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Autoren:
Verlag:
Springer-Verlag Weitere Titel dieses Verlages anzeigen
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................................. | ||
6 | Das Symmetrieprinzip | 65 |
6.1 | Drehachsen | 67 |
6.2 | Spiegelebene | 71 |
6.3 | Inversionszentrum | 72 |
6.4 | Koppelung von Symmetrieoperationen | 73 |
6.4.1 | Drehinversionsachsen | 75 |
6.4.2 | Drehspiegelachsen | 76 |
6.5 | Übungsaufgaben | 78 |
7 | Die 14 Translations-(Bravais-)gitter | 81 |
7.1 | Primitive Translationsgitter (P-Gitter) | 85 |
7.2 | Symmetrie der primitiven Translationsgitter | 98 |
7.2.1 | Symmetrie des triklinen P-Gitters | 100 |
7.2.2 | Symmetrie des monoklinen P-Gitters | 100 |
7.2.3 | Symmetrie des orthorhombischen P-Gitters | 102 |
7.2.4 | Symmetrie des tetragonalen P-Gitters | 104 |
7.2.5 | Symmetrie des hexagonalen P-Gitters | 106 |
7.2.6 | Symmetrie des kubischen P-Gitters | 108 |
7.3 | Zentrierte Translationsgitter | 108 |
7.4 | Symmetrie der zentrierten Translationsgitter | 114 |
7.5 | Übungsaufgaben | 115 |
8 | Die 7 Kristallsysteme | 125 |
9 | Die Punktgruppen | 129 |
9.1 | Die 32 kristallographischen Punktgruppen | 129 |
9.2 | Kristallsymmetrie | 133 |
9.2.1 | Kristallformen des tetragonalen Kristallsystems | 144 |
9.2.2 | Kristallformen des hexagonalen (trigonalen) Kristallsystems | 153 |
9.2.3 | Kristallformen des kubischen Kristallsystems | 162 |
9.2.4 Kristallformen des orthorhombischen, | ||
monoklinen und triklinen Kristallsystems | 162 | |
9.3 | Molekülsymmetrie | 163 |
9.4 | Punktgruppenbestimmung | 166 |
9.5 | Enantiomorphie | 171 |
9.6 | Punktgruppen und physikalische Eigenschaften | 171 |
9.6.1 | Optische Aktivität | 171 |
9.6.2 | Piezoelektrizität | 172 |
9.6.3 | Pyroelektrizität | 173 |
9.6.4 | Das Dipolmoment der Moleküle | 174 |
9.7 | Nichtkristallographische Punktgruppen | 174 |
9.8 | Übungsaufgaben | 178 |
10 | Die Raumgruppen | 201 |
10.1 | Gleitspiegelung und Schraubung | 201 |
10.1.1 | Gleitspiegelebenen | 202 |
10.1.2 | Schraubenachsen | 205 |
10.2 | Die 17 Ebenengruppen | 209 |
10.3 | Die 230 Raumgruppen | 213 |
10.4 | Eigenschaften der Raumgruppen | 218 |
10.5 | International Tables for Crystallography | 226 |
10.6 | Achsentransformationen | 232 |
10.7 | Raumgruppen und Kristallstruktur | 235 |
10.8 | Beziehungen zwischen Punkt- und Raumgruppen | 236 |
10.9 | Übungsaufgaben | 239 |
11 | Symmetriegruppen | 249 |
11.1 | Symmetrieoperationen in Matrizendarstellung | 249 |
11.2 | Eigenschaften einer Gruppe | 264 |
11.3 | Ableitung einiger Punktgruppen | 267 |
11.4 | Gruppentafeln | 270 |
11.5 | Gruppen - Untergruppen - Obergruppen | 272 |
11.5.1 | Gruppe-Untergruppe-Beziehungen | 272 |
11.5.2 | Gruppe-Obergruppe-Beziehungen | 284 |
11.5.3 | Strukturverwandtschaften | 286 |
11.5.4 | Beschreibung von displaziven Phasenübergängen | 290 |
11.6 | Übungsaufgaben | 292 |
12 | Grundbegriffe der Kristallchemie | 297 |
12.1 | Koordination | 298 |
12.2 | Metallstrukturen | 300 |
12.3 | Edelgas-und Molekülstrukturen | 304 |
12.4 | Ionenstrukturen | 305 |
12.4.1 | Ionenradien | 306 |
12.4.2 | Oktaederkoordination [6] | 309 |
12.4.3 | Hexaederkoordination [8] | 311 |
12.4.4 | Tetraederkoordination [4] | 313 |
12.5 | Kovalente Strukturen | 316 |
12.6 | Isotypie - Mischkristalle - Isomorphic | 316 |
12.7 | Polymorphie | 319 |
12.7.1 | Transformationen in 1. Koordination | 319 |
12.7.2 | Transformationen in 2. Koordination | 321 |
12.7.3 | Transformationen durch Ordnung-Unordnung | 322 |
12.7.4 | Transformationen durch Änderung des Bindungscharakters | 324 |
12.8 | Informationen über Kristallstrukturen | 324 |
12.9 | Übungsaufgaben | 325 |
13 | Röntgenographische Untersuchungen an Kristallen | 329 |
13.1 | Braggsche Gleichung | 329 |
13.2 | Debye-Scherrer-Verfahren | 330 |
13.3 | Reziprokes Gitter | 336 |
13.4 | Laue-Gruppen | 340 |
13.5 | Bestimmung einer Kristallstruktur | 342 |
13.6 | Übungsaufgaben | 346 |
14 | Kristallbaufehler | 347 |
14.1 | Punktdefekte | 348 |
14.2 | Liniendefekte | 349 |
14.3 | Flächendefekte | 351 |
15 | Anhang | 355 |
15.1 | Kristallographische Symbole | 355 |
15.2 | Symmetrieelemente | 356 |
15.3 Berechnung von Atomabständen und Winkeln | ||
in einer Kristallstruktur | 359 | |
15.4 | Kristallformen | 360 |
15.5 | Polyeder-Modellnetze | 363 |
16 | Lösungen der Übungsaufgaben | 375 |
Literaturverzeichnis | 405 | |
Sachverzeichnis | 409 | |
Ausschlagtafel (Wulffsches Netz) | 415 | |
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