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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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TL;DR: The relaxation time as well as relaxation strength increased anomalously in the vicinity of the gel-to-liquid crystal transition of 41.5 degrees C, which represents the first definite evidence of the critical slowing down in the lipid bilayer.
56 citations
TL;DR: In this article, the elastic anomalies associated with displacive phase transitions are explained in terms of coupling between strain components and the driving order parameter in Landau free energy expansions, and they are used to identify the underlying thermodynamic mechanism for a phase transition.
Abstract: Elastic anomalies that accompany cation ordering and displacive phase transitions can be understood in terms of coupling between strain components and the driving order parameter in Landau free energy expansions. Non-convergent cation ordering in spinel, MgAl2O4, is accompanied by changes in individual elastic constants, shear modulus, and bulk modulus that vary linearly with the order parameter. Convergent cation ordering, such as Al/Si ordering in anorthite, is expected to give changes in elastic properties that scale with the square of the order parameter. The elastic anomalies that develop in association with displacive phase transitions show greater diversity, due to the additional influence of the order parameter susceptibility. These are illustrated for the cases of the proper ferroelastic transition at high pressure in stishovite and the improper ferroelastic transition in SrTiO3 perovskite. Low temperature transitions in lawsonite show a more complex pattern of softening and stiffening that depends on coupling with both cation ordering and displacive processes. Variations of the spontaneous strain and elastic constants are indicative of the underlying thermodynamic mechanism for a phase transition. If any such transitions occur in minerals of the Earth’s crust or mantle they should be identifiable from their distinctive influence on seismic velocities.
56 citations
TL;DR: In this article, the tip-induced domain switching can be mapped on the Landau theory of phase transitions with the domain size as an order parameter, and the authors proposed that the early stages of the nucleation process when domain size is comparable with the tip radius of curvature requires exact field structure to be taken into account.
Abstract: Nanoscale polarization switching in ferroelectric materials by Piezoresponse Force Microscopy (PFM) in weak and strong indentation limits is analyzed using exact solutions for electrostatic and coupled electroelastic fields below the tip. It is proposed that the tip-induced domain switching can be mapped on the Landau theory of phase transitions with the domain size as an order parameter. For a point charge interacting with a ferroelectric surface, switching of both first and second order is possible depending on the charge-surface separation. For a realistic tip shape, the domain nucleation process is first order in charge magnitude and polarization switching occurs only above a critical tip bias. In pure ferroelectric or ferroelastic switching, the late stages of the switching process can be described using point charge/force model and arbitrarily large domains can be created; however, the description of the early stages of nucleation process when domain size is comparable with the tip radius of curvature requires exact field structure to be taken into account.
55 citations
01 Jan 2012
TL;DR: In this paper, the authors define a phase as homogeneous stable matter and classify phase transitions according to the Ehrenfest classification, and introduce a concept of an order parameter as a hidden variable responsible for symmetry changes during the transition.
Abstract: In this chapter, starting with the classical approach, we define a phase as homogeneous stable matter and classify phase transitions according to the Ehrenfest classification. Then we introduce a concept of an order parameter as a hidden variable responsible for symmetry changes during the transition. We consider different thermodynamic functions and choose the Gibbs free energy as a function of temperature, pressure, and order parameter (the Landau potential) to identify the equilibrium states in open systems. Using the concept of the order parameter, the phase transitions are considered as mathematical catastrophes of the Landau potential. The “catastrophic” approach helps us to classify the phase transitions and see how different forms of the Landau potential are applicable to different cases of phase transitions. We also look at the special lines and points of the phase diagram from the point of view of the “catastrophic” changes of the order parameter. We conclude the chapter with the analysis of the external field on the phase transition, using the properties of conjugation between the field and order parameter.
55 citations
TL;DR: In this paper, a number of unifying features are discussed in connection with the electronic structures of these elements, leading to a more precise understanding of the diversity of phase diagrams found for the elements of Group IVa.
Abstract: Displacive mechanisms are proposed for the high-pressure structural transitions which take place in Si, Ge, Sn, and Pb The mechanisms are analyzed in the framework of the Landau theory of phase transitions It reveals a number of unifying features which are discussed in connection with the electronic structures of these elements, leading to a more precise understanding of the diversity of phase diagrams found for the elements of Group IVa
55 citations