Elastic properties of ZnF2between 4.2 and 300 K

The elastic constants of single-crystal Zn${\mathrm{F}}_2$ were measured at 1 bar within the temperature range $4.2<T<\mathrm{}300\mathrm{}$ K using the method of pulse superposition. At room temperature the elastic moduli are, in units of ${10}^{11}$ ${\mathrm{d}\mathrm{y}\mathrm{n}\mathrm{e}\mathrm{s}/\mathrm{c}\mathrm{m}}^2$, $C_{11}=12.55\mathrm{}$, $C_{12}=9.18\mathrm{}$, $C_{13}=8.30\mathrm{}$, $C_{33}=19.22\mathrm{}$, $C_{44}=3.95\mathrm{}$, and $C_{66}=8.07\mathrm{}$. Near 300 K each $\frac{d{C}_{\mathrm{ij}}}{\mathrm{dT}}<0\mathrm{}$, but $\frac{d{C}_S}{\mathrm{dT}}>0\mathrm{}$, where $C_S=\frac{(C_{11}-C_{12})}{2}$. $C_{44}$ is found to have a maximum at 35 K, and to soften at lower temperature. The softening observed can be interpreted as an incipient ferroelectric transition. The room-temperature results are compared with the predictions of the rigidion model and of the Pandey model. The temperature dependence is compared to the behavior of the weak ferromagnet Ni${\mathrm{F}}_2$ and the antiferromagnet Mn${\mathrm{F}}_2$, as well as rutile (Ti${\mathrm{O}}_2$).