Fundamentals of the Physics of Solids / 16-back-matter

Name Index

Abrikosov, A. A. 4

Anderson, P. W. 6, 199,

466, 585

Baker, H. F. 441

Bardeen, J. 3, 4

Becquerel, H. 52

Bednorz, J. G. 6 Berezinskii, V. L. 555 Bernal, J. D. 22 Bethe, H. 3, 564, 642 Binnig, G. 270 Blech, I. 3, 315

Bloch, F. 3, 65, 186, 509, 523, 528 Bogoliubov, N. N. 542

Born, M. 88, 185

Bose, S. N. 396 Bouckaert, L. P. 647 Bragg, W. H. 2, 241 Bragg, W. L. 2, 241, 242 Brattain, W. H. 4 Bravais, A. 113 Brillouin, L. 3, 123, 436 Brockhouse, B. N. 439

Buckminster Fuller see Fuller, R. Buckminster

Burgers, J. M. 285, 286

Cahn, J. W. 3, 315

Chandrasekhar, S. 24

Clausius, R. J. E. 375

Coleman, S. 201

Cooper, L. N. 4

Curie, M. 52

Curie, P.	52
Curl, R. F., Jr. 30
Darwin, C. G. 38, 259
Debye, P.		267, 389, 442
de Haas, J. W. 45
Dirac, P. A. M.				32, 37, 92, 464
Dorda, D.		6
Drude, P.		1
Dulong, P. L.				384
Dyson, F. J.			531
Dzyaloshinsky, I. E. 4
Eckart, C.		53
Einstein, A.		45, 387, 396
Escher, M. C.				115
Evjen, H. M.			84
Ewald, P. P.			84, 120, 259, 264
Faigel, G.		252
Faraday, M.		513
Fedorov, J. S.				166
Fermi, E.	71
Feynman, R. P.				532
Fibonacci		317
Frank, F. C. 290, 297
Frenkel, J.		283, 470
Friedel, G.		24
Friedrich, W.			2, 241
Fuller, R. Buckminster 29
Gerber, Ch.		270
Ghosh, D. K.			577
Ginzburg, V. L.				4

680 Name Index

Goldschmidt, V. M. 236

Goldstone, J. 200

Gorkov, L. P. 4

Gossard, A. C. 6

Gratias, D. 3, 315

Gri th, R. B. 497

Grüneisen, E. 419, 425

Gutzwiller, M. C. 5

Haldane, F. D. M. 579

Hausdor , F. 441

Haüy, R.-J. 109

Heisenberg, W. 3, 92, 464, 470

Heitler, W. 90

Hermann, C. 125

Higgs, P. W. 201

Holstein, T. 530

Hooke, R. 365

Hubbard, J. 5

Hund, F. 42, 96

Ising, E. 472

Jordan, P. 533

Josephson, B. D. 497

Kadano , L. P. 498

Kamerlingh Onnes, H. 2

Kármán, T. von			185
Kasuya, T.	466
Kerr, J. 513
Kittel, C.	465, 466
Klitzing, K. von			6
Knight, W. D.			72
Knipping, P.		2, 241
Kondo, J.	5
Korringa, J.		71
Kosterlitz, J. M.			555
Kramers, H. A. 64, 182, 466
Kronig, R.	64
Kroto, Sir H. W. 30
Lamé, G.	365
Landé, A.	54
Landau, L. D.			3, 28, 199, 489
Landsberg, G.			434
Langevin, P.		50, 53
Larmor, J.	50
Laue, M. von		2, 241
Laughlin, R. B.			6

Leggett, A. J. 4

Lehmann, O. 24

Lennard-Jones, J. E. 81, 97

Lenz, W. 472

Lieb, E. 578

Lifshitz, E. M. 200

Lindemann, F. A. 413

London, F. 78, 90

Lorentz, H. A. 2, 374, 375

Lorenz, L. V. 375

Lyddane, R. H. 377

Madelung, E. 84

Majumdar, C. K. 577

Maleev, S. V. 531

Mandelstam, F. 434

Mattis, D. C. 578

Mauguin, C.-V. 125

Mayer, J. E. 88

Mermin, N. D. 411

Miller, W. H. 119

Mössbauer, R. L. 72

Mossotti, O.-F. 375

Mott, N. F. 6

Müller, K. A. 6

Mulliken, R. S. 96

Néel, L. 453, 461, 509

Noether, E. 191

Orowan, E. 285

Pauli, W. 3 Pauling, L. C. 236

Peierls, R. E. 3, 28, 193 Penrose, R. 323 Pepper, M. 6

Petit, A. T. 384

Pisano, L. see Fibonacci Planck, M. 387

Polányi, M. 285 Primako , H. 530 Purcell, E. M. 65

Quate, C. F. 270

Racah, G. 672

Raman, C. V. 434

Rashba, E. I. 38

Reinitzer, F. 24

Rohrer, H. 270

Ruderman, M. A. 465, 466

Rushbrook, G. S. 497

Russell, H. N. 40

Sachs, R. G. 377 Saunders, F. A. 40 Scherrer, P. 267 Schoenflies, A. M. 125, 166 Schrie er, J. R. 4 Schrödinger, E. 32 Schultz, T. D. 578 Schwinger, J. 532

Seitz, F. 3, 117, 157

Shechtman, D. 3, 315

Shockley, W. B. 4, 295

Shubnikov, A. V. 167 Shull, C. G. 439

Sklodowska, M. see Curie, M. Slater, J. C. 3, 101

Smalley, R. E. 30 Smoluchowski, R. 647 Sommerfeld, A. 3 Störmer, H. L. 6

Taylor, G. I. 285

Tegze, M. 252

			Name Index	681
Teller, E. P.		377
Thomson, J. J.			1
Thouless, D. J.			555
Tomonaga, S.			532
Tsui, D. C.		6
van der Waals, J. D. 78
Van Hove, L. 406, 656
Van Vleck, J. H. 6, 60
Voigt, W.		368
Volterra, V.		284
Voronoi, G.		117
Wagner, H.		411
Waller, I.	442
Weiss, Ch. S.			119
Weiss, P.	474
Widom, B.		498
Wigner, E. P.			3, 53, 117, 172, 533, 647
Wilson, A. H.			3
Wilson, K. G.			500
Yosida, K.		466
Zeeman, P.		2
Zener, C.	468

Subject Index

4-methoxy-benzilidene-4-butyl-aniline 24

A1 structure	204, 217
A15 structure	204, 209
A2 structure	204, 213
A3 structure	204, 226
A3 structure	204, 226
A4 structure	204, 221
A8 structure	204, 231, 232
A9 structure	204, 234

absorption edge	269
acoustic branch	343
acoustic vibrations 340, 360–361
actinoids 179, 218

AFM see atomic force microscope

Ah structure	204, 207
AlFe3 structure 220
alkali halides	76, 83, 219, 282
alkali metals	213
alkaline-earth metals 213, 218

almost periodic functions 311

amorphous materials		21, 303
angular frequency 339
angular momentum		665–672
anharmonicity	421
anisotropy
constant	507

magnetic 471–473, 504–513 annihilation operator

of antiferromagnetic magnon 542 of magnon 525

of phonon 394–395

anomalous dimension			499
antibonding state		98
antiferromagnetic ground state					see
ground state, of antiferromagnet
antiferromagnetic materials				453–459
antiferromagnetic ordering
Néel type
absence of in one-dimensional
systems	551
presence of in two-dimensional
systems	551
antiferromagnetism		453–459
in the Heisenberg model				464
antiferromagnon see			magnons,
antiferromagnetic
antiperiodic boundary conditions					see
boundary conditions, antiperiodic
antiphase boundary		300, 301
antiphase domains		301
antisite defects	283
anti-Stokes component			434
antiunitary operator			182
atomic force microscope 270
atomic form factor		249
atomic packing factor			see	packing
fraction
B1 structure	204, 219
B2 structure	204, 207, 208
B3 structure	204, 221
B4 structure	204, 228
B8 structure	204, 227, 228
Baker–Hausdor formula				441
basis 114

684	Subject Index
BCS theory			4
benzene-hexa-n-alkanoate 24
Berezinskii–Kosterlitz–Thouless
	phase		556
Berezinskii–Kosterlitz–Thouless
	transition				555
critical exponent in							see critical
	exponent, in Berezinskii–
	Kosterlitz–Thouless transition
Bernal model				22, 23, 304
Bernoulli numbers						618
Bessel functions					620
Bethe ansatz				564–566
biaxial nematic phase							26
BiF3 structure					220
bipartite lattice					520
BKT phase			see Berezinskii–
	Kosterlitz–Thouless phase
black-and-white group							167
black-and-white lattice							167
Bloch equations					65
Bloch T 3/2 law					528
corrections to					529
Bloch’s theorem					186
Bloch wall			509
body-centered cubic structures
	210–214
Bogoliubov transformation
application of					546
for antiferromagnets							542
Bohr magneton					44, 588
Bohr radius			50, 588
bonding state					98
Born–Mayer approximation								88
Born–von Kármán boundary condi-
	tion	see		boundary conditions,
	Born–von Kármán
Bose–Einstein statistics							396
boundary conditions
antiperiodic					186
Born–von Kármán						185, 186, 338
twisted		186
Bragg condition					243
Bragg peaks			243
shape of			252
temperature dependence of								443–444
Bragg plane			245
Bravais cell			117, 118, 144
Bravais group					140

Bravais lattices				113
types in three dimensions							141,
146–154
types in two dimensions							140,
142–145
Brillouin function				57
Brillouin scattering					436–437
Brillouin zone			123, 190
of bcc lattice				212
of fcc lattice			216
size of, in antiferromagnets							519
buckyball	30
bulk defects see volume defects
bulk modulus			365, 369
bulk susceptibility					see
susceptibility, volume
Burgers circuit			286, 287
Burgers dislocation
see screw dislocation
Burgers vector			286, 287
C1 structure			204, 219
C14 structure			204
C15 structure			204, 223
C1b structure			223
C2 structure			204
C3 structure			204, 209, 210
C4 structure			204
calamitic nematic phase						25
Cauchy relations				369
ccp structure see cubic crystal
structures, close-packed
center-of-mass order					19
cesium chloride
Madelung energy of 87
structure		204, 207
chain-like structures					229–233
character table
of Oh group			648
of the double group O†						648
chemical shift			72
chiral nematic			phase
see cholesteric phase
cholesteric phase				26
Clausius–Mossotti relation						375
Clebsch–Gordan coe cients							671
close packing
cubic	217
hexagonal		226

closure domains			511
coherent scattering				439–443
cohesive energy			77
of covalent crystals					105
of ionic crystals				84
of molecular crystals						81–83
coincident-site lattice					299, 300
Coleman’s theorem				201, 411
color center		282
color group
black-and-white 167
gray	167
columnar phase			28
compatibility condition						639
compressibility			365
compressional waves 366
compression		modulus
see bulk modulus
condensed phases				13
configurational entropy						276
configuration interaction						100
constant
sti ness see sti ness constant
continuous groups				642–646
conventional unit cell					117, 144
coordination number					208
correlation function				16
correlation length				494–496
coupling
jj	40
LS	40
Russell–Saunders				40
covalent bond 89–105
covalent crystal			89
covalent radius			233
creation operator
of antiferromagnetic magnon 542
of magnon		525
of phonon		394–395
critical exponent			491, 496–500
in Berezinskii–Kosterlitz–Thouless
transition			555
critical temperature
of antiferromagnets					481
of ferrimagnets				461
of ferromagnets				475
cross section		653–656
of coherent scattering						439–443
crowdion 280

			Subject Index					685
crystal class	162
crystal family			141
crystal field	174
crystal-field splitting					174
crystal momentum					189
crystal structure
types of	203
crystal systems			140
hierarchy	of,		in	three
dimensions				156
hierarchy of, in two dimensions								155
crystallite	21
CsCl structure			208, 237
Cu structure		217
Cu3Au structure				204, 208
CuAu structure			300
cubic crystal structures						205–224
body-centered				210–214
close-packed			217
face-centered			214–221
simple 205–210
cubic lattice	153
cuprite structure				204, 210
Curie’s law	52
deviation from				182
Curie susceptibility					53
Curie temperature				450, 475
of ferrimagnetic materials							461
of ferromagnetic materials							451–453
Curie–Weiss law				476
cyclic group	130
D0 structure		204
D03 structure			220
D09 structure			209
D2 structure		204
D21 structure			209
D23 structure			221
D2e structure			209
D2f structure			220
D8 structure		204
dangling bonds			305
Debye frequency				401
Debye function			416, 611
Debye model		389–390
Debye–Scherrer method						267
Debye temperature					412, 596
Debye–Waller factor					442

686	Subject Index
defects see also line defects; pla-
	nar defects; point defects;
	volume defects
dislocations			283–292
grain boundaries 298
degeneracy
accidental			173
lifting of		173
delta function			615
dense random packing model 304
density of states
integrated			399
of phonons			398–409
destruction		operator
	see annihilation operator

dhcp structure see hexagonal crystal structures, double close-packed

diamond structure		204, 221–224
di raction
dynamical theory of 258–260
theory of 242–260
digamma function		619
dihedral group	130
dimerized chain	337, 345–348

dipole–dipole interaction 70, 80, 463, 661

Dirac delta function 615

direct	exchange
see exchange, Heisenberg
direct lattice			122
director		25
Dirichlet’s construction				117
in reciprocal lattice				123
disclinations			290
screw		291
wedge		291
discotic columnar phase				28
discotic nematic phase				25, 26
dislocation line 284
dislocations			283–292
edge	284, 285
mixed		285, 286
partial
Frank		297
Shockley			295
screw		285
dispersion relation

for antiferromagnetic magnons 520, 543

for ferromagnetic magnons 518, 524

for phonons		395
for spinons
in an isotropic
antiferromagnet 571
for XY model		573
distribution function
Bose–Einstein		see
Bose–Einstein statistics
divacancy	280
domain wall	504
width of	511
domains 508–513
double exchange		468–469
double group 179, 641–642

double hexagonal close-packed structure see hexagonal crystal structures, double close-packed

Drude–Lorentz model			2
Dulong–Petit law		384
dynamical interactions			534
dynamical matrix		356
dynamical structure factor				440, 659
Dyson–Maleev transformation					531
and the Hamiltonian of interacting
magnons	534
E2 structure	204
E21 structure	209
easy axis of magnetization				472
easy plane of magnetization				472
edge dislocation		284, 285
e ective magnetic moment				58
e ective magneton number				58
Einstein model	387–389
elastic constants
Lamé see Lamé constants
of crystals	367–371
Voigt see Voigt elastic constants
elastic waves	363–367
electron paramagnetic resonance					61
electron–phonon interaction				193
electron spin resonance			61
elementary excitations
in magnetic systems			515
phonons see phonons
entropy
of vortices in XY model				554
EPR 61

equation of state
for crystal		418–420
equipartition theorem					384
equivalent wave vectors					190
ESR 61
Euler’s constant			see Euler–Mascheroni
constant
Euler’s equation			510
Euler’s gamma function					619
Euler–Lagrange equation 359
Euler–Mascheroni constant						620
Evjen’s method			84
Ewald construction				264–265
for Laue method				266
for powder method					268
for rotating-crystal method						267
Ewald’s method			84
Madelung energy of NaCl crystal 86
Ewald sphere		264
EXAFS	269, 309
exchange	463
direct	see exchange, Heisenberg
double	see double exchange
Heisenberg		463–464
RKKY	see RKKY interaction
super-	see superexchange
exchange energy			464
exchange integral			92
exchange interaction				42
extinction length			263
F -center	282
face-centered cubic structures						214–221
factorial function			619

faithful representation of point groups

130
Faraday e ect	513
Fermi contact term 71, 661
Fermi integral	612
Fermi pseudopotential		247, 439
ferrimagnetic materials		461–462
ferrimagnetism	461, 462
ferromagnetic materials		450–453
ferromagnetism	450–453, 470
Fibonacci chain	317–323
fine structure	40
of paramagnetic resonance 68
fine-structure constant		36

	Subject Index	687
first theorem of condensed-matter
physics	199
fixed point	502

flip-over process see umklapp process Floquet’s theorem 186 fluctuation–dissipation theorem 52

fluorite structure	204, 219
flux quantum 587
Fourier transform	601
Frank partial dislocation		297
free energy
of vortices in XY model		555

free enthalpy see Gibbs free energy

Frenkel defect		283
Fresnel’s equations			259
fullerene	30, 76
fullerite	30, 221
infrared absorption in				432
Raman scattering in				435
g-factor	45
gamma function		619
γ-selenium structure			204

gap

in magnon spectrum for antiferro-

magnets 546
Gaussian function
Fourier transform of		609
Gaussian system of units		590
Gell-Mann matrices	646
Gibbs free energy	277

Gibbs potential see Gibbs free energy

glass	21
metallic		see metallic glass
spin	see spin glass
glide line 158
glide plane		158
glide reflection 158
Goldstone bosons			200, 397
Goldstone’s theorem				200, 397, 546, 547
grain boundaries			293, 298
tilt	298
twist	298
graphite structure			204
gray groups		168
Gri ths inequality			497
ground state
of antiferromagnet				543–544
and the Néel state				543–544, 568

688	Subject Index
of crystal lattice			410–413
of ferromagnet			522
group theory		633–651
Grüneisen parameter				419
Grüneisen relation			425
gyromagnetic ratio			45
H1 structure		204
H11 structure		223
Haldane gap		579
half-Heusler structure				223
Hall e ect
quantum 6
Hamiltonian
of interacting magnons					534
Hankel functions			620
harmonic approximation					331–337
harmonic oscillator			392–393
Hartree energy		588
Hartree–Fock approximation 96

hcp structure see hexagonal crystal

structures, close-packed
Heaviside step function			608, 616
HEED 262
Heisenberg chain
anisotropic ferromagnetic
spin-1/2	560–566
antiferromagnetic
spin-1 578–580
spin-1/2	566–569
Heisenberg exchange			see exchange,
Heisenberg
Heisenberg model		469
Hamiltonian
eigenstates of		521–522, 526–527,
538, 540
quadratic and quartic parts
534–535
Heitler–London approximation 90
Helmholtz free energy			278
of phonon gas		414
Hermann–Mauguin symbols				125
Hermite polynomials			623
heteropolar bond		83
Heusler alloy see Heusler phase
Heusler phase	204, 220
hexa-n-alkoxy triphenylene				24
hexagonal crystal structures				224–229
close-packed	204, 224, 226

double close-packed					224, 226
simple	224
hexatic phase		28
Higgs bosons		201
high-temperature expansion						503–504
HMTTF-TCNQ			232
Holstein–Primako
transformation					530
and the Hamiltonian of interacting
magnons			534
application of			534, 546
homeopolar bond				89
homopolar bond			89
honeycomb lattice				113, 114
Hooke’s law		365, 368
Hubbard model			5
Hund’s rules		42
hybrid states		103–105, 233
hydrogen bond			106
hyperfine structure				69
icosahedral group				131
ideal crystal		14, 109
improper rotation				126
incoherent scattering					660
incommensurate structures						312
magnetic		see spiral structures
indirect	exchange			see
RKKY interaction
inelastic neutron scattering						see
neutron scattering, inelastic, 547
infrared absorption				431–433
infrared active mode					432
integrated density of states						399
interaction
electron–phonon				193
phonon–phonon				423–424
interfacial defects				274
international notation					see Hermann–
Mauguin symbols
interstitials		278–280
split	279
inversion	126
ionic bond 83
ionic–covalent bond				94
ionic crystals		83–89
optical vibrations in					373–377
ionic radius		236
irreducible representations						637

Ising model	472
and Mermin–Wagner theorem						551
two-dimensional			551
isomer shift	73
jj coupling	40
Jones symbol 130
Jordan–Wigner transformation						533
application of		572
Josephson constant			587
Josephson inequality				497, 499
junction transistor			4
kagome lattice		113, 114
Kerr e ect	513
kinematical interaction					536
Knight shift	72
Kondo e ect	5
Korringa law	71
Korringa relaxation			71
Kosterlitz–Thouless transition						see
Berezinskii–Kosterlitz–Thouless
transition
Kramers–Kronig relation					64
Kramers’ theorem			182
L1 structure	204, 207
L2 structure	204
L 3 structure	204
ladder operator		393
Lagrange’s equation				34, 359
Laguerre polynomials				624
Lamé constants		365
Landé g-factor		54
Landau–Peierls instability 28, 201
Landau theory of phase transitions
199, 489–492
Langevin diamagnetism					see Larmor
diamagnetism
Langevin function			57
Langevin susceptibility					53
lanthanoids	179, 218
Larmor diamagnetism				49
Larmor frequency			50
lattice parameters			229
lattice vibrations
classical description of					331–385
Einstein model			387–389
quantum description of					387–427

		Subject Index		689
lattices that are not Bravais lattices
113, 114
Laue condition		194, 244, 245
Laue method		265
Laves phase	204, 223
layered structures 229–233
LCAO method		97
LEED 262
Legendre polynomials 625
Lennard-Jones potential			81
level splitting in crystals			173–182
Lie groups	643

Lieb–Schultz–Mattis theorem							578, 582
lifetime
of magnons		536, 548
of phonons		424
Lindemann criterion				413
line defects	274, 283–292
linear chain
diatomic	341–345
dimerized		345–348
monatomic		337–341
liquid crystals		24–29
liquid phase		22–23
localized excitations
lattice vibrations				377–383
long-range order			14
longitudinal vibrations					341
Lorentz formula			374
Lorentz–Lorenz equation						375
Lorentzian function
Fourier transform of					609
low-angle grain boundary						298
low-dimensional			magnetic
systems		548f
LS coupling		40
Lyddane–Sachs–Teller relation							377
M -center	282
Madelung constant				87
Madelung energy			84
magnetic force microscope						513
magnetic form factor				249
magnetic group			see	color group,

black-and-white

magnetic lattice see black-and-white lattice

magnetic space groups see space groups, black and white