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Symmetry Relationships between Crystal StructuresApplications of Crystallographic Group Theory in Crystal Chemistry$
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Ulrich Müller

Print publication date: 2013

Print ISBN-13: 9780199669950

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199669950.001.0001

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Symmetry relations at phase transitions

Symmetry relations at phase transitions

Chapter:
(p.196) (p.197) 15 Symmetry relations at phase transitions
Source:
Symmetry Relationships between Crystal Structures
Author(s):

Ulrich Müller

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199669950.003.0015

Phase transitions in the solid state are classified as being continuous or discontinuous. According to Landau theory, continuous phase transitions require that there is a group-subgroup relation between the space groups of the involved crystal structures. They are driven by certain vibrational modes (soft modes) that must satisfy certain symmetry conditions. A phase transition which involves a symmetry reduction can often result in a topotactic texture consisting of domains. These are twin domains if there is a translationengleiche group-subgroup relation between the space groups of the phases, and antiphase domains if it is a klassengleiche relation. The index of the symmetry reduction determines how many kinds of domains may appear. Reconstructive phase transitions cannot proceed via a hypothetical intermediate phase whose symmetry is an assumed common subgroup of the two involved space groups.

Keywords:   phase transitions, topotactic texture, Landau theory, soft modes, twin domains, vibrational modes

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