Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package

Abstract

This paper presents the background for the calculation of anisotropic piezoelectric properties of single crystals and the graphical display of the results in two or three dimensions, and the calculation of the aggregate properties from constituent crystals and the texture of the aggregate in a coherent manner. The texture data can be obtained from a wide range of sources, including pole figure diffraction and single orientation measurements (electron backscattered diffraction, electron channelling pattern, Laue Pattern, optical microscope universal-stage). We consider the elastic wave propagation in piezoelectric crystals as an example of the interaction of electrical (2nd rank tensor), piezoelectric (3rd rank tensor) and elastic properties (4th rank tensor). In particular, we give explicit formulae for the calculation of the Voigt averaged tensor from individual orientations or from an orientation distribution function. For the latter we consider numerical integration and an approach based on the expansion into spherical harmonics. We illustrate the methods using single crystals, polycrystalline quartz measured using electron channelling patterns and ideal Curie limiting groups applied to quartz aggregates. This paper also serves as a reference paper for the mathematical tensor capabilities of the texture analysis software MTEX.

The variation and visualisation of elastic anisotropy in rock-forming minerals

“…We believe that publicly available and easy-to-use software tools like AnisoVis may be useful in teaching environments to guide understanding of the links between mineral properties (elastic, acoustic, optical) and their underlying symmetry and lattice structure. Following Nye's original text, other properties such as piezolectric and thermal conductivities, could also be added and visualised (Tommasi, 2001;Mainprice et al, 2015). Our AnisoVis MATLAB source code and sample elasticity files have been made available in open repositories so that other developers and researchers will optimise and extend the functionality, and that "given enough eyeballs, all bugs are shallow" (Raymond, 1999).…”

The variation and visualisation of elastic anisotropy in rock forming minerals

“…acoustic, optical) and their underlying symmetry and lattice structure. Following Nye's original text, other properties such as piezolectric and thermal conductivities, could also be added and visualised (Tommasi, 2001;Mainprice et al, 2015). Our AnisoVis MATLAB source code and sample elasticity files have been made available in open repositories so that other developers and researchers will optimise and extend the functionality, and that "given enough eyeballs, all bugs are shallow" (Raymond, 1999).…”

Towards an improved understanding of the mechanical properties and rheology of the lithosphere: an introductory article to ‘Rock Deformation from Field, Experiments and Theory: A Volume in Honour of Ernie Rutter’

“…These CPOs help determine seismic anisotropy in this complex metamorphic terrain, which is interpreted as an ancient extensional continental margin. Using microstructural parameters to obtain physical properties from tensor calculus applied to geological and geophysical problems, Mainprice et al (2014b) present elastic wave propagation in piezoelectric crystals as an example of interaction between electric, piezoelectric and elastic properties. Anisotropic piezoelectric properties are calculated for single crystals and corresponding aggregates from a range of fabric (or texture if using material science terminology) datasets that can be obtained from electron backscatter diffraction, electron channelling pattern, Laue pattern and optical microscope universal-stage analysis.…”