Dependence of the dielectric permittivity of single-crystal quartz on thermal deformation at cryogenic temperatures

Abstract

The whispering gallery mode technique applied to single-crystal quartz has been used as a precise method to determine the dependence of the dielectric permittivity of pure single-crystal quartz on temperature-induced dimensional changes at cryogenic temperatures. The anisotropic temperature coefficients of permittivity (TCP) perpendicular and parallel to the crystal axis have been determined between 4.7 and 280 K. The difference between TCPs perpendicular and parallel to the crystal axis, near 17 GHz, between 160 and 300 K is approximately half the thermal expansion coefficient perpendicular to the crystal axis. Over this temperature range, the fractional change in the relative permittivity values perpendicular and parallel to the crystal axis, as a result of thermal expansion of the perpendicular dimension of the crystal, only differs by a small constant value.