Arthur von Hippel

280 Pages·2008·45.91 MB·English

Dielectrics and Waves
Arthur von Hippel
Artech House
Boston. London
PREFACE TO THE SECOND EDITION
As a practicing engineer, I have used in my technical work the two-volume
von Hippel set as an indispensable reference for dielectric properties of materials.
When I realized that they were out of print, I sent copies of selected pages to
Artech House for evaluation with the recommendation that both volumes be re-
published for the benefit of other interested engineers. Several months later,
Artech House notified me that a decision had been made to republish, that the
rights to republish had been secr:red from the retired author, and that, as implau-
sible as it may seem, neither the previous publishers nor the author have any re-
maining copies of this set, as would be required for the republication process.
Therefore, I supplied the original editions to Artech House for reproduction. I
would like to thank the entire staff at Artech House for their professionalism in
the handling of this republication.
Huntinglon Beach, California Ar,pxnropR S. LABoITNSKY
August 1994 Principal engineer/scientist
McDonnell Douglas Aerospace
PREFACE TO THE FIRST EDITION
A treatise intended for physicists, chemists, and electrical engineers is likely
to disappoint three groups of readers. If an author, in spite of this danger, embarks
on such an adventure, intense compulsion must drive him. For a number of years
my demon has urged me to oppose the trend of specialization by helping to develop
a field of knowledge that belongs not only to physics and chemistry but is also of
vital importance for modern electrical engineering. We may call this subject "di-
electrics" by identifring with the name not a narrow class of so-called insulators,
but any nonmetal, and even metals as a boundary case, if their interaction with
electric, magnetic, or electromagnetic fields is under consideration. Dielectrics and
Waues has been chosen as the title of this book because wave phenomena play a
dominant part in our story, whether electromagnetic waves, probability waves of
quantum mechanics, or the elastic waves of crystal lattices.
The phenomena foolaization," tnagnetizatiort," and "conduction" are the
properties of matter at issue. For macroscopic physics and electrical engineering
this is a familiar subject when viewed from the standpoint of Maxwell's theory.
Matter appears here as a storage medium and wave gurde of electric and magnetic
energy and as a dissipator of such energy by conduction and other ineversible
processes. These properties are considered as given quantities that may be tabu-
lated by introducing some descriptive parameters, for example, the complex per-
mittivity and permeability used in this book. At this point the subject tnaterials"
vltl Pneface
is dismissed by the presentday eleclrical engineer in favor of his private world of
field vectors and equivalent circuits.
Ttre physicist and chenist have pushed on to the task of unraveling the mo-
lecular phenomena behind these macroscopic parameters. The structure and be-
havior of isolated atoms and molecules and the behavior of electrons and ions in
gases of low pressure are now relatively well understood; the dielectric properties
of gases at high pressures and of liquids and solids are still known only in rough
outlines. However, this task of "dielectric analysis" has progressed far enough to al-
low a successful beginning of "dielectric syntheses" in which the properties of materi-
als are tailored to order by combining the proper atoms and molecules into specified
arrangements.
This subject of dielectric synthesis is of vital importance to the electrical engr-
neer, promising him a variety of new tools and a release from shackling limita-
tions. Nobody, however, can leave his problens to others without losing control
over his destiny. Ttre electrical engineer has to remember that he is an applied sci-
entist and join his colleagues of physics and chemistry in a co-operative venture of
"molecular electrical engineering."
Seen from this point of view, I would want the book to be a tnrmpet of
Jericho; alas it may only loosen some bricks that will fall on the authot's head.
This is a surrrey book which carurot go into many important details and has to
leave unmentioned many significant contributions. Space does not permit to give
the molecular aspects of conduction more than a cursory glance. I hope to make
"Electric Conduction and Breakdown" the subject of a later volume.
To remedy some of these shortcomings a representative list of books covering
special fields has been added. Much additional information may also be found
in the companion book, Dielectric Materials and Applications, published simul-
taneously.
It is too much to hope that any reader will follow the unfolding of this biogra-
phy of dielectrics with t}ne puzzled attention nonnally reserved for a detective
story. But it may be of some help in bringtng physicists, chemists, and electrical
engineers closer together and provide a better understanding between the mode of
thinking of the theorist and the orperimentalist on dielectric problems.
In dedicating this book to Niels Bohr and James Franck I am fulfiUing a sim-
ple duty of gratitude to two masters of science who became my friends at decisive
junctures of my life and who have set, with their scientific genius and humanity,
an ideal for our generation.
C ambridg e, M os s achu sett s A. voN Hrpppr,
June 1954
ACKNOWLEDGMENTS
In writing a book, one accumulates a great amount of indebtedness. I owe
much to discussions with Professor J. C. Slater and with former and present co-
workers of our laboratory, especially Dr. S. C. Abraha,ms, Professor H. B. Callen,
M. E. Caspari, Professor D. J. Epstein, Dr. E. P. Gross, and'W. B. Westphal. My
co-workers Caspari and Epstein, together with our excellent draftsman, J. J. Mac-
carone, translated rough sketches into finished illustrations. Dr. L. G. Wesson
gave invaluable help, assisted by Mrs. H. B. Armstrong, Miss E. J. Busby, and
later by Miss A. Sils, in getting the book to the printer and seeing it through the
press. Dr. E. P. Gross worked with me in the preparation of the problem section;
Professor R. H. Cole read the major part of the manuscript in behalf of the pub-
lisher and made valuable comments. Dean F. G. Fasset, Jr., the director of the
Technology Press, which publishes the companion volume Dielectric Materials and,
Applicatio?as, gave helpful counsel.
The scientific work of the Laboratory for Insulation Research is supported
jointly by the ONR, the Army Signal Corps, and the Air Force under ONR Con-
tracts NSori-07801 and N5ori-07858. It is obvious that the book could not have
been written without this background of sponsored free researchl and it is a pleas-
ant duty to acknowledge gratefully the unfailing support of our sponsors in keep-
ing our research without restrictions and directed towards fundamental issues.
A number of figures have been adapted from publications of other authors as
indicated in the references. I am grateful to these colleagues and their publishers
for permission to use such rnaterial.
A. vox Hrpppr,
lx
CONTENTS
I . Macroscopic Approach 8 . The Structure of Atoms LL4
01 .. SCuormvepylex Permittivity and Permeability 31 190 .. AAttoommss iinn EMlaegctnreict icF iFeiledlsd;s S; tZaerekm Eanf fEecffte ct L12273
2 .Polarization and Magnetization 6 11 . The Energy Level Diagram of Atoms 131
3 . Coulomb and Dipole Fields 8 12 .Atoms in Electromagnetic Fields; the Dispersion
4 . Space-Charge Fields L2 Formula of Quantum Mechanics 135
5 . Correlations between Electric and Magnetic Phe- 13 . The Formation of Molecules 137
nomena 15 t4 . 'W'ave Functions of Molecules and the Concept of
6 . Maxwell's Field Equations 19 Quantum-Mechanical Resonance I4L
7 . Electromagnetic Waves in Unbounded Space 20 15 .Bond Energies and Dipole Moments of Diatomic
8 . Dimensions and Units 2l Molecules r44
I . Description of Dielectrics by Yarious Set"s of Pa- 16 . Static Dielectric Constants and Dipole Moments
rameters 26 of Polar Gases r48
10 . Forces 38 17 . Polyatomic Molecules 150
11 . Field Energy and Radiation 40 18 . Yibration and Rotation 155
12 . Polarized Radiation 43 19 .Electronic, Atomic, and Orientation Polarization
13 . Dipole Radiation 45 of Gas Molecules 161
14 . Boundary Conditions 48 20 . The Bandwidth of Spectral Lines 166
15 . Fresnel's Equations 50 21 . Microwave Spectroscopy 169
16 . Reflection and Refraction of Plane Waves by Loss- 22 . Pressure Broadening and Debye's Relaxation
17 . SFrtaened Diniegl eWctarivcess 5b3b 23 . TEhqe uMaotsioottni Catastrophe and the Local Field I17748
18 .Measurement of Dielectrics by Standing Waves; 24 . Formation and Structure of Liquids and Solids f81
fnterference Optics 58 25 . Various Models for the Discussion of Orientation
19 . Skin Efrect 61 Polarization in Liquids and Solids 187
20 . Reflection and Refraction by Media with Loss 64 26. Piezoelectricity 193
21 . Guided TV'aves 67 27. Dipole Moments, Piezoelectricity and Crystal
22 .Electromagnetic Fields in'W'ave Guides 69 Structure 198
23 .Measurement of Dielectrics in Shorted 'Wave 28. Ferroelectricity 202
Guides 73 29- Paramagnetism and Ferromagnetism 2L3
24 . Short-Circuited Guides and Cavity Resonators tt 30. Ferromagnetic Metals and Semiconductors 2Lg
25 . Treatment of Field Phenomena by Equivalent Cir- 31 . Inter{acial and SpaceCharge Polarization 228
cuits 82 32. Conduction and Breakdown 234
26 .Representation of Dielectrics by Lumped Circuit
Equivalents 86 Appendix
A . Problnms and Illustratiue Ernmples 253
II . Molecular Approach I . Macroscopic Approach 253
0.Survey 93 1 . Interrelation between the real and imag-
1 . Molecular Mechanisms of Polarization 95 inary part of the complex permittivity or
2 . The Clausius-Mosotti-Lorentz-Lorenz Equation 97 permeability 253
3 . Electronic Polarization 99 2 . Depolarization and demagnetization 254
4 . Anomalous Dispersion and Resonance Absorption 100 3 - Image dipole, image force, and electron
5 . Various Aspects of Electromagnetic Radiation t04 emlssron 254
6 . Bohr's Quantum Theory 108 4 . Wilson's bipolar thundercloud 256
7 . W'ave Mechanics il1 5 . Cyclotron and Betatron 256
-
t
xrl. Contents
6 . Maxwell's equations and the conservation 4 . The Kerr efrect 2M
of cha,rge 257 5 . The Faraday efrect 265
7 . Shrinkage of the wavelength of an electro- 6 .The ionic atmosphere in the Debye
magnetic wave in a semiconductor 258 Hiickel theory of strong electrol5rtes 266
8 . Dimensional analysis 28 7 . Dipole moments in polar liquids according
I . Macroscopic analysis of the frequency-re- to Onsager's theory 266
sponse characteristic of a ferrite 258 8 . The Franck-Condon principle 267
10 . Electric and magnetic balances 259 9 .Born's lattice theory and the compressi-
11 . Mass spectrographs 260 bility of ionic crystals 268
12 . The electromagnetic field energy and its 10 . The Born-Haber cycle 269
flow according to Maxwellts equations 260 11 . Electronic and heat conduction in metals
13 . Bouadary condition for the electric and according to the classical theory 270
magnetic flux densities 260 12 . Spacecharge-limited current flow 270
14 . Intederenee filters 26L
15 . Mierowave optics 26L B . El,srnmts of Veotnr Annlysis 27L
II . Molecular Approach 262 C . Vofups of PlWstnal Constfli,ts 273
1 . The Compton efrect 262
2 . Plasma reson&nce and dispersion of an D - Tablp ol Symbols 274
3 . e'Wleacvtero nfu ngacstions of the harmonic oscillator 262 E . Refermce List ol Booke ond Surnmartzing Artichs 276
in an electric field 263 Inder 279
I .MACROSCOPIC
APPROACH
oo Survey
In discussing electromagnetic waves and their inter- resonant circuits. Between meter and millimeter waves
action with dielectric materials, a comprehensive view the dimensions of the dielectric become comparable to
will be given without prejudice to the entrenched inter- those of the wavelength, the physical distinction be-
ests of the electrical engineer in the low-frequency range tween coil and condenser begins to disappear, and the
'We
or of the physicist in the optical spectrum. may material is customarily inserted into wave guides and
pretend that a dielectric can be exposed to electric or its characteristics are determined by standing-wave
UI
Rodio frequencies lnfrored vir Soft X roys
I Frequerygy in cycles per second
I I I
Scherins bridse
F H-f{,l ?it -,1 -tt$Sin+- rrovetins *oue -{ I
Detector
J.
ttnor a
generotor o{
Resonont circuit
Stonding wove Troveling wove
Fig. 0.1. Frequency ranges and measuring techniques.
magnetic fields of any frequencies by filling a capacitor patterns. As the wavelength shrinks further, we move
or a coil with the material in question and connecting out of this range of interference optics into that of geo-
it to a voltage source ranging in frequency from zero metrical optics and determine the dielectric properties
(direct current) to X-rays (=z 1018 cps). This Mun- of materials from infrared to ultraviolet by reflection
chausen device requires, of course, a number of equip- and transmission measurements. Finally, in the X-ray
ments for its practical realization (Fig. 0.1). region, we return once more to interference techniques
From direct cunent to about 108 cps a condenser or as the size of the atoms and the molecules and their sepa-
a coil represents a lumped circuit element; its proper- ration become comparable to the incident wave-length.
ties may be measured in the lower half of this range by This whole frequency spectrum is ruled by Maxwell's
bridge arrangements and at the higher frequencies in two field equations which describe quantitatively how
Macroscopic Approach
a time-varying electric field is accompanied by a time- analyzed in integral and differential formulation, and
varying magnetic field, and vice versa. Since both the divergence (V.Z') and the Laplacian (V2) are for-
fields may cause energy storage and energy dissipation mulated (Sec. 4).
in matter, two pairs of parameters are required to char- Thus far, electrieity and magnetism appear as two
acterize a dielectric as a carrier of electromagnetic new phenomena independent of each other and conse-
energy. quently requiring for their description the introduction
Various sets of such parameters have been introduced, of two new qua,ntities, an electric and a magnetic one,
depending on the specific interests of the observer. The for example, elnctric charge and magrutic dipole mommt.
scientist and the engineer concerned with the low- Actually, they are interlinked by Ampdre's circuital and
frequency range refer, in general, to permittivity (di- Faraday's induction law. The equivalence between the
electric constant) and permeability, and the communi- fields of magnetic dipoles and of circular currents allows
cation engineer to. the complex propagation factor; in us to attribute the existence of magnetic dipole moments
optics the complex index of refraction is used. Physi- to molecular currents and to reduce the dimensions of
cist and electrical engineer, allied in language through the magnetic quantities to electrical and mechanical
the advent of radar, rr&y, in addition, characterize a dimensions (Sec. 5). By extending Ampdre's and Fara-
dielectric by its complex impedance, and the chemist day's laws to all space, we obtain Maxwell's two field
may side with the power engineer in referring to dielec- equations; they can be written in complete symmetry
tric constant and power factor. (save for a negative sign) by the use of the complex
To establish order in this confusion of tongues, we permittivity and permeability (Sec. 6).
introduce, by lumped-circuit considerations, the com- From these field equations, the wave equations of the
plex permittivity e* and permeability p* as the funda- electromagnetic field are derived and solved for plane
mental parameters for the macroscopic description of a waves in unbounded space. A discussion of bhese waves
dielectric exposed to sinusoidal fields (Sec. 1) and then leads to the concepts complex propagation factor, wave-
proceed systematically in the development of the elec- length, phase velocity, and intrinsic impedance (Sec. 7).
tric and the magnetic field concepts. Herewith the prerequisites are at hand for a quantita-
The electrostatic field is due to the existence of posi- tive formulation of dimensions and units (Sec. 8) and
tive and negative charges. The total or true charge for the description of dielectrics by various sets of pa-
stored in a capacitor is only in part free to create an rameters, alternative to e* and tr"r*. Conversion formu-
external electric field; the remainder is bound by the las and nomographic charts are given in Sec. 9.
countercharges of the dielectric, that is, by polarization. After a short digression concerned with the forces op-
The true-, free-, and bound-charge densities are con- erative in electric and magnetic fields (Sec. 10), the
sidered to give rise to three vector fields, characterized energy of the electromaguetic field and its flow are con-
by the electric displacement D, the electric field strength sidered (Sec. 11). The state of polarization of a field is
E, and the polarizabion P, respectively. The field con- defined (Sec. 12), and the radiation emitted by an elec-
cept is extended throughout space by the definition tric dipole is calculated (Sec. 13). This extension of the
that the electric field strength is equivalent in magni- theory to light sources paves the way for a later dis-
tude and direction to the force per unit charge acting cussion of the dipole radiation of atoms and molecules.
on a detector charge. This dual role of E determines Electromagnetic fields are usually not observed in
the dimensions of the dielectric constant. After intro- free space, but within the confinement of boundaries.
duction of the electric dipole concept, the stage is set In fact, reflection and refraction of waves at boundaries
for a discussion of magnetic fields created by magnetic provide the essential means for measuring the interac-
dipoles. The magnetic field vectors, the magnetic flux tion between electromagnetic waves and dielectric ma-
density B, field strength H, and magnetization M be- terials. Boundary conditions are therefore introduced
come defined, and the dimensions of the magnetic dipole for static fields as well as for plane waves striking the
moment are determined by the torque equation (Sec. 2). interface between two media (Sec. 14). Snell's Iaws of
Formulating the potential concept, we arrive at Cou- reflection and refraction follow from the continuity of
lomb's law as a special case of the general force law for the tangential components of the E and H fields and
spherical symmetry and at the dipole field by the super- determine the direction of propagation of the reflected
position of the Coulomb fields of two opposite point and the refracted beams. Simultaneously, Fresnel's
charges. The differential operator V is introduced for equations are obtained which prescribe the amplitudes
the discussion of the potential gradient of the dipole of the reflected and the transmitted waves and their
field and of the general forces acting on a dipole in an states of polarization (Sec. 15). For dielectrics without
external field (Sec. 3). Next, space charge fields are loss, the phenomena of special interest are the disap-
Cornplex Perrnittivity and Perrneability
pearance of one pair of field components when the wave can be measured in such wave guides with great pre-
is reflected at Brewster's angle, and the occurrence of cision, whether by mapping with a traveling detector
total reflection accompanied by the formation of a the standing-wave pattern formed in front of the sample
guided surface wave with longitudinal components (Sec. (Sec. 23) or by evaluating the effect of the material on
16). At normal incidence, standing waves (Sec. 17) and the impedance of a cavity resonator (Sec. 24).
useful methods of measuring dielectric properties by Frequently it proves convenient to handle field phe-
interference (Sec. 18) result. nomena by an equivalence approach, in which the role
When electromagnetic waves strike a metal, nearly of the electric and the magnetic fields is assumed by
total reflection ensues, and the weak transmitted beam voltages and currents in electric circuits. By intro-
is rapidly attenuated (Sec. 19). The general case of ducing this complementarity we return to distributed
oblique incidence on media with loss is of great com- and lumped-circuit concepts (Sec. 25) and close the
plexity. The index of refraction becomes a function of macroscopic discussion with a formalistic representa-
the angle of incidence, and complicated phase shifts tion of dielectrics by lumped equivalent circuits (Sec.
arise because of the appearance of longitudinal field 26).
components (Sec. 20). Summarizing: Paft I of this book introduces the com-
Viewed from an alternative standpoint, the incident plex permittivity and permeability as the fundamental
w&ve, striking a boundary obliquely, forms, with the parameters, develops in rapid succession the essential
reflected wave, an interference pattern which glides field concepts, considers the propagation of electro-
along the interface with a phase velocity greater than magnetic waves in unbounded space and under suc-
that of the incident wave; the boundary acts as a wave cessively more stringent boundary conditions. In the
guide. To make such a guide more effective, a second course of this treatment we are logically led to alterna-
boundary may be placed parallel to the first one in one tive ways of describing the interaction between fields
of the dark interference fringes, and a parallel-plane and matter and to conversion formulas interlinking the
wave guide with cut-ofr properties results (Sec. 21). By various parameters. In addition to this quantitative
completing the enclosure we obtain hollow wave guides description of fields and dielectrics, the macroscopic
which behave like highly dispersive dielectrics and prop- theory provides a quantitative basis for measuring e*
agate characteristic wave types (Sec. 22). Dielectrics and pr*.
t Complex Permittivity and Permeability
A capacitor, connected to a sinusoidal voltage source and draws a charging current
U_ Tod" f (1.1) :# : :
I" iucs' Ior'("*t), (1.4)
of the angular frequency
a : 2ty (L.2) leading the voltage by a temporal phase angle of 90o
stores, when vacuum is its dielectric, a charge can forget this rotation in discussing their relative positions in
the complex plane.
Q - CoT, (1.3) 'We return from the complex functions to actual currents and
t Throughout this book we will use complex quantities in voltages by taking the real or the imaginary part: Re ('U) -
treating periodic phenomena and represent them in the complex Uo cos c,rl, Im (U) : Uo sin orJ. In dealing with products of com-
plane. Here the o-axis corresponds to the aris of reols and the plex functions it has to be kept in mind that the product of the
y-axis to the aris of imaginaries. The factor i : t/ -t n real parts of two complex quantities dr and dz is not equal to
front of a real quantity signifies an imaginary component ori- the real part of their product, but
ezn :t edr itn jtyhe p flyo-ttaexdi sin o rt h*eJ '-caoxmisp dleirxe pcltaionne . cAor rceosmpopnledxs qinu apnotiltayr Re (,4.f Re (.42) : L(At * A)(Az * Az).
caon-golerd din a: tetsa nto-l a(y r/ar)d ituosw avredcst othr ep r e: alt /a-xais?:l s o:z pinsice.lined by an AtT:h@e +sy mjbfoiel i,'4',.1th seignni fiAesr :t@he -c onjjuyg)ast-ei' t.of .A1; for example, if
seqTuheen tclyo mcpanle xb ef upnloctttieodn i7n) t:h eT Jcooemi'tp l:e xU pol(acnose ,ats *a ria sdiinu sa rvl)e ccoton-r The time average of a periodic function ,4. is E : * Io'O Or,
of length 1)s, the voltage amplitude, making an angle of col radians where ? is the period of the function. If ,4.r and Az are such
with the axis of reals. As long as the voltage and current vectors funetions, the product of the a,verages of their real parts is
rotoJ;e at the same angular velocity of ar radians per second, we Re (/il Re (dz) : I Re (AtAil.
Macroscopic Approach
(Fig. 1.1). Ce is the uaunwn (or geometrical) capaei'- the conductanee term need not stem from a migration
tance of the condenser. of charge carriers, but can represent any other energy-
'When filted with some substance, the condenser in- consuming process. It has therefore become customary
creases its capacitance to to refer to the existence of a loss eurrent in addition to
: z--, : a charging current noncommittally by the introduction
C Co Cox', (1.5) of a compler per-mittiuity
€O
€*:r'-jr"
(1.e)
where e' and es desiguate the real permitttiuities or dielec-
tric csnstnnds of the dielectric and of vacuum, respec- The total current .I of Eq. 1.7 may thus be rewritten
tively, and their ratio r' the relntiue dielectric constnnt of.
I^cos art 7 : (joxt * rr") C"" U : jaCsrc*'tJ, (1.10)
c0
where
tto sin ot - tc*=-€*:*'-j*" (1.1 1)
€0
is the compl,er relntiue permittiuitA of the material and
Fig. 1.1. Current-voltage relation in ideal capacitor
the material. Simultaneously, there may appear, in
addition to the charging current component 1", a loss
anrent component
It : GtJ (1.6)
in phase with the voltage; G represents the eonductance
of the dielectric. The total current traversing the con-
denser, A
I:1"*It:(jaC*G)t, (1.7)
I
oo
is inclined by a power factor angle d < 90o against the oc
applied voltage U, that is, by a Zoss angle D against the
Cotl
*J:axis (Fig. 1.2).
I"= jotCll log @+
Fig. 1.3. RC circuit and its frequency response.
e" and rc" the loss factor and relatiue loss factor, respec-
tively. The loss tangent becomes
e" K"
tan6:-:-. (1.12)
e' K'
et
Il"=
Since a parallel-plate condenser of the arca A and
Fig. 1.2. Capacitor containing dielectric with loss. the plate separation d, fringing effects neglected, has
the vacuum capacitance
It would be premature to conclude that the dielectric
material corresponds in its electrical behavior to a ca- Co: A (1.13)
pacitor paralleled by a resistor (RC circuit) (Fig. 1.3). iro,
The frequency response of this circuit, which can be
the current density J fiaversing a condenser under the
expressed by the ratio of loss current to charging cur-
rent, that is, the dissipation factor D or loss tangent applied field strength :,o/il
E (1.14)
tan D, as
It
D=tanf:-:-, 1 (1.8) becomes, according to Eq. 1.10,
I"
aRC
dE
S : (jae, * ac,,)E : ,* (1.15)
may not at all agree with that actually observed because A