Acoustic soft modes in KCNxBr1−x and KCNxCl1−x mixed crystals

Abstract

The ultrasonic velocity of [100] transverse waves has been measured as a function of temperature in $\mathrm{KC}{\mathrm{N}}_x{\mathrm{Br}}_{1-x}$ and $\mathrm{KC}{\mathrm{N}}_x{\mathrm{Cl}}_{1-x}$ crystals with $x<\mathrm{}{x}_c$, where $x_c$ is the critical C${\mathrm{N}}^{-}$ concentration required for a structural phase transition into an orientationally ordered phase. The shear stiffness $c_{44}$ in these samples and in others with $x\simeq x_c$ and $x>\mathrm{}{x}_c$ obeys an elastic Curie-Weiss law over a wide range of temperatures, with fitting parameters that agree with mean-field percolation theory. However, deviations from this Curie-Weiss behavior and also velocity dispersion are observed at low temperatures for samples with $x<\mathrm{}{x}_c$. The relationship between the $c_{44}$ soft mode and orientational ordering is discussed.