Lattice Parameter Local Determination for Trigonal, Hexagonal, and Tetragonal Crystal Systems Using Several Coplanar X-Ray Reflections

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Abstract
The method for determining the local lattice parameters using quasi-multiple X-ray diffraction (which was proposed and used only for crystals of the cubic system) has been expanded to measure the local crystal lattice parameters for the trigonal, hexagonal, and tetragonal systems. Local variations in the lattice parameters in the tetragonal paratellurite (TeO2) and trigonal lanthanum-gallium tantalate (La3Ga5.5Ta0.5O14) crystals have been investigated. Reflections necessary for implementing the quasi-multiple X-ray diffraction scheme are found for these crystals. The pairs of reflections that were found were used to complete quasi-multiple X-ray diffraction schemes on a laboratory X-ray source and determine the variation in the lattice parameter a along the surface of these crystals. The relative measurement error was 4 x 10-6 at a spatial resolution of 140 μm. The accuracy of the method and the parameters determining this characteristic were analyzed based on the results. The locality of the method and the limits of the spatial resolution of an X-ray diffraction measurement of lattice parameters are estimated.

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