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Landau theory

About: Landau theory is a research topic. Over the lifetime, 2882 publications have been published within this topic receiving 57078 citations.


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01 Feb 1997
TL;DR: In this paper, the authors proposed a collective mode of Pseudospins in Displacive Crystals and the Born-Huang Theory of Soft Modes, Lattice Anharmonicity and Pseudosphere Condensates in the Critical Region.
Abstract: Basic Concepts.- Thermodynamical Principles and the Landau Theory.- Order Variables, Their Correlations and Statistics: the Mean-Field Theory.- Collective Modes of Pseudospins in Displacive Crystals and the Born-Huang Theory.- Soft Modes, Lattice Anharmonicity and Pseudospin Condensates in the Critical Region.- Dynamics of Pseudospins Condensates and the Long-Range Order.- Experimental Studies.- Diffuse X-ray Diffraction and Neutron Inelastic Scattering from Modulated Crystals.- Light Scattering and Dielectric Studies on Structural Phase Transitions.- The Spin-Hamiltonian and Magnetic Resonance Spectroscopy.- Magnetic Resonance Sampling and Nuclear Spin Relaxation Studies on Modulated Crystals.- Structural Phase Transitions in Miscellaneous Systems.

65 citations

Journal ArticleDOI
TL;DR: A new Maier-Saupe-type model is developed, which explicitly shows the low-temperature saturation of the order parameters, and reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit.
Abstract: Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals---increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [Lopatina and Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.

65 citations

Journal ArticleDOI
TL;DR: In this article, the derivation of the Landau potential G = ½A θS [coth(θS/T) − coth(αS/TC)]Q2 + ¼BQ4 + … is derived as a solution of the general ϕ4 model.
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 = 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.

64 citations

Journal ArticleDOI
TL;DR: In this article, the authors give short and self-contained proofs of Γ-convergence results for Ginzburg-Landau energy functionals in two dimensions, in the logarithmic energetic regime.

64 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202317
202242
202142
202041
201949
201855