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2016 | OriginalPaper | Chapter

2. Theoretical Background

Author : Matias Acosta

Published in: Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

Publisher: Springer International Publishing

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Abstract

This chapter introduces the fundamental physics and concepts of dielectrics [1–10] and their classification [9–17], as well as of ferroelectrics [8–25], and relaxor ferroelectrics [26–32]. The information of many textbooks and review papers related to the physics of materials science was employed throughout these sections. Unless explicitly stated otherwise, mathematical relationships displayed throughout this work hold for linear and homogeneous materials. For more detailed mathematical treatments the reader is referred to Refs. [11, 12].

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Footnotes
1
Subscripts indicate tensor variables. In case no tensor notation is used, the variable is either a scalar or the norm of the variable considered. The Einstein convention of repeated indexes is used for all tensor relations.
 
2
For proper reading, indexes of tensor variables with subscripts are displayed as upper scripts.
 
3
The point group 432 is the only group with both a 4-fold and a 3-fold rotation axes. The 4-fold rotation axis leaves seven of the piezoelectric coefficients non-zero, and the 3-fold axis vanishes these coefficients leading to no coupling between \(D_{i}\) and \(\sigma_{ij}\).
 
4
The 333 mode describes the polarization and strain response of a sample poled in the measurement direction.
 
5
To the best of the author´s knowledge, none of the phase boundaries known in ferroelectrics is strictly in accordance with the definition of an MPB proposed by Goldschmidt.
 
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Metadata
Title
Theoretical Background
Author
Matias Acosta
Copyright Year
2016
Book
Strain Mechanisms in Lead-Free Ferroelectrics for Actuators

Print ISBN: 978-3-319-27755-4

Electronic ISBN: 978-3-319-27756-1

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-27756-1_2

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