A probabilistic analysis of the Walker-Vause model for liquid binary mixtures

A simple method to calculate the probability distribution for a binary fluid mixture is presented. The method is applid to the Walker-Vause binary liquid model and different temperature vs composition phase diagrams are obtained. These diagrams are obtained using catastrophe theory methods. Comparison with some experimental data are also discussed and a simplified model leading to closed-loop phase diagrams is considered.     

Phase studies and thermal stability of binary systems of cholesteric liquid crystals

The binary mixture of cholesteryl oleyl carbonate (COC) and cholesteryl nonanoate (CN) with different ratios has been characterized by differential scanning calorimetry (DSC) to determine the phase diagrams. Their normal shelf-life and accelerated stability studies were also examined. A novel microscopic Fourier-transform infrared (FT-IR) spectrometer equipped with DSC was also used to measure simultaneously the chemical structural variation and the thermal response of these liquid crystals. The results indicate that the binary mixture might transform from smectic to cholesteric and then to isotropic liquid (CN composition <50%); from solid to cholesteric and then to isotropic liquid (CN composition >50%). Therefore, the 50% CN composition might play a critical role in the phase transition of the binary COC-CN mixture. The microscopic FT-IR/DSCsystem could also confirm the phase transition, but could measure the phase trasition temperature of liquid crystals more easily and sharply than the DSC method. The long-term accelerated thermal stability of the COC-CN mixture seemed to be more constant when stored at 4 °C than in any other temperature conditions.     

Thermodynamic analysis of the decomposition of a supersaturated solid solution of the Fe-Cu system

The structure of Fe-5.5% Cu alloy is studied after eutectoid reaction and aging of the martensite. The thermodynamic analysis of decomposition of the supersaturated solid solution with copper release is peformed for different types of crystal lattice. The free energy of solid solutions and phase separation diagrams of the BCC and FCC phases of copper is calculated. Barriers for the nucleation of copper particles with BCC and FCC lattices are evaluated. The factors that favor the appearance of intermediate structural forms of copper preceding the formation of stable FCC phase are discussed.     

The phase behavior of mixed lipid membranes in the presence of the rippled phase

We propose a model describing liquid-solid phase coexistence in mixed lipid membranes by including explicitly the occurrence of a rippled phase. For a single component membrane, we employ a previous model in which the membrane thickness is used as an order parameter. As function of temperature, this model properly accounts for the phase behavior of the three possible membrane phases: solid, liquid and the rippled phase. Our primary aim is to explore extensions of this model to binary lipid mixtures by considering the composition dependence of important model parameters. The obtained phase diagrams show various liquid, solid and rippled phase coexistence regions, and are in quantitative agreement with the experimental ones for some specific lipid mixtures.     

A lattice-gas hamiltonian for micellar binary solutions

An explicit Ising-spin lattice Hamiltonian is proposed as a model for studying the phase diagrams of micellar binary solutions on the micellar length scale. Incorporating many essential features, it can be used to check the validity of a previously suggested scenario for nonuniversality at the consolute point.     

Pressure-temperature phase diagrams for several modified lead zirconate ceramics

Using dielectric constant and loss measurements we have determined the pressure-temperature phase diagrams of four ferroelectric ceramics based on lead zirconate (PbZrO₃). The materials chosen for study all have pressure-induced ferroelectric to antiferroelectric transitions at ∼0.3 GPa. In all four materials, five phases were identified by comparing our results with studies, previously published by other workers, of the phase behavior of modified PbZrO₃ materials as a function of composition and temperature. The observed phases are the ideal cubic perovskite paraelectric phase, two rhombohedral ferroelectric phases, and two antiferroelectric phases, one orthorhombic and one pseudotetragonal. Comparison is made with previous temperature-composition studies of modified PbZrO₃ materials.     

Phase separation of highly dissymmetric binary ionic mixtures

We study the phase separation of binary ionic mixtures involving two species of classical point ions in a rigid uniform neutralizing background of degenerate electrons. The thermodynamic properties of the ionic fluid are calculated on the basis of the HNC integral equation for the three partial pair distribution functions. We develop a systematic technique which allows the properties of mixtures of arbitrary composition to be expressed in terms of infinitely dilute solutions. Phase diagrams and critical parameters are determined for 12 different binary systems involving ionic charge ratios between 2 and 8. The dependence of the critical temperature on the ionic charges, on the pressure and an ionic quantum corrections is examined in detail.     

Computer-assisted analysis and calculation of phase diagrams of the Fe---Cr---O, Fe---Ni---O and Cr---Ni---O systems

Available thermodynamic and phase equilibrium data for the Fe---Cr---O, Fe---Ni---O and Cr---Ni---O systems are assessed and equations for the free energies of the phases as functions of composition and temperature are derived. With these mathematical expressions and with a computer program written for the purpose, phase diagram sections at constant temperature, or at constant log p_O2, or at constant P_co/P_co2 or p_H2/P_H2O ratios can be calculated at all compositions and over a wide range of temperature and oxygen potential. The representation and analysis of the phase equilibria are greatly facilitated through the use of isothermal log P_O2-composition phase diagrams which are discussed in some detail. Structural models for the spinel phases are examined.     

Universal intermediate phases of dilute electronic and molecular glasses

Generic intermediate phases with anomalous properties exist over narrow composition ranges adjacent to connectivity transitions. Analysis of both simple classical and complex quantum percolation shows how topological concepts can be used to understand many mysterious properties of high temperature superconductors, including the remarkably similar phase diagrams of La(2-x)Sr(x)CuO4 and C60(+y). Predictions are made for novel threshold behavior of the impurity band metal-insulator transition in two dimensions.     

Thermodynamics of III–V solutions with n components

A method has been developed for the calculation of phase diagrams of III–V mixtures with more than three components. The equations for the chemical potentials, activity coefficients and the free energy of the mixture and for the liquidus- and iso-solidus-concentration lines are given. The parameters, needed for the calculation, are the temperature of fusion, heats of fusion, and the interaction parameters. The interaction parameters can be fitted to datas of the binary or quasi-binary phase diagrams, or can be calculated using the electronegativities, energies of sublimation and molar volumes of the constituent elements.Two approaches for a mixture with n components are given, which give in the ternary and binary case the known equations. The two possible cases of quaternary III–V solutions are discussed explicitly.     

The Improved Subregular Model and the Phase Diagram of a Binary System

In thia paper an improved subregular model is proposed. Using the thermodynamic theory the equations describing liquid-solid phase equilibrium curve are obtained. For some typical phase diagrams of a binary system we give their predictive criteria of the phase diagram type. We enumerate 4 binary alkali halide systems, their phase diagrams are calculated respectively, this improved model is tested. The results calculated show that the agreement between the theoretical phase diagram and its corresponding experimental points is good.     

Thermodynamics of the phase equilibrium of multicomponent solid solutions containing nano-sized precipitates of the second phase

Based on the theory of regular solutions, the interphase boundary model for the case of an arbitrary number of components is developed. General relations for the calculation of the phase composition of multicomponent solutions containing nano-sized precipitates of the second phase are derived. By the example of binary and ternary solutions, it is shown that a considerable mutual enrichment of the conjugated phases by atoms of components dissolved in them occurs in the case if precipitates of the second phase are characterized by the sizes of the order of several nanometers.     

High temperature XRD studies of nanoscale AgI-CuI solid solutions

A preliminary high-temperature X-ray diffraction (HT-XRD) study of the nanometer-sized solid solution phases in the AgI-CuI system is reported through an extended range of temperatures (300-723K) covering phase transitions in both AgI and CuI. A major feature of this work is the observation of the coexistence of the zincblende and base-centred cubic phases of AgI over an extended range of temperatures the temperature width being a function of Cu content in the binary. The lattice parameters derived from HT-XRD data reflect systematics of phase transitions with progressive Cu substitution of AgI. The present results are discussed together with our earlier ionic conductivity, dilatometry and DSC data which have helped deduce phase diagrams for both the Ag-rich and Cu-rich regions of the binary.     

THERMODYNAMICS OF EQUILIBRIUM AND STABILITY

The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions of equilibrium and stability with the help of Lagrange's multipliers. The conditions of stability are expressed in several alternative forms. Next the equilibrium properties of a binary system arc considered, and some types of phase diagram are explained by means of equations. The theory is extended to the general heterogeneous equilibrium of a system consisting of any number of independent components. A system of equations for the change of temperature, pressure, and composition are obtained and are solved by means of determinants. Next Planck's theory of a binary solution is extended to a solution consisting of several solnte components, with the same conclusion regarding the lowering of freezing point as for a binary solution. Finally Planck's theory on the number of coexisting phases for aone-component system is extended to a system consisting of k components with the result that a state with, σ coexisting phases is more stable than one with σ-1 phases: where σ is an integer not greater than k + 2.     

Domain growth in ternary fluids: A level set approach

We analyze phase separation in ternary systems in the asymptotic hydrodynamic regime when the volume fractions and concentrations are constant. The multiphase Navier-Stokes equations are solved using a level set method. A new projection method was developed to treat multiple junctions for systems with more than two phases. It is found that surface tension ratios can alter the growth mechanism of a minority phase in the presence of two majority phases. When the minority phase wets the interface of the majority phases the domain growth rate of all three phases is initially similar to that of a symmetric binary fluid but slows down at later times.     

Mixed micellar aggregates of nonionic surfactants with short hydrophobic tails

Mixed micelle formation by aqueous mixtures of pentaethylene glycol monohexyl ether (C₆E₅) and diethylene glycol monohexyl ether (C₆E₂) has been investigated by determining the temperature-composition phase diagrams and measuring the intradiffusion coefficients. In binary aqueous solutions, C₆E₅ shows a high tendency to micellize, while C₆E₂, because of its too short hydrophilic head, presents a macroscopic phase separation in a water-rich and a surfactant-rich phases. The temperature-composition phase diagrams obtained for the ternary water-C₆E₅---C₆E₂ mixtures present a micellar region in which both surfactants co-aggregate. The dimensions of this micellar region depend on the relative ratio between the two surfactants molalities. By analysing the micelle intradiffusion coefficient, measured through the PGSE-NMR technique, the hydrodynamic radius of the aggregates has been estimated at 25 °C. It is similar to that of triethylene glycol monohexyl ether (C₆E₃) in binary aqueous solution. The experimental evidences suggest that in mixed ethoxylated surfactants the micellar behaviour is mainly determined by the mean number of ethoxylic units per surfactant molecule, independently of their distribution.     

Interaction properties of the periodic and step-like solutions of the double-Sine-Gordon equation

The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter epsilon. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter epsilon is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.     

Tuning the phase diagrams: the miscibility studies of multilactate liquid crystalline compounds

Design of binary and multicomponent liquid crystalline mixtures is a very powerful tool to reach the desired self-assembling properties. Beyond many advantages, this method has a distinct negativity – it is very material-consuming. While working with unique chiral materials in the research laboratory, this problem can be solved by applying miscibility study by the contact preparation method. In this work, the miscibility studies of lactic acid derivatives and non-chiral/chiral liquid crystalline molecules of different structure have been done in order to establish the phase diagrams. Special attention is focused on the ferro(antiferro)electric smectic phases.     

Composition and thermodynamic properties of thermal plasma with condensed phases

The initial relations of a method for calculating the composition and thermodynamic properties of a closed heterogeneous system in thermodynamic equilibrium at constant pressure and temperature are given. The gaseous phase is always present in the system, and substances in the condensed state can also be present, which are divided into several condensed phases. The essence of the method consists in the minimizing the Gibbs energy of a system in ideal state. The application possibilities of the method described are discussed in detail. The main aim of the article is to provide solutions to problems arising in the calculations of composition and thermodynamic properties. These problems are not only of physico-chemical nature but they also relate to the numerical calculations and stability. The nature of the problems is general and independent of computation method.     

X-Ray studies of phase diagrams of the system Mn-Cr-O in air

X-Ray analysis was made of solid solutions and heterogeneous compositions of the general formula Mn_3?xCr_xO_m (0?x ? 3, Δx = 0.05). Subsolidus portions of the high temperature phase equilibria diagram and the diagram of water-quenched phases of the system Mn-Cr-O in air were established in the temperature range 700–1400°C. Comparative analysis of these diagrams has revealed the mechanism of the processes occurring upon rapid cooling of the system (in water and in air in a ceramic crucible) from high temperatures to room temperature. Rapid cooling is shown to preserve the phase composition and crystal structure of nonspinel phases, but for equilibrium solid solutions with spinel or hausmannite structure, this is not always the case. Depending on the quench temperature and the solution composition the following phenomena are observed: (1) tetragonal distortion of a high temperature phase with spinel structure; (2) merging of a tetragonally distorted spinel and spinel and formation of a homogeneous phase with hausmannite structure; (3) decomposition of the homogeneous phase with spinel structure into two spinel-type phases with spinel and hausmannite structures. Possible causes of these phenomena are discussed.