Surveys recent theories on the transition between commensurate (C) and incommensurate (I) phases, and on properties of the I phase. The devil's staircase concept for the I phase is described. Differences between theories in two and three dimensions are discussed, together with those on chaotic structures.

https://iopscience.iop.org/article/10.1088/0034-4885/45/6/001/pdf

Commensurate phases, incommensurate phases and the devil's staircase

Experimental studies of structurally incommensurate crystal phases

Structural phase transitions can be studied by a variety of techniques; macroscopic fields, X-ray, light and neutron diffraction, and resonance methods. The information which can be obtained by these different techniques about the order parameter and susceptibility at structural phase transitions is described and compared. Landau theory coupled with the ‘soft mode’ concept provides a simple picture of many structural phase transitions in terms of relatively few phenomenological constants. A review is given of the application of this type of theory to the wide variety of different phenomena which can occur at structural phase transitions. In particular, emphasis is placed on the nature of the fluctuations within Landau-Ginzburg theory and on the role of secondary order parameters. The nature of incommensurate phases and of lock-in phase transitions are discussed using both the conventional lattice dynamical approach and the soft soliton theories. The parameters of the Landau theory can, in princip...

Structural phase transitions I. Landau theory

Recent theoretical and experimental studies on the critical properties of frustrated antiferromagnets with non-collinear spin order, including stacked-triangular antiferromagnets and helimagnets, are reviewed. Particular emphasis is put on the novel critical and multicritical behaviours exhibited by these magnets, together with the important role played by the `chirality'.

https://iopscience.iop.org/article/10.1088/0953-8984/10/22/004/pdf

Universality of phase transitions of frustrated antiferromagnets

A new investigation of the system Ni–Sn

The authors examined the behaviour of a wide variety of systems undergoing structural phase transitions to a phase incommensurate with the high-temperature structure. With the aid of renormalisation group methods they argued that, in the cases examined, either the critical behaviour is effectively that of the n=2 component Heisenberg model or the phase transition is first order.

https://iopscience.iop.org/article/10.1088/0022-3719/11/17/012/pdf

R A Cowley

Papers

The theory of structurally incommensurate systems. I. Disordered-incommensurate phase transitions