International tables for crystallography: Volume A Space-group symmetry
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| Ausgabe: | Sixth edition |
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| 245 | 1 | 0 | |a International tables for crystallography |n Volume A |p Space-group symmetry |c ed. by Theo Hahn |
| 246 | 1 | 3 | |a Space group symmetry |
| 250 | |a Sixth edition | ||
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c [2016] | |
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| adam_text | Titel: Bd. A. International tables for crystallography. Space-group symmetry
Autor: Aroyo, Mois I
Jahr: 2016
INTERNATIONAL TABLES FOR CRYSTALLOGRAPHY Volume A SPACE-GROUP SYMMETRY Edited by MOIS I. AROYO Sixth Edition Published, for THE INTERNATIONAL UNION OF CRYSTALLOGRAPHY by Wiley 2016
Contents PAGE Foreword to the sixth edition (C. P. Brock) ........................................................ xv Preface (M. I. Aroyo) .................................................................... xvii Symbols for crystallographic items used in this volume ................................................ xx PART 1. INTRODUCTION TO SPACE-GROUP SYMMETRY l 1.1. A general introduction to groups (B. Souvignier) .......................................... 2 1.1.1. Introduction .................................................................... 2 1.1.2. Basic properties of groups ............................................................ 2 1.1.3. Subgroups ...................................................................... 4 1.1.4. Cosets ........................................................................ 5 1.1.5. Normal subgroups, factor groups ........................................................ 6 1.1.6. Homomorphisms, isomorphisms ........................................................ 7 1.1.7. Group actions .................................................................... 9 1.1.8. Conjugation, normalizers ............................................................ 10 1.2. Crystallographic symmetry (H. Wondratschek and M. I. Aroyo, with Tables 1.2.2.1 and 1.2.2.2 by H. Arnold) ...................................................................... 12 I. 2.1. Crystallographic symmetry operations .................................................... 12 1.2.2. Matrix description of symmetry operations .................................................. 13 1.2.2.1. Matrix-column presentation of isometries .............................................. 13 1.2.2.2. Combination of mappings and inverse mappings .......................................... 15 1.2.2.3. Matrix-column pairs and (3 + 1) x (3 + 1) matrices........................................ 10 1.2.2.4. The geometric meaning of (W, w)
.................................................. 10 1.2.2.5. Determination of matrix-column pairs of symmetry operations ................................ IS 1.2.3. Symmetry elements ................................................................ 19 1.3. A general introduction to space groups (B. Souvignier)...................................... 22 1.3.1. Introduction .................................................................... 22 1.3.2. Lattices........................................................................ 22 1.3.2.1. Basic properties of lattices ...................................................... 22 1.3.2.2. Metric properties ............................................................ 23 1.3.2.3. Unit cells .................................................................. 24 1.3.2.4. Primitive and centred lattices...................................................... 24 1.3.2.5. Reciprocal lattice ............................................................ 27 1.3.3. The structure of space groups .......................................................... 28 13.3.1. Point groups of space groups ...................................................... 28 1.3.3.2. Coset decomposition with respect to the translation subgroup .................................. 29 1.3.3.3. Symmorphic and non-symmorphic space groups .......................................... 31 1.3.4. Classification of space groups .......................................................... 31 13.4.1. Space-group types ............................................................ 31 13.4.2. Geometric crystal classes ........................................................ 33 1.3.43. Bravais types of lattices and Bravais classes ............................................ 34 13.4.4. Other classifications of space groups ................................................ 37 1.4. Space groups and their descriptions (B. Souvignier, H.
Wondratschek, M. I. Aroyo, G. Chapuis and A. M. Glazer) .................................................................... 42 1.4.1. Symbols of space groups (H. Wondratschek) ................................................ 42 I.4.I.I. Introduction ................................................................ 42 vii
CONTENTS 1.4.1.2. Space-group numbers .......................................................... 42 1.4.1.3. Sehoenflies symbols............................................................ 42 1.4.1.4. Hermann-Mauguin symbols of the space groups .......................................... 43 1.4.1.5. Hermann-Mauguin symbols of the plane groups .......................................... 48 1.4.1.6. Sequence of space-group types .................................................... 49 1.4.2. Descriptions of space-group symmetry operations (M. I. Aroyo, G. Chapuis, B. Souvignier and A. M. Glazer)........ 50 1.4.2.1. Symbols for symmetry operations .................................................. 50 1.4.2.2. Seitz symbols of symmetry operations ................................................ 51 1.4.2.3. Symmetry operations and the general position .......................................... 53 1.4.2.4. Additional symmetry operations and symmetry elements .................................... 55 1.4.2.5. Space-group diagrams .......................................................... 56 1.4.3. Generation of space groups (H. Wondratschek) .............................................. 59 1.4.3.1. Selected order for non-translational generators .......................................... 60 1.4.4. General and special Wyckoff positions (B. Souvignier) .......................................... 61 1.4.4.1. Crystallographic orbits .......................................................... 61 1.4.4.2. Wyckoff positions ............................................................ 62 1.4.4.3. Wyckoff sets ................................................................ 64 1.4.4.4. Eigensymmetry groups and non-characteristic orbits........................................ 66 1.4.5. Sections and projections of space groups (B. Souvignier) ........................................ 67 1.45.1. Introduction
................................................................ 67 1.4.5.2. Sections .................................................................. 68 1.4.5.3. Projections ................................................................ 71 1.5. Transformations of coordinate systems (H. Wondratschek, M. I. Aroyo, B. Souvignier and G. Chapuis) 75 1.5.1. Origin shift and change of the basis (H. Wondratschek and M. I. Aroyo, with Table 1.5.1.1 and Figs. 1.5.1.2 and 1.5.1.5-1.5.1.10 by H. Arnold).......................................................... 75 1.5.1.1. Origin shift ................................................................ 75 1.5.1.2. Change of the basis............................................................ 76 1.5.1.3. General change of coordinate system ................................................ 83 1.5.2. Transformations of crystallographic quantities under coordinate transformations (H. Wondratschek and M. I. Aroyo) 83 1.5.2.1. Covariant and contravariant quantities ................................................ 83 1.5.2.2. Metric tensors of direct and reciprocal lattices .......................................... 84 1.5.2.3. Transformation of matrix-column pairs of symmetry operations ................................ 84 1.5.2.4. Augmented-matrix formalism...................................................... 84 1.5.2.5. Example: paraelectric-to-ferroeleetric phase transition of GeTe ................................ 86 1.5.3. Transformations between different space-group descriptions (G. Chapuis, H, Wondratschek and M. I. Aroyo) ........ 87 1.5.3.1. Space groups with more than one description in this volume .................................. 87 1.5.3.2. Examples .................................................................. 88 1.5.4. Synoptic tables of plane and space groups (B. Souvignier, G. Chapuis and H. Wondratschek, with Tables 1.5.4.1-1.5.4.4 by E. F.
Bertaut).................................................................... 91 1.5.4.1. Additional symmetry operations and symmetry elements .................................... 91 1.5.4.2. Synoptic table of the plane groups .................................................. 95 1.5.4.3. Synoptic table of the space groups .................................................. 95 1.6. Methods of space-group determination (U. Shmueli, H. D. Flack and J. C. FI. Spence) .............. 107 1.6.1. Overview ...................................................................... 107 1.6.2. Symmetry determination from single-crystal studies (U. Shmueli and H. D. Flack) ........................ 107 1.6.2.1. Symmetry information from the diffraction pattern ........................................ 107 1.6.2.2. Structure-factor statistics and crystal symmetry .......................................... 109 1.6.2.3. Symmetry information from the structure solution ........................................ 110 1.6.2.4. Restrictions on space groups ...................................................... Ill viii
CONTENTS I.6.2.5. Pitfalls in space-group determination ................................................ Ill 1.6.3. Theoretical background of reflection conditions (U. Siimueli) ...................................... 112 1.6.4. Tables of reflection conditions and possible space groups (H. D. Flack and U. Shmueli) ...................... 114 1.6.4.1, Introduction ................................................................ 114 1.6.4.2. Examples of the use of the tables .................................................. 114 1.6.5. Specialized methods of space-group determination (H. D. Flack) .................................... 114 1.6.5.1. Applications of resonant scattering to symmetry determination ................................ 114 1.6.5.2. Space-group determination in macromolecular crystallography ................................ 126 1.6.5.3. Space-group determination from powder diffraction ........................................ 127 1.6.6. Space groups for nanocrystals by electron microscopy (J. C. FI. Spence) ................................ 128 1.7. Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography (H. WONDRATSCHEK, U. MÜLLER, D. B. LlTVIN AND V. KOPSKY) ................................ 132 1.7.1. Subgroups and supergroups of space groups (H. Wondratschek) .................................... 132 1.7.1.1. Translationengleiche (or (-) subgroups of space groups ...................................... 133 1.7.1.2. Klassengleiche (or k-) subgroups of space groups ........................................ 134 1.7.1.3. Isomorphic subgroups of space groups ................................................ 134 1.7.1.4. Supergroups ................................................................ 134 1.7.2. Relations between Wyckoff positions for group-subgroup-related space groups (U. Muller) .................. 133 1.7.2.1. Symmetry relations between crystal
structures .......................................... 135 1.7.2.2. Substitution derivatives ........................................................ 135 1.7.2.3. Phase transitions ............................................................ 135 1.7.2.4. Domain structures ............................................................ 136 1.7.2.5. Presentation of the relations between the Wyckoff positions among group-subgroup-related space groups ...... 136 1.7.3. Relationships between space groups and subperiodic groups (D. B. Litvin and V. Kopsky) .................... 136 1.7.3.1. Layer symmetries in three-dimensional crystal structures .................................... 137 1.7.3.2. The symmetry of domain walls .................................................... 138 PART 2. THE SPACE-GROUP TABLES i ll 2.1. Guide to the use of the space-group tables (Th. Hahn, A. Looijenga-Vos, M. I. Aroyo, H. D. Flack, K. Momma and P. Konstantinov) ...................................................... 142 2.1.1. Conventional descriptions of plane and space groups (Th. Hahn and A. Looijenga-Vos)...................... 142 2.1.1.1. Classification of space groups...................................................... 142 2.1.1.2. Conventional coordinate systems and cells.............................................. 142 2.1.2. Symbols of symmetry elements (Th. Hahn and M. I. Aroyo) ...................................... 144 2.1.3. Contents and arrangement of the tables (Th. Hahn and A. Looijenga-Vos).............................. 150 2.1.3.1. General layout .............................................................. 150 2.1.3.2. Space groups with more than one description ............................................ 150 2.1.3.3. Headline .................................................................. 151 2.1.3.4. International (Hermann-Mauguin) symbols for plane groups and space groups ...................... 151 2.1.3.5.
Patterson symmetry (H. D. Flack) .................................................. 152 2.1.3.6. Space-group diagrams .......................................................... 154 2.1.3.7. Origin .................................................................... 158 2.1.3.8. Asymmetric unit.............................................................. 159 2.1.3.9. Symmetry operations .......................................................... 160 2.1.3.10. Generators ................................................................ 161 2.1.3.11. Positions.................................................................. 162 2.1.3.12. Oriented site-symmetry symbols .................................................. 163 2.1.3.13. Reflection conditions .......................................................... 163 2.1.3.14. Symmetry of special projections .................................................. 167 ix
CONTENTS 2.1.3.15. Monoclinic space groups ........................................................ 169 2.1.3.16. Crystallographic groups in one dimension ............................................ 172 2.1.4. Computer production of the space-group tables (R Konstantinov and K. Momma).......................... 172 2.2. The 17 plane groups (two-dimensional space groups) ........................................ 175 2.3. The 230 space groups .............................................................. 193 PART 3. ADVANCED TOPICS ON SPACE-GROUP SYMMETRY 697 3.1. Crystal lattices (H. Burzlaff, H. Grimmer, B. Gruber, P. M. de Wolff and H. Zimmermann) ........ 698 3.1.1. Bases and lattices (H. Burzlaff and H. Zimmermann) .......................................... 698 3.1.1.1. Description and transformation of bases .............................................. 698 3.1.1.2. Lattices .................................................................. 698 3.1.1.3. Topological properties of lattices.................................................... 698 3.1.1.4. Special bases for lattices ........................................................ 698 3.1.1.5. Remarks .................................................................. 699 3.1.2. Bravais types of lattices and other classifications (H. Burzlaff and H. Zimmermann) ........................ 700 3.1.2.1. Classifications .............................................................. 700 3.1.2.2. Description of Bravais types of lattices ...................... ........................... 700 3.1.2.3. Delaunay reduction and standardization .................... .......................... 701 3.1.2.4. Example of Delaunay reduction and standardization of the basis ................................ 707 3.1.3. Reduced bases (P. M. de Wolff) ........................................................ 709 3.1.3.1. Introduction
................................................................ 709 3.1.3.2. Definition.................................................................. 709 3.1.3.3. Main conditions .............................................................. 709 3.1.3.4. Special conditions ............................................................ 710 3.1.3.5. Lattice characters ............................................................ 712 3.1.3.6. Applications ................................................................ 713 3.1.4. Further properties of lattices (B. Gruber and H. Grimmer) ........................................ 714 3.1.4.1. Further kinds of reduced cells .................................................... 714 3.1.4.2. Topological characterization of lattice characters .......................................... 714 3.1.4.3. A finer division of lattices ........................................................ 715 3.1.4.4. Conventional cells ............................................................ 715 3.1.4.5. Conventional characters ........................................................ 717 3.1.4.6. Sublattices ................................................................ 718 3.2. Point groups and crystal classes (Th. Hahn, H. Klapper, U. Muller and M. I. Aroyo) .............. 720 3.2.1. Crystallographic and noncrystallographic point groups (Th. Hahn and H. Klapper) ........................ 720 3.2.1.1. Introduction and definitions ...................................................... 720 3.2.1.2. Crystallographic point groups...................................................... 721 3.2.1.3. Subgroups and supergroups of the crystallographic point groups ................................ 731 3.2.1.4. Noncrystallographic point groups .................................................. 731 3.2.2. Point-group symmetry and physical properties of crystals (H. Klapper and Th. Hahn)
...................... 737 3.2.2.1. General restrictions on physical properties imposed by symmetry................................ 737 3.2.2.2. Morphology ................................................................ 739 3.2.2.3. Etch figures ................................................................ 740 3.2.2.4. Optical properties ............................................................ 740 3.2.2.5. Pyroelectricity and ferroelectricity .................................................. 741 3.2.2.6. Piezoelectricity .............................................................. 741 3.2.3. Tables of the crystallographic point-group types (H. Klapper, Th. Hahn and M. I. Aroyo) .................... 742 3.2.4. Molecular symmetry (U. Muller)........................................................ 772 X
CONTENTS 3.2.4.1. Introduction ................................................................ 772 3.2.4.2. Definitions ................................................................ 772 3.2.4.3. Tables of the point groups........................................................ 773 3.2.4.4. Polymeric molecules .......................................................... 774 3.2.4.5. Enantiomorphism and chirality .................................................... 775 3.3. Space-group symbols and their use (H. Burzlaff and H. Zimmermann) ........................ ill 3.3.1. Point-group symbols ................................................................ Ill 3.3.1.1. Introduction ................................................................ Ill 3.3.1.2. Schoenflies symbols............................................................ Ill 3.3.1.3. Shubnikov symbols ............................................................ Ill 3.3.1.4. Hermann-Mauguin symbols ...................................................... Ill 3.3.2. Space-group symbols................................................................ 779 3.3.2.1. Introduction ................................................................ 779 3.3.2.2. Schoenflies symbols............................................................ 779 3.3.2.3. The role of translation parts in the Shubnikov and Hermann-Mauguin symbols ...................... 779 3.3.2.4. Shubnikov symbols ............................................................ 779 3.3.2.5. International short symbols ...................................................... 780 3.3.3. Properties of the international symbols .................................................... 780 3.3.3.1. Derivation of the space group from the short symbol ...................................... 780 3.3.3.2. Derivation of the full symbol from the short symbol........................................ 781 3.3.3.3.
Non-symbolized symmetry elements.................................................. 781 3.3.3.4. Standardization rules for short symbols................................................ 782 3.3.3.5. Systematic absences............................................................ 789 3.3.3.6. Generalized symmetry .......................................................... 790 3.3.4. Changes introduced in space-group symbols since 1935 .......................................... 790 3.4. Lattice complexes (W. Fischer and E. Koch).............................................. 792 3.4.1. The concept of lattice complexes and limiting complexes.......................................... 792 3.4.1.1. Introduction ................................................................ 792 3.4.1.2. Crystallographic orbits, Wyckoff positions, Wyckoff sets and types of Wyckoff set...................... 792 3.4.1.3. Point configurations and lattice complexes, reference symbols .................................. 793 3.4.1.4. Limiting complexes and comprehensive complexes ........................................ 794 3.4.1.5. Additional properties of lattice complexes .............................................. 795 3.4.2. The concept of characteristic and non-characteristic orbits, comparison with the lattice-complex concept ............ 796 3.4.2.1. Definitions ................................................................ 796 3.4.2.2. Comparison of the concepts of lattice complexes and orbit types ................................ 796 3.4.3. Descriptive lattice-complex symbols and the assignment of Wyckoff positions to lattice complexes ................ 798 3.4.3.1. Descriptive symbols............................................................ 798 3.4.3.2. Assignment of Wyckoff positions to Wyckoff sets and to lattice complexes .......................... 800 3.4.4. Applications of the lattice-complex
concept.................................................. 800 3.4.4.1. Geometrical properties of point configurations .......................................... 800 3.4.4.2. Relations between crystal structures.................................................. 823 3.4.4.3. Reflection conditions .......................................................... 823 3.4.4.4. Phase transitions ............................................................ 823 3.4.4.5. Incorrect space-group assignment .................................................. 824 3.4.4.6. Application of descriptive lattice-complex symbols ........................................ 824 3.4.4.7. Weissenberg complexes ........................................................ 824 3.5. Normalizes of space groups and their use in crystallography (E. Koch, W. Fischer and U. Muller) .. .. 826 3.5.1. Introduction and definitions (E. Koch, W. Fischer and U. Muller) .................................. 826 xi
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| spelling | International tables for crystallography Volume A Space-group symmetry ed. by Theo Hahn Space group symmetry Sixth edition Dordrecht [u.a.] Kluwer [2016] xxi, 873 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Aroyo, Mois I. edt Hahn, Theo 1928-2016 Sonstige (DE-588)143795198 oth Shmueli, Uri Sonstige oth Wilson, Arthur J. C. 1914- Sonstige (DE-588)118186191 oth Internationale Union für Kristallographie Sonstige (DE-588)4721-1 oth (DE-604)BV001208471 A HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027567676&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | International tables for crystallography |
| title | International tables for crystallography |
| title_alt | Space group symmetry |
| title_auth | International tables for crystallography |
| title_exact_search | International tables for crystallography |
| title_full | International tables for crystallography Volume A Space-group symmetry ed. by Theo Hahn |
| title_fullStr | International tables for crystallography Volume A Space-group symmetry ed. by Theo Hahn |
| title_full_unstemmed | International tables for crystallography Volume A Space-group symmetry ed. by Theo Hahn |
| title_short | International tables for crystallography |
| title_sort | international tables for crystallography space group symmetry |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027567676&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001208471 |
| work_keys_str_mv | AT aroyomoisi internationaltablesforcrystallographyvolumea AT hahntheo internationaltablesforcrystallographyvolumea AT shmueliuri internationaltablesforcrystallographyvolumea AT wilsonarthurjc internationaltablesforcrystallographyvolumea AT internationaleunionfurkristallographie internationaltablesforcrystallographyvolumea AT aroyomoisi spacegroupsymmetry AT hahntheo spacegroupsymmetry AT shmueliuri spacegroupsymmetry AT wilsonarthurjc spacegroupsymmetry AT internationaleunionfurkristallographie spacegroupsymmetry |