Showing papers on "Landau theory published in 1993"
TL;DR: Langmuir monolayers and freely suspended smectic films can exhibit a spontaneous breaking of chiral symmetry, which leads to the spontaneous formation of complex equilibrium patterns with either 1D or 2D modifications in the direction of molecular tilt.
Abstract: Langmuir monolayers and freely suspended smectic films can exhibit a spontaneous breaking of chiral symmetry. The order parameter that characterizes this symmetry breaking is coupled to variations in the direction of molecular tilt. As a result, chiral symmetry breaking leads to the spontaneous formation of complex equilibrium patterns with either 1D or 2D modifications in the direction of molecular tilt. A Landau theory for this pattern formation gives a general phase diagram, which includes a uniform nonchiral phase, a striped pattern, a square lattice, and a uniform chiral phase.
119 citations
TL;DR: In this paper, the authors investigated the relationship between the value of the gap and the softening of the order parameter in a weak crystallization of a liquid or a liquid crystal which is a first-order phase transition close to a continuous one.
82 citations
TL;DR: It is shown that for the set of properties studied one can single out six qualitatively different types of behavior of the model, and that this model can describe the gradual conversion of ferroelectric to antiferroelectric behavior.
Abstract: A simple phenomenological model with two coupled structural and ferroelectric order parameters is under consideration. The small-signal dielectric response, dielectric response to a strong electric field (hysteresis phenomena included), and the phase diagram in the presence of the bias field are analyzed in the framework of Landau theory. It is shown that for the set of properties studied one can single out six qualitatively different types of behavior of the model. It is also shown that, in the framework of a unified phenomenological scheme, this model can describe the gradual conversion of ferroelectric to antiferroelectric behavior. The application of the model to the description of real compounds with a sequence of phase transitions is discussed.
79 citations
TL;DR: In this article, the authors study interfacial fluctuations in a Ginzburg-Landau model for ternary oil-water-surfactant mixtures by Monte Carlo simulations.
Abstract: We study interfacial fluctuations in a Ginzburg-Landau model for ternary oil-water-surfactant mixtures by Monte Carlo simulations. Space has to be discretized in order to apply the Monte Carlo method. However, by an appropriate choice of the lattice constant of the background lattice, discretization effects can be largely avoided. Strong fluctuation effects on the phase diagram are observed, which can be explained by a fluctuation-induced lowering of the oil-water interfacial tension. We determine several quantities, which characterize the structure of the microemulsion, such as the internal interfacial area and the Euler characteristic. The microemulsion phase is shown to have a disordered bicontinuous structure. In the lamellar phase, we observe an increase of the interfacial area with increasing separation of the monolayers. A quantitative comparison with the predictions of the effective curvature model of Helfrich [J. Phys. (Paris) 46, 1263 (1985)] yields excellent agreement, when an exponential distance dependence of the interfacial tension is taken into account.
62 citations
TL;DR: In this article, conditions for single phase and multiphase equilibria are studied using Flory-Huggins free energy of mixing with χ representing the A-B interaction parameter.
Abstract: Ideal random AB copolymers with degree of polymerization N are mixtures of N+1 types of chains with different compositions (fractions fi of A monomers). Conditions for single phase and multiphase equilibria are studied using Flory–Huggins free energy of mixing with χ representing the A–B interaction parameter. The spinodal for one phase instability is given by χs=[2f(1−f)]−1 for all N, where f is the average A fraction in the system. The transition from one to two phases is continuous at χ=χs when f=0.5 and discontinuous at χ≤χs when f≠0.5. Three, four, and more phases become stable at larger values of χ. Our numerical solution suggests that the stability range for multiple phases approaches Δχ≊0.15 at large (but finite) N. Macroscopically and microscopically phase separated states are investigated with the Landau approach of Fredrickson, Milner and Leibler. The Landau method gives reasonable but inexact results for two macroscopic phases when the random copolymer has compositional symmetry (f=0.5). A dis...
45 citations
TL;DR: It is argued that the dynamics of a soft-spin Ising magnet, subject to the time-varying external magnetic field h(t)=h cosΩt, is argued to be inapplicable near the phase boundary line due to a critical slowing down.
Abstract: I consider the dynamics of a soft-spin Ising magnet, subject to the time-varying external magnetic field h(t)=h cos\ensuremath{\Omega}t. The system is modeled with a time-dependent Ginzburg-Landau equation and is studied at a mean-field level. The time-averaged magnetization (scrM) acts as the order parameter and divides the temperature-h plane into two phases. In contrast to a previous result that predicted a dynamical tricritical point separating a line of continuous and discontinuous transitions in scrM, I find that the transition is always continuous. The previous work utilized Glauber dynamics which, it is here argued, becomes inapplicable near the phase boundary line due to a critical slowing down.
41 citations
TL;DR: Seven structurally distinct condensed phases in the phase diagram of water-supported Langmuir monolayers are explained in the framework of the Landau theory of phase transitions.
Abstract: Seven structurally distinct condensed phases in the phase diagram of water-supported Langmuir monolayers are explained in the framework of the Landau theory of phase transitions. The present treatment, which covers two-dimensional hexatic and solid phases and describes the transitions between them, involves the coupling of three order parameters. One of the parameters governs the collective tilt of the molecules, while the other two describe one-dimensional «weak crystallisation» along the bond direction and normal to it with the herringbone ordering of the molecular backbone planes
41 citations
TL;DR: A model predicting the structure of repulsive, spherically symmetric, monodisperse particles confined between two walls is presented and the buckling transition of a single flat layer as the double layer state develops is studied.
Abstract: A model predicting the structure of repulsive, spherically symmetric, monodisperse particles confined between two walls is presented. We study the buckling transition of a single flat layer as the double layer state develops. Experimental realizations of this model are suspensions of stabilized colloidal particles squeezed between glass plates. By expanding the thermodynamic potential about a flat state of \( N \) confined colloidal particles, we derive a free energy as a functional of in-plane and out-of-plane displacements. The wavevectors of these first buckling instabilities correspond to three different ordered structures. Landau theory predicts that the symmetry of these phases allows for second order phase transitions. This possibility exists even in the presence of gravity or plate asymmetry. These transitions lead to critical behavior and phases with the symmetry of the three-state and four-state Potts models, the X-Y model with 6-fold anisotropy, and the Heisenberg model with cubic interactions. Experimental detection of these structures is discussed.
39 citations
TL;DR: In this paper, the properties of LaBGeO 5, a new ferroelectric with a stillwellite-type structure, were investigated and the specific heat, C p, showed one clear anomaly (Δ S =0114 R) at 8025 K, and an additional hump in C p was found in a different sample just above T c.
Abstract: Thermal and dielectric properties of LaBGeO 5 , a new ferroelectric with a stillwellite-type structure are investigated The specific heat, C p , shows one clear anomaly (Δ S =0114 R) at 8025 K The basic thermodynamic parameters are determined on the basis of the Landau theory However, an additional hump in C p was found in a different sample just above T c This dependence on samples is confirmed by the measurements of dielectric constants The appearance of the new intermediate phase may be caused by some impurities or defects The Rhodes-Wohlfarth plot suggests that the nature of the phase transitions is of the displacive-type
35 citations
01 Jan 1993
TL;DR: In this paper, a theoretical treatment based on the Landau-Devonshire expansion is presented for phase transitions in ferroelectric thin films, where a surface is characterised by a length δ, the negative of the logarithmic derivative of the order parameter at the surface.
Abstract: After a brief review of the experimental data concerning phase transitions in ferroelectric thin films, a theoretical treatment based on the Landau-Devonshire expansion is presented. A surface is characterised by a length δ, the negative of the logarithmic derivative of the order parameter at the surface. For negative δ, the critical temperature Tc of a film is increased above the bulk value, while for positive δ it is decreased. A careful discussion of depolarisation effects is presented. It is shown that these reduce Tc below the value found if depolarisation is neglected. Various possible extensions of the theory are pointed out.
28 citations
TL;DR: It is found that a new microscopically ``escaped'' structure for -1/2 wedge disclinations, in which the molecules point predominantly along the disclination line, which is metastable.
Abstract: The core structure of a disclination line defect in a nematic liquid crystal is simulated by a Monte Carlo technique in which molecules are represented as hard spherocylinders, with aspect ratios ranging from 5 to 15. For small aspect ratios (5 and 8), we confirm the mean-field Landau theory that the core is biaxial with negative order parameter at the center. The order parameter coherence length is small, of the order of the molecular diameter. For large aspect ratios, we discover a new microscopically ``escaped'' structure for -1/2 wedge disclinations, in which the molecules point predominantly along the disclination line. Free energy calculations demonstrate that the ``escaped'' structure is of lower energy than the unescaped ``flat'' structure, which is metastable. We expect the ``escaped'' structure to retard disclination mobility.
TL;DR: The high-temperature BaAl[sub 4] structure is monoclinic, C2/m, with lattice parameters, a = 6.1526 (15) [angstrom], b = 6,1730 (13) [ANGstrom], c = 6., 6.3290 (14) [Angstrom], [beta] = 118.026 (16).
Abstract: CaAl[sub 4] undergoes a reversible, structural transformation at 170[degrees]C according to high-temperature X-ray powder diffraction experiments. The high-temperature phase adopts the tetragonal BaAl[sub 4] structure (space group I4/mmm), while the low-temperature phase is monoclinic, C2/m, with lattice parameters, a = 6.1526 (15) [angstrom], b = 6.1730 (13) [angstrom], c = 6.3290 (14) [angstrom], [beta] = 118.026 (16). The Landau theory of phase transitions correctly provided a structural model for the low-temperature phase, which could be subsequently refined. Also, electronic structure calculations on both forms of CaAl[sub 4] allow rationalization of the transformation in terms of changes in local chemical bonding within the Al framework. 26 refs., 8 figs., 8 tabs.
TL;DR: In this paper, the influence of hydrostatic pressure on the temperature dependence of optical birefringence and ultrasonic velocities is studied in the vicinity of the phase transition temperatures of Cs2HgBr4, Cs 2CdBr4 and Cs1HgCl4 crystals.
Abstract: The influence of hydrostatic pressure on the temperature dependence of the optical birefringence and ultrasonic velocities is studied in the vicinity of the phase transition temperatures of Cs2HgBr4, Cs2CdBr4 and Cs2HgCl4 crystals. The new polycritical triple points which separate the normal, incommensurate and proper ferroelastic phases have been found in the P-T phase diagrams of all the compounds at applied pressures of 140 MPa, 100 MPa and 140 MPa, respectively. The origin of the triple points and the acoustic and optical properties near the phase transitions are discussed within the framework of phenomenological theory.
TL;DR: In this paper, the Brueckner-Hartree-Fock mean field is improved by infinitesimally advanced terms corresponding to fast hole-hole collisions and a criterion for the stability of motion is formulated.
TL;DR: In this paper, the successive phase transitions in (CH 3 NH 3 ) 3 Bi 2 Br 9 (MABB) single crystal have been investigated by measuring of dielectric and elastic dispersion and Brillouin and Raman scattering.
Abstract: The successive phase transitions in (CH 3 NH 3 ) 3 Bi 2 Br 9 (MABB) single crystal have been investigated by measuring of dielectric and elastic dispersion and Brillouin and Raman scattering Softening of the elastic constant c 66 and critical slowing down of the order parameter, which belongs to the E g representation, have been found in the phase I No optical soft mode has been observed The phase transition from the phase I to the phase II has been discussed by the Landau theory
TL;DR: The structure of the low-symmetry phase near the transition point depends on the number of arbitrary parameters, which is smaller than that determined by the space group G D of this phase as discussed by the authors.
Abstract: The structure of the low-symmetry phase near the transition point depends on the number of arbitrary parameters, which is smaller than that determined by the space group G D of this phase. Such a feature gives rise to some nontrivial structural effects in the vicinity of the transition point: there are numerical relationships among the displacements of the atoms belonging to different orbits of the G D group. In some cases, atoms may be displaced in a direction not singled out by symmetry in any of the 230 space groups. These effects are revealed by group-theoretical methods and the Landau concept of one irreducible representation
TL;DR: Landau theory provides a group-theoretical method for determining which symmetry changes can occur in second-order phase transitions in solids.
Abstract: Landau theory provides a group-theoretical method for determining which symmetry changes can occur in second-order phase transitions in solids. The irreducible representations of the space group of the higher-symmetry phase must satisfy certain conditions. For transitions to commensurate crystalline structures, the Landau and Lifshitz conditions must be satisfied. For transitions to incommensurate structures, the Landau and «weak Lifshitz» conditions must be satisfied. The irreducible representations of each of the 230 crystallographic space groups that violate these conditions are listed
TL;DR: The magnetic field versus temperature phase diagrams of axial triangular lattice antiferromagnets CsMnI 3 and CsNiBr 3 have been investigated by precise magnetization measurements.
Abstract: The magnetic field versus temperature phase diagrams of axial triangular lattice antiferromagnets CsMnI 3 and CsNiBr 3 have been investigated by the precise magnetization measurements. The location of the multicritical point ( T m , H m ) for each material has been determined, at which two successive phase transitions are merged into a single phase transition and a line of the spin-flop transition meets these three phase boundaries. In the vicinity of the multicritical point, the reduced phase diagrams for CsMnI 3 and CsNiBr 3 scaled by each value of T m and H m coincide with each other and three phase boundaries come in tangent to the line of the spin-flop transition. Observed phase diagrams are concluded to be common to the triangular lattice antiferromagnets with easy-axis anisotropy. Our experimental data suggest that the Landau theory gives a qualitatively correct phase diagram except for the vicinity of the multicritical point and that the scaling theory of Kawamura et al . is valid near the multicr...
TL;DR: In this article, an alternative approach for determining the Landau constants associated with the implementation of weakly nonlinear theories is presented, which is shown to be in agreement with the usual solvability condition for the case of exact resonance.
Abstract: This Brief Communication presents an alternative approach for determining the Landau constants associated with the implementation of weakly nonlinear theories. Results from this approach are shown to be in agreement with the usual solvability condition for the case of exact resonance. Away from resonance, the results are in agreement with a direct solution of the nonhomogeneous system. This approach also provides accurate results for the case of near resonance, in contrast to the approach currently in widespread use. Following this alternative approach, the Landau constants can be calculated accurately in a straightforward manner without requiring the solvability condition in some arbitrary neighborhood of resonance.
TL;DR: In this article, high-resolution Brillouin spectroscopy was used to study the elastic properties of (NH4)4LiH3(SO4) 4 (ALHS).
Abstract: High-resolution Brillouin spectroscopy was used to study the elastic properties of (NH4)4LiH3(SO4)4 (ALHS). The temperature dependences of eleven Brillouin modes from acoustic phonons, propagating in the (100), (001), (110) and (101) directions, were measured in the temperature range from 140 to 300 K. The greatest elastic anomaly was observed in the plane perpendicular to the (001) crystallographic axes. The soft elastic constant c2S was found to vanish at T approximately=232 K. A Landau-type free-energy expansion is postulated and discussed, in order to explain the observed elastic anomalies.
TL;DR: In this paper, it was shown that the Landau levels are split in a definite way if the field B is a monotonic function of the radial distance, which holds for the lowest Landau level even beyond perturbation theory.
TL;DR: In this paper, the structural transitions of CaCl2 and CaBr2 at 491 K and 778 K, respectively, represent clear examples of proper ferroelastic transformations of the optical type.
Abstract: The structural transitions of CaCl2 and CaBr2 at 491 K and 778 K, respectively, represent clear examples of proper ferroelastic transformations of the optical type. In both cases, the instability of the hightemperature rutile-type structure is caused by the softening of an optical phonon at the center of the Brillouin zone in combination with a symmetry-allowed, strong bilinear coupling of the eigenvector of that mode with distinct strain components. The order parameter of B1g symmetry induces the orthorhombic CaCl2-type structure in the low-temperature phase. Static effects on the structural parameters and dynamical effects on the phonon spectra, as seen by Raman spectroscopy, are discussed. Primary and secondary spontaneous strains, domain patterns, and implications to elastic properties are considered.
TL;DR: In this article, the paraelectric-incommensurate and incommensurate-comensurate phase transitions of the proper ferroelectric crystal Sn2P2Se6 were studied by thermal expansion measurement on crystals grown by two different techniques.
Abstract: The paraelectric-incommensurate and the incommensurate-commensurate phase transitions of the proper ferroelectric crystal Sn2P2Se6 are studied by thermal expansion measurement on crystals grown by two different techniques. For vapour-transport grown crystals the observed deviation around Ti from the Landau theory can be described by a small fluctuation correction, whereas for Bridgemann-method grown crystals this deviation is most likely to be due to random local field-type defects. For both types of crystals in the low-temperature region of the incommensurate phase an additional contribution to the spontaneous deformation above the Landau part has been revealed.
TL;DR: An experimental method to determine the parameters of the complex Ginzburg-Landau (CGL) equation for chemical reaction-diffusion systems, solely using measurements on homogeneous systems together with diffusion constants is described.
TL;DR: In this paper, the effects of elastic interactions and the associated orthorhombic distortion on the structural phase transitions in a two-dimensional Ising model were investigated and it was shown by means of Landau theory that the square-rectangular symmetry breaking may lead to a first-order transition between the orthoregressive single and double-cell phases at low temperatures.
Abstract: We investigate the effects of elastic interactions and the associated orthorhombic distortion on the structural phase transitions in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{\mathit{z}}$. Starting from a two-dimensional Ising model previously demonstrated to describe accurately the high-temperature phase boundaries, we show by means of Landau theory that the square-rectangular symmetry breaking may lead to a first-order transition between the orthorhombic single- and double-cell phases at low temperatures. This explains experimental observations of phase separation between orthorhombic phases, while retaining the simplicity and predictive power of the original model.
TL;DR: The modulation wave vector q=δ(T)c * of deuterated betaine calcium chloride dihydrate was measured as a function of the temperature for certain dc electric fields, using elastic neutron scattering, and the results obtained are compared with the behavior of the dielectric constant of electric-field-biased D-BCCD.
Abstract: The modulation wave vector q=δ(T)c * of deuterated betaine calcium chloride dihydrate (D-BCCD) was measured as a function of the temperature for certain dc electric fields, using elastic neutron scattering. The results obtained are compared with the behavior of the dielectric constant of electric-field-biased D-BCCD. The temperature range of stability of the polar phases with δ= 2/7, 4/15, 2/9, 2/11 increases with a dc electric field along b. The results are discussed qualitatively, in terms of Landau theory
TL;DR: A microscopic theory is proposed for transverse dynamics and zero-temperature attenuation in polarized Fermi liquids and a framework for a generalized nonlocal Landau theory is established.
Abstract: A microscopic theory is proposed for transverse dynamics and zero-temperature attenuation in polarized Fermi liquids. The transport equations are a set of two coupled equations in two ``partial transverse densities,'' which do not reduce to a single equation in a mixed component of a single-particle distribution. The effective interaction is linked to an irreducible vertex by an integral equation, and cannot be given as a limit of a full vertex. A framework for a generalized nonlocal Landau theory is established. The spectrum of attenuating spin waves is calculated at arbitrary polarizations and densities.
TL;DR: The Landau theory of phase transitions is developed for transitions between condensed phases of Langmuir monolayers in this paper, and the phase diagram is explained by the coupling between the order parameters describing collective tilt of the molecules and ordering of their backbone (zigzag) planes.
Abstract: The Landau theory of phase transitions is developed for transitions between condensed phases of Langmuir monolayers. The phase diagram is explained by the coupling between the order parameters describing collective tilt of the molecules and ordering of their backbone (zigzag) planes. If the latter ordering is considered as occurring between hexatic phases, then the predictions do not agree with X-ray data on the structure of phases of either fatty acid or long-chain alcohol monolayers on the water surface. However this transition can be explained as translational ordering with doubling of the unit cell realized either by herringbone ordering or by alternating orientations of the heads of the molecules in adjacent rows
TL;DR: In this article, a dual formulation of the Ginzburg-Landau model is employed to obtain a Landau description of the phase transition of three-dimensional type-II superconductors at zero magnetic field.
Abstract: Focusing on an order parameter that signals the breakdown of a global symmetry, we employ a dual formulation of the Ginzburg-Landau model to obtain a Landau description of the phase transition of three-dimensional type-II superconductors at zero magnetic field. In the superconducting phase the dual theory is a complex |ψ|4 theory interacting via a shielded Coulomb potential mediated by a massive vector mode which may be pictured as representing the magnetic field. In the normal, high-temperature phase the vector mode decouples and the theory reduces to a pure |ψ|4 theory with a broken global U(1) symmetry. The resulting massless Goldstone mode represents the photon. The phase transition between the two phases is continuous with critical exponents given by those of a superfluid with reversed temperature axis.
TL;DR: In this paper, a model for anisotropic singlet pairing in [ital A][sub 3]C[sub 60], using a realistic model for the Fermi surface in a hypothesized orientationally ordered doped crystal, is presented.
Abstract: We study a model for anisotropic singlet pairing in [ital A][sub 3]C[sub 60], using a realistic model for the Fermi surface in a hypothesized orientationally ordered doped crystal. Anisotropic solutions are studied by combining numerical solutions to the gap equation in the low-temperature phase with a Landau expansion near the mean-field critical temperature. We focus on a class of three-dimensional nodeless [ital d]-wave solutions to the model, which exhibit a fully developed gap everywhere on the Fermi surface, but non-BCS temperature dependence of the order parameter in the condensed state, a relatively large value of the low-temperature gap, 2[Delta]/[ital kT][sub [ital c]], and non-BCS structure in the quasiparticle spectrum near the gap.