Texture, 2D diffraction and piezoelectricity

Abstract

A computer-aided methodology for the approximate prediction of axially textured polycrystals’ properties is presented. The input data for the developed application consist of: (a) the two-dimensional diffraction pattern of the material under investigation and (b) the tensors of the elasto-piezo-dielectric properties of the single crystal case. Program ANAELU 2.0 allows the determination of the fiber axis inverse pole figure by means of a Rietveld-type procedure. The Material Properties Open Database (MPOD, http://mpod.cimav.edu.mx) provides free access to the experimentally determined values of the tensor properties for several crystal species. Practical estimates of polycrystals’ properties may be obtained by averaging single crystals’ properties tensors, with the orientation distribution function (the symmetry-axis inverse pole figure, in fiber textures) as a weight factor. This treatment, with the application of the Voigt, Reuss and Hill approaches, requires special precautions when it comes to the coupling properties (e.g. piezoelectricity, magnetostriction, magnetoelectricity). Some key physical, mathematical and computational aspects related to the considered topic are discussed. Program GISELLE systematizes the calculation of polycrystal properties under the considered treatments. The application of the proposed methodology to real-world events is illustrated by means of a case study.