Electromagnetic Properties of Heterostructures: Background and Calculation Methods covers the fundamental aspects of the electromagnetic properties of heterostructures and the theoretical knowledge of the computational techniques needed to understand dielectric phenomena in quantitative and physical terms. The book re-establishes the conceptual foundations of the physics associated with numerical simulation tools of the Laplace or the Poisson equations and shows their immediate implementation. It is relevant for all practicing engineers and materials scientists who develop composite materials that are capable of handling specified technological requirements by utilizing their electromagnetic properties.
1. Electromagnetic Heterostructures - p. i 2. Cover image - p. i 3. Title page - p. i 4. Table of Contents - p. i 5. Copyright - p. iv 6. Preface - p. xi 7. Acknowledgments - p. xix 8. Part One: Elementary concepts and definitions - p. xix 9. 1 Maxwell’s equations and conventional classical electromagnetic theory - p. 3 10. 2 Polarization in a static electric field - p. 35 11. Abstract - p. 35 12. 2.1 Electrostatic field and potential of a uniformly polarized homogeneous sphere in an infinite dielectric - p. 38 13. 2.2 Onsager derivation for the polarizability of a spherical homogeneous particle - p. 44 14. 2.3 Homogeneous polarizable ellipsoid in a uniform external electric field - p. 47 15. 2.4 Clausius-Mossotti relationship, Lorentz’s method for the treatment of dipolar interaction, and the local field representation - p. 56 16. References - p. 61 17. 3 Polarization and permittivity in an alternating electric field - p. 65 18. Abstract - p. 65 19. 3.1 Harmonic time dependence - p. 67 20. 3.2 Drude-Lorentz model and frequency-dependent electronic (ionic) polarizability - p. 71 21. 3.3 Frequency-dependent orientation polarizability - p. 75 22. 3.4 Frequency-dependent permittivity due to interfacial polarization (Maxwell-Wagner-Sillars) effects - p. 79 23. 3.5 Summary of frequency-dependent dielectric responses - p. 82 24. 3.6 Causality relationships between the real and imaginary parts of the permittivity of passive materials - p. 84 25. 3.7 Some considerations on the deviations from the Debye model of dielectric relaxation - p. 87 26. References - p. 91 27. Part Two: Analytical approaches - p. 94 28. 4 Prelude: A historical examination - p. 97 29. 5 Some preliminary definitions and considerations - p. 137 30. 6 Mixing laws for two-phase composite media - p. 153 31. 7 Effective medium approximation: Its basis and formulation - p. 165 32. Abstract - p. 165 33. 7.1 Exact results - p. 170 34. 7.2 Bruggeman effective equation - p. 173 35. 7.3 Virial series - p. 177 36. 7.4 Landau and Lifshitz analysis - p. 179 37. 7.5 McLachlan’s generalized effective media (GEM) equation - p. 181 38. 7.6 Bergman-Milton spectral representation of the effective permittivity - p. 183 39. 7.7 Multiple-scattering theory with infinite order perturbation summation - p. 187 40. 7.8 Iterated homogenization and differential effective medium theories - p. 190 41. 7.9 Asymptotic homogenization method and multiscale analysis - p. 192 42. References - p. 194 43. 8 Bounds for the homogenization of dielectric composite materials - p. 201 44. 9 Percolation: Crossing the great divide of bulk heterogeneous matter - p. 213 45. 10 Reciprocity relations and extensions - p. 237 46. Part Three: Computational approaches - p. 249 47. 11 Some preliminary considerations: The problem in context - p. 253 48. 12 Finite differences method - p. 257 49. 13 Finite-difference time-domain propagation - p. 263 50. 14 Finite element method - p. 279 51. 15 Integral equation approaches - p. 291 52. 16 Monte Carlo method - p. 305 53. 17 Other selected methods - p. 317 54. Appendix 1A Analogy between magnetism, thermal conduction, diffusion, flow in a porous medium, and electrostatics - p. 327 55. Appendix 1B Maxwell stress tensor and electrostatic force acting on an isolated body in an electric field - p. 331 56. Appendix 1C Electric dipole and polarizability - p. 337 57. Appendix 1D Solving Laplace’s equation for the CS spherical model - p. 345 58. Appendix 1E Electric modulus - p. 349 59. Appendix 1F Mie theory, quasistatic approximation, and discrete dipole approximation for calculating the optical properties of particles - p. 353 60. Appendix 2A Microstructure characterization and statistical descriptors - p. 361 61. Appendix 2B Equivalence between the definition of the effective permittivity using the average, Eq. (7.7), and the energy density, Eq. (7.10) - p. 365 62. Appendix 2C Selected mixing laws - p. 369 63. Appendix 2D Herglotz function and sum rules - p. 373 64. Appendix 2E Incremental MG formalism for homogenizing particulate composite media - p. 375 65. Index - p. 377
Electromagnetic Properties of Heterostructures: Background and Calculation Methods covers the fundamental aspects of the electromagnetic properties of heterostructures and the theoretical knowledge of the computational techniques needed to understand dielectric phenomena in quantitative and physical terms. The book re-establishes the conceptual foundations of the physics associated with numerical simulation tools of the Laplace or the Poisson equations and shows their immediate implementation. It is relevant for all practicing engineers and materials scientists who develop composite materials that are capable of handling specified technological requirements by utilizing their electromagnetic properties.
1. Electromagnetic Heterostructures - p. i 2. Cover image - p. i 3. Title page - p. i 4. Table of Contents - p. i 5. Copyright - p. iv 6. Preface - p. xi 7. Acknowledgments - p. xix 8. Part One: Elementary concepts and definitions - p. xix 9. 1 Maxwell’s equations and conventional classical electromagnetic theory - p. 3 10. 2 Polarization in a static electric field - p. 35 11. Abstract - p. 35 12. 2.1 Electrostatic field and potential of a uniformly polarized homogeneous sphere in an infinite dielectric - p. 38 13. 2.2 Onsager derivation for the polarizability of a spherical homogeneous particle - p. 44 14. 2.3 Homogeneous polarizable ellipsoid in a uniform external electric field - p. 47 15. 2.4 Clausius-Mossotti relationship, Lorentz’s method for the treatment of dipolar interaction, and the local field representation - p. 56 16. References - p. 61 17. 3 Polarization and permittivity in an alternating electric field - p. 65 18. Abstract - p. 65 19. 3.1 Harmonic time dependence - p. 67 20. 3.2 Drude-Lorentz model and frequency-dependent electronic (ionic) polarizability - p. 71 21. 3.3 Frequency-dependent orientation polarizability - p. 75 22. 3.4 Frequency-dependent permittivity due to interfacial polarization (Maxwell-Wagner-Sillars) effects - p. 79 23. 3.5 Summary of frequency-dependent dielectric responses - p. 82 24. 3.6 Causality relationships between the real and imaginary parts of the permittivity of passive materials - p. 84 25. 3.7 Some considerations on the deviations from the Debye model of dielectric relaxation - p. 87 26. References - p. 91 27. Part Two: Analytical approaches - p. 94 28. 4 Prelude: A historical examination - p. 97 29. 5 Some preliminary definitions and considerations - p. 137 30. 6 Mixing laws for two-phase composite media - p. 153 31. 7 Effective medium approximation: Its basis and formulation - p. 165 32. Abstract - p. 165 33. 7.1 Exact results - p. 170 34. 7.2 Bruggeman effective equation - p. 173 35. 7.3 Virial series - p. 177 36. 7.4 Landau and Lifshitz analysis - p. 179 37. 7.5 McLachlan’s generalized effective media (GEM) equation - p. 181 38. 7.6 Bergman-Milton spectral representation of the effective permittivity - p. 183 39. 7.7 Multiple-scattering theory with infinite order perturbation summation - p. 187 40. 7.8 Iterated homogenization and differential effective medium theories - p. 190 41. 7.9 Asymptotic homogenization method and multiscale analysis - p. 192 42. References - p. 194 43. 8 Bounds for the homogenization of dielectric composite materials - p. 201 44. 9 Percolation: Crossing the great divide of bulk heterogeneous matter - p. 213 45. 10 Reciprocity relations and extensions - p. 237 46. Part Three: Computational approaches - p. 249 47. 11 Some preliminary considerations: The problem in context - p. 253 48. 12 Finite differences method - p. 257 49. 13 Finite-difference time-domain propagation - p. 263 50. 14 Finite element method - p. 279 51. 15 Integral equation approaches - p. 291 52. 16 Monte Carlo method - p. 305 53. 17 Other selected methods - p. 317 54. Appendix 1A Analogy between magnetism, thermal conduction, diffusion, flow in a porous medium, and electrostatics - p. 327 55. Appendix 1B Maxwell stress tensor and electrostatic force acting on an isolated body in an electric field - p. 331 56. Appendix 1C Electric dipole and polarizability - p. 337 57. Appendix 1D Solving Laplace’s equation for the CS spherical model - p. 345 58. Appendix 1E Electric modulus - p. 349 59. Appendix 1F Mie theory, quasistatic approximation, and discrete dipole approximation for calculating the optical properties of particles - p. 353 60. Appendix 2A Microstructure characterization and statistical descriptors - p. 361 61. Appendix 2B Equivalence between the definition of the effective permittivity using the average, Eq. (7.7), and the energy density, Eq. (7.10) - p. 365 62. Appendix 2C Selected mixing laws - p. 369 63. Appendix 2D Herglotz function and sum rules - p. 373 64. Appendix 2E Incremental MG formalism for homogenizing particulate composite media - p. 375 65. Index - p. 377
