Second-order Phase Research Articles

Graphics simulation of a soap film catastrophe model

A soap film model is described that demonstrates catastrophic changes of the film pattern caused by continuous changes in configuration. The scope of the model is extended by the use of computer graphics both to animate the pattern changes of the films and to plot the corresponding movement on energy-configuration and other curves. Such energy-configuration curves are identical to those of systems that experience first-order and second-order phase changes.

Magnetic properties of ultrafine ferrihydrite clusters studied by Mossbauer spectroscopy and by thermodynamical analysis

Magnetic properties of ultrafine clusters of Fe5HO8·4H2O (ferrihydrite, FH), isolated in pores of polysorb, were studied by Mossbauer spectroscopy and by thermodynamical analysis. Thermodynamical analysis allowed the conclusion that magnetic properties of ultrafine clusters cannot be interpreted in terms of a secondorder magnetic phase transition or of superparamagnetic behavior alone but require the consideration of a jumplike first order magnetic phase transition (JMT). The critical radius R cr below which the JMT is to be expected in clusters was derived from thermodynamic criteria. It was determined as R cr = 2 α β η/(1 - T cc/T 0), where α, β and η are constants derived from surface energy, magnetostriction, compressibility and T cc = 3/2 Nκ B T o 2 ηβ 2 (N is the number of iron atoms, κ B is the Boltzmann constant, T o is the Curie temperature of the clusters). For the smallest FH clusters isolated in pores of polysorb, the critical radius and the JMT temperature were estimated by Mossbauer spectroscopy to be R cr ∼ 1.5–2.0 nm and T JMT ∼ 4.2–6 K, respectively. Satisfactory agreement between the value R cr, estimated from the experimental data and the one derived by thermodynamical analysis was achieved. Interfacial (cluster-surface) and intercluster interactions were found to destroy the JMT effect and to give rise to a second-order magnetic phase transition.

Second-Order Surface Phase Transitions in Electrode Kinetics

A theory, based on the Landau−Ginzburg formalism, shows that remarkable singularities in currents of electrode charge transfer reactions occur near the critical potentials where second-order surface phase transitions take place. This happens if the fluctuations of the order parameter, which describes the transition, are exponentially coupled to the reaction system via fluctuating tunneling or activation barriers. Coupling depending on the sign of the order parameter is considered; the corresponding singularities in Arrhenius and Tafel plots for electrode currents are predicted, and the perspectives for their experimental investigation are discussed.

Relaxational change of the phase transition character in ferroelectric-semiconductor

The effect of time evolution of second-order ferroelectric phase transition (PT), which is close to the Lifshitz point and the tricritical point in the phase diagram, to the sequential second-order and firstorder transitions has been found. As the data on time variations of the temperature dependence of dielectric constant for Sn2P2S6 ferroelectric-semiconductor show, the crystal exposure at fixed temperature in the paraphase in the vicinity of the second-order PT results in the appearance of an intermediate (incommensurate, hypothetically) state. Sample lighting benefits the formation of such state, whereas a constant electric field directed along the spontaneous polarization axis reduces its temperature range. Experimental data are described qualitatively by mean-field approximation within a framework of a model, that suggests the linear dependence of thermodynamic potential coefficients of the uniaxial proper ferroelectric with a single direction of modulation in the incommensurate phase vs the charge ...

Single-pass and double-pass propagation through complex paraxial optical systems

A generalized form of spectral representation theory is developed and used with the ABCD formulation of the Huygens–Fresnel integral for studying optical wave propagation through a random medium in the presence of any complex paraxial optical system that can be characterized by an ABCD ray matrix. Formal expressions are developed for the basic optical field moments and various related second-order statistical quantities in terms of three fundamental moments of the first- and second-order complex phase perturbations. Special propagation environments include line-of-sight propagation, single-pass propagation through arbitrary ABCD optical systems, and double-pass propagation through the same random medium in the presence of an ABCD optical system. For illustrative purposes the method is used in the development of expressions for the mean and the normalized variance of the irradiance associated with the Fourier-transform-plane geometry of a lens and the enhanced backscatter effect (EBS) associated with irradiance and phase fluctuations of a reflected Gaussian-beam wave from a Gaussian mirror. The EBS analysis accounts for both finite size and finite focal length of the mirror.

Soft modes and proper ferroelasticity-2: Paratellurite

Abstract The mechanism of the pressure-induced second-order proper ferroelastic phase transition (PFPT) in TeO2 is treated within a simple lattice dynamical model, which explains why this phenomenon arises without softening of any longwave optic phonon.

Soft modes and proper ferroelasticity-1: A background

Abstract Mechanisms of second-order structural phase transitions and the softening of Raman - active modes are considered with the emphasis to the role of the latter in proper ferroelasticity.

DSC study of superionic phase transition in (NH4)4H2(SeO4)3single crystals

Abstract DSC and complex impedance studies of the protonic conductor (NH4)4H2(SeO4)3, which undergoes a superionic phase transition of first order at Ts = 378 K show that the activation energy of ionic conductivity d(lg σ)/dt and the ordering enthalpy ΔCp of the crystal are proportional: d(lg σ)/dT = XΔCp/RTs + const, as found for MAg4I5 crystals undergoing a second-order superionic phase transition. Thus the short-range order environment of the species involved in fast-ion transport plays the main role in the superionic phase transition. This is also supported by the value of the entropy change at Ts, ΔS = 43 J/mole·K. A new metastable phase was found to be induced on heating the (NH4)4H2(SeO4)3 crystal above Ts.

Pattern formation at the traveling liquid-crystal twist grain boundary-smectic a interface

Pattern formation at phase boundaries moving in a temperature gradient is one of the major areas of nonequilibrium physics attracting considerable attention. While most of the early work concentrated on the moving solid-liquid interface, now the focus has changed to phase transitions characterized by broken continuous symmetry. Most recently we investigated consequences to interfacial patterns of a chirality-induced equilibrium length. Here we study patterns at another chiral interface where one of the phases has a chirality-induced defect lattice, the twist grain boundary (TGB) phase. The TGB state is analogous to the vortex lattice in Type-II superconductors predicted by the Gennes’ analogy between the nematic (N)-smectic A (A) transition and the normal-superconducting transition. In this analogy, a cholesteric A transition is analogous to the normal-superconducting transition in an external magnetic field and a theory has been developed for its analogous vortex lattice, the TGB phase, when this transition is Type II. We study patterns formed at the traveling TGB-A phase boundary. Different patterns are observed depending on whether TGB grows into A or A into TGB. Indeed, this maybe the first time a steady-state pattern is observed in directional melting (i.e. TGB growing into A). As these patterns have a broad band of wavelengths, they are difficult to characterize physically. Thus, we introduced a novel analysis (most simply but not rigorously described as) measuring the fractal dimension of the patterns at these traveling interfaces. Two lengths emerged from this analysis: a longer one set by sample thickness and a shorter one set by the smallest TGB unit that can grow into an oriented smectic A phase. We invoke our old dynamic arguments to account for why TGB cannot propagate at a second-order TGB-cholesteric phase transition so it is eventually squeezed out leaving behind a direct cholesteric-A transition.

Critical behavior of hyper-rayleigh scattering in the centrosymmetric phase of hexagonal barium titanate

Abstract Critical behavior of hyper-Rayleigh (second-harmonic) scattering was investigated for the first time for a new type of second-order displacive phase transition at Ta = 222 K in the hexagonal barium titanate, which is neither ferroelectric nor proper-ferroelastic in nature. It is found that the scattering intensity in a 90° scattering configuration increases strikingly in such a manner as I2ω ∼ (T-Ta)−2, the square of the generalized susceptibility also observed, as Ta is approached in the centrosymmetric phase, only for those polarizations enabling one to observe the relevant nonpolar soft phonon, while that for other polarizations the 90 intensity remains almost constant. These aspects newly found can be well accounted for with a model that residual point defects acting as strongly localizing “field” should induce microclusters in their vicinity such that development of a locally condensed order-parameter, the square of which I2ω is proportinal to, follows the generalized susceptibility.

Some structural and magnetic properties of Mn1 + ΔAs1−xPx single crystals

Lattice parameters and magnetic anisotropy of MnAs1−xPx single crystals with a nominal composition between 5 and 20 at% P are presented; samples are taken from two different growth apparatus. The magnetic phenomena suggest that distributions of exchange couplings are introduced. The generating random element of the lattice appears to be a displacement disorder of the Mn(As) atoms which might be a consequence of the anion mixture As/P and/or non-stoichiometry. The susceptibility anomaly at Tt which so far has been ascribed to a second-order NiAs-MnP displacive phase transition might alternatively be due to a magneto-volume effect which is linked to the exchange coupling distribution, at least for the mixed or non-stoichiometric crystals.

Excluded volume effects in heterogeneous catalysis: reactions between 'dollars' and 'dimes'

The authors introduce a lattice model of catalysis which involves a small particle (a dime) and a large particle (a dollar). The larger diameter of the dollar prevents its adsorption next to a site which is already occupied by a dollar. The catalytic process is the reaction and immediate desorption of nearest-neighbour dime-dollar adsorbates. As a function of the reaction rate and the relative deposition rates of the two species, this system exhibits a second-order kinetic phase transition which separates a dime-saturated phase from a reactive steady state. The features of the phase transition are examined by numerical simulations and analytic techniques, including a systematic mean-field cluster expansion.

Magnetoelastic and neutron-diffraction studies of Cr-Al-alloy single crystals.

Both magnetoelastic and neutron-diffraction studies have been performed on Cr-Al single crystals containing 1.2, 1.9, and 2.6 at. % Al. These concentrations lie in a controversial region of the magnetic phase diagram. For the crystals containing 1.2 and 1.9 at. % Al the transition at the N\'eel point is from a paramagnetic to an incommensurate spin-density-wave (ISDW) state while it is from the paramagnetic to a commensurate (C) SDW state for Cr+2.6 at. % Al. All magnetic transitions are observed as second-order phase changes within our experimental resolution. No ISDW-CSDW transition was observed in any of the crystals, and no evidence was found for the existence of mixed ISDW and CSDW phases in the alloys, as previously predicted. The temperature dependence of the elastic constants is described fairly well by existing thermodynamic models, while the magnetization ${\mathit{M}}^{2}$(T)/${\mathit{M}}^{2}$(0) of Cr + 1.9 at. % Al and Cr+2.6 at. % Al varies as [1-\ensuremath{\alpha}(T/${\mathit{T}}_{\mathit{N}}$${)}^{2}$+\ensuremath{\delta}(T/${\mathit{T}}_{\mathit{N}}$${)}^{4}$] at T${\mathit{T}}_{\mathit{N}}$. The values of \ensuremath{\alpha} and \ensuremath{\delta} compare fairly well with values obtained from magnetovolume data.

Novel current-mode all-pass phase shifter using a current conveyor

Using a single second-generation current conveyor (CC II), a current-mode second-order all-pass phase shifter network is proposed. The novelties of the network are the availability of high output impedance, the use of grounded capacitors, and the insensitivity of phase shift relative to the CC II device nonideality. >

Restoration of chiral symmetry in a model with dynamical spontaneous symmetry breaking at finite temperature and density.

The chiral-symmetry-restoring transition in a model proposed by Lurie is investigated at finite temperature and density. A method is given to establish the self-consistency equation satisfied by the order parameter and a convenient scheme is constructed for calculating the equation of state approximately. Study of the phase diagram shows the existence of a critical point separating the first-order from the second-order chiral phase transition. By calculating the energy density versus temperature, the order of the chiral phase transition is confirmed. A careful analysis of isotherms of pressure versus net baryon-number density suggests the existence of overheated and overcooled metastable states and the coexistence of a broken phase and a normal phase.

Dielectric Properties of the Phase Transitionin TlH2AsO4

The dielectric properties of TlH 2 AsO 4 powder pellet are investigated over the temperature range from 80 to 433 K. With respect to the form of the temperature dependence of complex dielectric constant, TlH 2 AsO 4 crystal shows much the same characteristics as with the TlH 2 PO 4 crystal. The results are indicative of a first-order antiferroelectric phase transition at 250.5 K (the lower phase transition point, T L ) with thermal hysteresis of 1.4 K, and of a second-order ferroelastic phase transition at about 390 K (the upper phase transition point, T U ).

Monte Carlo study of the generalized reaction-diffusion lattice-gas model system

The reaction-diffusion lattice-gas model is an interacting particle system out of equilibrium whose microscopic dynamics is a combination of Glauber (reaction) and Kawasaki (diffusion) processes; the Glauber rate c(s;x) at site x when the configuration is s satisfies detailed balance at temperature T, while the Kawasaki rate Fc(s;x, y) between nearest-neighbor sites x and y satisfies detailed balance at a different temperature T'. We report on the phase diagram of that system as obtained from a series of Monte Carlo simulations of steady states in two-dimensional lattices with arbitrary values for T', T, and F; this generalizes previous analytical and numerical studies for F--, oo and/or T' ~ oo. When the rates are implemented by the Metropolis algorithm, the system is observed to undergo various types of first- and second-order (nonequilibrium) phase transitions, e.g., one may identify Onsager (equilibrium) as well as Landau (mean-field) types of continuous phase transitions.

Nonequilibrium phase transition in the electronic transport of p-type germanium at low temperatures.

We investigate low-temperature impact-ionization breakdown of extrinsic germanium with the help of both time-averaged and time-resolved current-voltage measurements. Under variation of the lattice temperature as an appropriate thermodynamic control parameter, the underlying nonlinear physics displays a second-order nonequilibrium phase transition. The characteristic critical exponents evaluated reveal a scaling behavior consistent with the predictions of the Landau theory. Finally, an analogy to the well-known van der Waals gas equilibrium system is elucidated.

Elastic properties of CsDy1−xGd(Eu)x(MoO4)2in the region of structural phase transitions

Abstract An invesigation is made of the temperature dependences of relative changes in the sound velocities and dielectric permeability along the principle axes of CsDy1−x Gd(Eu) x (MoO4)2 system crystals in the region of second-order structural phase transitions. The absence of noticeable softening of the transverse moduli points to the antiferroelastic type of transition. One more first-order structural transition is detected in the temperature range 24 to 32 K.

Faraday effect aid birefringence in orthorhombic Li2Ge7O15 near the ferroelectric phase transition

Abstract The tensor of the Faraday effect and its temperature derivatives were determined from the temperature dependence of Faraday rotation and indices of refraction of orthorhombic Li 2Ge7O15 between 120K and 340K, wave length 633nm. A strong anomaly of the Verdet constant V 33 and of the index n 3 was observed passing through the transition at 284K. The ratio of the slopes of the Verdet constant V 33 above and below the transition is about -2. This value corresponds to a second-order ferroelectric phase transition.