International Tables for Crystallography, Volume A1

Symmetry relations between space groups
2. Auflage 2010
ISBN: 978-1-4020-8207-8
Verlag: Springer-Verlag GmbH

Buch, Englisch, 768 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: International Tables for Crystallography

The International Tables for Crystallography are jointly published with the International Union of Crystallography. Each print volume can be purchased individually. In addition the complete set of Vol A-G is available both in print and online (see right hand column).Volume A1 presents a systematic treatment of the maximal subgroups and minimal supergroups of the crystallographic plane groups and space groups. It is an extension of and a supplement to Volume A, Space-group symmetry, in which only basic data for sub- and supergroups are provided.Volume A1 consists of three parts. Part 1 presents an introduction to the theory of space groups at various levels and with many examples. It includes a chapter on the mathematical theory of subgroups. Part 2 gives for each plane group and space group a complete listing of all maximal subgroups and minimal supergroups. The treatment includes the generators of each subgroup as well as any necessary changes of the coordinate system. Maximal isomorphic subgroups are given in parameterized form as infinite series because of the infinite number for each group. Graphs that illustrate the group-subgroup relations are also presented. Part 3 lists the relations between the Wyckoff positions of every space group and its subgroups. Again, the infinite number of maximal isomorphic subgroups of each space group are covered by parameterized series. Volume A1 is a valuable resource for scientists engaged in crystal-structure determination, crystal physics or crystal chemistry. It is essential for those interested in phase transitions, the systematic compilation of crystal structures, twinning phenomena and related fields of crystallographic research.

Zielgruppe

Research

Autoren/Hrsg.

Wondratschek, H.

Müller, U.

Fachgebiete

• Naturwissenschaften Chemie Physikalische Chemie Chemische Kristallographie
• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Geowissenschaften Geologie Petrologie, Mineralogie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Werkstoffkunde, Materialwissenschaft: Forschungsmethoden

Inhaltsverzeichnis

PART 1: SPACE GROUPS AND THEIR SUBGROUPS: Historical introduction.- General introduction to the subgroups of space groups.- Computer checking of the subgroup data.- The mathematical background of the subgroup tables.- Remarks on Wyckoff positions.- Trees of group-subgroup relations.- The Bilbao Crystallographic Server.- PART 2: MAXIMAL SUBGROUPS OF THE PLANE GROUPS AND SPACE GROUPS: Guide to the subgroup tables and graphs.- Tables of maximal subgroups of the plane groups.- Tables of maximal subgroups of the space groups.- Graphs for translationengleiche subgroups.- Graphs for klassengleiche subgroups.- PART 3: RELATIONS BETWEEN THE WYCKOFF POSITIONS: Guide to the tables.- Tables of the relations of the Wyckoff positions.- Appendix. Differences in the presentation of Parts 2 and 3.