Piezoelectricity in classical and modern systems /

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"Version: 20240601"--Title page verso.Includes bibliographical references.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 crystal2. 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 coordinates3. 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 wavespart 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 oscillations5. 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 string6. Vibrations of bars -- 6.1. Simple boundary conditions -- 6.2. Transverse vibrations of bars -- 6.3. Torsional waves in a bar7. Vibrations of membranes -- 7.1. Theory of vibrating membranes -- 7.2. Rectangular membrane with fixed edges8. 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 cylinderpart III. Piezoelectricity and applications. 9. A piezoelectric toy model -- 9.1. Non-piezoelectric system -- 9.2. Piezoelectric system10. Piezoelectricity in solid crystals -- 10.1. Piezoelectricity in cubic (diamond and zincblende) structures -- 10.2. Piezoelectricity in hexagonal structures11. 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 material12. 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 system13. 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 model14. 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 215. 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 frequencies16. 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 heterostructures17. 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 pulsePart IV. Appendices. Appendix A. Stiffness tables -- Appendix B. Piezoelectric constant tables -- Appendix C. Permittivity tables.Full-text restricted to subscribers or individual document purchasers.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 kp 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.Physics and engineering students; both upper undergraduate and graduate.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Morten Willatzen is Senior Professor of the Beijing Institute of Nanoenergy and Nanosystems as well as a Guest Full Professor of the Technical University of Denmark. He has won numerous awards and published more than 300 papers in international journals. He is the author of two books on "The k.p Method" published by Springer and "Separable Boundary-Value Problems in Physics" by Wiley. Morten Willatzen is a recipient of the first BHJ Award from the University of Southern Denmark in 2008, A Talent 1000 Foreign Expert, and the Great Wall Friendship Award.Title from PDF title page (viewed on July 15, 2024).

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1 online resource (various pagings) :illustrations (some color).

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English

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9780750355575

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537/.2446

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Nanostructured materials.
Nanotechnology.
Piezoelectricity.

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Morten Willatzen.

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