DEPENDENCE OF THE X-RAY ELASTIC CONSTANTS ON THE DIFFRACTION PLANE FOR POLYCRYSTALLINE CUBIC, HEXAGONAL AND TETRAGONAL THIN FILMS WITH ANY FIBER AXIS

Harald Wern

Hochschule für Technik und Wirtschaft des Saarlandes, Goebenstrasse 40, D-66117 Saarbrücken, Germany

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. The calculation procedure for the x-ray elastic constants for isotropic and quasiisotropic materials from single crystal data is usually based on the model of Voigt, Reuss or Eshelby-Krner. In this paper a new theoretical model is proposed. 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 yield compliances that deoend on the crystallographic orientation of the diffracting crystallites. The new theory is rigorous only for samples with ideal fiber texture which is often observed in thin films. Because the full tensors of the elastic stiffness and compliance have been calculated for the first time in analytical closed form, the new model can be applied to any fiber axis.