Intensity of X Rays Diffracted from an Elastically Vibrating Single-Crystal Plate

Abstract

The intensity of the x-ray beam diffracted from a single crystal changes when the crystal lattice is distorted. An elastically vibrating quartz plate driven piezoelectrically was used to study relationships between diffracted intensity and lattice distortions for the case of Laue geometry with μt∼1. The main advantages in studying the distortions of a plate vibrating at resonance are that the shape of the displacement of the lattice is amenable to mathematical analysis and that the amplitude of vibration can be varied continuously. Integrated intensity of the diffracted x-ray beam was measured as functions of the position in the crystal plate, the amplitude of vibration, and the phase of a vibration cycle. The following conclusions were drawn, which demonstrate and verify some predictions made by the dynamical theory of x-ray diffraction for a distorted single crystal for the nonabsorbing case: (1) For an intensity change to occur, the distortion in the net plane must have a component along the diffraction vector and have a nonzero second derivative in the plane of diffraction. (2) The measured integrated intensity is a monotonically increasing function of lattice distortions and closely follows the theoretical curve. (3) Increases in the diffracted intensity are independent of the sign of the second derivative of the displacement.