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, Ttr = 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, Six, gives Ttr − Tc = 0.49 K, which indicates an α ↔ β transition that is weakly first order and nearly tricritical in character (Q4 ∝ T). Strains give higher Ttr − Tc values (≃ 7 K). Other fitted parameters are the oxygen Oz 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. The structural analysis of quartz across the α ↔ β transition is satisfactorily modelled with Landau theory. Cation–cation contractions give rise to negative‐thermal expansion (NTE) in quartz and calcite.