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Book Chapter

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

By
David Mainprice
David Mainprice
1
Geosciences Montpellier UMR CNRS 5243, Université Montpellier 2, 34095 Montpellier Cedex 05, France
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Florian Bachmann
Florian Bachmann
2
Mathematische Geologie und Geoinformatik, Institut für Geophysik und Geoinformatik, Technische Universität Freiberg, 09596 Freiberg, Germany
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Ralf Hielscher
Ralf Hielscher
3
Fakultät für Mathematik, Technische Universität Chemnitz, 09126 Chemnitz, Germany
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Helmut Schaeben
Helmut Schaeben
2
Mathematische Geologie und Geoinformatik, Institut für Geophysik und Geoinformatik, Technische Universität Freiberg, 09596 Freiberg, Germany
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Geoffrey E. Lloyd
Geoffrey E. Lloyd
4
School of Earth and Environment, The University, Leeds LS2 9JT, UK
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Published:
January 01, 2016

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.

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Contents

Geological Society, London, Special Publications

Rock Deformation from Field, Experiments and Theory: A Volume in Honour of Ernie Rutter

D. R. Faulkner
D. R. Faulkner
University of Liverpool, UK
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E. Mariani
E. Mariani
University of Liverpool, UK
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J. Mecklenburgh
J. Mecklenburgh
University of Manchester, UK
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Geological Society of London
Volume
409
ISBN electronic:
9781862396975
Publication date:
January 01, 2016

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