Three-phase Coexistence Region Research Articles

Phase equilibria of SiO2–Ce2O3–CaO-25 wt %Al2O3 system at 1673 K–1773 K

The utilization of rare earth resources, especially secondary resources (e.g., RE-oxide system slag), has been limited by the lack of thermodynamic information. In order to supplement and improve the thermodynamic data related to rare earth, the equilibrium experiments of SiO2–Ce2O3–CaO-25 wt %Al2O3 system phase diagram was carried out at 1673 K and 1773 K by the high-temperature isothermal equilibration/quenching technique in current paper. The composition of seven phase regions were determined by FE-SEM, XRD, EPMA and XRF analysis on the samples obtained by high temperature equilibrium technology at 1673 K and 1773 K, including the primary crystal regions of three compounds (C2AS, 2CaO·SiO2, CaO·2Ce2O3·3SiO2) and three three-phase coexistence regions (L + C2AS + 2CaO·SiO2, L + C2AS + CaO·2Ce2O3·3SiO2, L + CaO·2Ce2O3·3SiO2+CeAl11O18) and a liquid region. The phase relations and isotherms of SiO2–Ce2O3–CaO-25 wt %Al2O3 system obtained in current work are beneficial to the recycling of rare earth resources containing cerium.

Multiphase coexistence and enhanced piezoelectric properties in (1−x)(K0.45Na0.55)(Nb0.965Sb0.035)O3−xBi0.5(K0.91Li0.09)0.5(Hf0.3Zr0.7)O3 lead-free ceramics

A new lead-free piezoelectric solid solution system with the formula of (1−x)(K0.45Na0.55)(Nb0.965Sb0.035)O3−xBi0.5(K0.91Li0.09)0.5(Hf0.3Zr0.7)O3 were prepared using a conventional solid-phase sintering method, and we investigated the relationship between the composition, microstructure, phase structure and electrical properties of the ceramics. It was found that adding Bi0.5(K0.91Li0.09)0.5(Hf0.3Zr0.7)O3 induced the ceramics transition from a single orthorhombic structure to a coexistence of multiple phases, and a three-phase coexistence of rhombohedral, orthorhombic and tetragonal phases was present in the composition range x = 0.03 to 0.035. Enhanced piezoelectric properties were obtained for the ceramics near the three-phase coexistence region, with the largest piezoelectric constant d33 of 253 pC/N and the highest planar electromechanical coupling coefficient of 0.36. Additionally, a rough phase diagram for the solid solution system was established by using the critical temperatures determined by the temperature-dependent dielectric properties. The authors believe that these results can provide a useful reference for the development of (K,Na)NbO3-based lead-free piezoelectric ceramics.

Construction of Ti-Nb-Ti2Cu pseudo-ternary phase diagram.

The aim of this study was to construct a Ti-Nb-Cu ternary phase diagram that plays the role of a map for developing new titanium alloys with excellent machinability and mechanical properties. Fifteen experimental Ti-Nb-Cu ternary alloys composed of Ti-5-30%Nb-2-20%Cu were designed, and ingots made using Ar-arc melting furnace before casting to generate specimen. The alloy castings were evaluated in terms of their microstructures and alloy phases. A Ti-Nb-Ti2Cu pseudo-ternary phase diagram was constructed using X-ray diffractmetry results. Three alloy phases (α-Ti, β-Ti and Ti2Cu) were established within the specimen. Furthermore, the prescence of two-phase coexistence regions (α+Ti2Cu, α+β and β+Ti2Cu), and three-phase coexistence region (α+β+Ti2Cu) was noted. The findings obtained through microstructural observation corresponded well with the constructed phase diagram.

Effects of BaHfO3 addition on the phase transition and piezoelectric properties of (K,Na)NbO3-based ceramics

Lead-free piezoelectric ceramics based on (1–x)(K0.48Na0.48Li0.04)Nb0.95Sb0.05O3–xBaHfO3 were designed and prepared by a conventional ceramic fabrication method. An investigation was conducted to judge the effects of BaHfO3 content on the ceramics' phase structure, microstructure, phase transition temperatures, and piezoelectric properties. It was found that all the ceramics possessed a perovskite structure in the studied composition range, despite the fact that they experienced gradual transitions from orthorhombic symmetry to rhombohedral symmetry upon increases of BaHfO3 content. Furthermore, a three-phase coexistence of rhombohedral–orthorhombic–tetragonal phases was identified in the composition range of 0.05 ≤ x ≤ 0.055, based on X-ray diffraction results together with the temperature dependence of dielectric properties. In the three-phase coexistence region, the ceramics displayed effectively enhanced piezoelectric activity, with the maximum values of the piezoelectric constant d33, and planar electromechanical coupling coefficient, being 268 pC/N and 0.432 respectively. In addition, the Curie temperature of the ceramics was found to decrease in accordance with increases of BaHfO3 content. We believe that this work can provide a valuable reference for researchers to further improve the piezoelectric properties of (K,Na)NbO3-based ceramics.

Glucosylceramide Reorganizes Cholesterol-Containing Domains in a Fluid Phospholipid Membrane

Glucosylceramide (GlcCer), one of the simplest glycosphingolipids, plays key roles in physiology and pathophysiology. It has been suggested that GlcCer modulates cellular events by forming specialized domains. In this study, we investigated the interplay between GlcCer and cholesterol (Chol), an important lipid involved in the formation of liquid-ordered (lo) phases. Using fluorescence microscopy and spectroscopy, and dynamic and electrophoretic light scattering, we characterized the interaction between these lipids in different pH environments. A quantitative description of the phase behavior of the ternary unsaturated phospholipid/Chol/GlcCer mixture is presented. The results demonstrate coexistence between lo and liquid-disordered (ld) phases. However, the extent of lo/ld phase separation is sparse, mainly due to the ability of GlcCer to segregate into tightly packed gel domains. As a result, the phase diagram of these mixtures is characterized by an extensive three-phase coexistence region of fluid (ld-phospholipid enriched)/lo (Chol enriched)/gel (GlcCer enriched). Moreover, the results show that upon acidification, GlcCer solubility in the lo phase is increased, leading to a larger lo/ld coexistence region. Quantitative analyses allowed us to determine the differences in the composition of the phases at neutral and acidic pH. These results predict the impact of GlcCer on domain formation and membrane organization in complex biological membranes, and provide a background for unraveling the relationship between the biophysical properties of GlcCer and its biological action.

Anisotropy of local stress tensor leads to line tension.

Line tension of three-phase contact lines is an important physical quantity in understanding many physical processes such as heterogeneous nucleation, soft lithography and behaviours in biomembrane, such as budding, fission and fusion. Although the concept of line tension was proposed as the excess free energy in three-phase coexistence regions a century ago, its microscopic origin is subtle and achieves long-term concerns. In this paper, we correlate line tension with anisotropy of diagonal components of stress tensor and give a general formula of line tension. By performing molecular dynamic simulations, we illustrate the formula proposed in Lennard-Jones gas/liquid/liquid and gas/liquid/solid systems, and find that the spatial distribution of line tension can be well revealed when the local distribution of stress tensor is considered.

Budding of domains in mixed bilayer membranes.

We propose a model that accounts for the budding behavior of domains in lipid bilayers, where each of the bilayer leaflets has a coupling between its local curvature and the local lipid composition. The compositional asymmetry between the two monolayers leads to an overall spontaneous curvature. The membrane free energy contains three contributions: the bending energy, the line tension, and a Landau free energy for a lateral phase separation. Within a mean-field treatment, we obtain various phase diagrams which contain fully budded, dimpled, and flat states. In particular, for some range of membrane parameters, the phase diagrams exhibit a tricritical behavior as well as a three-phase coexistence region. The global phase diagrams can be divided into three types and are analyzed in terms of the curvature-composition coupling parameter and domain size.

Phase separation and charge-ordered phases of thed=3Falicov-Kimball model at nonzero temperature: Temperature-density-chemical potential global phase diagram from renormalization-group theory

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.

Charged bilayer membranes in asymmetric ionic solutions: Phase diagrams and critical behavior

We consider the phase separation in an asymmetrically charged lipid bilayer membrane consisting of neutral and negatively charged lipids that are in contact with in and out ionic solutions having different ionic strengths. The two asymmetric leaflets are coupled through electrostatic interactions. Based on a free-energy approach, the critical point and phase diagrams are calculated for different ionic strengths of the two solutions and coupling parameter. An increase of the coupling constant or asymmetry in the salt concentration between the in and out solutions yields a higher phase-separation temperature because of electrostatic interactions. As a consequence, the phase-coexistence region increases for strong screening (small Debye length). Finally, possible three-phase coexistence regions in the phase diagram are predicted.

X-ray Kinematography of Phase Transformations of Three-Component Lipid Mixtures: A Time-Resolved Synchrotron X-ray Scattering Study Using the Pressure-Jump Relaxation Technique

By using the pressure-jump relaxation technique in combination with time-resolved synchrotron small-angle X-ray diffraction (TRSAXS), the kinetics of lipid phase transformations of ternary lipid mixtures serving as model systems of heterogeneous raftlike membranes were investigated. To this end, we first established the temperature-pressure phase diagram of a model lipid raft mixture, 1,2-dioleoyl- sn-glycero-3-phosphatidylcholine (DOPC)/1,2-dipalmitoyl- sn-glycero-3-phosphatidylcholine (DPPC)/cholesterol (1:2:1), using Fourier transform infrared spectroscopy and SAXS, covering the pressure range from 1 bar to 10 kbar at temperatures in the range from 7 to 80 degrees C. We then studied the kinetics of interlamellar phase transitions of the ternary lipid system involving transitions from the fluidlike (liquid-disordered, l d) phase to the liquid-ordered (l o)/liquid-disordered (l d) two-phase coexistence region as well as between the two- and three-phase coexistence regions of the system, where also solid-ordered phases (s o) are involved. The phase transition from the all-fluid l d phase to the l o+l d two-phase coexistence region turns out to be rather rapid. Phases appear or disappear within the 25 ms time resolution of the technique, followed by a slow lattice relaxation process, which, depending on the pressure-jump amplitude, takes several seconds. Contrary to many one-component phospholipid phase transitions, the kinetics of the l d <--> l o+l d transition follows a similar time scale and mechanism for the pressurization and depressurization direction. A similar behavior is observed for the phase transition kinetics of the s o+l o+l d <--> l o+l d transformation and even for the s o+l o+l d <--> l d transformation, jumping across the l o+l d two-phase region. All transitions are fully reversible, and no intermediate states are populated. As indicated by the complex relaxation profiles observed, the overall rates observed seem to reflect the effect of coupling of various dynamical processes through the transformation, involving fast conformational changes in the sub-millisecond time regime and slow relaxation of the lattices growing, probably being largely controlled by the transport and redistribution of water into and in the new phases of the multilamellar vesicle assemblies.

Influence of Monolayer-Monolayer Coupling on the Phase Behavior of a Fluid Lipid Bilayer

We suggest a minimal model for the coupling of the lateral phase behavior in an asymmetric lipid membrane across its two monolayers. Our model employs one single order parameter for each monolayer leaflet, namely its composition. Regular solution theory on the mean-field level is used to describe the free energy in each individual leaflet. Coupling between monolayers entails an energy penalty for any local compositional differences across the membrane. We calculate and analyze the phase behavior of this model. It predicts a range of possible scenarios. A monolayer with a propensity for phase separation is able to induce phase separation in the apposed monolayer. Conversely, a monolayer without this propensity is able to prevent phase separation in the apposed monolayer. If there is phase separation in the membrane, it may lead to either complete or partial registration of the monolayer domains across the membrane. The latter case which corresponds to a three-phase coexistence is only found below a critical coupling strength. We calculate that critical coupling strength. Above the critical coupling strength, the membrane adopts a uniform compositional difference between its two monolayers everywhere in the membrane, implying phase coexistence between only two phases and thus perfect spatial registration of all domains on the apposed membrane leafs. We use the lattice Boltzmann simulation method to also study the morphologies that form during phase separation within the three-phase coexistence region. Generally, domains in one monolayer diffuse but remain fully enclosed within domains in the other monolayer.

Local Surface Potentials in the Three-Phase Coexistence Region of a Langmuir Monolayer

The relative surface potentials of Langmuir monolayer phases at the air/water interface have been determined in the three-phase coexistence region gas/liquid expanded/liquid condensed of methyloctadecanoate. The monolayer is assumed to be in hydrostatic equilibrium. A force balance applied to the morphology of the monolayer observed with fluorescence microscopy directly yields the relative surface potentials. This enables the determination of surface potential variations on a micron scale.

Phase behavior of three-component ionic fluids

We study the phase behavior of solutions consisting of positive and negative ions of valence z to which a third ionic species of valence Z>z is added. Using a discretized Debye-Hueckel theory, we analyze the phase behavior of such systems for different values of the ratio Z/z. We find, for Z/z>1.934, a three-phase coexistence region and, for Z/z>2, a closed (reentrant) coexistence loop at high temperatures. We characterize the behavior of these ternary ionic mixtures as function of charge asymmetry and temperature, and show the complete phase diagrams for the experimentally relevant cases of Z/z=2 and Z/z=3, corresponding to addition of divalent and trivalent ions to monovalent ionic fluids, respectively.

Quark-hadron three-phase mixture of baryonic matter

The phase diagrams of strongly interacting baryonic matter are constructed in a phenomenological model assuming three phases: hadrons, quarkgluon plasma and constituent quarks. Three-phase mixture states are considered in detail and it is shown that these states cover a finite area in the energy density-baryonic density plane. Possible hydrodynamic expansion processes involving the three-phase coexistence region in relativistic heavy-ion collisions are outlined.

Low-temperature analysis of three-phase coexistence.

We study the properties of an isotropic lattice model by low-temperature expansion. In particular, the interface between ferromagnetic phases for the case when a third modulated phase is in thermodynamic equilibrium is considered. Throughout the three-phase coexistence region the interfacial tension between all three phases is very low and actually vanishes at zero temperature. This reflects the fact that the surface of the finite-temperature three-phase equilibria arises from a curve of zero-temperature multiphase points. We show that throughout the three-phase region and in the limit of low temperature, the modulated phase never wets the interface between the ferromagnetic phases.