Temperature Dependence Of Order Parameter Research Articles

Magnetic order in 2D antiferromagnets revealed by spontaneous anisotropic magnetostriction

The temperature dependent order parameter provides important information on the nature of magnetism. Using traditional methods to study this parameter in two-dimensional (2D) magnets remains difficult, however, particularly for insulating antiferromagnetic (AF) compounds. Here, we show that its temperature dependence in AF MPS3 (M(II) = Fe, Co, Ni) can be probed via the anisotropy in the resonance frequency of rectangular membranes, mediated by a combination of anisotropic magnetostriction and spontaneous staggered magnetization. Density functional calculations followed by a derived orbital-resolved magnetic exchange analysis confirm and unravel the microscopic origin of this magnetization-induced anisotropic strain. We further show that the temperature and thickness dependent order parameter allows to deduce the material’s critical exponents characterising magnetic order. Nanomechanical sensing of magnetic order thus provides a future platform to investigate 2D magnetism down to the single-layer limit.

Elastic and dielectric responses of VDF70/Tr30 near ferroelectric phase transition

The infra-low frequency elastic modulus and the complex dielectric permittivity of vinylidene fluoride trifluoroethylene VDF70/Tr30, are studied within the temperature range of 20 ÷ 140 °C. The experimental results are used to determine the temperature dependence of order parameter η near the Curie temperature (T c). It is revealed that spontaneous polarization P s and spontaneous strain xs are linearly coupled. The dielectric dispersion, due to the relaxation dynamics of polar microregions in the vicinity of the T c, is found. The average relaxation time follows the Arrhenius law with activation energy depending on temperature.

Induced order and collective excitations in three-singlet quantum magnets

The quantum magnetism in a three-singlet model (TSM) with singlet crystalline electric field (CEF) states interacting on a lattice is investigated, motivated by its appearance in compounds with 4f^2 and 5f^2 electronic structure. Contrary to conventional (semi-classical) magnetism there are no preformed moments above the ordering temperature Tm. They appear spontaneously as induced or excitonic moments due to singlet-singlet mixing at Tm. In most cases the transition is of second order, however for large matrix elements between the excited states it turns into a first order transition at a critical point. Furthermore we derive the excitonic mode spectrum and its quantum critical soft mode behaviour which leads to the criticality condition for induced order as expressed in terms of the control parameters of the TSM and discuss the distinctions to the previously known two-singlet case. We also derive the temperature dependence of order parameters for second and first order transitions and the exciton spectrum in the induced magnetic phase.

Impact of different extended components of mean-field models on transport coefficients of quark matter and their causal aspects

The role of different extensions of the Nambu-Jona-Lasinio (NJL) model-like addition of vector interaction, Polyakov loop extended version (PNJL), and the entangled PNJL (EPNJL) models on transport coefficients, such as shear viscosity, bulk viscosity, electrical conductivity, and thermal conductivity are critically analyzed. We have considered the standard expressions of transport coefficients, obtained in relaxation time approximation of kinetic theory. Influence of temperature-dependent order parameters on the temperature profile of transport coefficients are analyzed. The causal aspect of the massless case to these different extended components of mean-field models are also picturized where an approximated lower and upper bound are drawn for shear relaxation time.

Cluster Variation Method Analysis of Correlations and Entropy in BCC Solid Solutions

Solid solutions occur when multiple chemical species share sites of a common crystal lattice. Although the single site occupation is random, chemical interaction preferences bias the occupation probabilities of neighboring sites, and this bias reduced the entropy of mixing below its ideal value. Sufficiently strong bias leads to symmetry-breaking phase transitions. We apply the cluster variation method to explore solid solutions on body centered cubic lattices in the context of two specific compounds that exhibit opposite ordering trends. Employing density functional theory to model the energetics, we show that CuZn exhibits an order-disorder transition to the CsCl prototype structure, while AlLi instead takes the NaTl prototype structure, and we evaluate their temperature-dependent order parameters, correlations and entropies.

Effects Associated with Confined Geometry in Nanocomposites Based on Mesoporous 2D-SBA-15 and 3D-SBA-15 Matrices Containing Sodium Nitrite Nanoparticles

Temperature dependences of the ferroelectric order parameter for nanostructured sodium nitrite under heating and cooling were obtained by analyzing the temperature evolution of diffraction spectra of neutron scattering by composites obtained by introducing sodium nitrite into pores of mesoporous 2D-SBA-15 (the average pore diameter is 69(4) A) and 3D-SBA-15 (94(5) A) matrices. It was demonstrated that the phase transition to the paraelectric phase in the process of heating occurs at TC = 433 ± 1 K in both nanocomposite materials. It was found that these sizes decrease at approaching to the ferroelectric phase transition point on heating. Temperature hysteresis (~15–20 K) in the temperature dependence of the order parameter between the heating and cooling regimes was revealed.

Investigation of the viscoelastic properties of 4-propoxy-biphenyl-4-carbonitrile

ABSTRACTWe report on the temperature-dependent measurements of dielectric permittivity, birefringence, elastic constants and rotational viscosity for 4-propoxy-biphenyl-4-carbonitrile in the nematic region. The temperature dependence of the three elastic constants was determined from studies of the Freédericksz transition. The thermal dependence of elastic constants shows features similar to the literature (bend > splay > twist). Elastic constants are proportional to the square of the order parameter. Temperature-dependent dielectric characterisation was carried out at a frequency of 10 kHz. The compound shows positive dielectric anisotropy in the nematic phase. The rotational viscosity is found to be relatively low. Temperature dependence of order parameter is estimated using Haller’s method. The figure of merit was also calculated as a function of temperature.

Graphical representations of the Maier–Saupe mean field theory in nematic liquid crystals

ABSTRACTWe have developed the graphical representation to analyse the Maier–Saupe (MS) mean field theory in nematic molecular system. Based on the molecular field theory, the transcendental equations for the Helmholtz free energy and the orientational order parameter are derived and graphically represented for several physical parameters, from which the critical values of temperatures and order parameters are uniquely determined. The empirical formulae based on a four-parameter power law for temperature dependence of order parameter are presented and compared with the MS theory, of which a modified Haller equation of the form yields the best result in a large portion of nematic range within ~0.5% deviation from the mean field theory. We also present the comparison of the MS theory with the Landau–de Gennes theory for universal ratios of the characteristic order parameters.

Эффекты, связанные с ограниченной геометрией, в нанокомпозитах на основе мезопористых матриц 2D-SBA-15 и 3D-SBA-15, содержащих наночастицы нитрита натрия

The temperature dependences of the ferroelectric order parameter for nanostructured sodium nitrite on heating and cooling have been obtained from the analysis of the temperature evolution of diffraction spectra of neutron scattering on nanocomposites, produced by embedding of sodium nitrite into the pores of the mesoporous matrices 2D-SBA-15 (average pore diameter 69 (4) Å) and 3D-SBA-15 (average pore diameter 94 (5) Å ). It is shown that on heating the phase transition from the ferroelectric phase to the paraelectric one occurs at TC = 433 ± 1 K for both nanocomposite materials. The sizes of nanoparticles in both nanocomposites are determined and it is established that their size decreases on heating at approaching to the ferroelectric phase transition temperature. Temperature hysteresis (~ 15–20 K) have been found in the temperature dependence of the order parameter between heating and cooling regimes.

Optical and dielectric parameters of a laterally difluorinated phenylbicyclohexane liquid crystalline compound

The temperature variation of the refractive indices in the nematic range of a laterally difluorinated phenylbicyclohexane liquid crystalline compound was determined using the thin prism technique. Birefringence and effective geometry parameter of this LC compound was calculated from the measured refractive indices. Using a four-parameter model, the temperature variation of the refractive indices and birefringence was theoretically fitted. The compound is found to have low value of birefringence and high value of effective geometry parameter. Using refractive index data, three different methods were used in this work to obtain temperature dependence of order parameter, namely Vuks’ method, Haller approximation method, and method based on effective geometry parameter. All of them show the same trend. The temperature variation of dielectric permittivities of the compound was done at frequency 1 kHz by an LCR meter. The temperature variation of dielectric anisotropy of the compound was calculated from the experimentally measured values of dielectric permittivities. The compound shows moderate negative dielectric anisotropy.

Flexoelectric Effect in Biaxial Nematics

The flexoelectric (FE) effect provides a linear coupling between electric polarization and orientational deformation in liquid crystals. It influences many electrooptical phenomena and it is used in some bistable nematic devices. A statistical theory of dipole FE polarization in biaxial nematic liquid crystals is used to calculate temperature dependence of order parameters, elastic constants, and FE coefficients. The splitting of the two Meyer FE coefficients and the appearance of new FE coefficients is obtained at the uniaxial-biaxial nematic transition. The ordering of the splited FE coefficients corresponds to the ordering of the splited elastic constants.

Elucidation of the Orientational Order and the Phase Diagram of p-Quinquephenyl

The orientational order in the nematic phase of p-quinquephenyl, the pentamer of p-phenylene, has been determined by means of birefringence measurements and by wide-angle X-ray scattering (WAXS). The experimentally determined order parameters <P(2)> are compared with the temperature-dependent order parameter predicted by the Maier-Saupe theory. The order parameters derived from the birefringence at different temperatures in the nematic phase of p-quinquephenyl were in excellent agreement with the Maier-Saupe predictions. The <P(2)> values calculated from the azimuthal profiles derived from WAXS measurements were significantly lower than those determined by the birefringence measurements, especially at higher temperatures. For the birefringence measurements, alignment of the director is achieved by using polyimide alignment layers, whereas director alignment for the WAXS experiments was achieved by a magnetic field. We assign the low overall order parameters that were measured by WAXS to a lower macroscopic orientational order. In addition, upon reinvestigating the mesophase behavior of p-quinquephenyl, a monotropic smectic A phase has been observed upon cooling at 390 °C, just before the crystallization temperature is reached.

Probing the exciton condensate phase in 1T-TiSe2 with photoemission

We present recent results obtained using angle-resolved photoemission spectroscopy performed on 1T-TiSe2. Emphasis is put on the peculiarity of the bandstructure of TiSe2 compared to other transition metal dichalcogenides, which suggests that this system is an excellent candidate for the realization of the excitonic insulator phase. This exotic phase is discussed in relation to the BCS theory, and its spectroscopic signature is computed via a model adapted to the particular bandstructure of 1T-TiSe2. A comparison between photoemission intensity maps calculated with the spectral function derived for this model and experimental results is shown, giving strong support for the exciton condensate phase as the origin of the charge density wave transition observed in 1T-TiSe2. The temperature-dependent order parameter characterizing the exciton condensate phase is discussed, both on a theoretical and an experimental basis, as well as the chemical potential shift occurring in this system. Finally, the transport properties of 1T-TiSe2 are analyzed in the light of the photoemission results.

Temperature-dependent optical constants and birefringence of nematic liquid crystal 5CB in the terahertz frequency range

We have measured the frequency dependence and temperature dependence of the optical constants of a liquid crystal 4′-n-pentyl-4-cyanobiphenyl (5CB) in both nematic and isotropic phases by using terahertz time-domain spectroscopy. The extinction coefficient of 5CB is less than 0.02 and without sharp absorption features in the frequency range of 0.2–1.0 THz. The extraordinary and ordinary indices of refraction at 25 °C are around 1.77 and 1.58, respectively, giving rise to a birefringence of 0.20±0.02 in this frequency range. The temperature-dependent order parameter extracted from birefringence agrees with the results from the visible region quite well.

Flexoelectric effect modelling

AbstractA statistical theory of dipole flexoelectric (FE) polarization in liquid crystals is used to calculate temperature dependence of order parameters, elastic constants and FE coefficients. Two systems with polar wedge-shaped and banana-shaped molecules are investigated. In both cases, the FE coefficients are proportional to the dipole moment component parallel to the molecule symmetry axis. It results from the symmetries of interactions and of the Mayer function. The origin of the FE effect and microscopic pictures of the distorted phases are discussed.

Presmectic wetting and supercritical-like phase behavior of octylcyanobiphenyl liquid crystal confined to controlled-pore glass matrices

The influence of controlled-pore glass (CPG) confinement on the phase behavior of octylcyanobiphenyl liquid crystal (LC) is studied by means of x-ray scattering and high precision calorimetry. For CPG samples with pore diameter 2R>24 nm, the smectic order parameter temperature dependence eta(T) reveals apparent presmectic ordering far above the bulk smectic A-nematic (SmA-N) phase transition for both nontreated and silane-treated CPG matrices. The behavior of eta(T) is qualitatively similar in all samples, well obeying the mean field approach (MFA) in which the surface wetting tendency plays the dominant role. In contrast, the critical fluctuations remain important in the specific heat data, which cannot be described within the MFA. We show experimentally that randomness and surface wetting become dominant over finite-size effects for 2R approximately<10 nm, in agreement with theoretical analysis. In nontreated samples, the noncritical character of the static disorder and the interfacial LC-CPG coupling almost completely suppress the quasi-SmA-N and nematic-isotropic phase transitions at 2R approximately 15.1 and approximately 7.5 nm, respectively.

Lattice Boltzmann scheme for modeling liquid-crystal dynamics: Zenithal bistable device in the presence of defect motion

A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng [Phys. Rev. E 58, 7475 (1998)] equations for the evolution of the velocity and tensor order-parameter fields. The resulting algorithm is able to include five independent Leslie viscosities, a Landau-deGennes free energy which introduces three or more elastic constants, a temperature dependent order parameter, surface anchoring and viscosity coefficients, flexoelectric and order electricity, and chirality. When combined with a solver for the Maxwell equations associated with the electric field, the algorithm is able to provide a full "device solver" for a liquid crystal display. Coupled lattice Boltzmann schemes are used to capture the evolution of the fast momentum and slow director motions in a computationally efficient way. The method is shown to give results in close agreement with analytical results for a number of validating examples. The use of the method is illustrated through the simulation of the motion of defects in a zenithal bistable liquid crystal device.

Dynamics of cyanoadamantane molecules confined in the space between carbon nanotubes: MD study

Results of molecular dynamics (MD) simulation are presented for cyanoadamantane molecules embedded in the space between two surfaces composed of single-wall nanotubes. The dynamics of the simulated system has been investigated by inspecting plots of the translational velocity autocorrelation functions. The temperature dependences of order parameter, total dipole moment and rotational autocorrelation functions have been analyzed as indicators of phase transitions.

Kinetics of Glass Transition Simulated by Path Probability Method

Kinetics of glass transition is simulated within the Path Probability Method (PPM) which is the natural extension of the Cluster Variation Method (CVM) to time domain. Temperature dependences of order parameter during continuous cooling are calculated as a function of cooling rate. When the temperature dependence of viscosity is introduced in the mobility term in the PPM, the order parameter is frozen as approaching the ideal glass transition temperature. Furthermore, a preliminary calculation which incorporates the cooling rate dependence into the viscosity reproduces the experimental tendency of the glass transition temperature. Together with the previous studies of thermodynamic frameworks of glass transition based on the CVM, it is confirmed that the combination of the CVM and PPM provides a unique theoretical tool to study glass transition in a consistent manner covering thermodynamics and kinetics.

Neutron diffraction study of NaNO 2 ferroelectric nanowires

For the first time the temperature evolution of the structure of ferroelectric nanowires of NaNO 2 was studied by neutron diffraction from room temperature up to melting, i.e. in ferro- and paraelectric phases. Samples were produced in natural chrysotile asbestos with average channel diameter 6±1.5 nm. It is demonstrated that in the ferroelectric phase the structure is consistent with the bulk but is strongly textured. The temperature dependence of order parameter in the ferroelectric phase is determined for the confined sodium nitrite. It is shown that this dependence follows a power law with T c=413.0±2.5 K and β=0.34±0.05, and differs from the same for the bulk material.