Calculation of the damping constant and the relaxation time of the LA mode in the incommensurate phase of quartz

Abstract

The damping constant (linewidth) of the LA mode is calculated as a function of temperature for the incommensurate (INC) phase of quartz by using the models of the pseudospin-phonon (PS) coupled and the energy fluctuation (EF). For this calculation, the observed linewidth (${\mathrm{\Gamma }}_{LA}$) data are used at $\mathrm{P}=0$ and $80.5\mathrm{MPa}$ from the literature. Close to the incommensurate phase between the $\alpha$ and $\beta$ phases of quartz, the observed ${\mathrm{\Gamma }}_{LA}$ and the frequency shifts ($\mathrm{\Delta }{\upsilon }_{LA}$) are also analyzed by the power-law formula for both pressures ($\mathrm{P}=0$ and $80.5\mathrm{MPa}$). By using the ${\mathrm{\Gamma }}_{LA}$ and $\mathrm{\Delta }{\upsilon }_{LA},$ the inverse relaxation time (${\tau }_{LA}^{-1}$) is predicted as a function of temperature ($\mathrm{P}=0$ and $80.5\mathrm{MPa}$) in the incommensurate phase of quartz and the values of the activation energy ($E_a$) are deduced. Our calculated ${\mathrm{\Gamma }}_{LA}$ from both models (PS and EF) explain adequately the observed behavior of the linewidth of the LA mode in the incommensurate phase of quartz. Also, our predicted ${\tau }_{LA}^{-1}$ can be compared with the measurements in the INC phase of this molecular crystal.

Keywords:

• Damping constant
• Brillouin LA mode
• PS and EF models
• power-law formula
• relaxation time
• incommensurate phase
• quartz