First-order Phase Boundary Research Articles

Multicritical phase diagrams of the Blume–Emery–Griffiths model with repulsive biquadratic coupling including metastable phases: the pair approximation and the path probability method with pair distribution

As a continuation of the previously published work, the pair approximation of the cluster variation method is applied to study the temperature dependences of the order parameters of the Blume–Emery–Griffiths model with repulsive biquadratic coupling on a body centered cubic lattice. We obtain metastable and unstable branches of the order parameters besides the stable branches and phase transitions of these branches are investigated extensively. We study the dynamics of the model by the path probability method with pair distribution in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. We present the metastable phase diagram in addition to the equilibrium phase diagram and also the first-order phase transition line for the unstable branches of the quadrupole order parameter is superimposed on the phase diagrams. It is found that the metastable phase diagram and the first-order phase boundary for the unstable quadrupole order parameter always exist at the low temperatures which are consistent with experimental and theoretical works.

Phase transitions in a ferrofluid at magnetic-field-induced microphase separation.

In the presence of a magnetic field applied perpendicular to a thin sample layer, a suspension of magnetic colloidal particles (ferrofluid) can form spatially modulated phases with a characteristic length determined by the competition between dipolar forces and short-range forces opposing density variations. We introduce models for thin-film ferrofluids in which magnetization and particle density are viewed as independent variables and in which the nonmagnetic properties of the colloidal particles are described either by a lattice-gas entropy or by the Carnahan-Starling free energy. Our description is particularly well suited to the low-particle-density regions studied in many experiments. Within mean-field theory, we find isotropic, hexagonal and stripe phases, separated in general by first-order phase boundaries.

Finite-temperature phase diagram of the Hubbard model

The finite-temperature phase diagram of the Hubbard model in d=3 is obtained from renormalization-group analysis. It exhibits, around half filling, an antiferromagnetic phase and, between 30%-40% electron or hole doping from half filling, a new τ phase in which the electron hopping strength t asymptotically becomes infinite under repeated rescalings. Next to the τ phase, a first-order phase boundary with very narrow phase separation (less than 2% jump in electron density) occurs. At temperatures above the τ phase, an incommensurate spin modulation phase is indicated. In d=2, we find that the Hubbard model has no phase transition at finite temperature.

Maximum solubility of cholesterol in phosphatidylcholine and phosphatidylethanolamine bilayers

In any lipid bilayer membrane, there is an upper limit on the cholesterol concentration that can be accommodated within the bilayer structure; excess cholesterol will precipitate as crystals of pure cholesterol monohydrate. This cholesterol solubility limit is a well-defined quantity. It is a first-order phase boundary in the phospholipid/cholesterol phase diagram. There are many different solubility limits in the literature, but no clear picture has emerged that can unify the disparate results. We have studied the effects that different sample preparation methods can have on the apparent experimental solubility limit. We find that artifactual demixing of cholesterol can occur during conventional sample preparation and that this demixed cholesterol may produce artifactual cholesterol crystals. Therefore, phospholipid/cholesterol suspensions which are prepared by conventional methods may manifest variable, falsely low cholesterol solubility limits. We have developed two novel preparative methods which are specifically designed to prevent demixing during sample preparation. For detection of the cholesterol crystals, X-ray diffraction has proven to be quantitative and highly sensitive. Experiments based on these methods yield reproducible and precise cholesterol solubility limits: 66 mol% for phosphatidylcholine (PC) bilayers and 51 mol% for phosphatidylethanolamine (PE) bilayers. We present evidence that these are true, equilibrium values. In contrast to the dramatic headgroup effect (PC vs. PE), acyl chain variations had no effect on the cholesterol solubility limit in four different PC/cholesterol mixtures.

The melting line of diamond determined via atomistic computer simulations

The diamond melting line was determined for a model system based on Brenner’s bond order potential for hydrocarbon systems. The location of this first-order phase boundary was found by a free energy calculation of the diamond and liquid phases, using atomistic simulation methods. The melting line was found to have a positive slope consistent with the present understanding. The location at lower pressure was also consistent with experiment and a number of other theoretical approaches. The slope is found to increase with pressure. The structure of the liquid is examined as a function of density and is suggestive of a liquid–liquid phase boundary.

First-order phase transition in unfolding a collapsed polymer: A histogram Monte Carlo simulation

The phase transition associated with stretching a collapsed polymer chain (consisting of N monomers) is investigated in detail using the histogram Monte Carlo simulation method and the bond-fluctuation model. The distribution functions for the number of contacts and end-to-end distances are obtained. The free energy profile associated with the transition is explicitly computed. Our results on the energy cumulants and free energy profiles provide direct evidence for the first-order nature of the phase transition. The phase transition occurs in the whole poor solvent regime below the $\ensuremath{\Theta}$ point, $\ensuremath{\chi}>{\ensuremath{\chi}}_{c}.$ The free energy barrier at the transition is found to scale with $N(\ensuremath{\chi}\ensuremath{-}{\ensuremath{\chi}}_{c}).$ Phase diagram for the first-order transition phase boundary is also obtained. We find that the mean-field theory results give only a qualitatively correct picture for the phase transition.

Phase diagram of a spin-1 magnetic bilayer by cluster variational theory: Exact results for a BEG model on a Bethe lattice with five-fold coordination

The complete global phase diagram for a magnetic spin-1 bilayer, whose interactions are described by the Blume Emery Griffiths model (BEG), is studied by cluster variational theory within the pair approximation. The results obtained, are also the exact results pertaining to the BEG model on a Bethe lattice having coordination number, z=5. Useful analytic expressions are derived for trajectories in phase space containing the second-order (continuous) phase boundaries. The physical existence of these second-order boundaries, together with the location of the first-order phase boundaries, are determined from a Gibbs free energy analysis. Detailed comparison of the results with those of other workers on this, and closely related systems, is made.

Neutron studies of nuclear magnetism at ultralow temperature

Nuclear magnetic order in copper and silver has been investigated by neutron diffraction. Antiferromagnetic order is observed in these simple, diamagnetic metals at temperatures below 50 nK and 560 pK, respectively. Both crystallize in the FCC-symmetry which is fully frustrated for nearest-neighbour interactions. Silveris a good example for a frustrated, spin 1 2 Heisenberg system. The antioferromagnetic structure is of type I with a very simple phase diagram. In copper the exchange interaction is similar to silver, but there the dipolar interaction has comparable strength. This leads to a very complex phase diagram in applied fields. The low- and the high-field structures are of type I, while in intermediate fields the unconventional ordering vector q - 2π(1, 1 3 ), 1 3 ) is observed. Strong hysteresis effects indicate first-order phase boundaries in copper.

Interlayer tunneling in a non-Fermi-liquid metal.

We study the effect of interlayer tunneling in the gauge theory describing a quasi-two-dimensional paramagnetic metal close to a second-order or weakly first-order antiferromagnetic phase boundary. In that theory, two species of fermions have opposite (rather than equal) charges with respect to the gauge field. We find that single-particle interlayer tunneling is suppressed at low energies. The effect of pair tunneling is analyzed within the $(3-d)$ expansion. The resulting phase diagram has superconducting and non-Fermi-liquid normal phases, and so is compatible with that of the copper-oxide superconductors.

Singularities near critical and tricritical end points: thermodynamics and applications

Systems where a phase transition is induced by biquadratic coupling of two different modes, like some types of ferroelectric materials, are analyzed utilizing a Landau-type free energy. The phase diagram associated with this free energy has a critical line that meets a first-order phase boundary surface at a point that can be either a critical end point or a tricritical end point. Scaling arguments indicate that, close to a critical or to a tricical end ppoint, the first-order phase boundaries exhibit nonanalyticities associated with the singularities of that critical line or of that tricritical point. Explicit expressions for the phase boundaries in the model for ferroelectric materials are computed and checked for singularities. The association with the nonanalyticities of the critical line and of the tricritical point is also verified, confirming our phenomenological predictions.

Singularities near critical and bicritical end points: applications to an isomorphous transition

We study a system that has an isomorphous transition using an eighth-order Landau-type free energy function. The phase diagram of such system has a critical line that meets a first-order phase boundary at a critical end point. This phase boundary is also limited by two other critical lines that meet at a bicritical end point. We showed that this phase boundary close to the end point exhibits a nonanalytic behavior associated with the singularities of the critical line, confirming similar result we previously obtained using scaling arguments. Related universal amplitude ratios are then computed. Next, the critical lines near the bicritical end point are also analyzed and checked for singularities.

A–B phase transition in rotating superfluid 3He

Quantized vortices, when formed in rotating 3He, can effectively be studied by NMR. Vortices of different structure have been identified, depending on the superfluid phase and the external conditions. Here we discuss what happens when the first-order phase boundary, which separates the A and B phases, traverses through a rotating container which initially contains an equilibrium vortex array. The measurements imply that a vortex layer is formed in front of a slowly propagating interface and part of the newly formed phase behind the interface is left devoid of vortices.

Line tension near multicritical wetting transitions

Abstract The interface displacement model previously employed for calculating the line tension near first-order and critical wetting transitions is applied to multicritical wetting transitions. For short-range forces (with exponential decay) the line tension is negative in the partial wetting regime close to the multicritical point, and vanishes as the first power of the contact angle θ. For long-range forces (with algebraic decay) the vanishing of the line tension is qualitatively similar, but the power of θ is less than unity and depends both on the range of the forces and on the order of the multicriticality. Furthermore, the exponents characterizing the vanishing of the line tension, when approaching multicriticality along selected first-order wetting phase boundaries, are calculated for both short- and long-range forces.

The vortices of superfluid 3He

In the superfluid phases of [sup 3]He quantized vortex lines have been investigated under uniform rotation, when they form a regular array of rectilinear objects. A large diversity exists in the structure and properties of vortices, owing to the complicated nature of symmetry breaking in the different superfluid phases. A review is presented here on the various experimentally verified types of vortices. Recent measurements open a puzzling problem about their interaction and interconnection at the first-order phase boundary separating the A and B phases of superfluid [sup 3]He.

Melting pressure of solid 3He through the magnetic-ordering transitions.

Magnetic ordering in solid $^{3}\mathrm{He}$ has been studied by measuring the melting pressure through the various phase transitions. We find a discontinuity in entropy at the high-field--paramagnetic phase transition at low fields, indicating that it is first order. The entropy discontinuity decreases as the field increases and the transition broadens, becoming second order above a field of about 0.65 T. The first precise determination of the first-order phase boundaries has been made, from which thermodynamic data not previously available are obtained.

High-pressure ultrasonic determination of the phase diagram of antiferromagnetic Cr-0.3 at.% Ru alloy single-crystal

The temperature and hydrostatic pressure dependences of anomalies observed in the ultrasonic wave velocity have been used to determine (i) the boundary corresponding to the paramagnetic (P) to commensurate transition and (ii) the first-order phase boundary between the commensurate (C) and incommensurate (I) spin-density wave (SDW) phases on the pressure-temperature phase diagram for monocrystalline Cr-0.3 at.% Ru alloy. The paramagnetic-commensurate phase boundary is linear with a negative gradient d T PC /d P= -358±4 K/ GPa. Both T CI and T IC increase approximately linearly with pressure, the mean values of dT CI / dP and dT IC / dP being 333±3 K/GPa and 277±5 K/GPa respectively. The position of the triple point is estimated as (315±5 K, 0.22±0.02 GPa). In the commensurate SDW state the alloy shows the extraordinary property that when pressure is applied it becomes easier to squeeze.

SUSCEPTIBILITY SINGULARITIES AT FIRST-ORDER PHASE TRANSITIONS

Problems associated with analyticity of thermodynamic functions close to first-order phase transitions are briefly reviewed. The bubble model for correlation functions is then applied to planar Ising-like models at subcritical temperatures (T<Tc) with a bulk magnetic field h. The fluctuation sum is used to calculate the susceptibility χ(h) from the bubble correlation function. We show that χ(h), calculated this way, must contain an essential singularity at h=0 i.e. at the first-order phase boundary. This has important implications to metastability, where we demonstrate that if the ensemble is restricted such that the magnetization stays positive when h goes negative, χ(h) has an infinite number of poles along the negative real axis with a limit-point at h=0. For an unrestricted ensemble, a Yang-Lee circle theorem is derived.

Finite-size-scaling derivation of the Widom critical-exponent relation for surface tension.

By introducing finite-size-scaling corrections into the Kelvin equation for the location of the shifted first-order phase boundary (condensation line) for a fluid confined between two parallel plates, the critical exponent \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{} for the liquid-gas surface tension is shown to satisfy the Widom exponent relation \ensuremath{\mu}\ifmmode \tilde{}\else \~{}\fi{}=2-\ensuremath{\alpha}-\ensuremath{\nu}. In contrast to most previous arguments, no assumptions of bulk and surface hyperscaling are required in the present derivation.

Thermodynamic measurements in magnetically ordered solid3He

Measurements of the melting pressure and constant-volume pressure of solid3He have been made in the vicinity of the various magnetic-ordering transitions. Data have been obtained at several magnetic fields for both the low-field phase and the high-field phase, with particular attention given to the region of the polycritical point. The absence of a latent heat indicates that the transition from the paramagnetic to the high-field phase is second order or λ type. A spin-wave velocity of 6.95 cm/sec was obtained from theT4 temperature dependence of the melting pressure in the high-field phase forB=0.495 T. These data provide the entropy and volume discontinuities as functions of field along the first-order low-field phase boundary. The volume dependence of the transition temperatures has been extracted from these and other data.

Magnetocaloric Measurements on Dysprosium Phosphate (DyPO4)

DyPO4 orders below 3.39 K as a two-sublattice Ising antiferromagnet with its moments along the crystallographic c-axis. Measurements of the specific heat and the magnetocaloric effect with the magnetic field applied along c are performed to determine the phase diagram. A new intermediate ferrimagnetic phase is found at the metamagnetic transition from the antiferromagnetic to the paramagnetic state below 0.82 K. Although this phase extends only over a field range of about 20 mT, it is clearly seen since for crystals with finite demagnetising factor it produces additional mixed phases at the first-order phase boundary. The measured phase diagram is verified by mean-field calculations and the possibility of even more ferrimagnetic phases is discussed.