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The present book provides a detailed account of the fundamental physics, group symmetry, and concepts from elasticity to establish the general properties of mechanical and electromagnetic wave propagation in crystals. The interaction of mechanical fields and electromagnetic waves in the so-called quasistatic approximation allows to determine the complete set governing equations for applications of piezoelectricity in sensors and actuators. The theory puts strong emphasis to the general allowed forms of material tensors (stiffness, permittivity, piezoelectric stress and strain tensors) for the 32 crystal classes in three dimensions. Piezoelectricity is first introduced using a toy model to emphasize the requirement of non-centrosymmetry of a system for the system to be piezoelectric. The book devotes a chapter to flexoelectricity which is another electromechanical effect that recently has attracted substantial interest in nanostructure applications where strain gradients can be large such as in two-dimensional materials applications (graphene-like materials).
The last part of the book discusses the modern theory of piezoelectric properties using first-principles atomistic calculations and the use of Berry phases. The Berry phase method is a general method that allows various physical properties of solids to be calculated including flexoelectricity. Other atomistic methods for strain calculations such as the Keating model for cubic structures and the Birman-Nusimovici model for wurtzite hexagonal structures are presented. Strain and piezoelectric properties of zincblende and wurtzite pyramidal quantum-dot structures and their influence for electronic eigenstates are discussed by use of the k.p electronic bandstructure method. Following this, optical properties are derived with emphasis to the influence of piezoelectricity. The last chapter of the book presents another subtle effect, sonoluminescence, displaying the mixture of ultrasonics, usually generated by the piezoelectric effect, thermodynamics of fluids, quantum mechanics, and optics.
Key Features:
- Includes an introduction with basic concepts of sound and vibrations
- Presents the fundamental theory of polarization and piezoelectricity
- Explains group symmetry applied to electromechanical system
- Describes piezoelectricity in novel applications such as nanotechnology, optics, and quantum mechanics
- Provides examples and computer code throughout the text
Piezoelectricity is a phenomenon in which materials respond to a mechanical strain by generating electrical polarization or, conversely, respond to an applied external electric field by generating a mechanical strain. While this effect was discovered in the 1880s, this subject remains very active, since it allows for a variety of applications in sensing, actuating, transducing, energy harvest and conversion.
Willatzen’s book is an introduction to the basic concepts of piezoelectricity. It is a pleasure to read and contains careful discussions of symmetry operations, since the lack of centrosymmetry is essential for piezoelectric materials. Optics and photonics students will find a complete chapter dedicated to the optical properties of piezoelectric materials. I highly recommend this book as primary source for graduates and scientists involved in this area of research and engineering.
Christian Brosseau, Optica, September 2024
1. Background
2. Simple zero-dimensional oscillator systems
3. Transverse vibrations of strings
4. Vibrations of beams and membranes
5. Vibrations of plates and cylindrical rods
6. Fluid acoustics and dynamics
7. Strain and stress in solids
8. Group symmetry in mechanical systems
9. A toy model of piezoelectricity
10. Piezoelectricity and symmetry
11. Piezoelectric constitutive relations
12. Classical piezoelectric theory and applications
13. Equivalent circuit diagrams of piezoelectric materials
14. Reciprocal piezoelectric transducer systems
15. Ultrasonic motors
16. Nanotechnology piezoelectric theory and applications
17. Modern theory of polarization
18. Piezoelectric cantilevers
19. Piezoelectric properties of nanosystems
20. Piezoelectric two-dimensional materials
21. Flexoelectricity and polarization
22. Piezoelectricity and electronic bandstructure
23. Acoustic and piezoelectric effects on optical properties
24. Acoustic gain in piezoelectric materials
25. Index
26. Appendices