3.1 Structural phase transitions

Physical properties of crystals

Second Online Edition (2013)

Part 3. Symmetry aspects of phase transitions, twinning and domain structures

  1. J.‐C. Tolédano4,†,
  2. V. Janovec2,‡,
  3. V. Kopský5,§,
  4. J. F. Scott3,¶,
  5. P. Boček1,‖

Published Online: 19 DEC 2013

DOI: 10.1107/97809553602060000915

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Tolédano, J.-C., Janovec, V., Kopský, V., Scott, J. F. and Boček, P. 2013. Structural phase transitions. International Tables for Crystallography. D:3:3.1:358–396.

Author Information

  1. 1

    Ecole Polytechnique, Route de Saclay, 91128 Palaiseau CEDEX, France

  2. 2

    Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic

  3. 3

    Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Prague 8, and Department of Physics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic

  4. 4

    Earth Sciences Department, University of Cambridge, Downing Street, Cambridge CB2 3EQ, England

  5. 5

    Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, 182 08 Praha 8, Czech Republic

Publication History

  1. Published Online: 19 DEC 2013



Aspects of phase transitions in crystals that are of interest to crystallographers are described in this chapter. The chapter starts with a brief introduction aimed at defining the field of structural transitions and the terminology used. The theory of structural phase transitions is then described. This theory relates the symmetry characteristics of the transitions to their physical characteristics. The application of the symmetry principles that derive from this theory is illustrated by the results contained in Tables and The first of these two tables concerns the simple but experimentally widespread situation in which a structural transition is not accompanied by a change in the number of atoms per primitive crystal cell. The second table concerns the general case, in which the number of atoms changes, and which corresponds to the onset of superlattice reflections at the phase transition. This table provides, for a set of hypothetical transformations, the various symmetry‐based predictions of the theory. The important topic of soft modes, which is related to the microscopic mechanism of a structural transition, is then discussed. The final section of the chapter is an introduction to the accompanying software package Group Informatics.


  • Curie temperature;
  • Landau theory;
  • Landau–Devonshire theory;
  • domain states;
  • enantiomorphism;
  • equitranslational phase transitions;
  • equitranslational subgroups;
  • ferroelastic materials;
  • ferroelastic phases;
  • ferroelastic transitions;
  • ferroelectric materials;
  • ferroelectric phases;
  • ferroelectric transitions;
  • ferroic classes;
  • ferroic domain states;
  • ferroic phases;
  • ferroic single‐domain states;
  • ferroic symmetry;
  • ferroic transitions;
  • free energy;
  • high‐symmetry phases;
  • high‐temperature superconductors;
  • irreducible representations;
  • low‐symmetry phases;
  • non‐equitranslational phase transitions;
  • order parameter;
  • parent phases;
  • parent symmetry;
  • phase transitions;
  • physical property tensors;
  • prototype phases;
  • soft modes;
  • superconductors;
  • tensor parameter