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Transition‐Active k = O Representations and the Microscopic Description of Phase Transitions
Author(s) -
Agyei A. K.,
Birman J. L.
Publication year - 1977
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220800212
Subject(s) - phase transition , crystal (programming language) , condensed matter physics , point group , mathematics , tensor (intrinsic definition) , irreducible representation , mathematical physics , physics , pure mathematics , combinatorics , computer science , programming language
Cell preserving transitions that give rise to localized physical quantities are considered from the standpoint of the phase transformations of the individual crystal sublattices. Such transitions are shown to be associated not with irreducible crystal point‐group representations, but with certain generalized transitive imprimitive representations of the transitive permutation groups of the “transforming” sublattices. These representations allow a microscopic treatment of any such transition, and it is shown, in particular, that the thermodynamic order of a crystal transition depends on the microscopic structures of the transforming sublattices. Further, it is shown on the basis of a Landau‐type crystal free‐energy expansion that at least one linear combination of the components of the (generalized) zero‐field inverse susceptibility tensor, χ +1 , of the crystal should go to zero at the transition temperature T c . The case of structural transitions, for which χ +1 is the elasticity tensor, is considered in some detail. It is shown that if a structural transition is brought about by the spontaneous distortion of a sublattice of site point group H ⊆ D 4h , then either one of the shear moduli c s = 1/2 ( c 11 – c 12 ) and c 44 will go to zero at T c .