherency strains between the domains. When both the magnitude of the $P overline{1} $ pattern of displacements of the tetrahedral framework become smaller and the influence of the structural coherency between anti-phase domains becomes significant, the thermodynamic behavior becomes 2nd-order in character, the c-type reflections disappear, and the orientation of the spontaneous strain changes.