Diffuse scattering anisotropy and the P2₁/a ↔ A2/a phase transition in titanite, CaTiOSiO₄

Diffuse scattering in titanite has been measured at three temperatures, 0.951T_c, 1.053T_c and 1.177T_c, using synchrotron radiation. T_c = 487 K is the temperature of the antiferroelectric paraelectric phase transition. Charge-coupled device (CCD) intensity measurements were centred about the 01 reciprocal-lattice position (space-group setting P2₁/a) and extended beyond the neighbouring 11 and 1 fundamental positions. Planar diffuse scattering intensity is observed normal to [100] with a lens-shaped maximum centred at 01. On approaching T_c from above, the intensity of the maximum at 01 increases, while intensity scattered into the planes decreases at large distances to the critical zone-boundary position. The intensity distribution is interpreted in terms of a two-dimensional spin-1/2 Ising model, in which individual spin states represent the collective displacement of octahedrally coordinated Ti atoms parallel to [100].