Showing papers on "Landau theory published in 1998"

Elastic anomalies in minerals due to structural phase transitions

Abstract: Landau theory provides a formal basis for predicting the variations of elastic constants associated with phase transitions in minerals. These elastic constants can show substantial anomalies as a transition point is approached from both the high-symmetry side and the low-symmetry side. In the limiting case of proper ferroelastic behaviour, individual elastic constants, or some symmetry­ adapted combination of them, can become very small if not actually go to zero. When the driving order parameter for the transition is a spontaneous strain, the total excess energy for the transition is purely elastic and is given by: which has the same form as a Landau expansion. In this case, the second-order elastic constant Cik softens as a linear function of temperature with a slope in the low-symmetry phase that depends on the thermodynamic character of the transition. If the driving order parameter, Q, is some structural feature other than strain, the excess energy is given by: G = ia(T Tc )Q2 + ±bQ4 + . . . + .LAi,m,neFQn + i � Ci%eiek l,m,n l,k In this case, the effect of coupling, described by the term in AemQn, is to cause a great diversity of elastic variations depending on the values of m and n (typically 1, 2 or 3), the thermodynamic character of the transition and the magnitudes of any non-symmetry-breaking strains. The elastic constants are obtained by taking the appropriate second derivatives of G with respect to strain in a manner that includes the structural relaxation associated with Q. The symmetry properties of second-order elastic constant matrices can be related to the symmetry rules for individual phase transitions in order to predict elastic stability limits, and to derive the correct form of Landau expansion for any symmetry change. Selected examples of \"ideal\" behaviour for different types of driving order parameter, coupling behaviour and thermodynamic character have been set out in full in this review. Anomalies in the elastic properties on a macroscopic scale can also be understood in terms of the properties of acoustic phonons. These microseopie processes must be considered if elastic anomalies due to dynamical effects are to be accounted for 0935122 1/98/00 10-0693 $ 30.00 001:1 0.1127/ejm/1 0/4/0693 © 1998 E. Schweizerbart'sche Verlagsbuchhandlung, D-70176 Stuttgart

Ferroelectric Phenomena in Crystals: Physical Foundations

Abstract: 1. General Characteristics of Structural Phase Transitions in Crystals.- 1.1 First- and Second-Order Structural Phase Transitions.- 1.2 Structural Phase Transitions of Displacive and Order-Disorder Types.- 1.3 The Domain Structure.- 1.4 Ferroelectric Phase Transitions.- 1.5 Basic Types of Ferroelectric Crystals.- 2. Phenomenological Theory of Second-Order Structural Transitions in Crystals.- 2.1 The Incomplete Thermodynamic Potential.- 2.2 Structural Phase Transitions Described by a One-Component Order Parameter.- 2.3 Structural Phase Transitions Described by Two- and Three-Component Order Parameters.- 3. Proper Ferroelectrics: Anomalies of Physical Properties in Phase Transitions.- 3.1 Anomalies of Thermal and Electrical Properties (One-Component Order Parameter).- 3.2 Anomalies of Electrical Properties (Multicomponent Order Parameter).- 3.3 First-Order Phase Transitions Close to Second-Order Transitions.- 3.4 The Tricritical Point.- 4. Dielectric Anomalies in Structural Nonferroelectric and Improper Ferroelectric Phase Transitions.- 4.1 Nonferroelectric Phase Transitions: Dielectric Anomalies.- 4.2 Improper Ferroelectric Phase Transitions: Dielectric Anomalies.- 5. Anomalies of Elastic and Electromechanical Characteristics of Crystals in Second-Order Phase Transitions.- 5.1 One-Component Order Parameter: Elastic Properties of an Isotropic Liquid.- 5.2 One-Component Order Parameter: Elastic Properties of an Anisotropic Crystal.- 5.3 Ferroelectric-Ferroelastics: One-Component Order Parameter with Transformation Properties of the Component of a Second-Rank Tensor and the Polar Vector.- 5.4 Temperature Dependences of "Morphic" Moduli of Elasticity.- 5.5 Two-Component Order Parameter: Elastic Properties of Crystals.- 5.6 Piezoelectric Effect and Electrostriction in the Case of One-Component Order Parameter and Centrosymmetric Paraelectric Phase.- 5.7 Piezoelectric Effect in the Case of One-Component Order Parameter and Noncentrosymmetric Paraelectric Phase.- 6. Fluctuations of the Order Parameter in Phenomenological Theory.- 6.1 Spatially Inhomogeneous Fluctuations of the Order Parameter in the Incomplete Thermodynamic Potential.- 6.2 Applicability of Landau Theory to Nonferroelectric Structural Phase Transitions.- 6.3 Applicability of Landau Theory to Phase Transitions in Uniaxial Ferroelectrics.- 6.4 Fluctuational Phenomena in Ferroelectric-Ferroelastics and in Phase Transitions in Multiaxial Ferroelectrics.- 7. Structural Phase Transitions in the Single-Ion Model.- 7.1 Problems of the Microscopic Theory.- 7.2 The Single-Ion Model of a Diatomic Crystal.- 7.3 Phase Transitions of Displacive and Order-Disorder Types in the Single-Ion Model.- 7.4 Applicability of the Landau Theory to Phase Transitions of Displacive and Order-Disorder Types.- 8. Statistical Theory of Ferroelectric Phase Transitions of the Order-Disorder Type.- 8.1 The Hamiltonian of a Uniaxial Ferroelectric with an Order-Disorder Phase Transition.- 8.2 The Free Energy of an Order-Disorder Crystal in the Self-Consistent Molecular Field Approximation.- 8.3 Tunneling Effects in Hydrogen-Containing Ferroelectrics.- 8.4 The Cluster Approximation: Crystals of the KH2P04 Group.- 9. Dynamics of Displacive and Order-Disorder Phase Transitions.- 9.1 The Equation of Motion of the Order Parameter.- 9.2 Dynamic Dielectric Constant: Order-Disorder Phase Transitions.- 9.3 Dynamic Dielectric Constant: Displacive Phase Transitions.- 9.4 Microscopic Theory of Dynamic Processes in Displacive Phase Transitions.- 9.5 Microscopic Theory of Dynamic Processes in Order-Disorder Phase Transitions.- 9.6 Dielectric Constant and Soft Mode: The Lyddane-Sachs-Teller Relation.- 10. Domain Structure and Defects.- 10.1 Nucleation of Domains in a Structural Phase Transition.- 10.2 Domain Wall Structure: One-Component Order Parameter.- 10.3 Domain Wall Structure: Two-Component Order Parameter.- 10.4 Motion of the Domain Wall in an Ideal and a Real Crystal.- 10.5 Motion of the Domain Wall: Account of the Discreteness of the Crystal.- 10.6 Domain Walls and Defects.- 10.7 Defects in the Symmetrical Phase.- 10.8 Domains in Proper Ferroelectrics.- 10.9 Domains in Ferroelastics.- 10.10 Domains in Polyaxial Ferroelectrics.- 11. Ferroelectrics with an Incommensurate Phase.- 11.1 Phase Transitions into an Incommensurate Phase.- 11.2 Phenomenological Theory of Phase Transitions into an Incommensurate Phase.- 11.3 Specific Features of Crystal Lattice Vibrations in an Incommensurate Phase.- 11.4 The Incommensurate Phase in a Real Crystal.- 11.5 The Commensurate-Incommensurate Phase Transition: A Special Type of Phase Transition.- 11.6 Evolution of the Structure of the Incommensurate Phase (General Picture).- 11.7 Evolution of the Structure of the Incommensurate Phase (the Continuum Approximation).- 12. Ferroelectric Liquid Crystals.- 12.1 Basic Types of Orientational Ordering in Liquid Crystals.- 12.2 Conditions for Existence of Dipolar Ordering in Liquid Crystals.- 12.3 Phenomenological Theory of Phase Transition SmA* -? SmC*.- 12.4 The Behavior of a Ferroelectric Smectic Liquid Crystal in an External Electric Field.- 13. Crystallochemical Aspects of the Theory of Ferroelectric Phenomena.- 13.1 Calculation of the Constants of the Hamiltonians of Some Crystals.- 13.2 An Approach Based on the Classical Theory of Ionic Crystals.- 14. Recommended Literature.- References.

Landau theory of stripe phases in cuprates and nickelates

Abstract: We consider a Landau theory of coupled charge and spin-density-wave order parameters as a simple model for the ordering that has been observed experimentally in the La{sub 2}NiO{sub 4} and La{sub 2}CuO{sub 4} families of doped antiferromagnets. The period of the charge-density wave is generically half that of the spin-density wave, or equivalently the charges form antiphase domain walls in the antiferromagnetic order. A sharp distinction exists between the case in which the ordering is primarily charge driven (which produces a sequence of transitions in qualitative agreement with experiment) or spin driven (which does not). We also find that stripes with noncollinear spin order (i.e., spiral phases) are possible in a region of the phase diagram where the transition is spin driven; the spiral is circular only when there is no charge order, and is otherwise elliptical with an eccentricity proportional to the magnitude of the charge order. {copyright} {ital 1998} {ital The American Physical Society}

Analysis of ferroelectric switching in finite media as a Landau-type phase transition

Abstract: A detailed analysis of polarization reversal in ferroelectrics has been performed, in the framework of the Landau model for phase transitions. Some important characteristics of homogeneous switching have been emphasized and later used in studying the more general case of inhomogeneous switching. The two extremes of switching current correspond to the inflexion points of the dielectric hysteresis loop. Hysteresis loops of poled ferroelectric samples are expected to include negative-susceptibility regions, for high-frequency applied electric fields. The switching current minimum is eliminated by the experimental method used for recording the switching responses. Equivalent Landau coefficients and electric fields have been defined, in order to integrate the size effects and inhomogeneity contribution to switching of the global order parameter. We correlated the size effects on the critical parameters of the switching (the coercive field) and the ferroelectric-to-paraelectric phase transition (the Curie temperature). Polarization reversal in small-size ferroelectrics can be regarded as a diffuse phase transition, whereas its character is closer to normal for large-size samples. The size dependencies of the reversal speed and maximum current result from the size dependencies of the equivalent Landau coefficients and electric field inducing reversal.

The temperature dependence of the cation distribution in synthetic hercynite (FeAl2O4) from in-situ neutron structure refinements

Abstract: The temperature dependence of the cation distribution in synthetic hercynite (FeAl 2O4) has been determined using in-situ time-of-flight neutron powder diffraction. The sample was synthesized from the oxides under controlled oxygen fugacity and then quenched in air. Neutron diffraction patterns were then collected under vacuum on heating from room temperature to 1150 8C, and the cation distribution was determined directly from site occupancies obtained by Rietveld refinement. The degree of inversion, x, decreased from 0.135(4) at room temperature to 0.112(4) at 600 8C. Thereafter the degree of inversion increases smoothly with increasing temperature, reaching a value of 0.219(5) at 1150 8C. The decrease in x on heating to 600 8C is a kinetic phenomenon caused by the system moving toward its equilibrium degree of order from the relatively disordered state main- tained after quenching from the synthesis temperature. The equilibrium ordering behavior between 600 and 1150 8C has been analyzed using both the O'Neill-Navrotsky and Landau thermodynamic models. Although the data could be fitted with both models over the tem- perature range of the measurements, Landau theory predicts the incorrect curvature of the equilibrium x-T curve, leading to a significant discrepancy in the calculated behavior when the model is extrapolated outside the calibrated temperature range. The correct x-T cur- vature is predicted by the O'Neill-Navrotsky model, and values of the model coefficients a5 31.3 6 1.1 kJ/mol and b5 19.7 6 3.4 kJ/mol were obtained by least-squares fitting to the equilibrium data. This confirms the results of a previous study using quenched material, which suggested that the sign of the b coefficient in FeAl 2O4 is opposite to that found in other 2-3 oxide spinels.

Crystalline structures and phase transition of the ferroelectric P(VDF-TrFE) copolymers, a neutron diffraction study

Abstract: Neutron investigations have been performed in order to study the crystalline structure of the ferroelectric and paraelectric phases of random copolymers of vinylidene fluoride and trifluoroethylene P(VDF-TrFE) and to investigate the influence of co-monomer composition. Structural information in the crystal is essential to understand the mechanism of the phase transition. In the ferroelectric phase, the increase of TrFE content from 20% to 40% clearly affects the crystalline order and leads to an anisotropic expansion of the lattice. At high temperature, complementary studies of diffraction and diffuse scattering, on oriented and deuterated samples, allow us to specify a structural description of the highly disordered paraelectric phase and to propose a model describing the conformational disorder of the chain. From these results we present a thermodynamical analysis of the ferroelectric to paraelectric transition based on the Landau theory which enables to evaluate the different energetic contributions to the structural instability in the crystalline regions of the polymer.

Onset of superconductivity in decreasing fields for general domains

Abstract: Ginzburg–Landau theory has provided an effective method for understanding the onset of superconductivity in the presence of an external magnetic field. In this paper we examine the instability of the normal state to superconductivity with decreasing magnetic field for a closed smooth cylindrical region of arbitrary cross-section subject to a vertical magnetic field. We examine the problem asymptotically in the boundary layer limit (i.e., when the Ginzburg–Landau parameter, k, is large). We demonstrate that instability first occurs in a region exponentially localized near the point of maximum curvature on the boundary. The transition occurs at a value of the magnetic field associated with the half-plane at leading order, with a small positive correction due to the curvature (which agrees with the transition problem for the disc), and a smaller correction due to the second derivative of the curvature at the maximum.

Low-temperature phase diagrams: non-linearities due to quantum mechanical saturation of order parameters

Abstract: At low temperatures, the behaviour of structural phase transitions is modified by the influence of quantum fluctuations. Such fluctuations enhance the stability of the high-symmetry phase, reducing the observed transition temperature. The effect on phase diagrams of temperature versus some other control parameter (e.g. pressure or chemical composition) is described. A simple low-temperature extension of Landau theory is used, where the extent of quantum mechanical effects is characterized by a saturation temperature . The theory is used to model the phase diagrams of the mineral anorthoclase , the ferroelectric materials ( for the 20 K transition), and SbSI . The saturation temperature is related to the extent to which changes in the hard phonon modes influence the transition mechanism.

The puzzle of the nematic-isotropic phase transition

Abstract: The low value of , where is the nematic-isotropic phase transition temperature and denotes the virtual transition temperature, is a long-standing puzzle in the physics of liquid crystals. The present review presents experimental and theoretical results on this long-standing problem. New experimental and theoretical results for the critical behaviour in the isotropic phase of nematogens are reviewed. We calculate in a unified approach the low value of , at both critical and tricritical points. The possibility of tricritical behaviour at the nematic-isotropic transition is also discussed by means of Landau theory. The various predictions are compared with the available experimental results.

Multidimensional Bosonization

Abstract: Bosonization of degenerate fermions yields insight both into Landau Fermi liquids, and into non-Fermi liquids We begin our review with a pedagogical introduction to bosonization, emphasizing its applicability in spatial dimensions greater than one After a brief historical overview, we present the essentials of the method Well known results of Landau theory are recovered, demonstrating that this new tool of many-body theory is robust Limits of multidimensional bosonization are tested by considering several examples of non-Fermi liquids, in particular the composite fermion theory of the half-filled Landau level Nested Fermi surfaces present a different challenge, and these may be relevant in the cuprate superconductors We conclude by discussing the future of multidimensional bosonization

Thickness Transitions of Ferroelectricity in Thin Films: II

Abstract: The disappearance of ferroelectricity in thin films is discussed in the framework of the Landau theory. The way in which ferroelectricity is lost with decreasing film thickness has the properties of a phase transition. The polarization profiles, the average energy density and the average polarization, which depend on the film thickness, are analytically obtained for various boundary conditions.

Derivation of the Time-Dependent Ginzburg-Landau Equation on the Line

Abstract: We give a rigorous derivation of the time-dependent one-dimensional Ginzburg—Landau equation.

Coupling between membrane tilt-difference and dilation: A new “ripple” instability and multiple crystalline inclusions phases

Abstract: A continuum Landau theory for the micro-elasticity of membranes is discussed, which incorporates a coupling between the bilayer thickness variation and the difference in the two monolayers' tilts. This coupling stabilizes a new phase with a rippled micro-structure. Interactions among membrane inclusions combine a dilation-induced attraction and a tilt-difference–induced repulsion that yield 2D crystal phases, with possible coexistence of different lattice spacings for large couplings. Inclusions favoring crystals are those with either a long-convex or a short-concave hydrophobic core.

Asymptotic behavior of the solutions to a Landau-Ginzburg system with viscosity for martensitic phase transitions in shape memory alloys

Abstract: In this paper, we investigate the system of partial differential equations governing the dynamics of martensitic phase transitions in shape memory alloys under the presence of a (possibly small) viscous stress. The corresponding free energy is assumed in Landau--Ginzburg form and nonconvex as a function of the order parameter. Results concerning the asymptotic behavior of the solution as time tends to infinity are proved, and the compactness of the orbit is shown.

Scaling of the interfacial tension of microemulsions: A Landau theory approach

Abstract: We have calculated the structure and the interfacial tension of microemulsions on the phase inversion path, using a single-order parameter Landau theory. We show that the observed scaling behavior of the interfacial tensions [T. Sottmann and R. Strey, J. Chem. Phys. 106, 8606 (1997)] is described by a simple theoretical model based on the assumption that the ratio of the length scales characterizing microemulsions is a universal function of the reduced temperature, on the phase inversion path. This assumption is based on the results of small angle neutron scattering experiments on this series of systems, at the optimal microemulsion temperature [T. Sottman, R. Strey, and S.-H. Chen, J. Chem. Phys. 106, 6483 (1997)] and on the scaling properties of the Landau free energy on the phase inversion path.

Landau theory of social clustering

Abstract: We discuss the Landau theory for a nonlinear equation that can describe social changes, such as an influence of the social environment on individual. The models can explain why the minority can survive inside the majority population. It is described in terms of the complex intermittent clusters behavior in the stationary limit.

On the nature of the γ-α transition in cerium

Abstract: In 1964 Davis and Adams established that the large increase of the thermal expansion and compressibility in the critical region of the γ-to α-Ce phase transition occurs predominantly in the α phase. This provides strong evidence that a tricritical point is realized in Ce. This also means that the aforementioned transition is not isomorphic and that α-Ce should have a distorted fcc structure. A careful examination of Jayaraman’s data (1965) shows that a second-order transition line continues beyond the tricritical point to the vicinity of a triple point on the melting curve. The phase boundary with the tricritical point and the minimum of the melting curve are reconstructed within the framework of Landau theory.

Fluctuation-induced phase in in a transverse magnetic field: experiment

Abstract: The new magnetic phase of recently found by specific heat measurements has been investigated by means of neutron diffraction. This new phase is found very close to the critical temperature and it widens to a few tenths of a degree Kelvin in very high magnetic fields. The availability of a new strong steady-state magnet with a nominal strength of 14.5 T provided us with the opportunity to investigate the magnetic structure. We found that the new phase is also incommensurate, but that it no longer has the triangular antiferromagnetic structure. A proposal for the structure derived from a Landau theory put forward in the following theory paper by Jacobs and Nikuni is compared to the experimental results. The order of the transitions observed will be discussed, as well as our failure to observe a predicted commensurate phase.

Fluctuation-induced phase in in a transverse magnetic field: theory

Abstract: is a quantum triangular antiferromagnet, ferromagnetically stacked, with an incommensurate (IC) structure due to a Dzyaloshinskii-Moriya interaction. Because of the classical degeneracy caused by the frustration, fluctuations in have extraordinarily large effects, such as the phase transition in longitudinal magnetic field (normal to the planes, parallel to the IC wavenumber q) and the plateau in q in transverse field (perpendicular to q). We argue that fluctuations are responsible also for the new IC phase discovered in transverse field near the Neel temperature , by Werner et al (Werner T, Weber H B, Wosnitza J, Kelnberger A, Meschke M, Schotte U, Stuser N, Ding Y and Winkelmann M 1997 Solid State Commun. 102 609). We develop and analyse the corresponding minimal Landau theory; the ground-state reconstruction due to fluctuations is described phenomenologically, by means of a biquadratic term. The Landau theory gives two IC phases, one familiar from previous studies; the properties of the new IC phase, which occupies a pocket of the temperature-field phase diagram near , agree qualitatively with those of the new phase found experimentally.

Improved analysis of the Landau theory of the uniaxial-biaxial nematic phase transition

Abstract: A phenomenological theory is developed for uniaxial and biaxial nematic phases, based on a two component tensor order parameter. Phase diagrams are plotted and investigated in the plane of two thermodynamic parameters. Anomalies in thermal properties are studied in the vicinity of an isolated four-phase critical point. The temperature dependences of the order parameter and the thermodynamic quantities are also calculated theoretically for the first time.

Instability of a Landau - Fermi liquid as the Mott insulator is approached

Abstract: We examine a two-dimensional Fermi liquid with a Fermi surface which touches the Umklapp surface first at the four points as the electron density is increased. Umklapp processes at the four patches near lead the renormalization group equations to scale to strong coupling, resembling the behaviour of a two-leg ladder at half-filling. The incompressible character of the fixed point causes a breakdown of Landau theory at these patches. A further increase in density spreads the incompressible regions so that the open Fermi surface shrinks to four disconnected segments. This non-Landau state, in which parts of the Fermi surface are truncated to form an insulating spin liquid, has many features in common with phenomenological models recently proposed for the cuprate superconductors.

Self Diffusion in Solid 4He and 3He-4He Mixtures Near the bcc-hcp Phase Transition

Abstract: We report experiments on the plastic flow of solid 4 He and 3 He- 4 He mixtures of 1.4% and 2.8% near the bcc-hcp transition. Plastic flow was generated by moving a wire through a macroscopic single crystal. We found that the plastic flow rate both in pure 4 He and in mixture helium crystals is enhanced in vicinity of the bcc-hcp phase transition. The results are interpreted in terms of self diffusion in the solid. Values of the self diffusion coefficient Ds at the respective transition temperatures of pure 4 He and of the mixtures are very close, and reach that found in normal liquids. The activation energy for self diffusion in the mixtures is lower by up to 3 K than in pure 4 He. We suggest that similar to what is observed in bcc metals, self-diffusion in solid He takes place through phonon assisted atom-vacancy exchange. The enhancement of the diffusion near the bcc-hcp transition is a result of the softening of a short wavelength transverse phonon. The temperature dependence of the energy of the phonon calculated using our data is in accord with the Landau theory of a phase transition driven by a soft mode. Work hardening was observed in mixture crystals, but not in pure 4 He. This implies that 3 He impurities pin dislocation lines.

Fluctuation-induced phase in CsCuCl3 in transverse magnetic field: Theory

Abstract: CsCuCl3 is a quantum triangular antiferromagnet, ferromagnetically stacked, with an incommensurate (IC) structure due to a Dzyaloshinskii-Moriya interaction. Because of the classical degeneracy caused by the frustration, fluctuations in CsCuCl3 have extraordinarily large effects, such as the phase transition in longitudinal magnetic field (normal to the planes, parallel to the IC wavenumber q) and the plateau in q in transverse field (perpendicular to q). We argue that fluctuations are responsible also for the new IC phase discovered in transverse field near the Neel temperature T_N, by T. Werner et al. [Solid State Commun. 102, p.609 (1997)]. We develop and analyse the corresponding minimal Landau theory; the effects of fluctuations on the frustration are included phenomenologically, by means of a biquadratic term. The Landau theory gives two IC phases, one familiar from previous studies; properties of the new IC phase, which occupies a pocket of the temperature-field phase diagram near T_N, agree qualitatively with those of the new phase found experimentally.

Effect of chiral interactions on the structure of Langmuir monolayers

Abstract: Structural changes in monolayers of the enantiomer and the racemic mixture of 1-hexadecyl-glycerol with temperature and surface pressure variations are compared. On compression, both monolayers exhibit a variation of the tilt azimuth from the direction to the nearest neighbor to the next nearest neighbor. In the monolayer of the racemate, this variation occurs as a first order transition. In the monolayer of the enantiomer, the unit cell is oblique, and continuously passes from a state close to the low-pressure state of the racemate to a state close to its high-pressure state. The azimuths of the unit-cell distortion and that of the tilt remain almost equal to each other. The effect of chirality decreases when the temperature is increased. Structural changes are explained in detail within the framework of the Landau theory of phase transitions.