Dependence of the X-Ray Elastic Constants on the Diffraction Plane

The calibration constants that link the peak-shift measured with X-rays to the macroscopic stress acting on the material are termed X-ray elastic constants. These terms contain both material parameters such as the elastic stiffness or compliance terms and configurational parameters caused by the Miller indices of the diffracting plane of the corresponding crystal structure. The configurational parameters can cause significant variations on the X-ray elastic constants. In this paper a new theoretical model is proposed for the calculation of the average X-ray elastic constants from single crystal data and its extensions will be compared and discussed with respect to the known Voigt and Reuss model. It uses a modification of the Voigt assumption and takes into account the fact that not all grains in a polycrystalline aggregate contribute to the data obtained by diffraction but only those which are selected by Bragg's law for a given reflection. It is shown that this restriction yields compliances that depend on the crystallographic orientation of the diffracting crystallites. The new model is demonstrated for polycrystalline cubic, hexagonal and tetragonal materials but also can be extended to any crystal structure. It is called constraint Voigt (CV) model.