Solid state crystal physics at very low temperatures

The mechanical dissipation (Q) and resonant frequency of a 15 kg silicon crystal were measured at cryogenic temperatures. In the experiment described, temperature control was incorporated to reduce the time derivative of the temperature. The results of the Q measurements with and without this temperature control are quite different. Measurements of the resonant frequency of the fundamental longitudinal mode of the silicon crystal from 6 to 300 Kelvin are presented and discussed with respect to temperature, df/dT. It is observed that frequency increases as temperature decreases down to about 16 Kelvin, i.e. dt/dT is negative. However, below this temperature the frequency decreases as temperature decreases, i.e. dt/dT is positive. It is suggested that this behavior is related to the coefficient of thermal contraction of silicon, which changes sign at 18 Kelvin. Continuation of these experiments to 20 mK is discussed.