空间群
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在数学和物理学中,空间群是空间中(通常是三维空间)一种形态的空间对称群。在三维空间中有219种不同的类型,或230种不同的手性类型。对超过三维的空间中的空间群也有研究,它们有时被称作比贝尔巴赫群,并且是离散的紧群,具有欧氏空间的等距同构。
在晶体学中,空间群也被称为费奥多罗夫群,是对晶体对称型的一种描述。三维空间群的权威参考文献是《国际晶体学表》(Hahn(2002))。
参考资料[编辑]
- Barlow, W, Über die geometrischen Eigenschaften starrer Strukturen und ihre Anwendung auf Kristalle, Z. Kristallogr., 1894, 23: 1–63
- Bieberbach, Ludwig, Über die Bewegungsgruppen der Euklidischen Räume, Mathematische Annalen, 1911, 70 (3): 297–336, ISSN 0025-5831, doi:10.1007/BF01564500
- Bieberbach, Ludwig, Über die Bewegungsgruppen der Euklidischen Räume (Zweite Abhandlung.) Die Gruppen mit einem endlichen Fundamentalbereich, Mathematische Annalen, 1912, 72 (3): 400–412, ISSN 0025-5831, doi:10.1007/BF01456724
- Brown, Harold; Bülow, Rolf; Neubüser, Joachim; Wondratschek, Hans; Zassenhaus, Hans, Crystallographic groups of four-dimensional space, New York: Wiley-Interscience [John Wiley & Sons], 1978, ISBN 978-0-471-03095-9, MR0484179
- Burckhardt, Johann Jakob, Die Bewegungsgruppen der Kristallographie, Lehrbücher und Monographien aus dem Gebiete der exakten Wissenschaften 13, Verlag Birkhäuser, Basel, 1947, MR0020553
- Burckhardt, Johann Jakob, Zur Geschichte der Entdeckung der 230 Raumgruppen, Archive for History of Exact Sciences, 1967, 4 (3): 235–246, ISSN 0003-9519, doi:10.1007/BF00412962, MR0220837
- Conway, John Horton; Delgado Friedrichs, Olaf; Huson, Daniel H.; Thurston, William P., On three-dimensional space groups, Beiträge zur Algebra und Geometrie. Contributions to Algebra and Geometry, 2001, 42 (2): 475–507, ISSN 0138-4821, MR1865535
- Fedorov, E. S., Symmetry of Regular Systems of Figures, Zap. Mineral. Obch., 1891, 28 (2): 1–146
- Fedorov, E. S., Symmetry of crystals, ACA Monograph 7, American Crystallographic Association, 1971
- Hahn, Th., Hahn, Theo, 编, International Tables for Crystallography, Volume A: Space Group Symmetry A 5th, Berlin, New York: Springer-Verlag, 2002, ISBN 978-0-7923-6590-7, doi:10.1107/97809553602060000100
- Hall, S.R., Space-Group Notation with an Explicit Origin, Acta Cryst., 1981, A37: 517–525
- Janssen, T.; Birman, J.L.; Dénoyer, F.; Koptsik, V.A.; Verger-Gaugry, J.L.; Weigel, D.; Yamamoto, A.; Abrahams, S.C.; Kopsky, V., Report of a Subcommittee on the Nomenclature of n-Dimensional Crystallography. II. Symbols for arithmetic crystal classes, Bravais classes and space groups, Acta Cryst. A, 2002, 58 (Pt 6): 605–621, doi:10.1107/S010876730201379X
- Kim, Shoon K., Group theoretical methods and applications to molecules and crystals, Cambridge University Press, 1999, ISBN 978-0-521-64062-6, MR1713786
- Litvin, D.B., Tables of crystallographic properties of magnetic space groups, Acta Cryst. A, May 2008, 64 (Pt 3): 419–24, Bibcode:2008AcCrA..64..419L, PMID 18421131, doi:10.1107/S010876730800768X
- Litvin, D.B., Tables of properties of magnetic subperiodic groups, Acta Cryst. A, May 2005, 61 (Pt 3): 382–5, Bibcode:2005AcCrA..61..382L, PMID 15846043, doi:10.1107/S010876730500406X
- Neubüser, J.; Souvignier, B.; Wondratschek, H., Corrections to Crystallographic Groups of Four-Dimensional Space by Brown et al. (1978) [New York: Wiley and Sons], Acta Cryst. A, 2002, 58 (Pt 3): 301, doi:10.1107/S0108767302001368
- Opgenorth, J; Plesken, W; Schulz, T, Crystallographic Algorithms and Tables, Acta Cryst. A, 1998, 54 (Pt 5): 517–531, doi:10.1107/S010876739701547X
- Plesken, Wilhelm; Hanrath, W, The lattices of six-dimensional space, Math. Comp., 1984, 43 (168): 573–587
- Plesken, Wilhelm; Schulz, Tilman, Counting crystallographic groups in low dimensions, Experimental Mathematics, 2000, 9 (3): 407–411, ISSN 1058-6458, MR1795312
- Schönflies, Arthur Moritz, Theorie der Kristallstruktur, Gebr. Bornträger, Berlin., 1891
- Souvignier, Bernd, The four-dimensional magnetic point and space groups, Z. Kristallogr., 2006, 221: 77–82
- Vinberg, E., Crystallographic group, (编) Hazewinkel, Michiel, 数学百科全书, Springer, 2001, ISBN 978-1-55608-010-4
- Zassenhaus, Hans, Über einen Algorithmus zur Bestimmung der Raumgruppen, Commentarii Mathematici Helvetici, 1948, 21: 117–141, ISSN 0010-2571, doi:10.1007/BF02568029, MR0024424[永久失效連結]
外部链接[编辑]
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维基共享资源中相关的多媒体资源:空间群 |
- International Union of Crystallography
- Point Groups and Bravais Lattices
- [1] Bilbao Crystallographic Server
- Space Group Info (old)
- Space Group Info (new)
- Crystal Lattice Structures: Index by Space Group
- Full list of 230 crystallographic space groups
- Interactive 3D visualization of all 230 crystallographic space groups
- Huson, Daniel H., The Fibrifold Notation and Classification for 3D Space Groups (PDF), 1999
- The Geometry Center: 2.1 Formulas for Symmetries in Cartesian Coordinates (two dimensions)
- The Geometry Center: 10.1 Formulas for Symmetries in Cartesian Coordinates (three dimensions)
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