Showing papers on "Landau theory published in 1987"

Theory of first-order phase transitions

Abstract: An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described. Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets of a new phase, etc.).

The Landau theory of phase transitions : application to structural, incommensurate, magnetic, and liquid crystal systems

Abstract: The contents of this book stems from three different objectives. First, it is an introduction to the basic principles and techniques of Landau's theory, which is intended for teaching purposes. A second purpose of the book provides the practical methods for applying Landau's theory to complex systems. The last objective of the book is to incorporate the developments which have arisen in the last fifteen years from the extensive application of the theory to a variety of physical systems.

Wetting on cylinders and spheres

Abstract: A fluid (or Ising-like) system in contact with a uniformly curved substrate, such as a cylinder or sphere, exhibits a surface phase diagram which is different from that when the substrate is flat. Using both an interface model and a Landau theory that includes surface field and surface coupling enhancement parameters, we find that the effects of curvature may be subsumed into an effective bulk (ordering) field. Complete and critical wetting transitions are thus suppressed. At bulk coexistence, the mean-field phase diagram exhibits curvature-induced prewetting and critical prewetting transitions. In d=3, finite-size effects smear the prewetting transitions that would otherwise take place in cylindrical or spherical geometries. The Landau theory employs a nonanalytic, piecewise parabolic approximation to the usual quartic polynomial in the free-energy functional. This approximation produces a global surface phase diagram with the correct topology, even though it is unsuited for the description of multicritical phenomena, such as wetting tricriticality. Other strengths and weaknesses of the approximation are described.

In situ observation of the polytypic phase transition 2H-12R in PbI2: investigations of the thermodynamic structural and dielectric properties

Abstract: A reversible phase transition between the two polytypic phases 2H and 12R was found in PbI2 near 367K which proves that these polytypes are thermodynamic equilibrium phases and not the result of growth processes. Disordered stackings were observed in samples which were annealed at temperatures above 420K. The phase transition is kinetically hindered with an activation energy of 3.8 eV. The character of the phase transition is first order with a latent heat of around 276 J mol-1. The absence of dielectric anomalies with electric fields along the hexagonal c axis indicates that dipole-dipole interactions are not involved in the transition mechanism. The nature of the inter-layer forces are exclusively based on short-range interactions leading to a description of the phase transition in terms of pseudo-spin models. The elastic energy released during the phase transition is 1.2 J mol-1 as determined from the observed jump of the c lattice parameter. A thermodynamic description of the phase transition leads to the conclusion that its driving forces are related to the gain of phonon energy and elastic energy during the transformation. The entropy gain is due to the differences of the phonon frequencies between the two phases. Higher polytypes, if thermodynamically stable phases, can be described as mixtures of structural elements of the basic polytypes with additional stabilisation energies. The temperature evolution of the free energies of the different phases is anticipated. The experimental results are expressed in terms of the Landau theory which shows that the phase transition 2H-12H must be first order as observed. The Landau theory also explains the disordered polytype as a common para-phase for all ordered polytypes. Further insight into the origin of polytypism can be derived from the current understanding of ANNNI models.

Thermodynamics of plagioclases I: Theory of the $$I\bar 1 - P\bar 1$$ phase transition in anorthite and Ca-rich plagioclases

Abstract: Landau theory of the $$P\bar 1 - I\bar 1$$ phase transition in Ca-rich plagioclases reveals the sensitivity of the phase transition behaviour to a) Al, Si disorder, b) structural replacement of Ca by Na, and c) inhomogeneities of lattice strains. The following effects are predicted: The role of inhomogeneous Al, Si distributions and lattice relaxations are discussed including possible structural modulations.

Finite-density Onsager-type theory for the isotropic-nematic transition of hard ellipsoids.

Abstract: We propose a simple density-functional theory for the isotropic-nematic transition of a system of hard ellipsoids which yields results in fair agreement with the computer simulation studies and which reduces exactly to Onsager's theory in the limit of infinitely dilute systems of infinitely long ellipsoids When the free energy is expanded with respect to the Maier-Saupe quadrupole order parameter an explicit Landau theory is produced which yields good results for small nonsphericities The theory also predicts a Lindemann rule for orientational freezing

Comments on the region of applicability of the landau theory for structural phase transitions

Abstract: The Landau theory of phase transitions1 is known to ignore (in its main approximation) long-wave fluctuations of the order parameter. In this aspect this theory is equivalent to the theory of the mean (molecular, self-consistent) field. True, starting from the Landau theory one can calculate contributions of the long-wave fluctuations as well but only if the contributions are small enough. This is not the case in the immediate vicinity of a second-order phase transition. At present the fluctuation theory of phase transitions, or more specifically, the scaling1,2 or renormalization group3-5 theory, is widely used for this region

Ferroelastic Phase Transition in (NH4)3H(SeO4)2

Abstract: Optical observation of twin structures, X-ray examinations and the measurement of the dielectric constant of (NH 4 ) 3 H(SeO 4 ) 2 were carried out in reference to the phase transition at 29°C ( T c ). It was found that (NH 4 ) 3 H(SeO 4 ) 2 undergoes the improper ferro-elastic phase transition at T c . The crystal is determined to be monoclinic withthe space group A 2/ a below T c and trigonal with the space group R \bar3 m above T c . The crystal has spontaneous strain ( e 22 - e 11 )/2=-3.0×10 -3 and e 13 =3.3×10 -3 at room temperature. It was clarified by both observation of domains and symmetry consideration that the crystal exhibits twin structures with two types of domain walls and three kinds of domain orientations at room temperature. The behaviour of the dielectric constant observed near T c is well explained by the Landau theory.

Structural states of Mg-cordierite II: Landau theory

Abstract: Mg-cordierite undergoes a ferroelestic phase transitionP6/mmc-Cccm. The order parameterQ is proportional to the spontaneous strain as reflected by changes of the lattice parametersa andb during the phase transition. The order parameter,Q od, which describes the Al, Si ordering, isnot directly involved in the phase transition and only “triggers” the structural collapse. Landau theory predicts that cordierite can exist in stable or metastable states with hexagonal, orthorhombic or monoclinic symmetry. Hexagonal cordierite can develop modulated structures which have been found by Putnis et al. (1987). The phase transition is predicted to be accompanied by singularities of the elastic constantsC 11,C 22 andC 12 leading to an elastic softening of the crystal structure.

Some remarks on ferroelectricity, soft modes and related problems

Abstract: The contents of the author's papers devoted to the phenomenological theory of ferroelectrics and the soft-mode concept are elucidated. Some remarks are made concerning the range of applicability of the Landau theory in the case of ferroelectric phase transitions. Connection between ferroelectricity, soft modes and high-temperature superconductivity is also discussed.

Spin-orbit coupling in Fermi-liquid theory.

Abstract: The Landau theory of Fermi liquids is extended to include spin-orbit coupling. After constructing the general form of the quasiparticle interaction (which allows spin-orbit coupling), forward-scattering sum rules, static properties such as the sound velocity and magnetic susceptibility, and the stability conditions are derived. Some possible applications of this theory are considered.

X-Ray and Dielectric Studies of Commensurate-Incommensurate Phase Transition in Rb2ZnCl4

Abstract: The commensurate (C)-incommensurate (IC) phase transition in Rb 2 ZnCl 4 has been investigated through studies of the X-ray diffraction and the P - E hysteresis loop Simultaneous observation of the P - E hysteresis loop and the misfit parameter reveals that the double hysteresis loop observed in the IC phase corresponds to the field induced C-IC transition The “triple”-like hysteresis loop observed in the vicinity of the C-IC phase transition temperature corresponds to the coexistence of the IC and the C state near E =0 followed by the field induced C-IC transition at a finite value of E The effect of pinning on the electric field dependence of the misfit parameter and the polarization is considered on the basis of the Landau type theory The tendency of the calculated results agrees well with that of the experimental results

Diffraction and imaging studies of the charge-density-wave-modulated phases of 1T-TaS2

Abstract: New results are presented on 1T-TaS2. They were obtained by combining convergent-beam electron diffraction with high-quality satellite dark-field imaging. In the nearly commensurate 1T2 state linear defects were analysed as displacement faults and the fault planes and vectors were determined. The visibility of these faults was found to be strongly temperature dependent. Temperature-dependent sequences were obtained in chosen areas to follow the dynamic changes which occurred on cooling. Direct dislocation interaction between crystal dislocations and the 1T1/1T2 interface was observed. Radiation damage effects were detected and investigated using a 300 kV electron microscope with variable operating voltage. The first detailed TEM investigation has been carried out on the T phase often obtained on warming the material from its low-temperature locked-in (1T3) state. Detailed comparison of the results obtained has been made with previously reported X-ray results and although there is considerable agreement some differences were detected. A simple Landau theory argument is developed to account for the out-of-plane components of the satellite vectors in the T phase. Some further investigation of the 1T3 phase was carried out and the results discussed in relation to earlier TEM and X-ray investigations.

Critical-point dewetting

Abstract: Already within Landau theory with short-ranged substrate-adsorbate forces, complete wetting is not necessary near critical points. Preferential adsorption, but only partial wetting all the way to the critical point, and even critical-point dewetting are possible. Physical systems displaying such behavior include uniaxial magnets with triplet surface fields, and special choices of adsorbed liquid-vapor systems, binary mixtures, liquid crystals, and critical-end-point systems.

Dipole-dipole interactions and the critical resistivity of gadolinium.

Abstract: Results are presented for the electrical resistivity of a c-axis single crystal of high-purity gadolinium metal in the immediate vicinity of the Curie temperature. Numerical analysis reveals that the data are not well described by the usual power laws in (T-T/sub c/)/T/sub c/ but tend to exhibit a change in effective slope at T/sub c/ which can be described by classical Landau theory with logarithmic corrections. This is interpreted in terms of the dipole-dipole interactions, which are shown to become important at about 1 K above T/sub c/. We suggest that gadolinium is a uniaxial dipolar ferromagnet in the asymptotic critical-behavior regime.

II → III Phase transitions in triammonium hydrogen disulfate (NH4)3H(SO4)2

Abstract: The second-order phase transition at 265 K in the triammonium hydrogen disulfate compound (NH4)3H(SO4)2 has been observed by X-ray diffractometry. The space group below 265 K is identified to be P2/b. The recorded X-ray diagrams show a doubling of the primitive unit cell. The observed symmetry change has been described by the Landau theory of continuous phase transitions. The implied high-symmetry point of the corresponding first Brillouin zone shows other possible space groups for the low-temperature structure which are in agreement with Landau and Lifshitz criteria. All the theoretical results are discussed and compared with the obtained space group.

Spontaneous polarization of helicoidal ferroelectric smectic C* liquid crystals

Abstract: Measurements of the spontaneous polarization of DOBAMBC in helicoidal smectic C* phase is presented. It is shown that the polarization shows an anomalous temperature dependence characterized by one square root behaviour close to Tc and by another one far from Tc. This behaviour is explained theoretically to be a consequence of a nonchiral biquadratic coupling between the polarization and the tilt of molecules in the Landau expansion of the free-energy density. Also the tilt is predicted to exhibit a (less pronounced) crossover region of the same type as the polarization within the proposed model. It is also noted that this crossover region coincides with the temperature interval where the pitch of the helix displays anomalous properties.

Magnetism and liquid crystals

Abstract: Superficial similarities and essential differences between nematic liquid crystals and magnetically ordered systems as well as some magnetic-field effects in nematics are recalled. Magnetic anisotropy, field alignment, and the determination of elastic constants of nematics are discussed briefly. Landau theory is used to discuss the effect of a magnetic field on the nematic-isotropic phase transition; the predictions are compared with experiment.

Internal structure of a Landau quasiparticle wave packet.

Abstract: : Starting from the conventional definition of the state of a Fermi system containing a quasiparticle of momentum k, we construct a state with a quasiparticle wave packet (QPWP) by the usual superposition. We have studied the distributions of charges and currents in such a state to first order in the inter-particle interaction. The dressed QPWP state contains a charge e-bar which is less than the bare charge, e. (The charge e-bar is different from an incorrect value previously proposed on different grounds.) The remaining charges resides at infinity. In more dimensions than one, the charge density of the QPWP also contains anisotropic components that fall off as 1/r-cubed away from the center of the wave packet. Similar conclusions hold for the current density. We have verified that the continuity equation is satisfied at every point in space. The relationship of these results to the classical formal Landau theory is discussed. The Landau quasi particle distribution function, n(k,r), can not be interpreted in terms of the QPWP's defined here. Finally, experimental consequences of the work presented in this paper are briefly discussed.

Effects of Applied Electric Field on Some Incommensurate Phase Transitions

Abstract: Electric-field induced phase diagrams are discussed for the group of crystals like NaNO 2 and SC(NH 2 ) 2 having incommensurate phases, on the basis of a relevant Landau-type thermodynamic potential. Several different phase diagrams derived from it are presented.

Continuous solid-solid phase transitions driven by an eight-component order parameter: Hamiltonian densities and renormalization-group theory.

Abstract: Continuous solid-solid phase transitions driven by an eight-component order parameter are investigated. We list the active eight-dimensional physically irreducible representations we find among the 230 crystallographic space groups and the matrix images onto which they map the symmetry operations. We obtain the Landau potential (to fourth degree) as well as the Landau-Ginzburg-Wilson Hamiltonian for each case. We obtain the recursion relations in renormalization-group (RG) theory, and calculate the fixed points. We find that none of the fixed points are stable. Thus for transitions driven by an eight-component order parameter, none can be continuous according to RG theory.

Anderson localisation in a strong magnetic field: self-consistent theory in high Landau levels

Abstract: Transport properties of a disordered 2D noninteracting electron gas in a strong external magnetic field (integer quantum Hall regime) are studied using a diagrammatic self-consistent theory. The case when the Fermi energy lies in the nth disordered broadened Landau level, for n large, is considered. In this limit two-particle Green function diagrams can be classified using 1/n as an expansion parameter. It is shown that the renormalised static diffusion constant D vanishes everywhere within the Landau band except at one energy, the band centre. A self-consistent calculation of conductivities and the localisation length is also discussed.

Even and odd moments: intrinsic properties of helical compounds

Abstract: Many helical compounds can be thought of as a deformation of a highly symmetric structure. This deformation is governed by only one mode, i.e. one irreducible representation, from the high-symmetry phase so that the Landau theory for phase transitions is applicable. It will be shown that the resulting helix has to be described by two (local) symmetry modes, an even and an odd one (with respect to inversion) which are in resonance. The description of a helix with even and odd modes is a consequence only of its geometry. With even and odd components, expressions (chiral functions) which are typical for a helix can be formed. These expressions lead to fourth-order Landau invariants. As examples the helical compounds Se and Te as well as HgO, HgS and HgSe will be treated. The cholesteric state of liquid crystals will be briefly discussed and a generalization will be made for multiple coaxial helices.

Exactly soluble model of phase transition with cubic anisotropy

Abstract: By using the method of an approximating Hamiltonian the properties of a three-dimensional two-component model are studied. In the region of exact solubility the model turns out to belong (in the classical approximation) to the universality class of the spherical model.