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    Kristallographie

    Eine Einführung für Naturwissenschaftler

    Kristallographie
    Eine Einführung für Naturwissenschaftler

    Autoren:

    Verlag:
    Springer-Verlag   Weitere Titel dieses Verlages anzeigen

    Auflage: 8., überarbeitete und aktualisierte Auflage 2013.
    Erschienen: September 2013
    Seiten: 414
    Sprache: Deutsch
    Preis: 29.99 €
    Illustration: 612 schwarz-weiße Abbildungen
    Maße: 241x169x20
    Einband: Taschenbuch
    Reihe: Springer-Lehrbuch
    Zum Buch: Book
    ISBN: 9783642348105

    Inhaltsverzeichnis

    1 Einleitung.........................................
    2 Der Kristallzustand..................................
    2.1 Übungsaufgaben.................................
    3 Das Raumgitter und seine Eigenschaften...................
    3.1 Gittergerade....................................
    3.2 Gitterebene ....................................
    3.3 Raumgitter.....................................
    3.4 Bezeichnung von Punkten, Geraden und Ebenen im Raumgitter
    3.4.1 Gitterpunkt uvw............................
    3.4.2 Gittergerade [uvw] ..........................
    3.4.3 Gitterebene (Netzebene) (hkl)...................
    3.5 Zonengleichung.................................
    3.5.1 Anwendungen der Zonengleichung...............
    3.6 Übungsaufgaben.................................
    4 Die Kristallstruktur..................................
    4.1 Übungsaufgaben.................................
    5 Die Morphologie....................................
    5.1 Korrespondenz von Kristallstruktur und Morphologie.......
    5.2 Grundbegriffe der Morphologie ......................
    5.3 Wachsen der Kristalle.............................
    5.4 Stereographische Projektion.........................
    5.5 Reflexionsgoniometer.............................
    5.6 Wulff sches Netz.................................
    5.7 Indizierung eines Kristalls..........................
    5.8 Gnomonische und orthographische Projektion............
    5.8.1 Gnomonische Projektion......................
    5.8.2 Orthographische Projektion....................
    5.9 Übungsaufgaben.................................
    6Das Symmetrieprinzip65
    6.1Drehachsen67
    6.2Spiegelebene71
    6.3Inversionszentrum72
    6.4Koppelung von Symmetrieoperationen73
    6.4.1Drehinversionsachsen75
    6.4.2Drehspiegelachsen76
    6.5Übungsaufgaben78
    7Die 14 Translations-(Bravais-)gitter81
    7.1Primitive Translationsgitter (P-Gitter)85
    7.2Symmetrie der primitiven Translationsgitter98
    7.2.1Symmetrie des triklinen P-Gitters100
    7.2.2Symmetrie des monoklinen P-Gitters100
    7.2.3Symmetrie des orthorhombischen P-Gitters102
    7.2.4Symmetrie des tetragonalen P-Gitters104
    7.2.5Symmetrie des hexagonalen P-Gitters106
    7.2.6Symmetrie des kubischen P-Gitters108
    7.3Zentrierte Translationsgitter108
    7.4Symmetrie der zentrierten Translationsgitter114
    7.5Übungsaufgaben115
    8Die 7 Kristallsysteme125
    9Die Punktgruppen129
    9.1Die 32 kristallographischen Punktgruppen129
    9.2Kristallsymmetrie133
    9.2.1Kristallformen des tetragonalen Kristallsystems144
    9.2.2Kristallformen des hexagonalen (trigonalen) Kristallsystems153
    9.2.3Kristallformen des kubischen Kristallsystems162
    9.2.4 Kristallformen des orthorhombischen,
    monoklinen und triklinen Kristallsystems162
    9.3Molekülsymmetrie163
    9.4Punktgruppenbestimmung166
    9.5Enantiomorphie171
    9.6Punktgruppen und physikalische Eigenschaften171
    9.6.1Optische Aktivität171
    9.6.2Piezoelektrizität172
    9.6.3Pyroelektrizität173
    9.6.4Das Dipolmoment der Moleküle174
    9.7Nichtkristallographische Punktgruppen174
    9.8Übungsaufgaben178
    10Die Raumgruppen201
    10.1Gleitspiegelung und Schraubung201
    10.1.1Gleitspiegelebenen202
    10.1.2Schraubenachsen205
    10.2Die 17 Ebenengruppen209
    10.3Die 230 Raumgruppen213
    10.4Eigenschaften der Raumgruppen218
    10.5International Tables for Crystallography226
    10.6Achsentransformationen232
    10.7Raumgruppen und Kristallstruktur235
    10.8Beziehungen zwischen Punkt- und Raumgruppen236
    10.9Übungsaufgaben239
    11Symmetriegruppen249
    11.1Symmetrieoperationen in Matrizendarstellung249
    11.2Eigenschaften einer Gruppe264
    11.3Ableitung einiger Punktgruppen267
    11.4Gruppentafeln270
    11.5Gruppen - Untergruppen - Obergruppen272
    11.5.1Gruppe-Untergruppe-Beziehungen272
    11.5.2Gruppe-Obergruppe-Beziehungen284
    11.5.3Strukturverwandtschaften286
    11.5.4Beschreibung von displaziven Phasenübergängen290
    11.6Übungsaufgaben292
    12Grundbegriffe der Kristallchemie297
    12.1Koordination298
    12.2Metallstrukturen300
    12.3Edelgas-und Molekülstrukturen304
    12.4Ionenstrukturen305
    12.4.1Ionenradien306
    12.4.2Oktaederkoordination [6]309
    12.4.3Hexaederkoordination [8]311
    12.4.4Tetraederkoordination [4]313
    12.5Kovalente Strukturen316
    12.6Isotypie - Mischkristalle - Isomorphic316
    12.7Polymorphie319
    12.7.1Transformationen in 1. Koordination319
    12.7.2Transformationen in 2. Koordination321
    12.7.3Transformationen durch Ordnung-Unordnung322
    12.7.4Transformationen durch Änderung des Bindungscharakters324
    12.8Informationen über Kristallstrukturen324
    12.9Übungsaufgaben325
    13Röntgenographische Untersuchungen an Kristallen329
    13.1Braggsche Gleichung329
    13.2Debye-Scherrer-Verfahren330
    13.3Reziprokes Gitter336
    13.4Laue-Gruppen340
    13.5Bestimmung einer Kristallstruktur342
    13.6Übungsaufgaben346
    14Kristallbaufehler347
    14.1Punktdefekte348
    14.2Liniendefekte349
    14.3Flächendefekte351
    15Anhang355
    15.1Kristallographische Symbole355
    15.2Symmetrieelemente356
    15.3 Berechnung von Atomabständen und Winkeln
    in einer Kristallstruktur359
    15.4Kristallformen360
    15.5Polyeder-Modellnetze363
    16Lösungen der Übungsaufgaben375
    Literaturverzeichnis405
    Sachverzeichnis409
    Ausschlagtafel (Wulffsches Netz)415

    Register

    Sachverzeichnis
    A
    A-Gitter, 110
    Abelsche Gruppe, 266
    Achsenabschnitte, 16
    Achsenabschnittsgleichung, 18
    Achsenkreuz, 12,125
    Achsentransformation, 232
    Achsenverhältnis, 53, 126, 127
    Ag, Au, 318
    AI2O3, 310
    AIB2, 29, 376
    allgemeine Form, 145
    allgemeine Netzebene, 81
    allgemeine Punktlage, 219
    a-Polonium, 11, 304
    amorph, 8, 9
    Ängström, 27
    anisotrop, 4, 36
    Antifluorittyp, 310
    Äquatorebene, 40, 44
    äquivalent, 68
    Aragonit, 137
    Aragonittyp, 320
    asymmetrisch, 171
    asymmetrische Einheit, 220, 227, 228
    asymmetrische Flächeneinheit, Atombindung, 297
    Atomradien, 301, 307
    Auslöschungen, 334, 342
    Avogadro-Konstante, 27
    Azimut, 44
    B
    B-Gitter, 110
    Basis, 25
    BaS04, 328, 402
    Baufehlern, 347
    Bauprinzipien der Kristalle, 297, 303
    Benzol, 142, 164, 238
    Blickrichtung, 86, 125, 135
    Braggsche Gleichung, 329
    Bravaisgitter, 113,114
    Bravais-Miller-Indizes, 153
    Buerger, 224, 319, 322
    Burgers-Vektor, 349
    C-Gitter, 108, 113
    C60, 306
    CaF2,311,312,314
    Calcit, 140
    Calcit-Typ, 320
    charakteristische Symmetrieelemente, 126, 166
    chiral, 171
    Cordierit, 3
    Coulomb-Gesetz, 306
    Coulomb-Kraft, 305
    Cristobalit, 314
    CsCl-Typ, 28, 311, 312, 314, 320
    Cu-Typ, 300, 301,303
    Cu20, 29, 376
    Cu3Au,318
    CuAu, 318
    Cuprit, 29
    Debye-Scherrer-Verfahren, 330
    Deckoperation, 11, 65
    Determinantenschema, 20
    Diadochie, 318
    Diamantstruktur, 298, 316, 324, 326, 399
    Dichte, 27
    Sachverzeichnis


    dilatative Umwandlung, 320
    Dipolmoment der Moleküle, 174
    Diskontinuum, 5
    displazive Umwandlung, 321
    dissymmetrisch, 171
    Disthen, 4
    ditetragonale Dipyramide, 147,148
    ditetragonale Pyramide, 151
    ditetragonales Prisma, 147,149
    ditrigonales Skalenoeder, 371
    Dolomit, 139
    Drehachse, Drehinversion, 75
    Drehinversionsachse, 75, 78, 79, 381, 382
    Drehspiegelachse, 76
    Drehung, 66, 67
    Ebenengruppe, 81, 209
    Edelgasstruktur, 304
    Eigensymmetrie, 163
    einfach primitiv, 13
    Einheitsfläche, 53
    Einheitsmatrix, 250
    Einkristall, 38
    elektrische Leitfähigkeit, 304
    Elementarmasche, 12
    Elementarzelle, 13
    Enantiomere, 171
    Enantiomorphie, 135
    erzeugende Symmetrie, 163
    Ethylen, 238
    Eulers che Polyederformel, 177
    Ewald-Konstruktion, 339
    Ewald, P.P., 336
    F-Gitter, 111, 113
    Fehlordnung, 348
    Festkörperreaktionen, 349
    Flächendefekt, 351
    Flächennormale, 34, 38-40
    Flächenpol, 39
    Flächensymmetrie, 145,148
    Flächenwinkel, 39
    flächenzentriert, 110, 111
    Fluorittyp, 310, 312, 314
    Flüssigkeit, 5, 6
    formbeständig, 5
    Forsterit, 311
    Freiheitsgrad, Frenkel-Fehlordnung, 348
    Fullerene, 305
    G
    Galenit, 32, 54, 61, 364
    Gangunterschied, 329
    Gas, 5, 6
    Gesetz der Winkelkonstanz, 37
    Gips, 4, 66
    Gitter, 12, 13,25, 113
    Gitterebene, 12,16
    Gittergerade, 11,15, 31
    Gitterparameter, 12, 13
    Gitterpunkt, 11, 13
    Gitter-Translation, Gitter-Translation, Glanzwinkel, 329
    gleichwertig, 68, 81
    Gleitspiegelebene, 201, 202
    Gleitspiegelung, 201, 204
    Gleitvektor, 202
    gnomonische Projektion, 54
    Goniometer, 41
    Graphit-Struktur, 324, 326, 399
    Grenzform, 146
    Großkreis, 40, 43
    Gruppen, 264
    Gruppen endlicher Ordnung, 266
    Gruppen unendlicher Ordnung, 266
    Gruppenaxiome, 264
    Gruppentafel, 270
    H
    Habitus, 33, 36
    Hermann-Mauguin-Symbolik, 133
    heteropolare Bindung, 297
    Hexaederkoordination, 299, 311
    hexagonal, 96,113, 153, 157,166, 170
    hexagonal dichteste Kugelpackung, 300, 302, 305, 353
    hexagonale Dipyramide, 195, 368
    hexagonale Pyramide, 194, 368
    hexagonales Prisma, 194, 368
    hexagonales Trapezoeder, 372
    HgNH4Cl3,328, 401
    (hkil), 153, 157
    (hkl), 16, 145, 333
    Sachverzeichnis

    homogen, 7
    I-Gitter, 110, 113
    Idealkristall, 347
    identisch, 12, 68
    Ikosaeder, 177, 374
    Indizierung, 48,150
    innenzentriertes Gitter, 110,113
    International Tables for Crystallography, 226
    Internationale Symbolik, 133,168, 216
    invers, 250
    Inversion, 67, 72
    Inversionszentrum, 67, 72
    Ionenbindung, 297
    Ionenradien, 306, 307
    Ionenstruktur, 305
    isometrisch, 33
    isomorphe Gruppen, 270
    Isomorphic, 319
    isotrop, 4
    Isotypie, 316
    JCPDS-Kartei, 335
    K
    Keim, 35
    Keimbildung, 35
    Kleinkreis, 43
    Kleinwinkelkorngrenze, 351
    Kombination, 73
    Komplikationsregel, 51
    Konformation, 140,165
    Kontinuum, 5
    Koordinatensystem, 12, 255
    Koordination, 298
    Koordinationspolyeder, 298
    Koordinationszahl, 298, 320
    Koppelung, 73, 201
    Korund-Typ, 310
    kovalente Bindung, 297
    kovalente Struktur, 316
    kreistreu, 44
    Kristall, Kristallaggregat, 38
    Kristallbaufehler, 347
    Kristallfläche, Kristallform, 33, 144
    Kristallkante, 31
    kristallographische Achse, 12, 125
    Kristallstrukturbestimmung, 342
    Kristallstrukturen, 25, 26, 31, 221, 235, 301, 303, 342
    Ag, Au, 318
    AI2O3, 310
    AIB2, 29, 376
    a-Polonium, 11,303, 304
    Antifluorit, 310
    BaS04,328,402
    Benzol, 238
    CaF2, 311, 312, 314
    Cristobalit, 314
    CsCl-Typ, 28, 311, 312, 314, 320
    Csl, 28
    Cu-Typ, 300, 303
    Cu20, 29, 376
    Cu3Au, 318
    CuAu, 318
    Cuprit, 29, 376
    Diamant, 316, 324, 326, 399
    Ethylen, 238
    Fluorit, 310,312,314
    Forsterit, 311
    Graphit, 324, 326, 399
    hexagonal dichteste Kugelpackung, 300, 302, 303, 305, 353
    HgNH4Cl3,328, 401
    Korund-Typ, 310
    kubisch dichteste Kugelpackung, Mg-Typ, 300, 302, 303, 305
    NaCl-Typ, 309
    NiAs-Typ, 310, 315, 316
    Pyrit, 327, 401
    Quarz (Hoch), 323
    Quarz (Tief), 323
    Rutil, 235,312,315
    Si02,315
    Sn02, 342
    Spinell-Typ, 309
    Stishovit, 315
    TiC>2, 235, 312, 315
    Tridymit, 323
    Urotropin (Hexamethylentetramin), 238
    W-Typ, 303
    Wurtzit, 313
    Zinkblende, 313, 319
    ZnS, 313, 319
    Sachverzeichnis

    Kristallsymmetrie, 133
    Kristallsystem, Kristallwachstum, 35
    kubisch, 98,113, 158, 162, 166, 170
    kubisch dichteste Kugelpackung, Kuboktaeder, 299, 303
    L
    Lagensymmetrie, Laue-Gruppen, Laue-Symbol, 333
    Liniendefekt, 349
    M
    Matrix, 260
    Metallbindung, 297
    Metallstruktur, 300
    Methan, 143, 167
    Mg-Typ, 300, 302, 303, 305
    Miller sehe Indizes, 16
    Mischkristalle, 316, 348
    Modellnetze, 363
    molare Masse, 27
    Molekülstruktur, 304
    Molekülsymmetrie, 163
    monoklin, 88,113, 130, 162, 166, 168
    Morphologie, morphologisches Achsenverhältnis, 53
    Mosaikbau, 354
    N
    NaCl, 3,143
    NaCl-Typ, 309, 312
    Netzebene, 12,16, 31, 85, 329
    Netzebenen, 85
    Netzebenenabstand, 331
    Netzebenenscharen, 329
    NiAs-Typ, 310, 315
    nichtkristallographische Punktgruppen, 164, 174, 175
    Normalenwinkel, 39
    O
    Obergruppe, 266, 284
    Oktaeder, 47, 195, 369
    Oktaederkoordination, 299, 309
    Oktaederlücke, 301
    optische Aktivität, Ordnung der Gruppe, 132
    orthographische Projektion, 55, 224
    orthorhombisch, 90,113,130,159,162,166,168
    P
    P-Gitter, 85,113
    P2/c, 229
    Packungs dichte, 302
    Pauling-Regel, 314
    Pentagondodekaeder, 177, 374
    periodisch homogen, 6, 7
    Phasenübergänge, 290
    Piezoelektrizität, Pinakoid, 33,147
    planar, 33
    plastische Verformung, 304
    Pleochroismus, 4
    polar, 166
    Poldistanz, 44
    Polymorphie, 319
    Polytypie, 324
    Präzessionsaufnahme, 341
    Prinzip der dichten Packung, 297
    prismatisch, 33
    Pulverdiagramm, 333
    Punktdefekt, 348
    Punktgitter, 11
    Punktgruppen, 129, 236, 237, 267
    Punktgruppenbestimmung, 166
    Punktsymmetrieelement, 77, 219
    Pyrit, 143
    Pyritstruktur, 327, 401
    Pyroelektrizität,
    Q
    Quarz, 36, 140, 172
    Quarz (Hoch), 290, 323
    Quarz (Tief), 140, 290, 323
    R-Gitter, 94,113
    Radienquotient, 299, 309, 311, 313
    Raumerfüllung, 302
    Raumgitter, Raumgruppen, 101, 213, 217, 237
    C2, 215, 229
    C2/c, 214, 229
    C2/m, 214, 229
    C2/m 2/m 2/m, 389
    Cc, 215, 229
    Cm, 215, 229, 243, 390
    Sachverzeichnis

    I2/m 2/m 2/m, 389
    Ibm2, 243, 391
    PI, 87, 101,245, 390, 394
    P2, 215
    P2/c, 214, 229
    P2/m, 88, 214, 222, 245, 395
    P2/m 2/m 2/m, 90,102, 103, 245, 395
    P2/m 2/n2i/a, 243, 391
    P2/m3, 392
    P2i/b2i/c2i/a, 393
    P2i/c, 229
    P4/m 2/m 2/m, 92, 93,104,105
    P4/m3 2/m, 391
    P4/m 3 2/m, 98, 109, 224
    P6/m 2/m 2/m, 96, 107
    P2i, 215
    P2i/a 3, 327,401
    P2i/b2/c2i/n, 262
    P2i/c,214
    P2i/m, 214
    P3 2/m, 94
    P42/m21/n 2/m, 227
    P42bc, 243, 391
    P6i, 223
    P422, 393, 394
    Pba2, 243, 390
    Pc, 215, 229
    Pca21,229
    Pm, 215, 245, 394
    Pmm2, 218
    Pna21,221
    Pnc2, 243, 390
    Realkristall, 347
    Rechtsschraube, 205
    Rechtssystem, 12, 205
    Reflexionsgoniometer, 41
    rekonstruktive Umwandlung, 320, 321
    reziprokes Gitter, 336
    Rhombendodekaeder, 3, 363
    rhombische Dipyramide, 195, 365
    rhombische Pyramide, 194, 365
    rhombisches Prisma, 194, 365
    Rhomboeder, 195, 370
    Rutil, 62, 139, 312, 379
    Rutil-Struktur, 235, 312, 315, 327, 400
    S
    Schönflies-Symbolik, 133, 134
    Schottky-Fehlordnung, 348
    Schraubenachse, 202, 205
    Schraubenversetzung, 349
    Schraubung, 201
    Schraubungsvektor, 205
    Si02,140
    Si02-Strukturen, 314, 315, 323
    Spaltbarkeit, 3
    Spaltenvektor, 251
    spezielle Form, 146
    spezielle Netzebene, 82
    spezielle Punktlage, 220
    Spiegelebene, 66, 71
    Spiegelung, 66, 71
    Spinell-Typ, 309
    Spinellzwilling, 352, 373
    Stapelfehler, 351
    statistisch homogen, 7
    Steno, 37
    Stereographische Projektion, 38
    strukturelle Achsenverhältnis, 53
    Strukturverwandtschaffen, 286
    Stufenversetzung, 349
    Substitutionsmischkristalle, 318
    Symmetrie, 65
    Symmetrieebene, 71
    Symmetrieelement, Symmetriegruppe, 249
    Symmetrieoperation, 65, 227, 264
    Symmetrieoperation in Matrizendarstellung, 249
    Symmetrieprinzip, 65, 297
    Symmetrierichtung, Symmetriesatz, 100
    Symmetriesatz I, 100, 272
    Symmetriesatz II, 100, 272
    Symmetriezentrum, 72
    T
    taflig, 33
    tautozonal, 34
    Tetraeder, 195, 369
    Tetraederkoordination, 299, 313
    Tetraederlücke, 301
    tetragonal, 92, 93, 113, 155, 166, 169
    tetragonale Dipyramide, 147,195, 366
    tetragonale Pyramide, 41, 151, 194, 366
    tetragonales Prisma, 41, 147,194, 366
    tetragonales Skalenoeder, 371
    thermische Leitfähigkeit, 304
    Sachverzeichnis

    Ti02, 139, 235,312
    Topas, 48
    Tracht, 33
    Transformationen durch Änderung des Bindungscharakters, 324
    Transformationen durch Ordnung-Unordnung, 322
    Transformationen in erster Koordination, 319
    Transformationen in zweiter Koordination, 321
    Translationenuntergruppe, 267
    Translations-Gitter, 81,113,114
    translatorisch gleichwertig, 12, 68
    Tridymit-Struktur, 323
    trigonal, 94, 113, 153,157, 166, 169
    trigonale Dipyramide, 195, 367
    trigonale Pyramide, 194, 367
    trigonales Prisma, 194, 367
    triklin, 87, 101, 113, 130, 162, 166, 168
    Turmalin, 140
    U
    Überstrukturen, 318
    Untergruppe, 132, 232, 266, 272, 286, 290
    Urotropin (Hexamethylentetramin), 238
    uvw, 13, 15
    V
    Van-der-Waals-Bindung, 297
    Versetzung, 349
    Vitamin Bi2, 305
    volumenbeständig, 5
    von Laue, 329
    W
    W-Typ, 303
    Wachstumsgeschwindigkeit, 36
    Wechselwirkungsprinzip, 297
    Weinsäure, 135
    Winkelkoordinate, 43, 44
    winkeltreu, 44
    Wulff sches Netz, 43
    Würfel, 195, 369
    Wurtzittyp, 313
    Wyckoff-Bezeichnung, 228
    X
    x, y, z, 25
    Zahl der Formeleinheiten pro Elementarzelle, 27, 334
    Zähligkeit, 67, 219
    Zeilenvektor, 252
    Zinkblendetyp, 313, 319
    ZnS, 313,319
    Zone, 33, 39
    Zonenachse, 34, 39, 45
    Zonengleichung, 18, 34
    Zonenkreis, 40, 46
    Zonenpol, 45
    Zwillinge, 291, 351
    Zwillingselement, 352
    Zwillingsgrenze, 351