Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package
David Mainprice, Florian Bachmann, Ralf Hielscher, Helmut Schaeben, Geoffrey E. Lloyd, 2016. "Calculating anisotropic piezoelectric properties from texture data using the MTEX open source package", Rock Deformation from Field, Experiments and Theory: A Volume in Honour of Ernie Rutter, D. R. Faulkner, E. Mariani, J. Mecklenburgh
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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.
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Ernie Rutter has made, and continues to make, a significant impact in the field of rock deformation. He has studied brittle and plastic deformation processes that occur within both the oceanic and continental crust, as well as other key properties such as the permeability and seismic velocities of these rocks. His approach has been one that integrates field observations, laboratory experiments and theoretical analyses. This volume celebrates Ernie’s key contribution to rock deformation and structural geology by bringing together a collection of papers that represent this broad approach. The papers within the volume address key issues that remain within these fields. These range from fundamental studies of brittle and plastic behaviour along with the resultant structures and microstructures from both the field and laboratory, to applied problems where a better understanding of the deformation and properties of the crust is still needed.