The ultrasonic velocity and attenuation of TA[100] acoustic waves have been measured as a function of temperature and frequency in ${\mathrm{K}}_{\mathit{x}}$${\mathrm{Na}}_{1\mathrm{-}\mathit{x}}$CN mixed single crystals. Relaxation behavior is revealed by comparing our ultrasonic ${\mathit{c}}_{44}$ elastic stiffness data with hypersonic ${\mathit{c}}_{44}$ data obtained from Brillouin scattering. Combining ultrasonic velocity and attenuation data we are able to determine the Kramers-Kronig ratio R in the disordered paraelastic phase and to estimate it in the orientational glass phase. For the regime ω${\mathrm{\tau }}_{\mathit{s}}$≪1, R is a direct measure of the cooperative quadrupolar clamped relaxation time ${\mathrm{\tau }}_{\mathit{s}}$, which can be represented by the empirical form ln${\mathrm{\tau }}_{\mathit{s}}$=${\mathit{A}}_{\mathit{s}}$-${\mathit{B}}_{\mathit{s}}$T in the paraelastic phase. Quadrupolar relaxation processes in the orientational glass state are also discussed.

• Received 14 March 1991

DOI:https://doi.org/10.1103/PhysRevB.44.6731