Method of measuring resonant frequencies of solids with parts per million resolution over a wide temperature range

An apparatus has been developed for the measurement of the ultrasonic resonances of a solid cube or parallelepiped, which involves a method of excitation and detection. The key point is that a small reentrant-type microwave cavity is used in the apparatus. The excitation of the sample vibration is due to the electrostatic force between a metal-coated sample surface and the outer surface of the cavity. The resonant frequency of the sample is measured by taking advantage of the amplitude modulation of the characteristic resonant frequency of the cavity. This modulation is caused by the capacitance change due to the sample vibration. The apparatus is so small that it is mounted in the "mK-stabilized cell" developed previously, which has a temperature stability and/or resolution of the order of 1 mK . The usefulness of the apparatus combined with the "mK-stabilized cell" has been demonstrated by the precise measurement of the resonant frequency of Ba Ti O 3 single crystal at its phase transition, which is relevant to the change of its elastic modulus at the critical point.