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Altmann S.L. — Band Theory of Solids: An Introduction from the Point of View of Symmetry
Altmann S.L. — Band Theory of Solids: An Introduction from the Point of View of Symmetry



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Название: Band Theory of Solids: An Introduction from the Point of View of Symmetry

Автор: Altmann S.L.

Аннотация:

The structure of much of solid-state theory comes directly from group theory, but until now there has been no elementary introduction to the band theory of solids using this approach. Employing the most basic of group theoretical ideas, and emphasizing the significance of symmetry in determining many of the essential concepts, this is the only book to provide such an introduction. Many topics were chosen with the needs of chemists in mind, and numerous problems are included to enable the reader to apply the major ideas and to complete some parts of the treatment. Physical scientists will also find this a valuable introduction to the field.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 304

Добавлена в каталог: 08.11.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C_3$      42
$C_3$, operations      42 F2—7.1
$C_3$, representations      43 T2—7.1
$C_3v$, as the group of ammonia      213
$C_3v$, character table      44 T2—7.2
$C_3v$, operations      44 F2—7.2
$C_4v$      106
$C_4v$, character table      111 T6—3.2
$C_6v$      40
$C_6v$, character table      41 T2—6.1
$C_6v$, operations      40 F2—6.1
$C_s$      109
$D_6h$      40
Abelian group      42
Acceptor levels      159
Acoustic bands      196
Acoustic branches      196
Active picture      28
Alloys      198
Alloys, rigid band model      198
Altmann      45 63 119 183 195 204 212 226
Ammonia      214
Amplitude      20
Antoncik      183
Apostol      212
Arfken      85
Ashcroft      22 63 85 165
Atkins      23 45
Augmented plane wave method      183
Austin      183
Austin — Heine — Sham pseudopotential      182 (10—4.15)
Austin — Heine — Sham pseudopotential, form of wave equation      181 (10—4.9)
Baldea      212
Band      17 95 see
Band gap      138
Band gap, Fermi level in it for semiconductors      159
Band gap, nearly free-electron method value      171 (10—1.33)
Band gap, states in it      227
Band gap, type I      173
Band gap, type II      173
Band label      99
bands      17 99
Bands, antibonding      232
Bands, bonding      232
Bands, condition for two bands to touch or cross at given k      111 116
Bands, conduction      140 158
Bands, continuity over the Brillouin zone      112
Bands, degeneracies      113 115
Bands, guesswork of trends      114
Bands, inversion symmetry with respect to k      118 (6—5.6)
Bands, periodicity of energy in reciprocal space      112 (6—4.1)
Bands, relation to free atomic levels      100 F5—6.1
Bands, valence      158
Bases      35 see
Bases of space group representations      103
Bases of space group representations, condition for same k to be repeated in same basis      111
Bases of space group representations, generated by k vectors      104
Bases of space group representations, group of the k vector      107
Bases of space group representations, importance of use of bases of invariant subgroup T      104
Bases of space group representations, separate all k vectors of Brillouin zone in disjoint sets      104
Bases of space group representations, small representations      110
Basis of a crystal pattern      50
Basis of a representation      35
Basis of a representation, direct sum      35
Basis of a representation, irreducible      37
Basis of a representation, reduction      36
Bassani      183
benzene      39
Benzene, energy levels      42 F2—6.2
Binary rotations      53
Blakemore      22 165
Bloch functions      97 (5—6.3)
Bloch functions, as eigenfunctions of the translations      97 (5—6.2)
Bloch functions, as modulated plane waves      98 (5—6.9)
Bloch functions, asymptotic relation to atomic states      99
Bloch functions, asymptotic relation to plane waves      99
Bloch functions, definition depends on form of translation representative      98
Bloch functions, effect of space group operators      102 (6—1.1)
Bloch functions, form for the wrong translation representatives      100 P5—7.2
Bloch sums      174 (10—2.6)
Bloch sums, for a lattice with basis      246 P14—5.8
Bloch sums, for linear chain      175 (10—2.12)
Bloch sums, use in tight-binding method      174 (10—2.7)
Boas      85
Body-centred cubic lattice      52 F3—3.2 77 84
Boon      45
Born-von Karman boundary conditions      8
Born-von Karman boundary conditions, in a periodic lattice      87
Bouckaert      119
Boundary conditions, Born-von Karman      8
Boundary conditions, box      21 P1—9.6—P1—9.9 249
Boundary conditions, periodic      11
Bozovic      212
Bra      79
Bradley      63 119
Bragg reflection      132
Bragg reflection, its relation to group velocity      136 see
Bragg scattering      193
Brass alloy phases      199
Brass alloy phases, Hume — Rothery rules      199
Brass alloy phases, Jones theory      199
Bravais lattice      51
Bravais lattice, must be a lattice without basis      53
Bravais lattice, of crystal pattern      52
Bravais lattice, synonymous with lattice and translational lattice      52
Bra—ket      79 (4—9.3)
Brillouin      101
Brillouin zone      92
Brillouin zone, all operations of P are covering operations      93
Brillouin zone, as centred primitive cell of the reciprocal lattice      92
Brillouin zone, basic domain      115
Brillouin zone, construction      143
Brillouin zone, folding back      147
Brillouin zone, for one-dimensional chain      100 P5—7.5
Brillouin zone, it has inversion symmetry from conjugator      118
Brillouin zone, it has no geometrical symmetry of its own      93 116
Brillouin zone, number of states inside      94 96
Brillouin zone, of higher order      141
Brillouin zone, open polyhedron property      93
Brillouin zone, permitted k vectors inside label all energy eigenstates      94
Brillouin zone, properties of faces      131
Brillouin zone, properties of faces, cusps      134
Brillouin zone, properties of faces, cusps, relation to group velocity      136
Brillouin zone, properties of faces, energy derivatives      133 (8—2.8)
Brillouin zone, properties of faces, k vectors      132
Brillouin zone, quantization of k vectors inside      95 F5—5.1
Brillouin zone, three—dimensional definition      143
Buerger      63
Bullett      183
Burns      63
Cell functions      98
Cell functions, asymptotic relation to atomic states      99
Celli      183
Cellular method      183
Centred primitive cell      50 92
CHARACTER      37 (2—4.17)
Character table      109 T6—3.1
Circular frequency      19 (1—8.7)
Circular wave number      19 (1—8.6)
class      24
Cochran      197
Cohen      183
Conduction band      140 158
Conductivity      184
Conductivity, relation to Fermi surface      185 (11—1.6)
Conductor      140
Configuration space      26
Configuration space operator      28
Conjugate element      24
Conjugate representations      251 P2—7.6
Conjugator operator      32 (2—3.11)
Conjugator operator, commutes with symmetry operations      33
Conjugator operator, inverts k vector of Bloch functions      118 (6—5.1)
Conjugator operator, it is non linear      33
copper      161
Copper, band structure      162 F9—2.1
Copper, Brillouin zone      157 F9—1.3
Copper, crystal structure      162
Copper, density of states      162 F9—2.1
Copper, details      165 P9—4.2 P9—4.3
Copper, Fermi surface      163 F9—2.2 164
Copper, free-electron energies      165 P9—4.4
Core electrons      7
Cornwell      45
Cotton      45
Cottrell      22 183 200 212
Coulson      240
Covering operation      26
Cox      22
Cracknell      63 119
Crystal lattice      52 64
Crystal pattern      46
Crystal structure      46
Crystal vibrations      186
Current density      184
Cyclic groups      42 P2—7.3 215 250
Cyclic groups, partition space into disjoint cells      214 216
Cyclic groups, properties      215
Cyclic groups, their representations are faithful      216
d band      162
d band, in noble metal      164
d band, in transition metal      164
Dangling bond      230
De Haas — Van Alphen effect      148
Degeneracy      31
Density of states      14
Density of states, for free electrons      15(1—5.7)
Density of states, free-electron gas      16 Fl—5.1
Diamond crystal pattern      153 154
Diamond crystal pattern, bond lengths      165 P9—4.1
Diamond crystal pattern, Bravais lattice      154
Diamond crystal pattern, point group      154
Diamond crystal pattern, space group      155
Dimmock      183
Direct product      25 (2—1.7) (2—1.8)
Direct product, basis      204 (12—2.12)
Direct product, character      210 (12—4.3)
Direct product, matrix      204
Direct product, representations      38
Direct product, symmetrized      210
Direct sum, of bases      35
Direct sum, of matrices      35
Displacement vector      188
Donor levels      159
Electron density      14
Electron-phonon interactions      203
Electron-phonon scattering      192
Electrons      149
Electrons, relation to holes      149
Energy as a function of k      92 112
Energy as a function of k, contacts or crossings at given k      111
Energy as a function of k, inversion symmetry in reciprocal space      118
Energy as a function of k, periodicity in reciprocal space      112 (6—4.1)
Energy as a function of k, symmetry in reciprocal space due to the star      115
Energy eigenvalues      31 (2—3.3)
Energy eigenvalues, are labelled by k vector      92
Energy level surfaces      135
Energy level surfaces, discontinuities at the Brillouin zone edge      145 F8—7.1
Equivalent functions      213 215(13—1.7)
Equivalent functions, close formula      219(13—1.33)
Equivalent functions, construction      218 (13—1.20)
Equivalent functions, orthogonal for different cells      218
Equivalent k vectors      91
Exchange integral      176 (10—2.15) 231
Exchange interactions      166
Extended zone scheme      143 141
Extrinsic semiconductivity      159
Extrinsic semiconductor      140
Face-centred cubic lattice      76 F4—7.1
Face-centred cubic lattice, Brillouin zone      131 F8—1.1
Face-centred cubic lattice, its reciprocal      76 F4—7.1 84
Faithful representations      216
Falicov      44 212
Fermi energy      13 146
Fermi energy, for free electrons      16 (1—6.4)
Fermi sphere      14
Fermi surface      14
Fermi surface, displacement under electric field      185 F (11—1.1)
Fermi surface, experimental determination      148
Fermi surface, extremal cross-sections      148
Fermi surface, for simple square lattice      147 F8—7.2 148
fermions      13
First Brillouin zone      see Brillouin zone
Flores      247
Folding back      147
Forbidden energy gap      138
Fourier coefficients      81 (4—9.19)
Fourier series      78 81
Fourier series, for lattice with basis      82 (4—9.25)
Fractional translation      55
Free-electron approximatio      167
Function products, transformation properties      204(12—2.12) 266 269
Function space operator      28 29
Function space operator, isomorphic to configuration space operators      30(2—2.8)
Function space operator, wrong form      45
Function transformation      28
Function transformation, wrong form      45
Functional transformations      29
G, a group      24
G, a space group      56
Garcia Moliner      247
General k vector      116
General k vector, bands cannot touch or cross at them      116
Glazer      63
Glide reflection      55
Gold      63 119 212
Green function      237
Green function, explicit form      239 (14—3.30)
Group      24
Group of the k vector      107
Group of the k vector, varies over star      110
Group velocity      20 (1—8.13)
Group velocity, from energy gradient      135 (8—3.2)
Group velocity, it is normal to level surfaces of energy      135 F8—3.1
Group velocity, not always parallel to momentum      135
Group, associative condition      24 (2—1.2)
Group, closure      24
Group, conjugate element      24
Group, identity      24 (2—1.3)
Group, inverse element      24(2—1.4)
Group, product of elements      24
Groves      63 85
Hamcrmcsh      45
Hamiltonian      9
Hamiltonian, vibronic      203(12—2.8)
Harmonic approximation      188
Harmonic oscillations      186
harmonic oscillator      186
Harmonic oscillator, eigenvalues      186 (11—2.3)
Harmonic oscillator, quantum mechanical Hamiltonian      186 (11—2.1)
Harris      212
Harrison      183
Hash      67
Heine      44 181 183
Hermite functions      186
Herring      183
Hexagonal close-packed structure      83 F4—9.1
Hexagonal close-packed structure, phase change      211 P12—4.5
Hexagonal close-packed structure, two dimensional (lattice)      73 F4—5.1
Hiickel approximation      177
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