Showing papers on "Landau theory published in 1991"

Order-parameter saturation and low-temperature extension of Landau theory

Abstract: The temperature evolution of the structural order parameter in displacive phase transitions with high transition temperatures (e.g. quartz, As2O5, LaAlO3, CaCO3, NaNO3, Pb3(PO4)2 etc.) follows a Landau-type behaviour over large temperature intevals. Below a saturation temperatureT s , however, the order parameter tends to become temperature independent. A quantitative analysis shows the correlationk B T s =ħΩ/4, where Ω is the frequency of the relevant local excitation atT s . A general Landau-type expression for the Gibbs energy is given which includes the effects of order-parameter saturation.

Landau Fermi-Liquid Theory: Concepts and Applications

Abstract: Landau Fermi-Liquid Theory and Low Temperature Properties of Normal Liquid 3He Low Temperature Properties of Dilute Solutions of 3He in Superfluid 4He Further Developments Index.

Elastic properties of NiTi

Abstract: The authors present measurements of the elastic constants on a single crystal of the shape-memory alloy NiTi in a wide temperature range. Step-like anomalies and hysteresis are detected at the austenitic-martensitic phase transition which provide evidence for the strain-order parameter coupling in the pre-martensitic phases. The results are discussed in the framework of existing Landau theory models.

Effect of Confinement on Wetting and Drying Between Opposing Boundaries

Abstract: We study quasi-wetting transitions in confined systems in which capillary condensation is suppressed. In particular, we are concerned with adsorbates between opposing walls (one wall favours wetting, the other drying). We employ an Ising model and calculate the global phase diagram for a slab of width L and boundaries with opposite surface fields, in Landau theory. We find novel first-order, critical, and tricritical quasi-wetting transitions, which converge smoothly, for L → ∞, to the familiar wetting transitions. We question the recently proposed novel mechanism for critical-point shifts in films.

Paraelectric-antiferroelectric phase transition in titanite, CaTiSiO5. I, A high temperature X-ray diffraction study of the order parameter and transition mechanism

Abstract: The paraelectric to antiferroelectric phase transition in titanite at ∼500 K involves a displacement of the titanium atom from the center of the [TiO6] octahedron in the paraelectric phase (A2/a) to an off-center position in the antiferroelectric (P2 1/a) phase. We have carried out a detailed single crystal high temperature x-ray diffraction study of the phase transition including structure refinements at 294, 350, 400, 430, 440, 450, 500, 600, and 700 K. The unit cell dimensions show a pronounced hysteresis effect in the 450–500 K range on heating and cooling during the first cycle along with a reduction of the transition temperature, T c from 495 ± 5 K on heating to 445 ± 5 K on cooling. The hysteresis effect disappears on further heating and the superstructure reflections show residual intensities above T c (445 K). An order parameter treatment of the phase transition is presented in terms of Landau theory and induced representation theory. The Ti-displacements parallel and antiparallel to a are taken as the primary order parameter η, which transforms as the Y 2 + representation. A coupling of Y 2 + with T 1 + results in the linear-quadratic coupling of the spontaneous strain components, ɛ ij with η. The Ti-displacements are coupled linearly to the Cadisplacements. Both sets of displacements predicted from induced representation theory are observed experimentally. The phase transition is initially driven by the soft mode at the zone boundary point Y 2 + ; near T c critical fluctuations set in and an order-disorder mechanism finally drives the phase transition, whereby parallel and antiparallel Ti-displacements related by [0, 1/2, 1/2] in adjacent domains are dynamically interchanged. Immediately above T c , the high temperature (A2/a) phase is a statistical average of small dynamic antiphase domains of the low temperature (P2 1/a) phase. Vacancies and defects pinning the domain boundaries may drastically alter the transition behavior and affect the domain mobility.

Crystallography and structural phase transitions, an introduction

Abstract: Structural phase transitions which involve the generation of lattice strain (i.e. in ferroelastic and co-elastic crystals) are reviewed. Landau–Ginzburg theory is found to lead to an appropriate description of order parameters following the theoretical predictions over large temperature intervals. A quantum extension of Landau–Ginzburg theory is presented which describes the saturation of order parameters at low temperatures. Coupling between different order parameters is relevant if more than one phase transition (or lattice instability) occurs in a crystal. Finally, the importance of microstructures and kinetic processes for the structural behaviour of crystals is pointed out.

Landau theory of the nematic-smectic-A phase transition under shear flow

Abstract: Shear flow distorts the microstructure of fluids if the Deborah number scrD becomes comparable to 1. In complex fluids, exotic hydrodynamics effects are often seen in this regime. We compute within Landau theory the structure factor S(q) of a sheared nematic liquid crystal close to the nematic to smectic-A (N--Sm-A) phase transition. As a function of increasing Deborah number, the pretransitional smectic-A fluctuation clusters become increasingly geometrically restricted, evolving from their usual three-dimensional ellipsoidal shape for scrD\ensuremath{\ll}1 to an extremely anisotropic one-dimensional shape for scrD\ensuremath{\gg}1. We discuss the predictions of Landau theory for x-ray diffraction experiments for various orientations of the nematic director. The suppression of pretransitional critical fluctuations by shear flow is found to raise the transition temperature ${\mathit{T}}_{\mathit{N}--\mathrm{Sm}\mathrm{\ensuremath{-}}}$A, and peculiarly, ${\mathit{T}}_{\mathit{N}--\mathrm{Sm}\mathrm{\ensuremath{-}}}$A is found to depend on the orientation of the director. The presence of the microscopic fluctuation clusters under the shear flow is also reflected on the macroscopic level. The classical theory of the hydrodynamics of nematic liquid crystals, due to Ericksen, Leslie, and Parodi (ELP), is found to be incomplete. We compute the new fluctuation-induced forces that must be added to ELP nematic hydrodynamics and we discuss their consequence, in particular for large scrD, the analog of shear-thinning for liquid crystals.

Elastic Properties of Interfaces in a Ginzburg-Landau Theory of Swollen Micelles, Droplet Crystals and Lamellar Phases

Abstract: Using a Ginzburg-Landau free energy for oil-water-surfactant mixtures, we show that the Helfrich Hamiltonian describes the free energy of the amphiphilic monolayers at the oil/water interface, and calculate the bending rigidity, the saddle splay modulus and the spontaneous radius of curvature. The results are used to discuss the phase diagram obtained from Landau theory, which contains a lamellar phase, a hexagonal phase of cylinders, and a droplet crystal. It is found that the interaction of the monolayers plays an important role in stabilizing the lamellar phase.

The bifurcation of a hot round jet to limit-cycle oscillations

Abstract: The onset of self‐excited or limit‐cycle oscillations in an axisymmetric hot jet is studied experimentally as the jet density is systematically decreased below the value at which absolute instability first appears in the potential core region By transient measurements at different supercritical jet densities, this bifurcation is demonstrated to be of the Hopf type That is, close to the critical density, the oscillation amplitude at a fixed point in space is shown to be described by a Landau equation All coefficients of the equation, ie, linear temporal growth rate, linear frequency, and the Landau constant, are determined

Methods of the theory of singularities in the phenomenology of phase transitions

Abstract: A review is presented on the methods of the theory of singularities applied to the Landau phenomenological theory of phase transitions. Constructive algorithms are presented that eliminate arbitrariness in the choice of the Landau potential and make it possible to exclude from consideration models with nonphysical results. The methods of singularity theory are illustrated by application to several real thermodynamic systems.

Scaling hypothesis and nonzero-field critical invariants

Abstract: Assuming the static scaling hypothesis, a proof is given for the existence of invariants (Q) associated with the extrema of the thermodynamic functions: nonzero-field susceptibility, nonzero-field specific heat, nonzero-wave-vector correlation function. In the framework of the Landau theory, the value of the invariant Q related to the susceptibility is found to be Q=2. Experimental measurements of the maxima of the nonzero-electric-field susceptibility for a ferroelectric triglycine sulfate TGS crystal give a value 1.87\ifmmode\pm\else\textpm\fi{}0.05 for the invariant Q. This result provides new evidence of a deviation from Landau theory in the thermodynamic behavior of the TGS crystal.

Coupled order parameters in the Landau theory of phase transitions in solids

Abstract: We discuss the role of both primary and secondary order parameters in a transition between two solid phases. We show how microscopic distortions which appear at the transition can be calculated using group-theoretical methods. We also show how the form of the coupling term in the Landau free energy influences the behavior of secondary order parameters.

Derivation of Landau theories and lattice mean-field theories for surface and wetting phenomena, from semi-infinite Ising models

Abstract: The phenomenological aspects of surface and interfacial phenomena such as wetting phase transitions are commonly studied using the classification scheme provided by the Landau theory. Although this approach is very meaningful, it is also important to establish a firm connection between the phenomenology and the microscopic models of statistical mechanics. This is true, especially in view of the remarkable sensitivity of wetting phenomena to the details of the substrate-adsorbate interactions. We study such connections and derive a variety of lattice mean-field theories, which make a bridge between the Landau theory and the semi-infinite Ising model with a surface. We discuss standard mean-field approximations (MFA) and improvements thereof, renormalization group techniques, reaction-field approximations, and cluster variation methods. We pay special attention to the derivation of the newly introduced triplet surface field h 3 in the Landau theory for wetting.

Elastic properties of Rb4LiH3(SO4)4 and K4LiH3(SO4)4

Abstract: High-resolution Brillouin spectroscopy was used to study the elastic properties of Rb4LiH3(SO4)4 and K4LiH3(SO4)4 crystals. In contrast to earlier studies of the former compound, the present results indicate that the ferroelastic phase transition, which occurs at approximately 115 K, is of the 4 to 2 type rather than 4 mm to mm2 as previously believed. An appropriate theoretical model using a two-component order parameter free energy expansion has been presented based on the Landau theory. K4LiH3(SO4)4 does not appear to be ferroelastic in the temperature range examined and only exhibits a slight change in slope of the temperature plots for elastic constants associated with longitudinal phonons.

The molecular origin of ferroelectricity in FLC: A challenge for dielectric spectroscopy at microwave frequencies

Abstract: Broadband dielectric spectroscopy delivers in the frequency regime from 10 Hz to 10 GHz two collective relaxation processes (soft— and Goldstone—mode) and one molecular relaxation (β-relaxation). The latter does not split or broaden at the phase transition SmA*/SmC*. Its dielectric strength does not decline - in pronounced contrast to the (generalized) Landau theory of the phase transition SmA*/SmC* in FLC. Our experimental findings contradict the common explanation of the spontaneous polarization which is based on the existence of a free rotation inside the SmA* phase and its strong hindrance in the ferroelectric SmC* phase.

Dynamics of patterns in ferroelastic-martensitic transformations. I. Lattice model

Abstract: A lattice model and its nonlinear dynamics for ferroelastic-martensitic transformations is proposed. The lattice model presented involves the necessary interactions required in a cubic-tetragonal transformation for proper ferroelastic materials for which the strain tensor is merely the order parameter. Basically, the lattice model is a two-dimensional system including both nonlinear and competing interactions. The latter are considered as two kinds: (i) interactions by particle pairs and (ii) noncentral interactions or bending forces. A one-dimensional version is derived from the two-dimensional system, with the former possessing the anisotropic nature of the original lattice. The equations of motion are deduced as a set of difference-differential equations placing thus the discrete macroscopic and microscopic stresses in evidence. Moreover, upon investigating homogeneous states of deformation of the lattice, a comparison can be made with the Landau theory for ferroelastic phase transitions. On the basis of this reduced one-dimensional model the softening of the transverse-acoustic-phonon branch is examined, leading to two important results: (i) the partial softening of this branch of dispersion at a nonzero wave number and (ii) the positive curvature of the dispersion curve at the long-wavelength limit. All these effects are usually observed by means of neutron-inelastic-scattering techniques and this suggests pretransitional effects characterized by modulated lattice distortions.

Smectic order and backbone anisotropy of a side-chain liquid crystalline polymer by Small-Angle Neutron Scattering

Abstract: We have simultaneously measured, for the first time, the extension of the polymer backbone of a side-chain liquid crystalline polymer and the intensity of the 001 Bragg reflection, which gives the smectic order parameter Ψ as a function of temperature in the smectic phase. We have qualitatively demonstrated that the more the smectic phase is ordered, the more the polymer backbone is localized between the mesogenic layers. It is shown that the Landau theory allows us to relate the radius of gyration parallel to the magnetic field of the polymer backbone to the smectic order parameter. We also show that the Renz-Warner theory is suitable at low temperatures.

Magnetic phase diagrams of spin‐frustrated stacked triangular antiferromagnets: Application to ABX3 compounds (invited)

Abstract: A review is given of our recent results on magnetically ordered states occuring in geometrically frustrated stacked triangular (simple hexagonal) antiferromagnets based on phenomenological Landau theory, molecular field theory, and Monte Carlo simulations. Novel multicritical behavior in magnetic field‐temperature phase diagrams is demonstrated for systems with axial and planar anisotropy (weak and strong). Crossover effects are discussed in terms of the new chiral universality classes recently proposed by Kawamura. Comparison of theory and simulation results with the observed magnetic ordering and phase diagrams in a wide variety of ABX3 compounds is made.

Analysis of Electric Fields, Space Charges, and Polarization of Thin-Film Ferroelectric Capacitors Based on Landau Theory

Abstract: This paper describes a detailed physical analysis of the electric fields, space charges, and polarization of thin-film ferroelectric devices. The analysis is based on a previously developed model of the electric field dependent polarization, permittivity, and hysteresis of the thin-film polycrystalline ferroelectric, which was derived from the Landau-Devonshire theory. This paper includes the macroscopic effects related to device structure and composition, including potential barriers at contacts, domain relaxation, grain boundary surface charge, and interactions between the space charges and the non-linear polar displacement.

On the structural phase transitions in the incommensurate Cs2CdBr4

Abstract: In the series of incommensurate A2BX4 halides with the β-K2SO4 type structure, Cs2CdBr4 exhibits an unusual behaviour since the “lock-in” phase transition occurs at the centre of the Brillouin zone The observed phase sequence is the following: Pnma (Z = 4)⇔INC(k0 ≈ 1/6a∗)⇔P21/n(Z = 4)⇔P1 (Z = 4) These phase transitions have been studied by means of Raman scattering and ultrasonic measurements It is shown that the Pnma⇔INC⇔P21/n sequence is governed by order-disorder processes due to CdB2-4 tetrahedra reorientations coupled with translations of the Cs+ cations, and that the low-temperature P21/n⇔P1 transition is of a displacive nature, governed by a soft optical mode The “pseudo-proper” ferroelastic character of these transformations is clearly established A model potential developed in the framework of Landau theory is proposed; this model is able to reproduce the general trends observed in the temperature dependence of the soft-modes and of the elastic constants in the different phases

Susceptibility scaling functions for landau critical and tricritical points

Abstract: In the framework of Landau theory the equations for susceptibility scaling function for critical and tricritical points are derived above and below Tc, respectively. They are used to calculate the nonzerofield critical invariants Q for the critical (Q = 2) and tricritical (Q = 4/3) points. Q is equal to the ratio χ(τmax, E = 0)/χ(τmax, E), where τmax(E) is the reduced temperature of maximum of nonzerofield susceptibility χ(τ, E) for a given value of electric field E. It is concluded that behaviour of TGS and TGSe ferroelectrics is not in agreement with either the Landau critical or tricritical scaling prediction and that the experimental nonlinearity in the Landau critical and tricritical equations for susceptibility scaling functions is a measure of invariant Q (4/3 < Q < 2). It is suggested that the nonlinearity method (determination of Q) is more sensitive for detection of deviations from classical behaviour than the exponent ratio method (determination of Δ/γ) and both methods should be used simultane...

Wetting and adsorption at substrates and grain boundaries

Abstract: Wetting near grain boundaries is a fairly new topic in comparison with wetting at substrates (or walls). A Landau theory is reviewed that describes the wetting and interfacial unbinding transitions near grain boundaries (or defect planes). The results are compared with those for wetting at substrates. Restricting attention to short-range substrate-adsorbate forces, critical-point wetting (as conjectured by Cahn) applies for substrates, but not for grain boundaries, unless the grain boundary remains ordered at the bulk critical point. It is argued that, quite generally, surface order at the bulk critical point implies critical-point wetting. In this article I review some key results of our studies of adsorption and wetting near grain boundaries [1, 2]. At the same time I present new arguments and conjectures, which clarify and update the framework of understanding that is emerging.

Perspectives of the theory of spin-polarized quantum systems : beyond the standard boltzmann equation

Abstract: Problems and the latest achievements in the theory of spin-polarized quantum systems are briefly discussed. The current agreement with the experimental data is quite good, but the further improvement of the accuracy of theory is hindered by fundamental problems of the kinetic theory. One of the main goals was to go beyond the simplest Boltzmann equation and a rederivation of the improved versions of this equation for different polarized systems with the emphasis on virial, non-local and non-exchange terms. Some specific applications and boundary effects are presented. The basic problem for polarized dense Fermi-liquids is an applicability of the Landau theory to transverse phenomema. For dilute degenerate systems (e.g., low-temperature liquid mixtures of helium isotopes) the problem is how to go beyond the lowest approximations in density/interaction. Most of the attempts in this direction, especially with regard to superfluid transition in helium mixtures are still unconvincing; this transition remains one of the most intriguing problems of (ultra) low-temperature physics.

A theory of the phase diagram around the N–A–C point in liquid crystals

Abstract: A phenomenological model is proposed for the nematic-smectic A–smectic C transition. Two order parameters which are biquadratically coupled are involved. The first one is primary and characterizes the appearance of layers in the smectic phases. The second order parameter is triggered by the first one and can be identified with the tilt angle. Analytic expressions are obtained for lines and points in the phase diagram. These expressions are used to reconstruct completely the non-equilibrium Landau potential.

Phase transitions between partial wetting states in the Landau theory and the Van der Waals theory of adsorbed fluids

Abstract: Adsorption phase transitions between distinct partial wetting states (or 'thin-thick' transitions at bulk two-phase coexistence) are studied systematically in the phenomenological Landau theory for Ising models, as well as in the Sullivan model, a more microscopic Van der Waals theory for fluids. In the Landau theory the previously proposed mechanism of competing surface fields is examined in detail and confirmed. In the generalized Sullivan model with combined exponential and square-well wall-fluid potentials thin-thick transitions are found already if the potential is purely square-well. A mapping of the Van der Waals to the Landau theory suggests that the mechanism of competing surface fields can largely explain the new phase transitions.