The influence of surface effects on Frederiks transition in nematic liquid crystal doped with ferroelectric nanoparticles

Motivated by our recent work,in this work,we present the numerical study of the anchoring effect on the Frederiks threshold field in a nematic liquid crystal doped with ferroelectric colloidal nanoparticles.Assuming weak anchoring conditions,we employ the relaxation method and Maxwell construction to numerically solve the Euler–Lagrangian differential equation for the total free energy together the Rapini–Papoular surface energy to take into account anchoring of nematic liquid crystal molecules at the substrates.In this study,we focus our attention on obtaining the phase diagrams of Frederiks transition for different values of anchoring strength which have been not computed in our previous work.In this way,the effect of nanoparticle radius,nanoparticle volume fraction,nanoparticle polarization,and cell thickness on the Frederiks transition for different values of anchoring conditions are summarized in the phase diagrams.The numerical results show that by increasing the nanoparticles size and nanoparticle volume fraction in the ferronematic system,the Frederiks threshold field is strongly reduced.     

Molecular field theory for nematic liquid crystal film with finite layers

The nematic liquid crystal film composed of n molecular layers is studied based upon a spatially anisotropic pair potential, which reproduces approximately the elastic free energy density. On condition that the system has perfect nematic order, as in the Lebwohl—Lasher model, the director in the film is isotropic. The effect of the temperature is investigated by means of molecular field theory. Some new results are obtained. Firstly, symmetry breaking takes place when taking account of the temperature, and the state with the director along the normal of the film has the lowest free energy. Secondly, the N—I phase transition temperature increases as an effect of finite sizes instead of decreasing as in the Lebwohl—Lasher model. Thirdly, the nematic order is induced in the layers near the surface in the isotropic phase.     

Thermodynamics of Phase Transitions of a Kerr Nonlinear Blackbody

We study the thermodynamics of phase transitions of a blackbody whose interior is filled by a Kerr nonlinear crystal. There is a transition temperature To, above which the Kerr nonlinear blackbody is in the normal thermal radiation state, and below which it is in the squeezed thermal radiation state. At To, the Gibbs free energy of the two phases is continuous but the entropy density of the two phases is discontinuous. Hence, there is a jump in the entropy density and this leads to a latent heat density. The photon system undergoes a first-order phase transition from the normal to the squeezed thermal radiation state.     

First Principles Study on Electronic Structure of PbFe0.5Nb0.5O3

The full potential linearized augmented plane wave (FLAPW) method is used to study the crystal structure and electronic structure properties of PbFeo.5 Nbo.5O3 (PFN). The optimized crystal structure, density of states, band structure and electron density distribution have been obtained to understand the ferroelectric behaviour of PFN.The analysis result of the density of states shows there is an obvious change of Nbd states in the paraelectric-to-ferroelectric phase transition. The polarization result shows that the contribution to ferroelectricity of Nb atoms is larger than that of Fe atoms. In ferroelectric phase there is a hybridization of Fed-Op and Nbd-Opin ferroelectric PFN. This is consistent with the result of the electronic band structure. This hybridization is responsible for the tendency to its ferroelectricity.     

Epitaxy surface effect on the first-order phase transition properties in a ferroelectric thin film

By modifying the interchange interactions and the transverse fields on the epitaxy surface layer,this paper studies the phase transition properties of an n-layer ferroelectric thin film by the Fermi-type Green’s function technique based on the transverse Ising model with a four-spin interaction.The special attention is given to the effect of the epitaxy surface layer on the first-order phase transition properties in the parameter space constructed by the ratios of the bulk transverse field and the bulk four-spin interaction to the bulk two-spin interaction with the framework of the higher-order decoupling approximation to the Fermi-type Green’s function.The results show that the first-order phase transition properties will be changed significantly due to the modification of interchange interaction and transverse field parameters on the epitaxy surface layer.The dependence of the first-order phase transition properties on the thickness of ferroelectric thin films is also discussed.     

Vapour-to-Liquid Nucleation in Associating Lennard-Jones Fluids with Multiple Association Sites

The excess Helmholtz free energy functional for associating Lennard-Jones （L J） fluid is formulated in terms of a weighted density approximation for short-ranged interactions and a Weeks-Chandler-Andersen approximation for long-range attraction. Within the framework of density functional theory, phase equilibria, vapour-liquid surface tension and vapour-liquid nucleation properties including the density profile, work of formation, excess number of particles and critical supersaturation are investigated for associating LJ fluids with different numbers of association sites （M =1,2, 3, 4） per particle. The influences of association energy and association sites on phase equilibria, surface tension and vapour-liquid nucleation properties are discussed.     

Ginzburg–Landau Free Energy of Crystalline Color Superconductors:A Matrix Formalism from Solid-State Physics

The Ginzburg–Landau(GL) free energy of crystalline color superconductors is important for understanding the nature of the phase transition to the normal quark matter and predicting the preferred crystal structure. So far the GL free energy at zero temperature has only been evaluated up to the sixth order in the condensate. To give quantitative reliable predictions we need to evaluate the higher-order terms. In this work,we present a new derivation of the GL free energy by using the discrete Bloch representation of the fermion field. This derivation introduces a simple matrix formalism without any momentum constraint,which may enable us to calculate the GL free energy to arbitrary order by using a computer.     

Paraelectric--ferroelectric interface dynamics induced by latent heat transfer and irreversibility of ferroelectric phase transitions

The temperature gradients that arise in the paraelectric--ferroelectric interface dynamics induced by the latent heat transfer are studied from the point of view that a ferroelectric phase transition is a stationary, thermal-electric coupled transport process. The local entropy production is derived for a ferroelectric phase transition system from the Gibbs equation. Three types of regions in the system are described well by using the Onsager relations and the principle of minimum entropy production. The theoretical results coincides with the experimental ones.     

The hysteresis loops of a ferroelectric bilayer film with surface transition layers

Based on the transverse Ising model in the framework of the mean field approximation,this paper discusses a ferroelectric bilayer film with the surface transition layers within each constituent slab and an antiferroelectric interfacial coupling between two slabs.The hysteresis loop of a bilayer film is investigated.The results show that the surface transition layer in a ferroelectric bilayer film plays a significant role in realizing the multiple-state memory.     

First-Principles Study of the γ Angle Deformation Path in the Wurtzite-to-Rocksalt Phase Transition in Aluminum Nitride

A new transition path （γ angle deformation path） is put forward and used to characterize the wurtzite-rocksalt transition in AlN. The enthalpy surface and the contour plot of enthalpy difference at equilibrium pressure are obtained by first-principles pseudopotential method within the generalized gradient approximation. The phase transition is needed to overcome two barriers and a metaphase arises between them. The total barrier height is 0.26eV. The pressure region of the phase transition is estimated to be 13.9-23.5 GPa, in which the experimental result is well located. Along the least barrier path, the changes of density of states and the fields of charge density difference are investigated. The similarities and differences between γ angle deformation path and the orthorhombic deformation path are analyzed.     

Condensate fraction of asymmetric three-component Fermi gas

In this paper, we investigate the condensate fraction （CF） of fermionic pairs in the BCS-BEC crossover for three- component Fermi gas with both asymmetric interactions and unequal chemical potentials in two-dimensional free space. By using the functional-path-integral method, we have analytically derived the number densities and bound-state energy, from which the off-diagonal long-range order is analyzed in terms of the asymptotic behavior of the two-body density matrix. The explicit formula of CF is obtained as a function of the bound-state energy and population imbalance. It is demonstrated that the CF spectrum with respect to the bound-state energy can be used to characterize the quantum phase transition between the two kinds of Sarma phases as well as the transition from three-component to two-component superfluid. Moreover we obtain the same analytic formula of CF in the BCS superfluid phase as that of homogeneous Fermi gas with equal chemical potentials.     

Bubble dynamics in a strong first-order quark-hadron transition

We investigate the dynamics of a strong first-order quark-hadron transition driven by cubic interactions via homogeneous bubble nucleation in the Friedberg-Lee model.The one-loop effective thermodynamic potential of the model and the critical bubble profiles have been calculated at different temperatures and chemical potentials.By taking the temperature and the chemical potential as variables,the evolutions of the surface tension,the typical radius of the critical bubble,and the shift in the coarse-grained free energy in the presence of a nucleation bubble are obtained,and the limit on the reliability of the thin-wall approximation is also addressed accordingly.Our results are compared to those obtained for a weak first-order quark-hadron phase transition;in particular,the spinodal decomposition is relevant.     

Lattice Boltzmann Simulation of 3D Nematic Liquid Crystal near Phase Transition

Phase transition between nematic and isotropic liquid crystal is a very weak first order phase transition.We avoid to use the normal Landau-de Gennes‘s free energy that reduces a strong first order transition,and set up a data base of free energy calculated by means of Tao-Sheng-Lin‘s extended molecular field theory that can explain the experiments of the equilibrium properties of nematic liquid crystal very well.Then we use the free energy method of lattice Boltzmann developed by Oxford group to study the phase decomposition,pattern formation in the flow of the liquid crystal near transition temperature.     

Anomalous Optical and Electronic Properties of CaTiO3 Perovskites

With the help of the first-prlnciples full potential linearized augmented plane wave method, absorption coefficients, reflect/vity, dielectric behavior and electronic properties, including electronic energy bands, density of states and charge density distributions, are studied for the tetragonal and cubic CaTiO3. By considering the thermal expansion effects, an approximate method is proposed for the study of the stability of ground state and a tendency of phase transition, based on the minimum free energy principle. Subsequently, numerical calculations are carried out by using the first-principles perturbation method. We demonstrate that the high-temperature phase is cubic. It is shown that optical spectra in tetragonal phase exhibit single-peak feature and differ from multi-peak character in cubic. We find that strong orbital hybridization results in the co-valent bonds between Ti 3d and O 2p electrons and forms two-type dipoles （Ti-Ol and Ti-02） in tetragonal, while the Ti-O dipoles are identical in cubic. It is argued that crystal structure determines the dipole distributions and leads to some electron states among which the dipole-dipole transit/on forbidden is a key, causing such anomalous optical phenomena with the insulator characteristics. The predicted charge density distribution and the tendency of phase transition from tetragonal to cubic are in good agreement with experimental observations.     

Magnetic field induced phase branches of the superconducting transition in two-dimensional square π-loop arrays

Based on the results of explicit forms of free energy density for each possible arrangement of magnetization fluxes in large-scale two-dimensional （2D） square π-loop arrays given by Li et al [2007 Chin. Phys. 16 1450], the field-cooled superconducting phase transition is further investigated by analysing the free energy of the arrays with a simplified symmetrical model. Our analytical result is exactly the same as that obtained in Li＇s paper by means of numerical calculations. It is shown that the phase transition splits into two branches with either ferromagnetic or anti-ferromagnetic flux ordering, which depends periodically on the strength of external magnetic flux φe through each loop and monotonically on the screen parameter β of the loops in the arrays. In principle, the diagram of the phase branches is similar to that of its one-dimensional counterpart. The influence of thermal fluctuation on the flux ordering during the transition from normal to superconducting states of the π-loop arrays is also discussed.     

Effects of Shock Pressure on Transition Pressure in Zr

Measurements of free surface velocity profiles of high-purity Zr samples under shock-wave loading are performed to study the dynamic strength and phase transition parameters. The peak pressure of the compression waves is within the range from 9 to 14 GPa, and the Hugoniot elastic limit is 0.5 GPa. An anomalous structure of shock waves is observed due to the α - ω phase transition in Zr. Shock pressure has effects on transition pressure which increases with increasing compression strength, and the stronger shocks have a lower transit time.     

Expanding the thermodynamical potential and analysis of the possible phase diagram of decon nement in the FL model

Decon nement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of decon nement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

Expanding the thermodynamical potential and analysis of the possible phase diagram of deconfinement in the FL model

Deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, phase transition can only be first order in the whole μ-T phase plane. Using a Landau expansion, we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in the FL model. From our analysis, if the cubic term in the Landau expansion could be cancelled by the higher order fluctuations, second order phase transition may occur. By an ansatz of the Landau parameters, we obtain a possible phase diagram with both the first and second order phase transitions, including the tri-critical point which is similar to that of the chiral phase transition.     

Characterization of Phase Transition in Heisenberg Fluids from Density Functional Theory

The phase transition of Heisenberg fluid has been investigated with the density functional theory in mean-field approximation （MF）. The matrix of the second derivatives of the grand canonical potential Ω with respect to the particle density fluctuations and the magnetization fluctuations has been investigated and diagonalized. The smallest eigenvalue being 0 signalizes the phase instability and the related eigenvector characterizes this phase transition. We find a Curie line where the order parameter is pure magnetization and a spinodal where the order parameter is a mixture of particle density and magnetization. Along the spinodal, the character of phase instability changes continuously from predominant condensation to predominant ferromagnetic phase transition with the decrease of total density. The spinodal meets the Curie line at the critical endpoint with the reduced density p＊=pσ3=0.224 and the reduced temperature T＊ =kT/ε=1.87 （σ is the diameter of Heisenberg hard sphere and e is the coupling constant）.     

Magnetic-field-induced metal-insulator quantum phase transition in CaFeAsF near the quantum limit

The quantum limit, where only the lowest Landau level is occupied by electrons, can be achieved under a high magnetic field when the Landau level splitting is comparable with the Fermi energy. The rather small Fermi pockets and Fermi energy in CaFeAsF reported recently make this compound a good candidate for investigating the electrical transport near the quantum limit.Here, we report high-field experiments up to 65 T on a single-crystalline CaFeAsF, which shows a metal-insulator quantum phase transition tuned by the out-of-plane magnetic field. The obtained critical exponent zν through the finite-size scaling analysis is very close to 4/3. This transition is closely associated with the evolution of electronic states approaching the quantum limit.The resistivity behaviors as a function of field and temperature were evaluated based on Adams-Holstein theory(A-H theory).Moreover, the in-plane component of the field, which does not affect the transport behavior in the classical region, suppressed the magnetoresistance near the quantum limit.