Ferroelastic phase transitions: structure and microstructure

Abstract

Landau-type theories describe the observed behaviour of phase transitions in ferroelastic and co-elastic minerals and materials with a high degree of accuracy. In this review, the derivation of the Landau potential G = 1 2 A S [coth( S /T) À coth( S /T C )]Q 2 + 1 4 BQ 4 + F F F is derived as a solution of the general 0 4 model. The coupling between the order parameter and spontaneous strain of a phase transition brings the behaviour of many phase transitions to the mean-®eld limit, even when the atomistic mechanism of the transition is spin-like. Strain coupling is also a common mechanism for the coupling between multiple order parameters in a single system. As well as changes on the crystal structure scale, phase transitions modify the microstructure of materials, leading to anomalous mesoscopic features at domain boundaries. The mesostructure of a domain wall is studied experimentally using X-ray diffraction, and interpreted theoretically using Ginzburg±Landau theory. One important consequence of twin mesostructures is their modi®ed transport properties relative to the bulk. Domain wall motion also provides a mechanism for superelastic behaviour in ferroelastics. At surfaces, the relaxations that occur can be described in terms of order parameters and Landau theory. This leads to an exponential pro®le of surface relaxations. This in turn leads to an exponential interaction energy between surfaces, which can, if large enough, destabilize symmetrical morphologies in favour of a platelet morphology. Surface relaxations may also affect the behaviour of twin walls as they intersect surfaces, since the surface relaxation may lead to an incompatibility of the two domains at the surface, generating large strains at the relaxation. Landau theory may also be extended to describe the kinetics of phase transitions. Time-dependent Landau theory may be used to describe the kinetics of order±disorder phase transitions in which the order parameter is homogeneous. However, the time-dependent Landau theory equations also have microstructural solutions, explaining the formation of microstructures such as tweed.

First-principles calculations of the high-temperature phase transformation in yttrium tantalate

“…To expand the above equation for YTaO 4 , the relation between the tetragonal and the monoclinic lattice parameters must be formulated using an irreducible representation and then the spontaneous strains can be derived. The crystal symmetries of the high-temperature tetragonal and low temperature monoclinic phases of YTaO 4 are reported to be (I 41 /a) and (C 2 /c) respectively [27][28][29] .…”

“…This is believed to be the basis for the unusually high fracture toughness of YSZ thermal barrier coating at elevated temperatures 7 . In the search for other oxides capable of ferroelastic toughening, we have been studying the transformations in YTaO 4 to determine whether it, too, exhibits a ferroelastic phase transition. From in-situ X-ray diffraction experiments, the high symmetry scheelite-YTaO 4 (I 41 /a) is stabilized over monoclinic fergusonite-YTaO 4 (C 2 /c) phase above 1426…”

Identification of the Domain Walls Configuration in the Ferroelastic Nanosize Material La0.95Sr0.05Ga0.9Mg0.1O3-x

“…According to [28][29][30][31][32] they maintain their distribution in the crystal and determine the reversibility of strain fields because of their insignificant migration at comparatively low temperatures (≈ 700 K). At the transition to the paraelastic phase (or ferroelastic phase as in our case) the defect distribution remains unchanged and the same configuration of domains walls on cooling to the low temperature ferroelastic phase occurs [33]. In case of LSGM05 a phase transition from one ferroelastic phase to another one takes place, but the mechanism of reversibility of domain wall configurations is the same.…”

Structural evolution, strain and elasticity of perovskites at high pressures and temperatures

“…Each of q 1 , q 2 , ... can then be related to angles of rotation about different tilt axes. Details of Landau theory applied to minerals have been described in many reviews, including, for example, Salje (1991Salje ( , 1992, Carpenter (1988Carpenter ( , 1992Carpenter ( , 2000Carpenter ( , 2002, Carpenter et al (1998a), Carpenter and Salje (1998), Redfern (2000) and Salje et al (2005). Selected results for perovskites are given below without further explanation.…”