Calculation of the Raman Linewidths of Lattice Modes Close to the α-β Transition in Quartz

Abstract

The Raman frequencies of the lattice modes (147 cm 1 and 207 cm 1 / are analyzed for the˛-ˇtran-sition in quartz according to a power-law formula with the critical exponent by using the experimental data. The temperature dependence of the Raman frequency is associated with the order parameter (polarization P ) for this transition in the quartz crystal. The damping constant of the lattice modes studied here is calculated using the Raman frequencies at various temperatures for the˛-ˇtransition in quartz (T c D 846 K) using the soft mode -hard mode and the energy fluctuation models. Our calculations for the damping constant (bandwidths) give an evidence that the lattice mode of the 147 cm 1 exhibits a soft mode behavior for the˛-ˇtransition in quartz.

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

“…The behavior of the soft mode which vanishes at the transition temperature in ferroelectrics, as given in Cohran's theory [5] was also studied using Raman frequencies of the lattice modes of 147 and 207 cm -1 for the a-b transitions in quartz [31]. Using the observed data [31] for the Raman frequencies of the lattice modes (147 and 207 cm -1 ), which exhibit the soft mode behavior in quartz, we have calculated recently the Raman linewidths of those phonon modes by relating the Raman frequency to the order parameter (spontaneous polarization) as in ferroelectric materials [24].…”

“…We have studied the Raman frequency shifts and linewidths in quartz [21,24], and in SiO 2 -moganite [40] previously. We have also studied the critical behavior of the specific heat C p near the a-b transition [39] and we have established the Pippard relations [38] in quartz by analyzing the experimental data [25,35].…”

Temperature Dependence of the Raman Frequency of an Internal Mode for SiO2-Moganite Close to theα-βTransition

“…For the α-β transition in quartz, we were able to predict the divergence of the 147 cm −1 and 207 cm −1 Raman modes in the vicinity of the transition temperature (T C = 846 K) using the models considered above, as studied in our recent work [11]. We also indicated in that work [11] that the 147 cm −1 Raman mode exhibits a soft mode behavior for the α-β transition in quartz. In the case of moganite, the temperature dependence of the vibrational frequency and of the linewidth of the 501 cm −1 mode can be further investigated to explain its α-β transition.…”

“…More recently, the experimental analyses have identified a first-order character to the phase transition between α-quartz and the intermediate incommensurate phase [7][8][9]. In our recent study, we have calculated the temperature dependence of the Raman frequency shifts and the linewidths for the optical lattice vibrations of the 128 cm −1 and 466 cm −1 in the α-phase of quartz from the anharmonic self-energy [10]; we have also calculated [11] the temperature dependence of the damping constant (Raman bandwidths) for the lattice modes of 147 cm −1 and 207 cm…”

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

“…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 .…”