Technology management assessment procedure : a guide for supporting technology management in business

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The book discusses homogenisation principles and mixing rules for the determination of the macroscopic dielectric and magnetic properties of different types of media. The effects of structure and anisotropy are discussed in detail, as well as mixtures involving chiral and nonlinear materials. High frequency scattering phenomena and dispersive properties are also discussed.

The book includes analysis of special phenomena that the mixing process can cause, such as the difference in character between a mixture and its constituent parts. Mixing results are applied to different materials in geophysics and biology. Reference is also made to the historical perspectives of dielectric modelling. Examples are included throughout the text.

Aimed at students with research interests in electromagnetics or materials science, the book is also useful as a textbook in universities, as a handbook of mixing principles, and as a sourcebook for composite material design.

Author Notes

Ari Sihvola is Professor of Electromagnetics at Helsinki University of Technology He is Vice-Chairman of the Finnish National Committee of URSI (International Union of Radio Science) and served as the Secretary of the 22nd European Microwave Conference, held in August 1992, in Espoo, Finland. Ari received the degrees of Diploma Engineer in 1981, Licentiate of Technology in 1984 and Doctor of Technology in 1987, all in Electrical Engineering, from the Helsinki University of Technology, Finland. Besides working for HUT and the Academy of Finland, he was visiting engineer at the Research Laboratory of Electronics of the Massachusetts Institute of Technology in 1985-1986, and a visiting scientist at Pennsylvania State University in 1990-1991. In 1996, he was visiting scientist at Lund University, Sweden.

Preface	p. xi
1 Introduction	p. 1
1.1 The philosophy of homogenisation of mixtures	p. 1
1.2 Historical background	p. 5
1.3 Literature	p. 9
1.4 Outline of the book	p. 11
References	p. 12
I To observe the pattern: Classical and neoclassical mixing	p. 17
2 Physics behind the dielectric constant	p. 19
2.1 Polarisation phenomena in matter	p. 19
2.2 Conduction and complex permittivity	p. 23
2.2.1 Field relations	p. 23
2.2.2 Time-harmonic fields	p. 25
2.2.3 Dispersion	p. 26
2.2.4 Complex resistivity	p. 28
2.3 Higher-order polarisation mechanisms	p. 29
2.3.1 Anisotropy and multipole moments	p. 29
2.3.2 Magnetic polarisation	p. 30
2.3.3 Other polarisation effects	p. 32
Problems	p. 35
References	p. 36
3 Classical mixing approach	p. 39
3.1 Average fields and Maxwell Garnett rule	p. 40
3.2 Polarisability of dielectric sphere	p. 41
3.2.1 Polarisability and dipole moment	p. 41
3.2.2 Consistency of the field solutions	p. 42
3.2.3 Dipole moment as solution for the external problem	p. 44
3.3 Mixture with spherical inclusions	p. 45
3.3.1 Clausius-Mossotti formula	p. 45
3.3.2 Maxwell Garnett mixing rule	p. 47
3.3.3 Q[subscript 2] function for mixture analysis	p. 49
3.4 Discussion on basic field concepts	p. 51
3.4.1 Macroscopic and microscopic fields	p. 52
3.4.2 Shape of the cavity in a crystal	p. 55
3.4.3 The internal dipoles	p. 56
3.4.4 Alternative routes to Maxwell Garnett formula	p. 57
Problems	p. 58
References	p. 59
4 Advanced mixing principles	p. 61
4.1 Multiphase mixtures	p. 61
4.2 Ellipsoidal inclusions	p. 63
4.2.1 Depolarisation factors	p. 63
4.2.2 Polarisability components of an ellipsoid	p. 66
4.2.3 Aligned orientation	p. 67
4.2.4 Random orientation	p. 68
4.2.5 Orientation distribution	p. 70
4.3 Inhomogeneous inclusions	p. 71
4.3.1 Polarisability of a layered sphere	p. 72
4.3.2 Continuously inhomogeneous inclusions	p. 75
4.3.3 Nonhomogeneous ellipsoids	p. 78
4.4 Lossy materials	p. 79
Problems	p. 82
References	p. 84
5 Anisotropic mixtures	p. 85
5.1 Anisotropy in dielectric materials	p. 85
5.2 Elementary dyadic analysis	p. 88
5.2.1 Notation and definitions	p. 88
5.2.2 Operations and invariants	p. 90
5.2.3 Examples	p. 93
5.3 Polarisability of anisotropic sphere	p. 94
5.3.1 Reinterpretation of scalar polarisability	p. 94
5.3.2 Depolarisation and the shape effect	p. 97
5.4 Mixtures with anisotropic inclusions	p. 101
5.5 Mixtures with anisotropic background medium	p. 102
5.5.1 Affine transformation	p. 102
5.5.2 Internal field and polarisability	p. 103
5.5.3 Homogenisation	p. 105
Problems	p. 107
References	p. 110
6 Chiral and bi-anisotropic mixtures	p. 113
6.1 Bi-anisotropic materials	p. 113
6.1.1 Bi-anisotropic constitutive relations	p. 114
6.1.2 Dissipation and reciprocity	p. 115
6.1.3 Renormalisation of field quantities	p. 116
6.2 Six-vector algebra	p. 117
6.3 Chiral mixtures	p. 119
6.3.1 Chiral and bi-isotropic materials	p. 119
6.3.2 Polarisability of chiral sphere	p. 121
6.3.3 Chiral Maxwell Garnett mixing formula	p. 122
6.3.4 Example: a racemic mixture	p. 123
6.4 Bi-anisotropic mixtures	p. 125
6.4.1 Polarisability of a bi-anisotropic sphere	p. 126
6.4.2 Bi-anisotropic mixing rules	p. 126
Problems	p. 127
References	p. 128
7 Nonlinear mixtures	p. 131
7.1 The characterisation of nonlinearity	p. 131
7.1.1 Examples of nonlinear mechanisms in matter	p. 131
7.1.2 Nonlinear susceptibilities	p. 133
7.1.3 Quadratic and cubic nonlinearities	p. 135
7.2 Mixing rules for nonlinear materials	p. 136
7.2.1 Polarisability components for a nonlinear sphere	p. 136
7.2.2 Dilute mixtures	p. 138
7.2.3 Towards denser mixtures	p. 139
7.2.4 Nonlinearity as perturbation to permittivity	p. 140
7.3 Characteristics of nonlinear mixtures	p. 141
Problems	p. 142
References	p. 143
II To transgress the pattern: Functionalistic and modernist mixing	p. 145
8 Difficulties and uncertainties in classical mixing	p. 147
8.1 Weak links in the mixing rule derivation	p. 148
8.1.1 Interaction between the scatterers	p. 148
8.1.2 Quasi-static approximation	p. 150
8.1.3 Correlation length	p. 151
8.2 Limits for the effective permittivity	p. 151
8.2.1 General bounds	p. 152
8.2.2 Hashin-Shtrikman bounds	p. 153
8.2.3 Higher-order bounds	p. 156
8.2.4 Anisotropic bounds	p. 156
Problems	p. 157
References	p. 158
9 Generalised mixing rules	p. 161
9.1 Bruggeman formula	p. 161
9.2 Coherent potential formula	p. 163
9.3 Unified mixing rule	p. 164
9.3.1 Spherical inclusions	p. 164
9.3.2 Ellipsoidal inclusions	p. 164
9.4 Other mixing models	p. 166
9.4.1 Power-law models	p. 166
9.4.2 Differential mixing models	p. 167
9.4.3 Periodical lattice models	p. 168
9.4.4 Random medium model	p. 169
9.5 Chiral and bi-anisotropic mixtures	p. 169
9.6 Numerical approaches for homogenisation	p. 170
Problems	p. 172
References	p. 174
10 Towards higher frequencies	p. 177
10.1 Rayleigh scattering contribution	p. 178
10.1.1 Rayleigh scattering of a single inclusion	p. 178
10.1.2 Rayleigh attenuation	p. 181
10.2 Mie scattering	p. 184
10.3 Scattering in random media	p. 188
10.3.1 Quasi-crystalline approximation	p. 188
10.3.2 Size-dependent polarisability approach	p. 189
Problems	p. 191
References	p. 192
11 Dispersion and time-domain analysis	p. 195
11.1 Constitutive relations as operators	p. 196
11.2 Susceptibility models	p. 198
11.2.1 Debye model	p. 198
11.2.2 Lorentz model	p. 200
11.2.3 Drude model	p. 201
11.2.4 Modified Debye model	p. 202
11.2.5 Other susceptibility models	p. 203
11.3 Mixing in time domain	p. 203
11.3.1 Quasi-static time-domain fields	p. 204
11.3.2 Deconvolution of kernels	p. 205
11.3.3 A mixture of two Debye materials	p. 206
11.4 Temporal dispersion in anisotropic and chiral materials	p. 208
Problems	p. 212
References	p. 213
12 Special phenomena caused by mixing	p. 215
12.1 Dispersion of the permittivity of mixtures	p. 215
12.1.1 Water and polar molecules	p. 215
12.1.2 Metals and Drude dispersion	p. 218
12.2 Polarisation enhancement	p. 219
12.2.1 Mossotti catastrophe	p. 220
12.2.2 Onsager model	p. 222
12.2.3 Single scattering and Frohlich modes	p. 223
12.3 Percolation	p. 226
12.3.1 Generalised mixing rule	p. 226
12.3.2 Effect of spatial dimension	p. 228
Problems	p. 232
References	p. 232
13 Applications to natural materials	p. 235
13.1 Water and ice	p. 235
13.1.1 Free and bound water	p. 235
13.1.2 Ice	p. 237
13.2 Snow	p. 239
13.2.1 Dry snow	p. 239
13.2.2 Wet snow	p. 242
13.3 Rocks and soil	p. 244
13.3.1 Porous bedrock	p. 245
13.3.2 Soil	p. 247
13.4 Rain attenuation	p. 249
13.5 Wood, trees, and canopies	p. 252
13.6 Biological tissues	p. 254
Problems	p. 257
References	p. 258
14 Concluding remarks	p. 261
Appendixes	p. 265
A Collection of dyadic relations	p. 265
B Collection of basic mixing rules	p. 267
Index	p. 271

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