Landau Expansion Of Free Energy Research Articles

Biaxiality of chiral liquid crystals.

Using the extended de Gennes--Ginzburg--Landau free energy expansion in terms of the anisotropic part ${\mathit{Q}}_{\mathrm{\ensuremath{\alpha}}\mathrm{\ensuremath{\beta}}}$(x) of the dielectric tensor field, a connection between the phase biaxiality and the stability of various chiral liquid crystalline phases is studied. In particular, the cholesteric phase, the cubic blue phases, and the phases characterized by an icosahedral space group symmetry are analyzed in detail. Also, a general question concerning the applicability of the mean-field approximation in describing the chiral phases is addressed. By an extensive study of the model over a wide range of the parameters, a class of phenomena, not present in the original de Gennes--Ginzburg--Landau model, has been found. These include (a) reentrant phase transitions between the cholesteric and the cubic blue phases and (b) the existence of distinct phases of the same symmetry but of different biaxialities. The phase biaxiality serves here as an extra scalar order parameter. Furthermore, it has been shown that, due to the presence of competing bulk terms in the free energy, the stable phases may acquire a large degree of biaxiality, also in liquid crystalline materials composed of effectively uniaxial molecules. A study of icosahedral space group symmetries provides a partial answer to the question of whether or not an icosahedral quasicrystalline state can be stabilized in liquid crystals. Although, in general, the stability of icosahedral structures could be enhanced by the extra terms in the free energy, no absolutely stable icosahedral phase has been found.

Phase transition and symmetry in BaAl2O4

Abstract Structural, optical, dielectric, and pyroelectric properties of crystals and ceramics of BaAl2O4 have been investigated. A refinement of the atomic positions has been carried out from X-ray powder diffraction data. BaAl2O4 is ferroelectric with TC=396K. The thermal behavior of Ps shows a broad maximum close to 220K without any phase transition. A model is proposed on the basis of the existence in the unit cell of two partial polarizations. A fit of the coefficients of the Landau free energy expansion allows the calculation of the thermal variations of these partial polarizations. A possible crystal structure is proposed for the paraelectric phase.

The stability of ferroelectric phase near critical size

The stability of ferroelectricity in ferroelectric films near the critical size (i.e. the size at which ferroelectricity disappears) is investigated using Landau free energy expansion. In the case of strong surface coupling, as the film thickness decreases, the ferroelectric phase becomes an unstable state before the critical size is reached, the size driven phase transition is of first order properties. When the surface coupling is weak, the ferroelectric phase is stable at any thickness larger than the critical size.

Brillouin scattering study of elastic properties in ferroelectric (CH3NH3)5Bi2Br11crystal

Abstract Elastic properties of (CH3NH3)5Bi2Br11 (MAPBB) orthorhombic (mm2) molecular-ionic crystal have been studied employing Brillouin scattering technique. The values of all elastic stiffness constants c ij were measured at room temperature. Dispersions of refractive indices in the visible region were determined at room temperature too. No anomaly of the longitudinal c 22− and the transverse c 44-mode frequency around the temperature of second order phase transition T c = 311.5 K was observed whereas the longitudinal c 33-mode frequency exhibits a step of 1.5% near 306 K. Results were analyzed in framework of Landau free energy expansion and with Landau-Khalatnikov approximation.

PHASE TRANSITION IN FERROELECTRIC FILMS WITH DOMAIN STRUCTURE

The phase transition characteristics of ferroelectric films with domain structure were studied using Landau free energy expansion. The existence of domain walls reduces both the spontaneous polarization and the Curie temperature, and increases the critical size. The reversal length moves away from the surfaces as temperature increases. As the film becomes thinner, the film will turn into single domain.

Surface effect on ferroelectric domain structure

Using Landau free energy expansion, the domain structure in a semi-infinite system was studied. The main result is that the domain wall only exists in the case of reduced surface polarization, no domain exists if the surface polarization is enhanced; and domain wall thickness was obtained as well as the reversal length.

Landau free energy and order parameter behaviour of theα/βphase transition in cristobalite

Cristobalite, the high-temperature phase of silica, SiO2, stable between1743 K and the melting point at 1898 K, exists in metastable form atlower temperatures. The cristobalite tetrahedral framework distorts fromcubic Fa3mBAR to tetragonal P4(1)2(1)2 symmetry at a strongly firstorder phase transition near 533 K with a latent heat of 1256 Jmol-1. Thetransition involves a large (5\%) volume discontinuity such that singlecrystals tend to shatter. We measured the thermal evolution of thestructural order parameter of the alpha/beta-cristobalite transition andthe unit cell strain by neutron time-of-flight and X-ray Guinier powderdiffractometry. The system is well described by a single-domain approachwith only one active order parameter component, and there is no evidencefor a coupling mechanism between the six possible order parametercomponents. The transition follows a Landau free energy expansion up to

Orientational-translational coupling for nematic-smectic-A tricritical point : A birefringence study

The high frequency dielectric permittivity is studied as a measure of orientational-translational coupling across the nematic-smectic A (NA) transition in the binary mixtures of N(p-n-alkoxybenzylidene)p-n-alkylaniline (nO.m) compounds viz..40.6/60.4. The difference in permittivity anisotropy value reflecting the orientational order parameter becomes minimum with a tricritical exponent β 2 = 1 in the vicinity of TCP to agree with mean field prediction. A universal scaling is demonstrated in the variation of dielectric anisotropy in the nematic phase of the binary mixtures exhibiting first and second order NA transitions. An analogy with 3He- 4He λ-line is discussed. The results are discussed in the light of Landau free energy expansion approach.

Pressure-induced temperature shift of the lock-in transition in someA2BX4crystals

The influence of hydrostatic stress on phase transitions of a ``Lifshitz type-I'' system is discussed. Taking into account third- and fifth-order coupling terms between the order parameter and the strains, we show that the two lowest-order terms in the Landau free-energy expansion are both pressure dependent. Within the ``phase-modulation-only'' approximation, a formula is derived, which gives the shift of the lock-in transition temperature under the effect of a stress. A numerical comparison with the Clausius-Clapeyron relation is shown.

Acoustic phonon softening of selected double sulphates

Abstract Theoretical analysis concerning 4 double sulphates: LiCsSO4, LiKSO4, LiNH4SO4 and LiRb5(SO4)31.5H2SO4 is presented. Symmetry-adapted Landau free energy expansions are given and discussed. Similarities and differences between the compounds are analyzed.

What do Landau free energies really look like for structural phase transitions?

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.

Spinodal Decomposition in Semiconductor Alloys

AbstractA generalization is proposed of the lattice gas model which takes into account the presence of free Fermions in the system. In the framework of this approach the Landau free energy expansion is constructed. The influence of the electron energy spectrum particularities on the spinodal decomposition in the semiconductor alloys is examined.

High-temperature enthalpy at the orientational order-disorder transition in calcite: implications for the calcite/aragonite phase equilibrium

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.

On the ferroelastic phase transition of LiNH4SO4: a Brillouin scattering study and theoretical modelling

Brillouin spectroscopy was used to study the elastic properties of LiNH4SO4 in the vicinity of the ferroelastic first-order transition occurring at approximately 285 K. Eleven acoustic modes were observed in the temperature range from 273 to 293 K. Their sound velocities and the temperature dependences of the corresponding elastic constants were calculated from the measured frequency shifts. The measured elastic constants exhibited step-like discontinuities at the transition temperature and were interpreted using a symmetry-adapted Landau free-energy expansion. The order parameter for the ferroelectric phase transition at 460 K was chosen to be an infrared-active soft mode; while for the ferroelastic phase transition at 285 K, a two-component soft mode from the X point of the Brillouin zone was chosen. Both of these order parameters are coupled to polarisation and strains.

Interaction between electric field and liquid crystals with spontaneous polarization: Derivation of suitable free energy expression for a cell with an applied voltage

Abstract The interaction between electric fields and liquid crystals is reconsidered, taking into account spatially varying anisotropic dielectric constant and ferro- resp. flexoelectricity. The general static case as well as planar samples with applied constant voltage is treated, and explicit formulas for the free energy are given. Some results: The consequences of the simple fact that the curl of the electric field is zero have been overlooked in many articles. The Landau free energy expansion for the chiral smectic C phase have been developed by R.B. Meyer1 and Pikin-Indenbom2. In the Pikin-Indenbom theory the P2-term, controlling the size of the spontaneous polarization, has been given the coefficient ½ χ, where χ is the dielectric susceptibility. However, there are several independent sources to the dielectric susceptibility, and not all of them do contribute to the formation of spontaneous polarization. This indicates that the size of the spontaneous polarization and the size of the induced polariz...

A phenomenological model for lipid-protein bilayers with critical mixing

A Landau expansion of free energy in terms of area/lipid has been used to obtain protein-lipid phase diagrams with critical mixing and a maximum phase separation concentration. Simulations using this model indicate that diffrential scanning calorimetry scan shapes and transition enthalpies observed for lipid-synthetic peptide mixtures are consistent with this type of phase diagram. The critical mixing point and the homogeneous mixture critical point are distinguished.

Acoustic anomalies in diglycine-nitrate

Abstract The behaviour of some elastic constants of diglycine nitrate across the ferroelectric phase transition were measured with Brillouin scattering. The results were compared with low frequency behaviour of one elastic constant. Results were analysed in the framework of Landau free energy expansion. Discrepancy was found between the relaxation time for the spontaneous polarization from dielectric measurements and our results.

Order-order and order-disorder transitions in the quantum spin-1 Ising-Heisenberg models

The critical properties of a quantum spin-1 ferromagnetic multidimensional Ising-Heisenberg model with uniaxial and single-ion anisotropy are examined in the framework of a mean-field approximation. A Landau free energy expansion is performed to identify critical lines and surfaces. The resulting phase diagram, defined in a three-dimensional space characterized by a single-ion anisotropy variable, a parameter measuring the interaction anisotropy and the temperature, is particularly interesting because it exhibits three different phases, one paramagnetic and two ferromagnetic; the latter two differing for the orientation of the dipolar ordering. The presence of both first order reorientation transitions (order-order transitions) and order-disorder transitions makes the present model promising for describing several physical systems.

Brillouin scattering studies of the ferroelastic phase transition in LiCsSO4.

Brillouin spectroscopy was used to study the elastic properties of ferroelastic ${\mathrm{LiCsSO}}_{4}$. The sound velocities, linewidths, and intensities of twelve acoustic modes were measured in the temperature range from 150 to 293 K. The mmm (${D}_{2h}$)\ensuremath{\rightarrow}2/m (${C}_{2h}$) phase-transition temperature was found to be 202 K. All nonzero components of the elastic stiffness tensor of the high-temperature phase were determined. The frequency, linewidth, and integrated intensity of the Brillouin line associated with the soft acoustic mode (characterized by ${c}_{66}$) were found to be strongly temperature dependent in the vicinity of ${T}_{c}$. In order to explain all experimental features, the fourth-order Landau free-energy expansion in all strain components was carried out. Using a non-Gaussian approach to critical fluctuations, the effective interaction range was calculated to be \ensuremath{\sim}10 nm.

Phase diagrams of cubic systems under uniaxial quadratic symmetry-breaking fields.

The effect of uniaxial quadratic symmetry-breaking fields on two- and three-component systems which possess cubic symmetry is studied. A Landau free-energy expansion which includes sixth-order terms in the order parameter is constructed and analyzed in the context of mean-field theory. A remarkably rich spectrum of complex phase diagrams featuring several ordered phases is predicted. The phase diagrams exhibit a variety of multicritical points including triple, bicritical, tetracritical, tricritical, and critical-end points. We also predict the existence of two consecutive tricritical points along phase boundaries separating ordered phases. Some of these phase diagrams may be realized in certain compounds corresponding to two- and three-component cubic systems such as ${\mathrm{Tb}}_{2}$(${\mathrm{MoO}}_{4}$${)}_{3}$ and ${\mathrm{BaTiO}}_{3}$.