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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

(p.196) (p.197) 15 Symmetry relations at phase transitions
Symmetry Relationships between Crystal Structures

Ulrich Müller

Oxford University Press

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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