International Tables for Crystallography, Volume A1: Symmetry relations between space groups (repost)

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International Tables for Crystallography, Volume A1: Symmetry relations between space groups (repost)

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This volume 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.

Group-subgroup relations, apart from their theoretical interest, are the basis of a number of important applications in crystallographic research:
(1) In solid-state phase transitions there often exists a group-subgroup relation between the symmetry groups of the two phases. According to Landau theory, this is in fact mandatory for displacive (continuous, second-order) phase transitions. Group-subgroup relations are also indispensable in cases where the symmetry groups of the two phases are not directly related but share a common subgroup or supergroup.
(2) Group-subgroup relations provide a concise and powerful tool for revealing and elucidating relations between crystal structures. They can thus help to keep up with the ever-increasing amount of crystal-structure data. Their application requires knowledge of the relations of the Wyckoff positions of group-subgroup related structures.
(3) Group-subgroup relations are of great importance in the study of twinned crystals, domain structures and domain boundaries.
(4) These relations can even help to identify errors in space-group assignment and crystal-structure determination.
(5) Subgroups of space groups provide a valuable approach to teaching crystallographic symmetry.