Anisotropic thermal expansion in yttrium silicate

In this study, crystals of Y₂SiO₅ were examined by high-temperature powder x-ray diffractometry to determine the changes in unit-cell dimensions with temperatures up to 1273 K for the X₁ phase (the low-temperature phase, space group P121/c1) and 1473 K for the X₂ phase (the high-temperature phase, space group I12/a1). The lattice deformations of both phases induced by thermal expansion were investigated by matrix algebra analysis to determine the directions and magnitudes of the principal distortions (λ_i, i = 1, 2, and 3). For the X₁ phase, λ₁ and λ₂ invariably showed a positive thermal expansion. On the other hand, λ₃ showed a negative thermal expansion below 1173 K; the maximum contraction of 0.10(4)% occurred at 685 K. The λ₂ axis invariably coincides with the crystallographic b axis. The directions of λ₁ and λ₃, defined by the acute angle λ₃ ^ c changed between 53(3)° (T = 394 K) and 45(1)° (T = 788 K). For the X₂ phase, all of the principal distortions steadily increased with increasing temperature. The angle λ₃ ^ c steadily decreased from 71(2)° to 62.1(1)° with increasing temperature. The mean linear thermal expansion coefficients were, when compared at the same temperatures, necessarily higher for the X₁ phase than for the X₂ phase. The lattice change of X₁–RE₂SiO₅ (RE = Y and Yb–La), which was induced by the substitution of rare-earth (RE) ions, showed a striking resemblance with the lattice deformation of X₁-Y₂SiO₅, which was caused by the thermal expansion. Because the lattice change of the former must be caused by the isotropic expansion of the RE sites, the anisotropic thermal expansion of the latter would be essentially attributable to the isotropic thermal expansion of the YO₉ and YO₇ polyhedron.