Fundamentals of Piezoelectric Sensorics (eBook)

Preface 5
Contents 7
References 11
Basic Piezoelectricity, Crystal Physics, Domains 11
Ferroelectricity 11
Ferroelectric Polymers 11
Ferroelectric Ceramics 12
Quartz Crystal Technology 12
Applications 12
1 Principles of Piezoelectricity 13
1.1 The Direct and the Converse Piezoelectric Effect 13
1.2 Discovery of Piezoelectricity 16
1.3 History of the Theory of Piezoelectricity and of Piezoelectric Materials 18
1.4 Applications of Piezoelectricity and Pyroelectricity 20
1.5 New Piezoelectric Materials 23
References 26
2 Introduction to Phenomenological Crystal Structure 27
2.1 Crystal Structure 27
2.1.1 Elements of Symmetry 28
2.1.1.1 Point Operations and Symmetry Elements 28
2.1.1.2 Space Symmetry Elements and Operations 30
2.1.2 Bravais Lattices 30
2.1.3 Directions and Planes in Crystals 33
2.2 Introduction to Tensors 33
2.2.1 Orthogonal Transformation 34
2.2.2 Transformation of the Coordinates of a Point 36
2.2.3 Scalars and Vectors 37
2.2.4 Second-Rank Tensors 38
2.2.5 Second-Rank Symmetrical Tensors, the Representation Quadric 39
2.2.6 Higher Rank Tensors 40
3 Elastic Properties of Crystals 43
3.1 The Strained Body 43
3.2 Stress 51
3.3 Hookes Law 55
3.4 Transformation Equations for Elastic Constants 59
3.5 Youngs Modulus and Poissons Ratio 60
3.6 Thermodynamics of Mechanical Deformation 61
References 65
4 Basic Thermodynamics of Piezoelectric Crystals 67
4.1 Dielectric Properties 67
4.2 Internal Energy of Elastic Dielectrics 68
4.3 Linear Constitutive Equations 69
4.4 Material Coefficients 71
4.5 Relations Between Different Material Coefficients 76
References 80
5 Piezoelectric Properties 81
5.1 Four Possibilities of Piezoelectric Effect 84
5.2 Crystallographic Symmetry Restrictions to Piezoelectricity 85
5.3 Transformation of Piezoelectric Coefficients 86
5.4 Pyroelectric Effect 87
5.5 Hydrostatic Piezoelectric Coefficient 90
5.6 Ferroelectricity 91
5.6.1 Special Properties of Ferroelectrics 92
5.6.2 Thermodynamic Theory 94
5.6.3 Microphysical Model of Ferroelectricity 102
5.6.4 Antiferroelectricity 108
5.6.5 Ferroics 109
References 111
6 Nonlinear Material Properties 113
6.1 General Considerations 113
6.2 Choice of State Variables 114
6.3 Definition of Third-Order Material Constants 117
6.4 Experiments on Nonlinear Effects 122
6.4.1 Third Order Permittivity and Electrooptic Effect 122
6.4.2 Piezooptic Effect and Electrostriction 122
6.4.3 Nonlinear Piezoelectricity and Electroelastic Effect 123
6.4.4 Nonlinear Elasticity 125
6.5 Interrelations Between Different Sets of Third-Order Material Constants 126
References 127
7 Piezoelectric Materials 131
7.1 Introduction 131
7.2 Desired Properties of Piezoelectric Materials 131
7.3 Quartz 133
7.3.1 Coordinate System Choice 134
7.3.2 Quartz's Material Properties 136
7.3.3 Synthetic Quartz Crystals 137
7.3.4 Twinning 139
7.3.5 Suppression of the Secondary Twinning 143
7.3.6 Temperature Dependence of Piezoelectric Coefficients 145
7.3.7 Nonlinear Electromechanical Properties of a-quartz 146
7.3.8 Piezoelectric Properties of ß-quartz 147
7.4 Crystals Homeotypic to Quartz 148
7.4.1 Gallium Orthophosphate (GaPO4) 149
7.4.2 Berlinite (AlPO4) 150
7.4.3 Crystals of CGG Group (Langasite, Langanite, Langataite) 150
7.5 Tourmaline 150
7.6 Lithium niobate (LiNbO3) and Lithium tantalate (LiTaO3) 154
7.7 Lithium Tetraborate (Li2B4O7) 155
7.8 Perovskite Structure 156
7.8.1 Barium titanate (BaTiO3) 158
7.8.2 Potassium niobate (KNbO3) 159
7.8.3 Lead titanate (PbTiO3) 159
7.8.4 PZN-PT and PMN-PT Single-Crystals 160
7.9 Miscellaneous Piezoelectric Crystals 162
7.10 Piezoelectric Textures 164
7.11 Piezoelectric Ceramics 164
7.11.1 PZT Ceramics 166
7.11.2 Non-PZT Ceramic Compositions 171
7.12 Thin Films 173
7.13 Ferroelectric Polymers 174
7.13.1 PVDF Polymer and Its Blends with TrFE 175
7.14 Piezoelectric Composites 176
7.14.1 0-3 Composites 182
7.14.2 1-3 Composites 183
7.14.3 2-2 Composites 186
7.14.4 Miscellaneous Composite Structures 187
7.14.5 Materials with Functionally Graded Properties 189
References 190
Appendix 199
Index 217