A dynamical model for the $$I\bar 1 - P\bar 1$$ phase transition in anorthite, CaAl2Si2O8

The non-ferroic triclinic to triclinic $$I\bar 1 - P\bar 1$$ phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R 1 + representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R 1 + order parameter of the high symmetry triclinic phase $$P\bar 1_0$$ (or equivalently $$I\bar 1$$ ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R 1 + order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x0,y0,z0) of $$P\bar 1_0$$ (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x0, y0, z0), an opposite displacement at (x0+1,y0+1,z0+1), and the same displacement at ( $$\bar x$$ 0+1, $$\bar y$$ 0+1, $$\bar z$$ 0+1) of $$P\bar 1_0$$ . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).