title: Quartz: structural and thermodynamic analyses across the α ↔ β transition with origin of negative thermal expansion (NTE) in β quartz and calcite.
abstract: 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 (Q(4) ∝ 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.
authors.affiliation: Department of Geoscience, University of Calgary, Calgary, Alberta, Canada T2N 1N4.
authors.forename: Sytle M
authors.initials: SM
authors.lastname: Antao
keywords: Landau theory; Rietveld refinement; high-temperature studies; negative thermal expansion (NTE); quartz; thermodynamic modeling