α-β Transition in Quartz: Temperature and Pressure Dependence of the Thermodynamic Quantities for β-Quartz and β-Cristobalite as Piezoelectric Materials

Abstract

Temperature and pressure dependencies of the thermal expansivity (a p ), isothermal compressibility (j T ) and the specific heat (C p -C v ) are studied for piezoelectric materials, in particular, for b-quartz. By analyzing the temperature (at 1 atm) and pressure (at 848 K) dependence of the observed volume V from the literature, the thermodynamic functions (a p , j T and C p -C v ) are obtained and the Pippard relations (C p -C v vs. Va p and a p vs. j T ) close to the transition from the b-quartz to the b-cristobalite are examined.

Raman opalescence of a destabilizing soft mode near the phase transition in quartz monocrystals

“…Selection rules and properties of symmetry for lattice modes in quartz were classified by using the group theory, taking into account the quartz crystalline structure . We present a more detailed information making allowance for the translational, librational, and internal modes.…”

“…Figure presents digitized isotemperature Raman spectra of a quartz single crystal in the x ( zz ) y scattering geometry at different temperatures. One can see three fundamental Raman maxima (1A 1 , 2A 1 , and 3A 1 ) in accordance with . Mode 1A 1 is due to libration of SiO 2 group and may be ascribed to a tilting type.…”

“…Quartz crystals were extensively studied by means of Raman spectroscopy . First results concerning temperature dependence of Raman spectra in crystalline quartz were obtained in Landsberg and Mandelstam .…”

“…Thus, by varying the neutron irradiation dose for quartz monocrystal one can control the phase transition temperature in the crystal. Influence of pressure on Raman spectra of crystalline quartz was investigated in Lider and Yurtseven . In Ranieri et al, solid solutions Si 1‐x Ge x O 2 were investigated and the possibility of controlling the phase transition temperature by changing the x‐concentration was demonstrated.…”

P‐Wave Velocities Across the α → β Quartz Transition at Lower Continental Crust Pressure and Temperature Conditions

“…Even though the actual physical meaning of a negative K ′ remains unclear (at least to the authors of this manuscript), the comparison of our experimental results with V p curves calculated with different K ′ values using the Abers and Hacker (2016) formalism (Figure 14) suggests that this parameter might be indeed overestimated in most databases. For instance, using molar volume measurements, Lider and Yurtseven (2014) have calculated the isothermal compressibility of β ‐quartz as a quadratic function of P: κ ( P ) = κ o + κ 1 × P + κ 2 × P 2 , where κ o and κ ( P ) are the compressibilities of β ‐quartz at room pressure and at a given pressure, respectively. Using their coefficients ( κ o = 0.035 GPa −1 ; κ 1 = −9.01 × 10 −4 GPa −2 ; κ 2 = −8.9 × 10 −5 GPa −3 ) yields a bulk modulus of β ‐quartz at room pressure and 1 GPa (and 878 K) equal to 28.57 and 29.4 GPa respectively, that is, a $${K}_{\beta }^{\prime }\sim $$ 0.8 only (close to the green dashed line in Figure 14).…”