On the elasticities of quartz across the α–β phase transformation

Abstract

The purpose of this paper is to describe the behavior of the elasticities of quartz across the α– β phase transformation at room pressure. In spite of the known dynamic behavior of quartz, we adhere to the prejudice that an equilibrium theory is sufficient for this task, and propose a Landau model based on a three-phase, two-order-parameter polynomial free energy. One of the order parameters, describing a suitable displacement of the oxygen atoms, produces an isostructural transition just above the temperature of the α– β phase transformation. Subsequently, the latter takes place with the joint contribution of the second structural order parameter, associated with another displacement of the oxygens. The free energy consists of the minimal number of monomials necessary to produce the two mentioned transitions and only those; in spite of this minimality, the results from theory appear to reasonably agree with the experimental data. A posteriori, we reconstruct the phase diagram in the plane of the coefficients of the quadratic monomials.