Velocities of First and Zero Sound in Quartz

Abstract

The temperature dependence of the velocity of sound in $X$-cut and $\mathrm{BC}$-cut natural quartz crystals has been measured in the range 4 to 75 \ifmmode^\circ\else\textdegree\fi{}K. Measurements were made at frequencies of 35, 100, and 1000 MHz. By assuming that at these frequencies the velocity is frequency independent at 4 \ifmmode^\circ\else\textdegree\fi{}K, these results can be used to obtain the frequency dependence of the velocity at higher temperatures. At temperatures below 20 \ifmmode^\circ\else\textdegree\fi{}K, or above about 65 \ifmmode^\circ\else\textdegree\fi{}K, there is no velocity dispersion in the frequency range studied, to within the experimental uncertainty. In the temperature range between 20 and about 65 \ifmmode^\circ\else\textdegree\fi{}K, the velocity is greater at 1000 MHz than at the lower frequencies, both for the $X$-cut and the $\mathrm{BC}$-cut crystals. These results are compared with theories of velocity dispersion due to interaction with thermal phonons, and qualitative agreement is obtained.