Displacement Parameter, Soft-Mode Frequency, and Fluctuations in Quartz Below Itsα−βPhase Transition

Abstract

The displacement parameter in $\alpha$-quartz consists of a rotation of the Si${\mathrm{O}}_4$ tetrahedra around their two-fold symmetry axis. Its magnitude is given by $x_0(\omega ,T)-x_0(\omega ,T_c)=A\left(\omega \right)\times {(T_c-T)}^{\beta }$, with $\beta =0.34\mathrm{}\pm 0.02$ as determined independently by x rays, ultrasound, and Raman scattering.