Calibration of excess thermodynamic properties and elastic constant variations associated with the alpha <-->beta phase transition in quartz

Abstract

Spontaneous strains for the ␣ ↔ ␤ transition in quartz were determined from lattice parameter data collected by X-ray powder diffraction and neutron powder diffraction over the temperature range ϳ5-1340 K. These appear to be compatible with previous determinations of the order parameter variation in ␣ quartz only if there is a non-linear relationship between the individual strains and the square of the order parameter. An expanded form of the 2-4-6 Landau potential usually used to describe the phase transition was developed to account for these strains and to permit calculation of the elastic constant variations. Calibration of the renormalized coefficients of the basic 2-4-6 potential, using published heat capacity data, provides a quantitative description of the excess free energy, enthalpy, entropy, and heat capacity. Values of the unrenormalized coefficients in the Landau expansion that include all the strain-order parameter coupling coefficients were used to calculate variations of the elastic constants. Values of the bare elastic constants were extracted from published elasticity data for ␤ quartz. Calculated variations of C 11 and C 12 match their observed variations closely, implying that the extended Landau expansion provides a good representation of macroscopic changes within the (001) plane of quartz. Agreement was not as close for C 33 , suggesting that other factors may influence the strain parallel to [001]. The geometrical mechanism for the transition involves both rotations and shearing of SiO 4 tetrahedra, with each coupled differently to the driving order parameter. Only the shearing part of the macroscopic distortions appears to show the same temperature dependence as other properties that scale with Q 2. Coupling between the strain and the order parameter provides the predominant stabilization energy for ␣ quartz and is also responsible for the first-order character of the transition.

Study of quantum effects on atomic displacements in quartz

“…We can consider a HT for quartz to be independent of temperature because the lattice parameter a exhibits only a slight temperature dependence in the high-temperature phase [1,6,7], as shown in Figure 2. In this case, we can treat e a as proportional to ∆a = a LT − a HT .…”

“…Recently, lattice-parameter measurements of SiO 2 have been performed in the temperature range of 10-900 K [6,7], and spontaneous strains along the a and c directions were shown to follow equation (4) for B = 0 [7].…”

Dauphiné twinning and texture memory in polycrystalline quartz. Part 3: texture memory during phase transformation

“…Bragg and Gibbs 1925) and are still being investigated (e.g. Smirnov and Mirgorodsky 1997;Carpenter et al 1998;Ericksen 2001;Kitahara 2001). Two models are proposed: one explains b-quartz as a dynamic average of microdomains related by the Dauphiné twin orientation and producing a disordered structure (e.g.…”

Imaging and visualising nanometre scale surface geometry of a crystalline mineral (SiO2) in monochromatic spectra

“…With the recent development of scientific tools many advanced researches are conducted to understand the physical natures of quartz. Agrosì et al (1992), Rink et al (1993), Onasch and Vennemann (1995), Stevens Kalceff and Phillips (1995), Carpenter et al (1998a), Götze et al (2001), Botis et al (2005) and Götze et al (2005) focused on different physical characteristics of quartz and its importance as a natural compound. Considering the physical importance of quartz in material and earth sciences we decided to perform an experiment on imaging for visualising nanomorphological characteristics or surface geometry this mineral by digital imaging.…”