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 fromP3221 (low-T, α quartz) toP6222 (high-T, β quartz) occurs at a transition temperature,Ttr= 847 K. TheTvariations of spontaneous strains and several structural parameters are fitted to an order parameter,Q, using Landau theory. The change in Si atom coordinate, Six, givesTtr−Tc= 0.49 K, which indicates an α ↔ β transition that is weakly first order and nearly tricritical in character (Q4∝T). Strains give higherTtr−Tcvalues (≃ 7 K). Other fitted parameters are the oxygen Ozcoordinate, Si—Si distance, Si—O—Si and φ angles, and intensity of the (111) reflection,I111. In α quartz, the Si—Si distance increases withTbecause 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 SiO4tetrahedra. The Si—Si distances contract withTand 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 withT, but the next-nearest Ca—Ca distance, which is of equal length to theaaxis, contracts withTand causes NTE along theaaxis. The thermal librations of the atoms in the rigid CO3group increase withTalong thecaxis.