Site symmetry in crystals: theory and applications
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Springer
1997
|
| Edition: | 2. ed. |
| Series: | Springer series in solid-state sciences
108 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 280 S. graph. Darst. |
| ISBN: | 3540614664 |
Staff View
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| 100 | 1 | |a Ėvarestov, R. A. |d 1937- |e Verfasser |0 (DE-588)113340788 |4 aut | |
| 245 | 1 | 0 | |a Site symmetry in crystals |b theory and applications |c R. A. Evarestov ; V. P. Smirnov |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1997 | |
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| 650 | 7 | |a Symétrie (physique) |2 ram | |
| 650 | 4 | |a Crystallography, Mathematical | |
| 650 | 4 | |a Solid state chemistry | |
| 650 | 4 | |a Solid state physics | |
| 650 | 4 | |a Symmetry (Physics) | |
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Record in the Search Index
| _version_ | 1804125480378433536 |
|---|---|
| adam_text | R. A. EVARESTOV V P SMIRNOV
SITE SYMMETRY
IN CRYSTALS
THEORY AND APPLICATIONS
SECOND EDITION
WITH 42 FIGURES
YYYYYY SPRINGE
R
CONTENTS
1. INTRODUCTION 1
2. FINITE GROUPS AND THEIR REPRESENTATIONS 5
2.1 ELEMENT
S OF GROU
P THEOR
Y 5
2.1.1 GROUPS
. GENERATOR
S AN
D GENERATIN
G RELATIONS.
SUBGROUPS
. COSETS. INVARIAN
T SUBGROUPS
.
TH
E FACTOR GROU
P 5
2.1.2 CONJUGAT
E ELEMENT
S AN
D CLASSES. FACTORIZATIO
N
OF GROUP
S 7
2.1.3 HOMOMORPHIS
M AN
D ISOMORPHIS
M OF GROUP
S 9
2.2 ELEMENT
S OF GROU
P REPRESENTATION THEOR
Y 10
2.2.1 REPRESENTATION
S OF A GROUP
. EQUIVALENT
, REDUCIBLE
AN
D IRREDUCIBL
E REPRESENTATIONS
. ORTHOGONALIT
Y RELATIONS.
REPRESENTATIO
N CHARACTER
S 10
2.2.2 DECOMPOSITIO
N OF REPRESENTATIONS
.
COMPLEX CONJUGAT
E REPRESENTATION
S 15
2.3 GENERATIO
N OF REPRESENTATION
S 17
2.3.1 DIRECT PRODUC
T OF REPRESENTATION
S 17
2.3.2 SUBDUCTIO
N OF REPRESENTATION
S 20
2.3.3 INDUCTIO
N OF REPRESENTATION
S 22
2.3.4 LITTLE GROU
P METHO
D
OF IRREDUCIBL
E REPRESENTATION GENERATIO
N 26
3
. SYMMETRY GROUPS AND THEIR REPRESENTATIONS 31
3.1 TH
E EUCLIDEA
N GROU
P AN
D ITS SUBGROUP
S 31
3.1.1 TRANSLATION GROU
P 31
3.1.2 ROTATIO
N GROU
P 32
3.1.3 INVERSION GROU
P 35
3.1.4 FULL ORTHOGONA
L GROU
P 35
3.1.5 EUCLIDEAN GROU
P 36
3.2 POIN
T SYMMETRY GROUP
S 39
3.2.1 SYMMETRY ELEMENT
S OF MOLECULES
AN
D CRYSTALLOGRAPHI
C POIN
T GROUP
S 39
3.2.2 SITE SYMMETRY SUBGROUP
S OF POIN
T GROUP
S 40
3.3 SPACE GROUP
S 43
3.3.1 SYMMETRY OF A MODE
L OF A
N INFINITE CRYSTAL
.
SYMMORPHI
C AN
D NONSYMMORPHI
C SPACE GROUP
S 43
X CONTENTS
3.3.2 SYMMETRY OF A CYCLIC MODEL OF A CRYSTAL 46
3.4 SITE SYMMETRY IN SPACE GROUPS 48
3.4.1 CRYSTALLOGRAPHIC ORBITS. WYCKOFF POSITIONS 48
3.4.2 ORIENTED SITE SYMMETRY GROUPS. CHOICE OF ORIGIN 51
3.4.3 CRYSTAL STRUCTURE TYPES. CRYSTALS WITH SPACE GROUP D T . 54
3.5 SYMMETRY OPERATIONS IN QUANTUM MECHANICS 55
3.5.1 SYMMETRY GROUP OF A QUANTUM MECHANICAL SYSTEM ...
. 55
3.5.2 WIGNER S THEOREM 56
3.5.3 TIME-REVERSAL SYMMETRY 57
3.6 IRREDUCIBLE REPRESENTATIONS OF ROTATION
AND FULL ORTHOGONAL GROUPS 59
3.7 REPRESENTATIONS OF POINT GROUPS 62
3.8 REPRESENTATIONS OF SPACE GROUPS 70
3.8.1 IRREDUCIBLE REPRESENTATIONS OF THE TRANSLATION GROUP.
THE BRILLOUIN ZONE 70
3.8.2 STARS OF WAVE VECTORS. LITTLE GROUP.
FULL REPRESENTATIONS OF SPACE GROUPS 76
3.8.3 SMALL REPRESENTATIONS OF A LITTLE GROUP.
PROJECTIVE REPRESENTATIONS OF POINT GROUPS 78
3.8.4 DOUBLE-VALUED REPRESENTATIONS OF SPACE GROUPS 79
3.8.5 DEPENDENCE OF THE LABELING OF THE IRREDUCIBLE
REPRESENTATIONS OF A SPACE GROUP ON THE SETTING 81
3.8.6 EXAMPLE: IRREDUCIBLE REPRESENTATIONS
OF SPACE GROUP D
L
F
H
. COMPATIBILITY TABLES 84
4. SITE SYMMETRY AND INDUCED REPRESENTATIONS OF SYMMETRY GROUPS 89
4.1 INDUCED REPRESENTATIONS OF POINT GROUPS.
CORRELATION TABLES 89
4.2 INDUCED REPRESENTATIONS OF SPACE GROUPS 91
4.2.1 INDUCTION FROM SITE SYMMETRY SUBGROUPS
OF SPACE GROUPS 92
4.2.2 INDUCED REPRESENTATIONS IN THE /C-BASIS.
BAND REPRESENTATIONS 93
4.2.3 SIMPLE AND COMPOSITE INDUCED REPRESENTATIONS 97
4.3 DOUBLE-VALUED INDUCED REPRESENTATIONS 99
4.4 GENERATION OF THE SIMPLE INDUCED REPRESENTATIONS
OF THE SPACE GROUP D I 100
4.5 THE TWENTY-FOUR MOST COMMON SPACE GROUPS: CRYSTAL
STRUCTURES AND TABLES OF SIMPLE INDUCED REPRESENTATIONS 103
4.5.1 TABLES OF SIMPLE INDUCED REPRESENTATIONS AND THEIR USE 103
4.5.2 SPACE GROUPS AND CRYSTAL STRUCTURES
WITH CUBIC LATTICES 106
4.5.3 SPACE GROUPS AND CRYSTAL STRUCTURES
WITH HEXAGONAL AND TRIGONAL LATTICES 111
4.5.4 SPACE GROUPS AND CRYSTAL STRUCTURES
WITH TETRAGONAL LATTICES 114
CONTENTS
XI
4.5.5 SPACE GROUPS AND CRYSTAL STRUCTURES
WITH ORTHORHOMBIC LATTICES 117
4.5.6 SPACE GROUP SETTING AND SIMPLE INDUCED REPRESENTATIONS
FOR MONOCLINIC SPACE GROUPS 121
5. APPLICATION OF INDUCED REPRESENTATIONS IN THE ELECTRON THEORY
OF MOLECULES AND CRYSTALS 125
5.1 ADIABATIC AND ONE-ELECTRON APPROXIMATIONS 125
5.1.1 SPACE SYMMETRY
OF THE ONE-ELECTRON APPROXIMATION HAMILTONIAN 129
5.2 INDUCED REPRESENTATIONS IN THE ELECTRON THEORY OF MOLECULES 131
5.2.1 CANONICAL, LOCALIZED AND HYBRIDIZED MOLECULAR ORBITALS 131
5.2.2 LOCALIZED TWO-CENTER BONDS AND HYBRIDIZED ORBITALS
IN AB
4
AND YYYY
YY
MOLECULES 136
5.2.3 MULTICENTERED BONDS IN THE 1,6-C
2
B
4
H
6
MOLECULE 139
5.2.4 CANONICAL AND LOCALIZED ORBITALS
IN THE MN0
4
MOLECULAR ION 140
5.2.5 LOCALIZED ORBITALS IN THE TETRAHEDRAL BI
4
MOLECULE 142
5.3 ONE-ELECTRON APPROXIMATION FOR CRYSTALS 144
5.3.1 CRYSTALLINE ORBITALS.
DEGENERATE AND NONDEGENERATE ENERGY BANDS 144
5.3.2 EQUIVALENT HAMILTONIANS
FOR THE SAME CRYSTAL STRUCTURES 146
5.3.3 K-P PERTURBATION METHOD IN THE ENERGY BAND THEORY .
. 147
5.3.4 ZERO-SLOPE POINTS OF ENERGY BANDS 150
5.3.5 ENERGY BANDS IN THE NEIGHBORHOOD
OF DEGENERACY POINTS 152
5.3.6 ADDITIONAL DEGENERACY OF ENERGY BANDS DUE
TO THE REALITY OF THE HAMILTONIAN 155
5.3.7 DENSITY OF STATES OF AN ENERGY BAND 155
5.4 INDUCED REPRESENTATIONS AND THE THEORY OF CHEMICAL BONDING
IN CRYSTALS 158
5.4.1 ENERGY BAND STATES AND LOCALIZED FUNCTIONS 158
5.4.2 LOCALIZED ORBITALS AND ATOMIC STATES IN CRYSTALS 159
5.4.3 HYBRIDIZED ORBITALS IN CRYSTALS 160
5.4.4 CRYSTALS WITH SPACE GROUP 0 161
5.4.5 CRYSTALS WITH SPACE GROUP 0 162
5.4.6 CRYSTALS WITH SPACE GROUP D L 163
5.4.7 ONE-ELECTRON STATES IN HIGH-T
C
SUPERCONDUCTORS 165
5.5 ENERGY BANDS AND LOCALIZED STATES 173
5.5.1 LOCALIZED ORBITALS AND PARAMETERS OF AN ENERGY BAND .
. 173
5.5.2 GENERATION OF LOCALIZED FUNCTIONS IN CRYSTALS 174
5.5.3 INTERPOLATION SCHEME USING LOCALIZED FUNCTIONS 175
5.6 LOCALIZED ORBITALS IN MOLECULAR MODELS OF CRYSTALS 179
5.6.1 CLUSTER MODEL OF PERFECT CRYSTALS 179
5.6.2 CLUSTER AND CRYSTAL LOCALIZED ORBITALS 180
XII CONTENTS
5.6.3 ENERGY BANDS OF AGBR FROM CLUSTER CALCULATIONS
OF [AG
14
BR,
3
]
+
181
5.6.4 CYCLIC MODEL AS A MOLECULAR MODEL OF CRYSTALS 182
5.6.5 LOCALIZED ORBITALS IN THE CYCLIC MODEL 183
6. INDUCED REPRESENTATIONS IN THE THEORY OF IMPERFECT CRYSTALS ...
. 185
6.1 POINT DEFECTS IN CRYSTALS 185
6.1.1 SINGLE DEFECT MODEL 186
6.1.2 CLUSTER MODEL OF IMPERFECT CRYSTALS 188
6.1.3 CYCLIC MODEL OF IMPERFECT CRYSTALS 189
6.1.4 BAND MODEL OF IMPERFECT CRYSTALS 189
6.1.5 LOCALIZED ORBITALS IN THE BAND MODEL OF POINT DEFECTS . 191
6.2 DIPERIODIC SPACE GROUPS. SURFACE ELECTRON STATES 192
6.2.1 DIPERIODIC (LAYER) SPACE GROUPS 192
6.2.2 SITE SYMMETRY IN LAYER GROUPS 195
6.2.3 IRREDUCIBLE REPRESENTATIONS OF DIPERIODIC GROUPS 197
6.2.4 INDUCED REPRESENTATIONS OF DIPERIODIC GROUPS 199
6.2.5 USE OF TRANSLATIONAL SYMMETRY IN THE COMPARISON
OF BULK AND SURFACE CRYSTALLINE STATES 201
7. APPLICATION OF INDUCED REPRESENTATIONS OF SPACE GROUPS
TO SECOND ORDER PHASE TRANSITIONS 205
7.1 SYMMETRY RULES IN THE LANDAU THEORY
OF SECOND ORDER PHASE TRANSITIONS 205
7.2 TENSOR FIELDS IN CRYSTALS AND INDUCED REPRESENTATIONS
OF SPACE GROUPS. TENSOR FIELDS FOR SPACE GROUP D^
H
207
7.3 VIBRATIONAL FIELD REPRESENTATION AND PHASE TRANSITIONS
IN HIGH-TEMPERATURE SUPERCONDUCTORS 210
8. INDUCED REPRESENTATIONS OF SPACE GROUPS
IN PHONON SPECTROSCOPY OF CRYSTALS 213
8.1 PHONON SYMMETRY ANALYSIS 213
8.2 INFRARED AND RAMAN SPECTRA SELECTION RULES 214
8.3 PHONON SYMMETRY AND OPTICAL SPECTRA SELECTION RULES
IN SEMICONDUCTOR SUPERLATTICES 215
8.3.1 (GAAS)
M
(ALAS)YY SUPERLATTICES 216
8.3.2 (SI)
M
(GE)YY SUPERLATTICES 221
8.3.3 EXPERIMENTAL APPLICATIONS 221
8.4 PHONON SYMMETRY IN HIGH-TEMPERATURE SUPERCONDUCTORS 227
8.5 PHONON SYMMETRY IN DIPERIODIC SYSTEMS 233
9. SITE SYMMETRY IN MAGNETIC CRYSTALS
AND INDUCED COREPRESENTATIONS 237
9.1 SHUBNIKOV SPACE GROUPS OF SYMMETRY OF MAGNETIC CRYSTALS . 237
9.2 SITE SYMMETRY IN MAGNETIC CRYSTALS 238
9.3 COREPRESENTATIONS OF SHUBNIKOV SPACE GROUPS 241
CONTENTS
XIII
9.4 INDUCED COREPRESENTATIONS OF MAGNETIC SPACE GROUPS 244
9.5 COREPRESENTATIONS OF THE SPACE GROUPS
OF ANTIFERROMAGNETIC LA
2
CU0
4
247
10. SITE SYMMETRY IN PERMUTATION - INVERSION SYMMETRY GROUPS
OF NONRIGID CRYSTALS 251
10.1 SYMMETRY GROUPS OF NONRIGID CRYSTALS 252
10.1.1 LABELING OF NUCLEI. SAMPLING OF COORDINATE SYSTEMS 252
10.1.2 DESCRIPTION OF PERMUTATION -
INVERSION SYMMETRY ELEMENTS 253
10.1.3 COORDINATE TRANSFORMATIONS INDUCED
BY PERMUTATION - INVERSION SYMMETRY ELEMENTS ..
. 255
10.1.4 SITE SYMMETRY GROUP OF A ROTATING MOLECULE
IN A NONRIGID CRYSTAL 256
10.1.5 PERMUTATION - INVERSION GROUP
OF A NONRIGID SODIUM NITRATE CRYSTAL 257
10.2 IRREDUCIBLE REPRESENTATIONS
OF A NONRIGID CRYSTAL SYMMETRY GROUP 260
10.2.1 GENERATION OF IRREDUCIBLE REPRESENTATIONS 260
10.2.2 IRREDUCIBLE REPRESENTATIONS
OF A SITE SYMMETRY GROUP 261
10.2.3 CLASSIFICATION OF STATES 263
10.3 GENERALIZED SYMMETRY OF HIGH-TEMPERATURE PHASE
OF FULLERITE C
60
264
10.3.1 PERMUTATION - INVERSION SYMMETRY GROUP
OF FULLERITE C
60
IN THE HIGH-TEMPERATURE PHASE ...
. 265
10.3.2 IRREDUCIBLE REPRESENTATIONS
OF THE GROUPS [N] AND P
C
265
10.3.3 CLASSIFICATION OF STATES OF NONRIGID FULLERITE C
60
..
. 266
REFERENCES 269
SUBJECT INDEX 277
|
| any_adam_object | 1 |
| author | Ėvarestov, R. A. 1937- Smirnov, Vjačeslav P. |
| author_GND | (DE-588)113340788 |
| author_facet | Ėvarestov, R. A. 1937- Smirnov, Vjačeslav P. |
| author_role | aut aut |
| author_sort | Ėvarestov, R. A. 1937- |
| author_variant | r a ė ra raė v p s vp vps |
| building | Verbundindex |
| bvnumber | BV010990529 |
| callnumber-first | Q - Science |
| callnumber-label | QC176 |
| callnumber-raw | QC176 |
| callnumber-search | QC176 |
| callnumber-sort | QC 3176 |
| callnumber-subject | QC - Physics |
| classification_rvk | UP 1100 UP 1200 UQ 1350 ZM 6000 |
| ctrlnum | (OCoLC)35331270 (DE-599)BVBBV010990529 |
| dewey-full | 530.4/11 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.4/11 |
| dewey-search | 530.4/11 |
| dewey-sort | 3530.4 211 |
| dewey-tens | 530 - Physics |
| discipline | Physik Werkstoffwissenschaften / Fertigungstechnik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV010990529 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:14Z |
| institution | BVB |
| isbn | 3540614664 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007356382 |
| oclc_num | 35331270 |
| open_access_boolean | |
| owner | DE-384 DE-20 DE-92 DE-703 DE-634 DE-11 |
| owner_facet | DE-384 DE-20 DE-92 DE-703 DE-634 DE-11 |
| physical | XIII, 280 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in solid-state sciences |
| series2 | Springer series in solid-state sciences |
| spelling | Ėvarestov, R. A. 1937- Verfasser (DE-588)113340788 aut Site symmetry in crystals theory and applications R. A. Evarestov ; V. P. Smirnov 2. ed. Berlin [u.a.] Springer 1997 XIII, 280 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in solid-state sciences 108 Chimie de l'état solide ram Groupes ram Physique de l'état solide ram Réseaux cristallins ram Symétrie (physique) ram Crystallography, Mathematical Solid state chemistry Solid state physics Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Kristallsymmetrie (DE-588)4136175-1 gnd rswk-swf Kristallgitter (DE-588)4139853-1 gnd rswk-swf Kristallsymmetrie (DE-588)4136175-1 s Gruppentheorie (DE-588)4072157-7 s DE-604 Kristallgitter (DE-588)4139853-1 s Symmetrie (DE-588)4058724-1 s 1\p DE-604 Smirnov, Vjačeslav P. Verfasser aut Springer series in solid-state sciences 108 (DE-604)BV000016582 108 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007356382&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ėvarestov, R. A. 1937- Smirnov, Vjačeslav P. Site symmetry in crystals theory and applications Springer series in solid-state sciences Chimie de l'état solide ram Groupes ram Physique de l'état solide ram Réseaux cristallins ram Symétrie (physique) ram Crystallography, Mathematical Solid state chemistry Solid state physics Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd Gruppentheorie (DE-588)4072157-7 gnd Kristallsymmetrie (DE-588)4136175-1 gnd Kristallgitter (DE-588)4139853-1 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4072157-7 (DE-588)4136175-1 (DE-588)4139853-1 |
| title | Site symmetry in crystals theory and applications |
| title_auth | Site symmetry in crystals theory and applications |
| title_exact_search | Site symmetry in crystals theory and applications |
| title_full | Site symmetry in crystals theory and applications R. A. Evarestov ; V. P. Smirnov |
| title_fullStr | Site symmetry in crystals theory and applications R. A. Evarestov ; V. P. Smirnov |
| title_full_unstemmed | Site symmetry in crystals theory and applications R. A. Evarestov ; V. P. Smirnov |
| title_short | Site symmetry in crystals |
| title_sort | site symmetry in crystals theory and applications |
| title_sub | theory and applications |
| topic | Chimie de l'état solide ram Groupes ram Physique de l'état solide ram Réseaux cristallins ram Symétrie (physique) ram Crystallography, Mathematical Solid state chemistry Solid state physics Symmetry (Physics) Symmetrie (DE-588)4058724-1 gnd Gruppentheorie (DE-588)4072157-7 gnd Kristallsymmetrie (DE-588)4136175-1 gnd Kristallgitter (DE-588)4139853-1 gnd |
| topic_facet | Chimie de l'état solide Groupes Physique de l'état solide Réseaux cristallins Symétrie (physique) Crystallography, Mathematical Solid state chemistry Solid state physics Symmetry (Physics) Symmetrie Gruppentheorie Kristallsymmetrie Kristallgitter |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007356382&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000016582 |
| work_keys_str_mv | AT evarestovra sitesymmetryincrystalstheoryandapplications AT smirnovvjaceslavp sitesymmetryincrystalstheoryandapplications |