Showing papers on "Phase transition published in 1983"

Crystalline ferroelectrics with glassy polarization behavior

Abstract: We report measurements of the optic index of refraction as a function of temperature, $n (T)$, in the crystalline ferroelectrics having the simple perovskite ($\mathrm{AB}{\mathrm{O}}_{3}$) structure. We show that these crystals possess a local, randomly oriented, nonreversible polarization below a temperature ${T}_{d}$ several hundred degrees above the ferroelectric phase-transition temperature ${T}_{c}$. Using a simple model, we account for this behavior and understand quantitatively the values of ${T}_{d}$. This model, we believe, contains the basic physical understanding of ferroelectrics with a diffuse phase transition.

Time-Resolved Reflectivity Measurements of Femtosecond-Optical-Pulse-Induced Phase Transitions in Silicon

Abstract: The reflectivity of silicon has been measured following excitation with intense 90-fsec optical pulses. These measurements for the first time clearly resolve in time the process of energy transfer to the crystal lattice and the dynamics of the phase transition to the melted state.

Temperature and pressure dependences of the dielectric constants of semiconductors

Abstract: The effects of temperature and hydrostatic pressure on the static dielectric constant (epsilon) were investigated for a group of crystalline semiconductors chosen to be representative of III-V compounds (GaAs and GaP), II-VI compounds (ZnS and CdS), and group-IV (Si) materials. When combined with earlier results on the temperature and pressure dependences of the high-frequency optical (i.e., electronic) dielectric constants (epsilon/sub infinity/), the present results allow, for the compound semiconductors, determination of the lattice contribution to these effects. The results are discussed from both the microscopic and macroscopic points of view. For all the crystals studied, the pressure effects are dominated by the change in polarizability with volume, and the temperature effects by anharmonicities. The pressure dependences of the lattice contributions to the dielectric constants (epsilon/sub 11/ and epsilon/sub 33/) of hexagonal CdS are anomalous in that they increase with pressure. This behavior is most likely due to coupling between the appropriate TO modes and the TA modes which are known to soften on approaching the pressure-induced phase transition in this crystal. The transverse dynamic effective charge was calculated for the compounds, and its pressure dependence was determined for GaAs and GaP. The results and their implications are discussed.

Theory of critical micelle concentration for solutions of block copolymers

Abstract: A simple microscopic model for micellar formation in mixtures of block copolymers and homopolymers is presented. The size, number of chains, and energy of formation of micelle are calculated. The fraction of copolymer chains aggregating into micelles is computed as a function of the overall copolymer content. A critical micelle concentration behavior is found for low copolymer contents even for weak incompatibilities of species. The similarity with an aborted phase transition is underlined.

Finite-size effects at first-order transitions

Abstract: Finite-size rounding of a first-order phase transition is studied in “block”- and “cylinder”-shaped ferromagnetic scalar spin systems. Crossover in shape is investigated and the universal form of the rounded susceptibility peak is obtained. Scaling forms on the low-temperature side of the critical point are considered both above and below the borderline dimensionality,d >=4. A method of phenomenological renormalization, applicable to both odd and even field derivatives, is suggested and used to estimate universal amplitudes for two-dimensional Ising models atT=Tc.

Phase transitions in stationary nonequilibrium states of model lattice systems

Abstract: We investigated the stationary nonequilibrium states of a lattice gas of interacting particles subject to an external field $\stackrel{\ensuremath{\rightarrow}}{E}$. The dynamics of the system are given by hoppings of particles to nearby empty sites with rates biased for jumps in the direction of $\stackrel{\ensuremath{\rightarrow}}{E}$. This system is often used to model fast ionic conductors. Using computer simulations of a two-dimensional lattice with nearest-neighbor interactions we studied the dependence of the structure function, current, etc., on temperature and $\stackrel{\ensuremath{\rightarrow}}{E}$. We found evidence for a transition line in the temperature-field plane at which the system develops (anisotropic) long-range order. $\stackrel{\ensuremath{\rightarrow}}{E}$ enhances the transition for attractive interactions and represses it for repulsive ones.

Kinetics of phase transitions: Theory of Ostwald ripening

Abstract: A new derivation is presented for the last stage of phase separation in the kinetics of a first order phase transition, precipitation, where Ostwald ripening is the dominant mechanism. We use a time scaling technique and derive the power law time dependence and distribution function for the size of the particles of the new phase. Equations are derived for the correction terms to the distribution function and power laws. The derivation clarifies and corrects prior work.

Transformation behaviour of a Ti50Ni47Fe3 alloy I. Premartensitic phenomena and the incommensurate phase

Abstract: The transformation behaviour of TiNiFe alloys of nominal composition Ti50Ni47Fe3 has been studied by transmission electron microscopy and diffraction, and electrical resistance measurements between room temperature and −196°C. Based on the present results and complementary neutron and X-ray diffraction data, charge density wave (CDW) phenomena and associated phase transitions were found to be involved in the ‘premartensitic’ behaviour of the Ti50Ni47Fe3 alloys. The crystal structure of the high-temperature parent phase was confirmed to he the CsCl (B2) structure with a0, = 3·02 A. On cooling from room temperature, 1/3(110) and 1/3(111) superlattice reflections appeared, coincident with the onset of the electrical resistance anomaly (increase). The ‘1/3’ superlattice reflections were observed to intensify with decreasing temperature, and close inspection showed that such reflections deviated slightly from the exact 1/3 positions relative to the parent CsCl structure, suggesting the formation of an...

Theoretical interpretation of resistive transition data from arrays of superconducting weak links

Abstract: The effects of a vortex-unbinding phase transition on the properties of a square lattice of superconducting weak links are discussed. Formulas relating bulk static quantities such as the penetration depth and transition temperature to single-junction parameters are given, as well as formulas for the current- and temperature-dependent resistance. Except for temperatures very near the transition temperature, these results can differ significantly from the continuum results of Halperin and Nelson, and thus may be more appropriate for description of junction arrays and some granular films.

High-pressure Raman study of zone-center phonons in PbTi O 3

Abstract: A complete study of the $\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}=\stackrel{\ensuremath{\rightarrow}}{0}$ optical phonons of the ferroelectric tetragonal PbTi${\mathrm{O}}_{3}$ as a function of hydrostatic pressure has been carried out using Raman spectroscopy. The coalescence, to the same frequency, of the high-energy [${A}_{1}(\mathrm{TO})$, $E(\mathrm{TO})$] pairs of phonons in the ferroelectric phase and the disappearance of the first-order Raman lines in the cubic phase has enabled us to determine the transition pressure ${P}_{c}$, as well as the second-order character of the phase transition. Our results also suggest the existence of a tricritical point in the ($P$,$T$) phase diagram. Using the Liddane-Sachs-Teller relation we calculate the static dielectric constant as a function of pressure and compare the results with previous dielectric measurements. Moreover, we discuss the soft phonons, their damping, and their behavior near the phase transition. It is found that the soft $E(\mathrm{TO})$ phonon damping function is nearly constant over a wide frequency range and that it appears to diverge near the phase transition.

Critical behaviour of the phase transition in the 2D Ising Model with impurities

Abstract: The problem of the effect of inhomogeneous impurities in a lattice structure on the critical behaviour of systems which undergo a second-order phase transition is studied on a model system, the 2D Ising Model with impurity bonds randomly distributed over the lattice. It is known that in the critical region the 2D Ising Model is equivalent to the model of free fermions. We show that the effect of impurities is to add a four-fermion interaction with the corresponding charge proportional to the concentration of impurities. The resulting fermion model is simple enough and can be studied exactly by renormalization group methods. We show that for any small concentration of impurity bonds a new critical regime is established if we go sufficiently close to the phase-transition point. In particular we find that the specific heat singularity changes from C ˜ ln 1/|τ|(τ=(Τ − Τc/Τc to C ˜ ln ln 1/|τ| for τ≪τi ˜ exp(−const/c i), c i being the concentration of impurities, while the spin-spin correlation functi...

On a sharp transition from area law to perimeter law in a system of random surfaces

Abstract: We introduce and study a phase transition which is associated with the spontaneous formation of infinite surface sheets in a Bernoulli system of random plaquettes. The transition is manifested by a change in the asymptotic behavior of the probability of the formation of a surface, spanning a prescribed loop. As such, this transition offers a generalization of the bond percolation phenomenon. At low plaquette densities, the probability for large loops is shown to decay exponentially with the loops' area, whereas for high densities the decay is by a perimeter law. Furthermore, we show that the two phases of the three dimensional plaquette system are in a precise correspondence with the two phases of the dual system of random bonds. Thus, if a natural conjecture about the phase structure of the bond percolation model is true, then there is a sharp transition in the asymptotic behavior of the surface events. Our analysis incorporates block variables, in terms of which a non-critical system is transformed into one which is close to a trivial, high or low density, fixed point. Stochastic geometric effects like those discussed here play an important role in lattice gauge theories.

Semi-infinite systems with first-order bulk transitions

Abstract: Semi-infinite systems are considered which undergo a first-order transition. The global phase diagram is discussed within the framework of Landau theory. Several types of phase transitions are found. At some of these transitions, critical surface phenomena occur since a variety of surface exponents may be defined although there are no bulk exponents.

Liquid–gas phase transition in nuclear matter

Abstract: Every self-bound Fermi liquid will exhibit a liquid–gas phase equilibrium at low temperatures, because the pressure is positive at low densities due to the kinetic energy of degeneracy, and falls to zero again at the equilibrium density. Nuclear matter is seldom found under conditions of two-phase equilibrium, however: in usual nuclear reactions, a heated (‘compound’) nucleus is produced out of equilibrium with its surroundings, which are at a much lower temperature. The most familiar example of a two-phase equilibrium occurs in the crust of neutron stars inside the neutron-drip line1, at temperatures of less than an MeV. In supernovas, in the crucial moments when the implosion is reversed to an explosion, densities comparable to those of neutron stars may be attained with associated temperatures of 5 to 10 MeV. An accurate knowledge of the properties of nuclear matter under these conditions is essential to the understanding of supernova dynamics2. This communication shows how laboratory observations with the latest generation of nuclear accelerators can be used to infer the surface tension of the liquid–gas interface in nuclear matter–an essential ingredient of the equation of state for which a reliable theoretical model is not available.

Reflection properties of phase transition and compositional change models of the 670-km discontinuity

Abstract: Seismic observations of the amplitude ratio amplitude P′670P′/amplitude P′P′ suggest a reflection coefficient R ∼ 7–13% for reflections from the underside of the 670-km discontinuity. This can be compared with calculated reflection coefficients to constrain the nature of the mantle transition region. Velocity and density profiles through the transition region were calculated for olivine, pyroxene, garnet, and olivine + garnet model mineral assemblages. For models with identical upper and lower mantle compositions, the computed reflection coefficients from the phase transitions pertinent to the 670-km discontinuity are less than 0.5%. These phase transitions produce their maximum R if they are effectively discontinuous, which gives R ∼ 2–3%, except for the garnet to perovskite transformation which gives R ∼ 8%. In general, given realistic impedance contrasts across a phase transition, the change in material properties must occur over a region less than 3 km thick for R to be of the order of 5%. A discontinuous change in chemical composition at 670-km depth, coupled with a change in phase, can also produce a reflection coefficient of the observed magnitude: R ∼ 2–3% for a first-order change in phase at 670 km with different iron concentrations on each side of the discontinuity, and R ∼ 4–6% for cases with a discontinuous increase in silica content. Based on our analysis, the thermal and chemical boundary layers which would occur across such a chemical discontinuity would probably have negligible effects on the reflection coefficient. Thus although limited by considerable uncertainties, the mineralogical and seismic data suggest a two-layered model of the mantle with a discontinuous change in both phase and composition at 670 km.

Wetting transitions at models of a solid-gas interface

Abstract: Using mean field free energy functionals of the type employed by Sullivan, we have investigated the nature of the transition from partial to complete wetting that occurs at a solid-gas interface. We show that this wetting transition can be a first or a second order phase transition. If it is first order, as predicted by Cahn, the coverage diverges discontinuously and the temperature derivative of the interfacial tension changes discontinuously at the transition whereas if it is second order these properties change continuously, as found by Sullivan. For a given model system the order of the transition depends strongly on the range of the solid-fluid potential. When the solid-fluid and fluid-fluid potentials are to be taken to be exponentially decaying functions of distance the transition is second order if the range of the solid-fluid potential is smaller or equal to that of the fluid-fluid potential but may be first order when the solid-fluid potential is of longer range. For the more realistic model, a ...

Superconducting phase transitions in indium/indium-oxide thin-film composites

Abstract: Low-frequency techniques are used to examine the predictions of the equilibrium Kosterlitz-Thouless theory of the vortex-pair unbinding transition in indium/indium-oxide composite superconducting thin films. The renormalized superfluid density obtained from independent measurements of the kinetic inductance and the exponent of the current-dependent resistance are in agreement. At the transition temperature ${T}_{c}$, the critical value of the superfluid density agrees with theory for a finite measurement length. Experimental sensitivity is such that the resistance near ${T}_{c}$, measured to be about 9 orders of magnitude below the normal resistance, is explained by the motion of a single thermally excited free vortex in a superfluid background renormalized by bound-vortex pairs. The corresponding critical magnetic field for flux entry is also measured. The resistance of the thermally excited free-vortex plasma and the correlation length above the transition temperature obey the qualitative prediction of the theory. Nonuniversal constants in the renormalization-group theory are obtained from the experiment and are found to be sample dependent.

Phase transitions on fractals. I. Quasi-linear lattices

Abstract: Magnetic spin models and resistor networks are studied on certain self-similar fractal lattices, which are described as 'quasi-linear', because they share a significant property of the line: finite portions can be isolated from the rest by removal of two points (sites). In all cases, there is no long-range order at finite temperature. The transition at zero temperature has a discontinuity in the magnetisation, and the associated magnetic exponent is equal to the fractal dimensionality, D. When the lattice reduces to a non-branching curve the thermal exponent v-1=y is equal to D. When the lattice is a branching curve, y is related, respectively, to the dimensionality of the single-channel segments of the curve (for the Ising model), or to the exponent describing the resistivity (for models with continuous spin symmetry).

Critical measurements in the spin glass CuMn

Abstract: We present experimental data on the magnetization M(H) of a CuMn 1 at. % in the range Tc≤ T ≤ 4 Tc, 0 < H < 7 teslas. We took special precautions in order to eliminate systematic errors and improve the reliability of the data. It was then possible to study the temperature dependence of the first coefficients A 1, A3, A5 in the expansion of the low field magnetization data in terms of odd powers of [FORMULA], in the range 1.1 Tc ≤ T ≤ 4 Tc. From the divergence of A3 and A5 (which vary over 3 and 6 orders of magnitude respectively in this range), we derive two exponents (γ = 3.25, β = 0.75 ± 0.25) which allow the rescaling of all our data points onto a universal function. The success of the scaling argument is strong evidence in favour of the existence of a phase transition in three dimensions for RKKY spin glasses.

Theory of Agglomeration of Ferromagnetic Particles in Magnetic Fluids

Abstract: For some magnetic fluids, large agglomerates of magnetic particles are formed when a weak magnetic field is applied. In this paper we regard this phenomenon as a kind of gas-liquid phase transition induced by the magnetic field, and study the condition for the formation of the agglomerates by a simple mean field theory. It is found that if the particle is small enough, no phase separation occurs even if the magnetic field is infinitely large, while if the particle is large, the liquid phase appears at certain magnetic field. The van der Waals attraction between the particles enhances the agglomeration.