Quartz: structural and thermodynamic analyses across the α ↔ β transition with origin of negative thermal expansion (NTE) in β quartz and calcite

The temperature variation, T, of the crystal structure of quartz, SiO₂, from 298 to 1235 K was obtained with synchrotron powder X-ray diffraction data and Rietveld structure refinements. The polymorphic transformation from P3₂21 (low-T, α quartz) to P6₂22 (high-T, β quartz) occurs at a transition temperature, T_tr = 847 K. The T variations of spontaneous strains and several structural parameters are fitted to an order parameter, Q, using Landau theory. The change in Si atom coordinate, Si_x, gives T_tr − T_c = 0.49 K, which indicates an α ↔ β transition that is weakly first order and nearly tricritical in character (Q⁴ ∝ T). Strains give higher T_tr − T_c values (≃ 7 K). Other fitted parameters are the oxygen O_z coordinate, Si—Si distance, Si—O—Si and φ angles, and intensity of the (111) reflection, I₁₁₁. In α quartz, the Si—Si distance increases with T because of cation repulsion, so the Si—O—Si angle increases (and φ decreases) and causes the thermal expansion of the framework structure that consists of corner-sharing distorted rigid SiO₄ tetrahedra. The Si—Si distances contract with T and cause negative thermal expansion (NTE) in β quartz because of increasing thermal librations of the O atom in the Si—O—Si linkage that occur nearly perpendicular to the Si—Si contraction. In calcite, CaCO₃, the short Ca—Ca distance expands with T, but the next-nearest Ca—Ca distance, which is of equal length to the a axis, contracts with T and causes NTE along the a axis. The thermal librations of the atoms in the rigid CO₃ group increase with T along the c axis.