Table of Contents: Piezoelectricity in classical and modern systems

Piezoelectricity in classical and modern systems [E-Book] / Morten Willatzen.

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 qu...

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Personal Name(s):	Willatzen, Morten, author
Imprint:	Bristol : IOP Publishing, [2024]
Physical Description:	1 online resource
Note:	englisch
ISBN:	9780750355575
DOI:	10.1088/978-0-7503-5557-5
Subject (LOC):	Piezoelectricity. Nanostructured materials.

part I. Strain and stress in solids. 1. Definition of strain and stress
1.1. Strain
1.2. Stress
1.3. Thermodynamics of deformation
1.4. Free energy of a solid crystal
2. Transformation properties of strain and stress
2.1. Orthogonal transformations
2.2. Transformation law for the stiffness matrix
2.3. Stiffness tensor of cubic crystal in rotated coordinates
2.4. equations-of-motion in rotated coordinates
3. Wave propagation in solids
3.1. Compressional wave propagation along the [110] direction in a cubic crystal
3.2. Hexagonal crystals
3.3. Unbounded isotropic media
3.4. Christoffel equation
3.5. Surface waves
part II. Dynamic deformation. 4. Simple oscillator systems
4.1. Case 1: underdamping
4.2. Case 2: overdamping
4.3. Case 3: critical damping
4.4. Forced oscillations
5. Transverse vibrations of strings
5.1. Wave equation of strings
5.2. Forced vibration of a semi-infinite string
5.3. Normal modes of the fixed-fixed string
6. Vibrations of bars
6.1. Simple boundary conditions
6.2. Transverse vibrations of bars
6.3. Torsional waves in a bar
7. Vibrations of membranes
7.1. Theory of vibrating membranes
7.2. Rectangular membrane with fixed edges
8. Cylindrical rod vibrations
8.1. Wave equations of cylindrical rods
8.2. Longitudinal vibrations
8.3. Elasticity equations
8.4. Torsional waves
8.5. Flexural waves
8.6. General three-dimensional dispersion equation for infinite cylindrical rods
8.7. Program for computing three-dimensional dispersion curves of infinite cylindrical rods
8.8. Circumferential waves in a hollow elastic cylinder
part III. Piezoelectricity and applications. 9. A piezoelectric toy model
9.1. Non-piezoelectric system
9.2. Piezoelectric system
10. Piezoelectricity in solid crystals
10.1. Piezoelectricity in cubic (diamond and zincblende) structures
10.2. Piezoelectricity in hexagonal structures
11. Group theory, transformation properties, and application to material properties
11.1. Group tables and material parameters
11.2. Stiffness matrices
11.3. Piezoelectric matrices
11.4. Permittivity matrices
11.5. Transformation matrices for the symmetry group generators
11.6. Transformation properties of the stiffness tensor using point-group symmetry
11.7. Transformation properties of the piezoelectric and permittivity tensors
11.8. Transformation of the permittivity tensor
11.9. Coupled electromagnetic and mechanical fields in piezoelectric materials
11.10. The quasistatic approximation
11.11. Solving the coupled field equations for a strain wave in a cubic material
12. Piezoelectric reciprocal systems coupled to fluids
12.1. Wave motion in fluids
12.2. The equation of continuity
12.3. The Euler equation
12.4. Wave propagation in fluids
12.5. Piezoelectric constitutive equations
12.6. Equation-of-motion in the 1D solid case
12.7. Mono-frequency case
12.8. A one-dimensional model of a classical piezoelectric transmitter
12.9. A one-dimensional model of a classical piezoelectric receiver
12.10. General time-dependent excitation of a reciprocal piezoelectric transducer system
13. Three-dimensional axisymmetric piezoelectric vibrations
13.1. Piezoelectric cylindrical rod
C mm 6v(6 ) crystal symmetry
13.2. Effective one-dimensional spatial model
13.3. Full two-dimensional numerical implementation
13.4. Numerical results using the effective one-dimensional model
14. Flexoelectricity and electrostriction
14.1. Flexoelectricity and symmetry properties of hexagonal crystals
14.2. Converse flexoelectricity
14.3. Electrostriction and symmetry properties of hexagonal crystals
14.4. Flexoelectricity and piezoelectricity in graphene
14.5. Set of dynamic equations for a two-dimensional membrane
14.6. Case study 1
14.7. Case study 2
15. Atomistic approach to piezoelectric properties
15.1. Modern theory of polarization
15.2. Berry phase
15.3. The three-dimensional system
15.4. Berry phase: example 1
15.5. Berry phase of a sequence of N states
15.6. Berry phase: example 2
15.7. Atomistic approach to strain and elasticity: valence force-field models
15.8. equation-of-motion and dynamical matrix
15.9. The dynamical matrix
15.10. CdS wurtzite case
15.11. Theory of the local electric field
15.12. Electric field from a polarized medium
15.13. Born-Huang theory
15.14. Piezoelectric vibrations at optical frequencies
16. Optical properties of piezoelectric materials
16.1. Optical absorption in a semiconductor
16.2. The k.p method
16.3. Piezoelectric potential
16.4. Electron Hamiltonian
16.5. Hole Hamiltonian
16.6. Zincblende
16.7. Wurtzite
16.8. Band structure of heterostructures
17. Sonoluminescence
17.1. Sonoluminescense due to bubble oscillations
17.2. Incompressible fluids
17.3. Derivation of the Rayleigh-Plesset equation
17.4. Momentum conservation
17.5. Boundary conditions
17.6. Adiabatic gases and perfect gas law
17.7. Derivation of Planck's black-body radiation law
17.8. The Planck formula
17.9. Stefan-Boltzmann law
17.10. Derivation of Wien's displacement law from Planck's black-body radiation law
17.11. Numerical solution of the Rayleigh-Plesset equation, i.e., bubble radius versus time for a given ultrasonic pulse
Part IV. Appendices. Appendix A. Stiffness tables
Appendix B. Piezoelectric constant tables
Appendix C. Permittivity tables.