Analysis of Stress-Strain Relationships and Line Broadening in Polycrystalline Materials Having Tetragonal Crystal System with [001] Fibre Texture by X-Ray Diffraction

Abstract

The stress and strain relationships for polycrystalline materials having tetragonal crystal system with [001] fibre texture, which are required for stress analysis by X-ray diffraction (XRD), were formulated within the framework of the Reuss model of elasticity. In formulating the relationships, two types of orientations of constituent crystallites in the specimen, which contribute to XRD, were shown to exist by taking into account the Laue classes of the crystallites. The formulae representing strains measurable by XRD were found to be different, depending on which the Laue class, 4/mmm or 4/m, the specimen belongs to, even though both Laue classes are in the tetragonal crystal system. The formula obtained for the Laue class 4/mmm shows that the profile observed by XRD is formed in a symmetrical shape so that the strain can be the average value of those for the two different types of crystallites. On the other hand, the formula for the Laue class 4/m shows that the profile is formed in an asymmetrical shape so that the strain can be determined by the magnitudes of the structure factors in the two different types of crystallites. Additionally, it is shown that some of the Debye-Scherrer lines change their widths with the measurement direction. The order of magnitude of such a line broadening is discussed for two materials, BaTiO3 and MgF2.