Effect of the worked layer in quartz-crystal plates on their frequency stabilities

This paper describes the direct measurement of the relation between the worked layers in quartz-crystal plates and their effect on the frequency stability. The rectangular fundamental 5-MHz A T-cut specimen plates lapped and polished with emery powder and cerium oxide, respectively, were placed in gap-type holders and connected with oscillator circuits, and their frequency stabilities were measured. The frequency stabilities are evaluated by the fractional frequency deviation to the nominal frequency ratio, power spectral density, and the Allan variance. The main results are: 1) The frequency drift due to the worked layer is dealt with as a relaxation process. It can be approximated by a sum of one to three terms of an exponential function. 2) The depth of the worked layer has a large effect not only on the long-term frequency stability but on the medium term in the Fourier frequency range of 10
⁻³
to 10
⁻⁷
Hz. 3) It does not have a dominant effect on the short-term stability with an averaging time of less than 10 s.