Showing papers on "Landau theory published in 1989"
TL;DR: In this paper, the enthalpy of calcite has been measured directly between 973 K and 1325 K by transposed-temperature-drop calorimetry, and the excess enthalp has been analysed in terms of Landau theory for this tricritical phase transition.
Abstract: The enthalpy of calcite has been measured directly between 973 K and 1325 K by transposed-temperature- drop calorimetry. The excess enthalpy has been analysed in terms of Landau theory for this tricritical phase transition. The zero-point enthalpy and entropy allow estimates of the parameters a and C in the Landau expansion for free energy which expresses excess free energy ΔG as a function of the order parameter Q and temperature T: ΔG 1/2a(T2c−T)Q2+1/6CQ6 with a=24 J·Kℒ·mol-1, C = 30 kJ·mol−Tc = 1260 ±5 K. The entropy of disorder below the transition has been formulated as a function of temperature allowing the calculation of the calcite/aragonite phase boundary when taking this extra entropy into account. There is remarkable agreement between the calculated equilibrium curve and previous experimental observations. The Landau theory predicts behaviour which fully accounts for the change in slope of the calcite/aragonite phase boundary, which is thus wholly due to the R¯3c –R¯3m transition in calcite.
95 citations
TL;DR: In this article, the global existence of smooth solutions for the system of partial differential equations governing the dynamics of martensic phase transitions in shape memory alloys is proved for the case where the free energy is assumed in Ginzburg-Landau form and nonconvex in the order parameter.
75 citations
01 Jan 1989
TL;DR: In this article, the authors investigated the orientational ordering transition in NaNO3 near 552 K using x-ray diffraction techniques and showed that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T > Ttr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO3-disorder, and a second order parameter linked with the spontaneous strain of this phase transition.
Abstract: The orientational ordering transition R\(R\bar 3m - R\bar 3c\) in NaNO3 near 552 K has been investigated using x-ray diffraction techniques. NaNO3 is a model system for CaCO3 and other minerals with orientational disorder of triangular molecules in a simple NaCl-type matrix. The temperature evolution of the integrated intensities of the superlattice reflection \(\bar 1\)23 and the fundamental reflection 110 are discussed in terms of Landau theory of two coupled order parameters. It is shown that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T > Ttr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO3-disorder, and a second order parameter linked with the spontaneous strain of this phase transition.
53 citations
TL;DR: In this article, a review of the use of time-dependent order parameter theory to describe the kinetics of order/disorder transitions is presented, which does not depend on the detailed structure of the material being examined and can be followed experimentally through its relationship with other properties, such as spontaneous strain, excess entropy, intensities of superlattice reflections, etc.
Abstract: Recent advances in the use of time-dependent order parameter theory to describe the kinetics of order/disorder transitions are reviewed. The time dependence of a macroscopic order parameter, Q, follows, to a good approximation: For systems in which the order parameter has a long correlation length (large ξ) and is not conserved (small ξC), the Ginzburg-Landau equation provides a general kinetic solution: Specific rate laws can be derived from this general solution depending on whether the crystals remain homogeneous with respect to the order parameter, Q. The advantages of the overall approach are, firstly, that it does not depend on the detailed structure of the material being examined; secondly, that the order parameter can be followed experimentally through its relationship with other properties, such as spontaneous strain, excess entropy, intensities of superlattice reflections, etc.; and, finally, that conventional Landau expansions in Q may be used to describe the thermodynamic driving forces. For a simple second-order transition in crystals which remain homogeneous in Q the rate law is: If the free energy of activation varies with the state of order of the crystal, this becomes: Simplifying assumptions can be introduced into the mathematics, or the integrals can be solved numerically. For crystals which remain homogeneous, the simplest solution valid only over small deviations from equilibrium is: For crystals which develop heterogeneities in Q, the rate laws change significantly and we find as an extreme case: where the A coefficient may be temperature dependent. Experimental data available for a limited number of minerals (omphacite, anorthite, albite, cordierite and nepheline) are used to demonstrate the practical implications of the overall approach. As anticipated from the theory, modulated structures commonly develop during kinetic experiments, the observed rate laws depend on whether the critical point of the ordering is located at the centre or boundary of the Brillouin zone, and the rate laws for ordering and disordering can be quite different. The importance of different length scales, not only in the different techniques for characterizing states of order (IR, NMR, calorimetry, X-ray diffraction, etc.) but also for interpreting observed mechanisms and rate laws, is also outlined. Use of the order parameter in Landau expansions and in Ginzburg-Landau rate laws provides, in principle, a means of predicting the equilibrium and non-equilibrium evolution of minerals in nature.
48 citations
TL;DR: Developpement d'un modele thermodynamique des transitions de phases de cristaux liquides multilamellaires formes de brioches de phospholipides dans l'eau par les interactions de the membrane.
Abstract: A thermodynamic model for phase transitions of multilamellar liquid crystals composed of phospholipid bilayers in water is developed. By means of a Landau theory of the thermally driven hydrocarbon chain-melting transition of an isolated membrane and a continuum model of the interactions between neutral phospholipid bilayers, the phenomenon of structural phase transitions induced by membrane interactions is described. The phenomenological parameters that appear in the theory may be readily determined by existing experimental techniques; an analysis of available data on several phospholipid systems is used here to estimate these quantities. Semiquantitative agreement is achieved with the experimental temperature-composition phase diagram as well as the variation of the characteristic dimensions of the lamellar crystals with water content. Possible origins of pseudocritical phenomena are suggested on the basis of the unusual topology of the phase diagram. The model highlights the central importance of the water-mediated ``hydration repulsion'' between membranes in the phase behavior of the lamellar systems.
43 citations
TL;DR: In this paper, the authors present a Landau theory for transitions among tilted hexatic phases in liquid-crystal films, and derive phase diagrams with four tilted Hexatic phases: hexatic I and hexatic F phases, an intermediate hexatic-L phase, and an unlocked phase.
Abstract: We present a Landau theory for transitions among tilted hexatic phases in liquid-crystal films. Using the renormalization group, we then derive phase diagrams with four tilted hexatic phases: the hexatic-I and hexatic-F phases, an intermediate hexatic-L phase, and an unlocked phase. If the films are crystalline rather than hexatic, all these phases except the unlocked phase still exist. These results are consistent with recent experiments on thermotropic and lyotropic liquid crystals. We also study the five-armed ``star'' defect close to the hexatic-to-hexatic transitions. Near the first-order transition from hexatic-I to hexatic-F, the thickness of the arms increases as \ensuremath{\Vert}T-${T}_{\mathrm{IF}}$${\ensuremath{\Vert}}^{\mathrm{\ensuremath{-}}1/3}$ through a process similar to wetting. This thickening should be observable in thin tilted hexatic films.
40 citations
TL;DR: In this article, it was shown that the coefficient of the fourth-order term is highly temperature dependent, relative to that of second-order terms, and this result is not due to critical fluctuations in the Ginzburg interval.
Abstract: Landau free-energy expansions are commonly used to describe systems undergoing structural phase transitions. The Landau free energy of a model solid with an anharmonic potential (often a double well) at each site and mean-field-like inter-site coupling has been calculated both analytically and from molecular dynamics simulation. The calculated free-energy function is not well described by a simple polynomial in the order parameter. This result is not due to critical fluctuations in the Ginzburg interval. If, however, such a polynomial is used the coefficient of the fourth-order term is found to be highly temperature dependent. For a certain range of model parameters this coefficient is small relative to that of the second-order term. These observations help to explain the occurrence of 'non-critical, non-standard' values of the exponent beta in the variation of the order parameter, x, with temperature: x varies as (Tc-T)beta . More importantly they also help to explain why so many natural systems behave in a tricritical-type manner with beta approximately=1/4.
32 citations
TL;DR: The systematics of the critical temperature and the critical angular momentum of the shape transitions as functions of neutron and proton number are investigated and simple rules are provided for the behavior of these quantities.
Abstract: The Landau theory of shape transitions in hot rotating nuclei is applied to even-even rare-earth nuclei from cerium to hafnium. The parameters of the Landau expansion are extracted from microscopic calculations based on the Nilsson-Strutinsky procedure, and are shown to follow simple systematics. In particular, the systematics of the critical temperature and the critical angular momentum of the shape transitions as functions of neutron and proton number are investigated. Simple rules are provided for the behavior of these quantities.
31 citations
TL;DR: Mise en evidence par diffraction RX a 1000 and 1115 C d'une transformation de premier ordre cubique-tetragonale-orthorhombique suivie d'un transformation de second ordre tetragonal-orthorehombiques for NbRu 1+x (x=0-0,13-0.27) and RhTi.
Abstract: Mise en evidence par diffraction RX a 1000 et 1115 C d'une transformation de premier ordre cubique-tetragonale suivie d'une transformation de second ordre tetragonale-orthorhombique pour NbRu 1+x (x=0-0,13-0,27) et RhTi. Ces resultats sont en accord avec les previsions de la theorie de Landau
29 citations
13 Mar 1989
28 citations
TL;DR: The ``nearly metamagnetic'' model of Bedell and Sanchez-Castro for the magnetic equation of state for polarized liquid and the predictions of this model, as well as the comparison to other existing models, are presented.
Abstract: In this article, we discuss the thermodynamics and Landau theory of spin-polarized Fermi systems. Then, we review the ``nearly metamagnetic'' model of Bedell and Sanchez-Castro for the magnetic equation of state for polarized liquid $^{3}\mathrm{He}$. The predictions of this model, as well as the comparison to other existing models, are presented.
TL;DR: In this paper, symmetry properties and structural phase transitions of the relaxor ferroelectric PbSc0.5Ta 0.5O3 are described using Landau theory.
Abstract: Symmetry properties and structural phase transitions of the relaxor ferroelectric PbSc0.5Ta0.5O3 are described using Landau theory. Symmetry reductions in disordered material occur via a ferroelastic (Pm3m-R3m) and a ferroelectric transition (R3m-R3m). Ordering involves the zone boundary instabilities Pm3m(Z=1)-Fm3m(Z=2) (R point), R3m(Z=1)-R3m(Z=2) (Z point) and R3m(Z=1)-R3m(Z=2) (Z point). The Landau potential includes the coupling between the three primary order parameters describing the cation ordering, the ferroelastic and the ferroelectric lattice distortions. Relaxor behaviour is related to the kinetic properties of order parameters with intermediate conservation lengths. Kanzig domains are related to inhomogenous solutions of the kinetic rate law.
TL;DR: In this article, a study of the dielectric constant at a constant frequency of 10 kHz as a function of temperature has been performed and the results reveal the existence of new intermediate high-order commensurate phases, in agreement with pyroelectric measurements.
Abstract: BCCD exhibits a sequence of structural phase transitions from a high-symmetry orthorhombic phase to different commensurate or incommensurate phases modulated along [001]. This work reports a study of the dielectric constant at a constant frequency of 10 kHz as a function of temperature. The results are discussed within the scope of Landau theory and reveal the existence of new intermediate high-order commensurate phases, in agreement with recent pyroelectric measurements.
TL;DR: In this article, the problem of phase transition can be formulated without introduction of some additional parameters into the free-energy density, and the theory proposed is an approximate one, based on integration of ''basic» measure densities.
Abstract: In terms of these variables the problem of phase transition can be formulated without introduction of some additional parameters into the free-energy density. In the present study at certain points there arise relations connected with Landau theory, Wilson's RG method and with the hierarchical Dyson's model [38, 41]. The theory proposed is an approximate one, based on integration of «basic» measure densities
TL;DR: In this paper, the complex dielectric permittivity of HDOBAMBC has been measured in the vicinity of the chiral smectic C-smectic A transition as a function of temperature and frequency.
Abstract: The complex dielectric permittivity of HDOBAMBC has been measured in the vicinity of the chiral smectic C-smectic A transition as a function of temperature and frequency. The Goldstone mode contribution has been clearly identified and its relaxation frequency has been determined over the whole S*C range. High accuracy tilt angle measurements have also been performed by using a new method which allows its determination in a direct and virtually continuous way. These experimental results together with additional measurements of the polarization and helical pitch have been compared with those of DOBAMBC and analized in the framework of the generalized Landau theory. As for DOBAMBC a reentrant behaviour S*C-SC-S*C has been observed under an electric field near the S*C-SA transition.
TL;DR: Using the Ginzburg criterion, it is demonstrated that the width of the critical region associated with the smectic-A-smectic C transition is dependent on the observable studied, which affords an explanation of the results obtained for terephthal-bis-p-p'-butylaniline.
Abstract: Using the Ginzburg criterion, we demonstrate that the width of the critical region associated with the smectic-A-smectic-C transition is dependent on the observable studied. This affords an explanation of the results obtained for terephthal-bis-p-p'-butylaniline, which shows specific-heat behavior consistent with a Landau-type model, unlike that of the elastic constants. This analysis could apply to other phase transitions
TL;DR: In this paper, the results of Brillouin scattering studies of single crystals of ferroelastic LiKSO2 in the range of temperatures from 140 to 300 K have been reported.
Abstract: The authors report on the results of Brillouin scattering studies of single crystals of ferroelastic LiKSO2 in the range of temperatures from 140 to 300 K. They have measured all the nonzero second-order elastic constants and found them to be essentially temperature-independent except for c66. The interesting hysteretic temperature dependence of c66, its incomplete softening at the transition temperature and other physical properties of LiKSO4 previously reported have motivated them to re-examine and extend the theoretical models adopted earlier. A Landau expansion of the free-energy involved strain components including spontaneous strain, polarisation and both order parameters for the two neighbouring transitions around 190 and 250 K. As a result of this analysis they have obtained good qualitative agreement with the reported experimental data.
TL;DR: In this paper, the phase sequence of betaine phosphate was interpreted with the Landau-type thermodynamic potential, and the experimental results confirmed two low temperature transitions in the Raman spectra.
Abstract: Successive phase transitions in betaine phosphate were studied by measuring the temperature and pressure dependence of dielectric constants, and by observing the temperature dependence of the Raman spectra. The experimental results confirmed two low temperature transitions. The phase sequence is phenomenologically interpreted with the Landau-type thermodynamic potential.
TL;DR: In this article, the properties of binary mixtures with closed-loop diagrams are discussed and the topology of the phase diagram of a binary mixture with hydrogen-bonding is obtained in the mean-field approximation of the lattice mixture Hamiltonian.
TL;DR: Using Landau theory, the possibility that two and three dimensional hexagonal structures can exist in cholesteric liquid crystals with positive dielectric anisotropy in an applied electric or magnetic field is considered as discussed by the authors.
Abstract: Using Landau theory, the possibility that two and three dimensional hexagonal structures can exist in cholesteric liquid crystals with positive dielectric anisotropy in an applied electric or magnetic field is considered. Both are found to be thermodynamically stable in different regions of the chirality-temperature-field phase diagram, in agreement with reported experimental data. Further, the theoretical results indicate that two different three dimensional hexagonal phases, having the same space group (P6222) but different structure factors, may exist. Ways of verifying this prediction by optical and N.M.R. studies are considered. Also noted is the need to develop further the theoretical model to allow for the existence of the experimentally observed body-centred tetragonal structure.
01 Jan 1989
TL;DR: In this article, the emergence of order out of disorder is studied in the context of phase transitions in the Landau theory, and symmetry breaking in phase transitions is discussed in particular.
Abstract: This chapter is concerned with the emergence of order out of disorder, and specifically with symmetry breaking in phase transitions in the framework of the Landau theory [3.1, 2].
TL;DR: In this paper, the successive phase transitions in hexagonal BaTiO 3 are discussed on the basis of the Landau-type free energy function, putting the emphasis on the transition between the intermediate phase II and the lowest temperature phase III.
Abstract: The successive phase transitions in hexagonal BaTiO 3 is discussed on the basis of the Landau-type free energy function, putting the emphasis on the transition between the intermediate phase II and the lowest temperature phase III. It is pointed out that to induce the phase III with the space group P2 1 the twelveth order term in the order parameters, transforming under the symmetry operations as the bases of the two-dimensional E 2 u representation of the 6/mmm group, is required.
TL;DR: Une fonctionnelle d'energie libre de type Landau, developpee au huitieme ordre dans la densite de spin, sert de base a l'etude des phases ordonnees magnetiquement du C 5 CoCl 3 a quasi-une dimension, de type Ising, et des composes qui s'y rattachent.
Abstract: Une fonctionnelle d'energie libre de type Landau, developpee au huitieme ordre dans la densite de spin, sert de base a l'etude des phases ordonnees magnetiquement du C 5 CoCl 3 a quasi-une dimension, de type Ising, et des composes qui s'y rattachent. Une variete de sequences des transitions successives sont predites, impliquant les phases d'ordre trois caracterisees par deux composantes de Fourier dominantes de la densite de spin. De plus, on etudie le diagramme de phase, et on trouve un nombre de points multicritiques inhabituels
TL;DR: The structural phase transitions in zirconia ZrO 2 are interpreted phenomenologically, based upon the Landau-type thermodynamic potential derived on the consideration of the change of translational as well as rotational symmetry of the unit cell as discussed by the authors.
Abstract: The structural phase transitions in zirconia ZrO 2 are interpreted phenomenologically, based upon the Landau-type thermodynamic potential derived on the consideration of the change of translational as well as rotational symmetry of the unit cell. The difference between Chan's model and ours is mentioned.
TL;DR: In this article, the equivalence of the two methods is discussed in the context of RPA collective modes in nuclear matter, and two different approaches to the theory, one due to Landau and the other to van Kampen, are discussed.
TL;DR: In this article, a coupled non-linear system of partial differential equations that models the dynamics of structural phase transitions in a one-dimensional non-viscous and heat-conducting solid is studied.
Abstract: In this paper we study a coupled non-linear system of partial differential equations that models the dynamics of structural phase transitions in a one-dimensional non-viscous and heat-conducting solid. The corresponding Helmholtz free energy density is assumed in Ginzburg–Landau form; to allow for phase transitions and hysteresis phenomena, it is not assumed convex in the order parameter. It is shown that the solution of the system depends continuously upon the data, and we prove an existence result for an associated optimal control problem.
TL;DR: It is demonstrated that the only peculiar feature of the harmonic atomic Debye-Waller factors is a space modulation, which becomes negligible as the amplitude of the structural modulation decreases.
Abstract: A general analysis of the dynamics of displacive incommensurately modulated structures within the harmonic approximation is presented. Superspace formalism is not used. The present approach is compared with the usual Landau model and some recent phenomenological predictions for hard internal modes. The characteristics of coherent inelastic neutron scattering are also analyzed. A compact expression for the one-phonon dynamic structure factor is derived which is valid for any form of the static modulation. The resulting expression for the atomic Debye-Waller factors generalizes those previously obtained in the frame of Landau theory. It is demonstrated that the only peculiar feature of the harmonic atomic Debye-Waller factors is a space modulation, which becomes negligible as the amplitude of the structural modulation decreases.
TL;DR: The problem of the hot-carrier distribution function in crossed electric and magnetic fields is treated for free carriers in a parabolic band and the master equation for the diagonal elements of the density operator is solved for three Landau levels, considering optical and acoustic deformation potential scattering.
Abstract: The problem of the hot-carrier distribution function in crossed electric and magnetic fields is treated for free carriers in a parabolic band. To account for the discrete structure of the energy spectrum (Landau levels), a fully quantum-mechanical treatment is employed. The master equation for the diagonal elements of the density operator is solved for three Landau levels, considering optical and acoustic deformation potential scattering. Numerical results are presented for the case of the light holes in p-type germanium. The total populations of the different Landau levels are discussed as well as the one-dimensional distribution functions in the Landau levels, and their dependencies on electric and magnetic field strengths are studied. Special attention is paid to the occurrence of a population inversion between Landau levels and to a comparison of the present approach to the classical picture of streaming motion.