An X-Ray Study of a Long X-Cut Quartz Crystal Vibrating Under the Transverse Piezoelectric Effect

The sixth order reflection from the (110) set of planes of a long X-cut quartz crystal of the $K\alpha$ radiation of Mo was photographed for the following conditions: (1) with the crystal non-oscillating, (2) with the crystal oscillating at its fundamental frequency under the transverse piezoelectric effect, and (3) with the crystal oscillating at its second harmonic frequency. From the microphotometer analysis of these lines it is shown that no increase in width of the lines reflected from the crystal oscillating at its fundamental frequency over the width of the lines reflected from the non-oscillating crystal is observed. This fact shows that there is no elastic deformation of the spacing of the (110) set of planes greater than 1.45×${10}^{-5\mathrm{}}$ per unit dimension. This value is the limit of the sensitivity of the spectrograph and microphotometer used. However, an appreciable increase in intensity in the lines reflected from the crystal oscillating at its fundamental frequency over the lines reflected from the non-oscillating crystal is shown. A microphotometer analysis of Laue spots obtained by passing a rectangular beam of x-rays through the middle of the crystal when it was oscillating at its fundamental frequency confirms the prediction made by the authors in an article recently published in this journal. The results seem to indicate that any increase in intensity of the reflected x-rays from any portion of a quartz crystal produced by piezoelectric oscillations of the crystal is due almost entirely to a reduction of secondary extinction.