CALIBRATION OF EXCESS THERMODYNAMIC PROPERTIES AND ELASTIC-CONSTANT VARIATIONS ASSOCIATED WITH THE ALPHA[--]BETA PHASE-TRANSITION IN QUARTZ

Spontaneous strains for the alpha <-> beta transition in quartz were d etermined from lattice parameter data collected by X-ray powder diffra ction and neutron powder diffraction over the temperature range simila r to 5-1340 K, These appear to be compatible with previous determinati ons of the order parameter variation in alpha quartz only if there is a non-linear relationship between the individual strains and the squar e of the order parameter. An expanded form of the 2-4-6 Landau potenti al usually used to describe the phase transition was developed to acco unt for these strains and to permit calculation of the elastic constan t variations. Calibration of the renormalized coefficients of the basi c 2-4-6 potential, using published heat capacity data, provides a quan titative description of the excess free energy, enthalpy, entropy, and heat capacity, Values of the unrenormalized coefficients in the Landa u expansion that include all the strain-order parameter coupling coeff icients were used to calculate variations of the elastic constants. Va lues of the bare elastic constants were extracted from published elast icity data far beta quartz. Calculated variations of C-11 and C-12 mat ch their observed variations closely, implying that the extended Landa u expansion provides a good representation of macroscopic changes with in the (001) plane of quartz. Agreement was not as close for C-33, sug gesting that other factors may influence the strain parallel to [001]. The geometrical mechanism for the transition involves both rotations and shearing of SiO4 tetrahedra, with each coupled differently to the driving order parameter. Only the shearing part of the macroscopic dis tortions appears to show the same temperature dependence as other prop erties that scale with Q(2). Coupling between the strain and the order parameter provides the predominant stabilization energy for alpha qua rtz and is also responsible for the first-order character of the trans ition.