Extensions and some recent applications of the Landau theory of phase transitions

Abstract

The basic concepts of the Landau theory of phase transitions are introduced through working examples. A number of rules governing the application of the theory to second and first-order transitions are given. The approach to magnetostructural transitions in magnetic mulltiferroic materials is detailed. Examples of transitions induced by replica of the same order-parameter in superconducting and liquid crystal systems, are described. The theory of reconstructive transitions is outlined and illustrated by the examples of the graphite-diamond transition and by the phase diagram of iron. An extention of the phenomenological approach to incommensurate structures to the crystal-amorphous transition is proposed (see also the chapter by Perez-Mato et al. for further discussion and applications).

Crystal symmetry of stripe-ordered La1.88Sr0.12CuO4

“…The emergence of CDW order can be interpreted as the consequence of a displacive continuous phase transition where the space group symmetries, before and after the transition, are connected by a group-subgroup relation. Group theory [21][22][23] indicates which of the possible modulated displacement patterns are consistent with the observed CDW ordering wave vectors. Symmetry analysis indicates that the stripe order observed in the LSCO system is not consistent with space group 64 as in this space group the [1, 0, 0] t and [0, 1, 0] t directions and all the CuO 6 octahedra are equivalent [24].…”

Monoclinic–orthorhombic first-order phase transition in K2ZnSi5O12 leucite analogue; transition mechanism and spontaneous strain analysis

“…All of these studies interpreted aspects of the phase transitions for natural leucite in terms of Landau Theory, which was developed initially for continuous second-order transformations. However, subsequent research showed that this approach could be extended to describe first-order and reconstructive phase transitions, and even to incommensurate phases (Tolédano and Tolédano, 1987; Tolédano, 2012). In the present case, as mentioned above, Group Theory shows that a phase transition from Pbca to P 2 1 /c is permitted to be second order as it satisfies both the Landau and Lifshitz criteria, but this does not preclude such a transition being first-order that is system dependent.…”

“…Aitta, 2009); such a first-order transition will be characterised by the presence of discontinuities in symmetry-breaking and non-symmetry breaking strains, and perhaps by the occurrence of a two-phase region (e.g. also see Salje, 1990; Hayward et al , 2000; Tolédano, 2012). Redfern and Henderson (1996) have already shown for T -site ordered KMg-Lc leucite that the symmetry relations for the P 2 1 /c to Pbca transition satisfy the general Landau and Lifshitz criteria and that discontinuities in both the volume and the shear strain (e 13 , see below) indicate a first-order mechanism.…”