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Superspace groups

Author

Listed:
  • Janner, A.
  • Janssen, T.

Abstract

Superspace groups have been introduced to describe the symmetry of n-dimensional incommensurate crystal phases. The (n + d)-dimensional Euclidean space in which these groups act as space groups has a distinguished n-dimensional subspace called position space. This implies that superspace groups are not merely (n + d)-dimensional space groups but that they have additional structure. Here the mathematical structure and properties of these groups is discussed. It is shown that the usual crystallographic concepts can be generalized. Taking into account the additional structure a definition is given for the equivalence of superspace groups. From this equivalence relation follow the equivalence relations for point groups and for lattices. A constructive method is given for the derivation of all (n + d)-dimensional superspace groups, their arithmetic and geometric crystal classes and their corresponding lattices starting from a knowledge of the n- and d-dimensional crystal classes.

Suggested Citation

  • Janner, A. & Janssen, T., 1979. "Superspace groups," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 99(1), pages 47-76.
    • Handle: RePEc:eee:phsmap:v:99:y:1979:i:1:p:47-76
    DOI: 10.1016/0378-4371(79)90124-9
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