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A general expression has been derived using anisotropic elasticity theory for the lattice strain which corresponds to the x-ray diffraction measurement on the polycrystalline specimen (cubic system) compressed nonhydrostatically in an opposed anvil device. The expressions for the various diffraction geometries emerge as the special cases of this equation. The strain calculated using isotropic elasticity theory corresponds to the macroscopic strain in the specimen, and can be obtained from the present equation by letting the anisotropy factor 2(S11−S12)/S44=1. Further, it is shown that the ratio of the lattice strain to the macroscopic strain (in the direction of the lattice strain) produced by the deviatoric stress component depends on the Miller indices (hkl) of the lattice planes and the elastic anisotropy factor. This ratio is unity only if the crystallites constituting the specimen are elastically isotropic, and increases with increasing anisotropy of the crystallites.
Ajay Singh (Sat,) studied this question.