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 = ½AθS [coth(θS/T) − coth(θS/TC)]Q2 + ¼BQ4 + … is derived as a solution of the general ϕ4 model. The coupling between the order parameter and spontaneous strain of a phase transition brings the behaviour of many phase transitions to the mean-field 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 modified 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 profile 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.

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Ferroelastic phase transitions: structure and microstructure.

On the basis of the bond valence model, an approach is established to determine the dopant occupancy in the lithium niobate (LN) crystallographic frame. The dopant location can be easily assigned by comparing the deviation of its normal and calculated valence states, when such a dopant is arbitrarily placed in both ${\mathrm{Li}}^{+}$ and ${\mathrm{Nb}}^{5+}$ sites, respectively. Further, the parameter Global Instability Index is used to characterize the structural instability of doped LN crystals. The dopant occupancy in the LN crystallographic frame and its interaction with the LN matrix are quantitatively understood by the structural stability. Calculated threshold values of various dopants are further obtained in the present work.

Dopant occupancy and structural stability of doped lithium niobate crystals

Structural study of Li1+x-yNb1-x-3yTix+4yO3 solid solutions

Nanoscale domain switching at crystal surfaces of lithium niobate

The structure of LaAlO3 has been investigated around the phase transition at T(c) ≃ 800 K by neutron powder diffraction in vacuum and by X-ray powder diffraction under nitrogen atmosphere as well as by a very high resolution synchrotron experiment in air. The results were analysed in frame of the Landau theory using the fluctuation-dissipation theorem to relate the susceptibility to the atomic displacement parameters. The room temperature structure is a rhombohedrally distorted perovskite structure, space group R3c, which undergoes a transition to the ideal perovskite structure, space group Pm3m, at high temperatures. The order parameter is a rotation of the O6-octahedron described by one χ(O)-parameter. This parameter and the spontaneous strain (c/a - √6), as well as the relevant atomic displacement parameter U(op) 11(O) in the order parameter system, show a critical behaviour in agreement with a second order phase transition. Although the critical exponents of the order parameter and strain show the expected coupling behaviour, there is a striking difference of the transition temperature: the metric becomes cubic roughly 30 K below the proper T(c). This is related to spontaneous formation of domains imposing the average cubic symmetry via internal stresses.

A powder diffraction study of the phase transition in LaAlO3

The structural changes of stoichiometric LiNbO3 at temperatures up to 1470 K have been investigated by neutron powder diffraction. At Tc ≈ 1460 K, LiNbO3 transforms from a paraelectric high-temperature (R3c) to a ferroelectric low temperature structure (R3c). The phase transition is of coupled order-disorder and displacive type. In the high-temperature phase, Li is highly disordered over two off-centre positions, whereas Nb takes a centrosymmetric position within O6 octahedra. An analysis of anisotropic displacement parameters shows that the probability density function of Li is extended along c, that of the oxygens is more or less perpendicular to the Nb-O bonds, and that of Nb is slightly extended in the a - b plane at high temperatures. An increase of the tilt angle of the NbO6 octahedra away from an h.c.p. arrangement towards a perovskite structure was observed. The octahedra become almost regular at high temperatures. Comparison with an earlier investigation of congruent lithium niobate shows a quite similar behaviour, however, all parameters of the latter are closer to those of the perovskite structure at same temperatures. Anomalies in the behaviour of the order parameters, a more complicated disorder and a high mobility of Li at high temperatures are explained by the competition of the order-disorder and displacive character of the phase transition.

A. Hewat

Papers

A neutron powder investigation of the high-temperature structure and phase transition in stoichiometric LiNbO3