Chapter

1.10 Tensors in quasiperiodic structures

Physical properties of crystals

Second Online Edition (2013)

Part 1. Tensorial aspects of physical properties

  1. T. Janssen

Published Online: 19 DEC 2013

DOI: 10.1107/97809553602060000909

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Janssen, T. 2013. Tensors in quasiperiodic structures. International Tables for Crystallography. D:1:1.10:246–268.

Author Information

  1. Institute for Theoretical Physics, University of Nijmegen, 6524 ED Nijmegen, The Netherlands

Publication History

  1. Published Online: 19 DEC 2013

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Abstract

This chapter is devoted to the symmetry‐related physical properties of quasiperiodic crystals. In the first part the symmetry properties are described: point groups, superspace groups and the action of symmetry groups. The second part concerns the properties of tensors in higher‐dimensional spaces, with emphasis on the particular cases of the piezoelectric, elastic and electric field gradient tensors. The last section gives tables of characters of some point groups for quasicrystals and of the matrices of the corresponding irreducible representations.

Keywords:

  • Fourier module;
  • compensating gauge transformations;
  • elastic constants;
  • electric field gradient;
  • icosahedral quasicrystals;
  • incommensurate structures;
  • irreducible representations;
  • metric tensor;
  • modulation wavevector;
  • octagonal quasicrystals;
  • piezoelectric tensor;
  • quasicrystals;
  • quasiperiodic structures;
  • superspace;
  • superspace groups;
  • tensors