Lattice parameters and melting behavior of the B2-phase in the ternary gold-cadmium-zinc system

Lattice parameter and DTA-measurements were performed in the range of the ternary B 2-phase in the gold-cadmium-zinc system. It could be shown that a continuous range of homogeneity exists between β′-AuCd and β′-AuZn. Lattice parameter values are reported for a number of compositions. The ternary liquidus projection is given between about 40 and 60 at % Au. The congruent melting point of the binary β′-AuZn phase was found to be at 51.5±0.5 at % Au and 758±3°C.     

Experimental investigation and thermodynamic prediction of the Al–Ge–Zn phase diagram

The knowledge of the phase diagram of the Al?CGe?CZn ternary system is of importance in the development of high temperature soldering materials. In this study, the phase diagram of the Al?CGe?CZn ternary system was calculated by the calculation of phase diagrams method using binary thermodynamic parameters included in the COST MP0602 thermodynamic database. Chosen alloys with compositions along two vertical sections with molar ratio Al/Ge?=?3/1 and 1/3 were measured using DTA (differential thermal analysis). The experimentally determined phase transition temperatures from this work and phase equilibria data from literature were compared with calculation results and good mutual agreement was noticed.     

A thermodynamic analysis on the coincidence of extrema conditions in the sorption equilibrium for ternary polymer systems

Flory-Huggins theory of polymer solutions has been used to express the condition of extrema values in the total sorption, as well as the inversion point in the preferential adsorption parameters for termary polymer systems. Two approaches have been followed, the first considers the binary and ternary interaction parameters independent of polymer concentration and solvent composition. In the second one, this dependence has been introduced. Our attention is focused on the volume fraction of solvent mixture dependence of the above parameters, in order to confirm or not the coincidence between the extrema values and the inversion point. Several cosolvent and cononsolvent ternary polymer systems, have been used to test the validity of the equations obtained. Also, it has been verified, from an experimental point of view, that in cosolvent ternary polymer systems there is coincidence in both compositions while in cononsolvent ternary polymer systems, such coincidence does not appear.     

The prediction of isothermal phase equilibria for non-ideal multicomponent mixtures from heats of mixing

A method is presented for predicting both vapor—liquid and liquid—liquid equilibria for multicomponent mixtures using heat of mixing data for the constituent binary pairs together with pure component vapor pressures. Its application to two highly non-ideal hydrocarbon ternary systems is discussed. The parameters of the hybrid local composition model of Renon and Prausnitz, known as the NRTL equation, were evaluated from heat of mixing data for the three binary pairs in each of the two ternary systems. The parameters thus obtained were used in the multicomponent form of the NRTL equation to predict the ternary vapor—liquid equilibrium data for the completely miscible system cyclohexane(1)—n-heptane(2)—touluene(3) and for the partially miscible system acetonitrile(1)—benzene(2)—n-heptane(3) without the need for any ternary or higher order parameters.This method predicted compositions of the single phase region of the partially miscible ternary system with a standard deviation of 10%. It also predicted compositions for the fully miscible system with a standard deviation of 4.6%. Total pressure curves for the partially miscible and miscible ternaries were predicted with standard deviations of 6.6% and 4.5% respectively. Poor predictions of the binodal curve for the partially miscible region were obtained. The method offers a means of predicting the whole range of ternary phase equilibria for miscible systems.     

Correlation and Calculation of Multicomponent Adsorption Equilibria Data Using a Generalized Adsorption Isotherm

Enhanced by the need for reliable and accurate data of multicomponent gas adsorption equilibria on porous solids like activated carbons or zeolites, a new method to measure and correlate coadsorption equilibria has been developed. This method is a combination of gravimetric or volumetric measurements of the total load of pure or multicomponent adsorbates (Staudt, 1994; Gregg and Sing, 1982) and a correlation and calculation procedure using a new adsorption isotherm (AI) (Keller, 1990). This AI is thermodynamically consistent and describes adsorbates with fractal dimension for single- or multicomponent systems and load dependent adsorption energies. This method allows calculation of partial loads of multicomponent coadsorption equilibria from pure component data and the total loads of the mixture adsorption equilibria. This will be demonstrated for binary and ternary adsorption equilibria of CH₄, C₂H₄ and C₂H₆ on activated carbon (Reich et al., 1980).     

Measurement of vapor-liquid equilibria and determination of azeotropic point

Hiaki, T., Tochigi, K. and Kojima, K., 1986. Measurement of vapor—liquid equilibria and determination of azeotropic point. Fluid Phase Equilibria, 26: 83–102.To measure the azeotropic point, a liquid-vapor ebullition type equilibrium still is developed. Vapor-liquid equilibria at 101.325 kPa are measured for the ternary azeotropic system benzene - cyclohexane - n-propanol, and the three constituted binary azeotropic systems. A method is introduced for graphical determination of the binary azeotropic point on the basis of experimental binary vapor-liquid equilibrium data. Also, a method is evolved for determination of the binary and ternary azeotropic points by using the extended Redlich-Kister equation applicable to the condition of constant pressure, and the azeotropic points are determined for three binary and one ternary systems.     

Subsolidus Phase Relations in the ZnO-BaO-V2O5 System

The subsolidus phase relations of the ZnO-BaO-V2O5 ternary systems were investigated by means of X-ray diffraction analysis. There are three ternary compounds, nine binary compounds and sixteen 3-phase regions found in this system. The crystal structure of the ternary compound Ba2ZnV2O8 was refined by Rietveld profile fitting method and the powder diffraction pattern is given. A new ternary compound Ba3.4Zn0.8V4O14.2 has been found by the powder diffraction pattern.     

Diphasic Domains Approach Method (DDAM)

If someone wants to plot an isobaric temperature-composition binary or an isobarothermal section of a ternary equilibria phase diagram he only needs to plot the limits of diphasic domains, it automatically gives the limits of the monophasic and triphasic fields. In such diagrams each diphasic domain is defined by two lines joining all the extremities of the tie-lines of the domain and limited by the first and the last one. These tie-lines are segments whose the extremities are in the plane of the diagram and can easily be determined by equilibria calculation codes. Then binary or ternary phase diagrams can be plotted only using conodes of the diphasic fields and the method used to determine the diphasic domains becomes the main point in binary and ternary phase diagrams plotting. A meshing of the surface of the diagram is certainly not the best way to obtain a rapid result. We propose an approach which consists to follow the curvature of the diphasic domains limits, the ‘Diphasic Domains Approach Method, DDAM’, which allows a rapid and robust determination of binary and ternary diagrams.     

Eine σ-Phase im System Chrom—Molybdän—Silicium

A ternary σ-phase (Cr_0.39–0.57Mo_0.47–0.29Si_0.14) has been detected in the chromium—molybdenum—silicon system at 1500 °C. The novel σ-phase, which displays only a small degree of ordering, undergoes eutectoid decomposition at ca. 1200 °C, into (Cr, Mo)+(Cr,Mo)₃Si. The relative stability bility of the ternary σ-phase and the non-existing binary σ-phases (Cr?Si, Mo?Si) were estimated from the observed equilibria. With respect to the coexistent phases there is an amount of 2500 cal/g atom metal necessary for stabilizing of the ternary σ-phases at 1500 °C. The slight deviation from completely random distribution reflects on the entropy change and there is fair agreement with the entropy change calculated from the temperature dependency of ΔG _{z, σ}.     

A modified clausius equation of state for calculation of multicomponent refrigerant vapor-liquid equilibria

Gow, A.S., 1993. A modified Clausius equation of state for calculation of multicomponent refrigerant vapor-liquid equilibria. Fluid Phase Equilibria, 90: 219-249.

A modified Clausius equation of state with a single temperature dependent energy-volume parameter a(T) in the attractive term was designed to describe the vapor pressure vs. temperature relationship of 39 pure refrigerant fluids including elementary cryogenic materials (e.g. He, Ar, N₂, CO₂, CH₄, etc.), chlorofluorocarbons (CFCs), hydrofluorocarbons (HFCs), hydrochlorofluorocarbons (HCFCs), fluorocarbons (FCs), and various other simple cryogenic compounds. The equation developed represents the vapor-liquid coexistence dome, and the superheated vapor compressibility factor and enthalpy for pure refrigerants.

The vapor-liquid equilibrium for refrigerant mixtures is calculated using a “phi-phi” method with “one fluid” van der Waals mixing and combining rules for the equation of state parameters a_M(T), b_M and c_M. A single interaction constant k₁₂ is used to describe non-ideal behavior of each binary. The binary interaction constant, which is a strong function of temperature, and the sign of which signifies the type of deviations from Raoult's law, is obtained by correlating experimental bubble point data for isothermal binary refrigerant mixtures. The proposed equation of state generally describes binary P-x,y data more accurately the higher the temperature for a given system. The method presented is extended to predict vapor-liquid equilibria for the R14-R23-R13 ternary system at 198.75 K using binary interaction constants at this temperature for the three binaries involved.     

Single crystal growth of Bi1−xSrxMnO3—Thermodynamics and experiment

The primary crystallization field of a perovskite solid solution Bi_1−xSr_xMnO_3−δ was delimited by calculating the respective phase equilibria in the quaternary Bi–Sr–Mn–O system. The calculations are based on the recent assessment involving all three ternary subsystems, a quaternary liquid approximated as a mixture of Mn, MnO, Mn₂O₃, SrO and Bi₂O₃ species with binary Redlich–Kister coefficients and the perovskite phase described in terms of a point defect model allowing Sr²⁺ for Bi³⁺ substitution, oxygen vacancy formation and the related Mn³⁺/Mn⁴⁺ mixing on Mn-sublattice. The crystallization path and the composition of the crystallized solid solution are compared with single crystal growth experiments performed by self-flux method from a Bi-rich melt. The crystallization path obtained for a selected feed composition for which the largest and high quality single crystal have been grown, turns out to end very close to the global eutectic point.     

Calculation for liquid-liquid equilibria of quaternary alkane-ethyl acetate-methanol-water systems used in counter-current chromatography

The calculation of liquid-liquid equilibrium compositions of solvent systems is very important for the work on counter-current chromatography (CCC), especially the phase composition and volume ratio obtained from liquid-liquid equilibrium calculation. In this work, liquid-liquid equilibria of quaternary Arizona solvent systems, alkane-ethyl acetate-methanol-water, and related ternary systems are correlated and predicted using the non-random two-liquid model (NRTL). Hexane, heptane and isooctane are the used alkanes. The parameters in the model are regressed only with the special systems considered. Detailed comparison with experimental data shows that liquid-liquid equilibria of these systems can be predicted with greatly improved accuracy as compared to the group contribution method (UNIFAC).     

Modification of the NRTL model for ternary and quaternary liquid-liquid equilibrium calculations

The original NRTL model is modified for the correlation of ternary liquid-liquid equilibria. The ternary expression of the modified NRTL model includes three additional ternary parameters and the ternary terms vanish when a ternary system degenerates to a binary. The ability of the modified NRTL model has been evaluated in the calculations of ternary vapor-liquid-liquid equilibria and quaternary liquid-liquid equilibria.     

Thermodynamic studies of drug-alpha-cyclodextrin interactions in water at 298.15 K: promazine hydrochloride/chlorpromazine hydrochloride + alpha-cyclodextrin + H(2)O systems

Data on osmotic coefficients have been obtained for a binary aqueous solution of two drugs, namely, promazine hydrochloride (PZ) and chlorpromazine hydrochloride (CPZ) using a vapor pressure osmometer at 298.15 K. The observed critical micelle concentration (cmc) agrees excellently with the available literature data. The measurements are extended to aqueous ternary solutions containing fixed a concentration of alpha-cyclodextrin (alpha-CD) of 0.1 mol kg(-1) and varied concentrations (approximately 0.005-0.2 mol kg(-1)) of drugs at 298.15 K. It has been found that the cmc values increase by the addition of alpha-CD. The mean molal activity coefficients of the ions and the activity coefficient of alpha-CD in binary as well as ternary solutions were obtained, which have been further used to calculate the excess Gibbs free energies and transfer Gibbs free energies. The lowering of the activity coefficients of ions and of alpha-CD is attributed to the existence of host-guest (inclusion)-type complex equilibria. It is suggested that CPZ forms 2:1 and 1:1 complexed species with alpha-CD, while PZ forms only 1:1 complexed species. The salting constant (ks) values are determined at 298.15 K for promazine-alpha-CD and chlorpromazine-alpha-CD complexes, respectively, by following the method based on the application of the McMillan-Mayer theory of virial coefficients to transfer free energy data. It is noted that the presence of chlorine in the drug molecule imparts better complexing capacity, the effect of which gets attenuated as a result of hydrophobic interaction. The results are discussed from the point of view of associative equilibria before the cmc and complexed equilibria for binary and ternary solutions, respectively.     

Freezing point and heating curve behavior for an organic reciprocal salt pair system

Binary and quasi-binary freezing point data have been obtained to establish the freezing point diagram for the ternary reciprocal salt pair system involving cyclohexylamine stearate, cyclohexylamine palmitate, 2,2'-dipyridylamine stearate, and 2,2'-dipyridylamine palmitate. The compositions and primary freezing points of the ternary peritectic and eutectic mixtures have been determined Apparent anomalies in the heating curves for selected compositions have been explained on the basis of the existence of metastable equilibria.     

Influence of solid surface on equilibria in polymer mixtures

The influence of solid disperse particles (aerosil) on phase equilibria in ternary (polymer-polymer-solvent) and binary (polymer-polymer) systems has been investigated using adsorption and gas chromatography techniques. The change in position and shape of the binodal for the ternary systems has been established. The region of thermodynamic compatibility of two polymers in a common solvent is broadened due to the selective adsorption of high molecular weight fraction of one of the polymers, this effect being dependent on the amount of solid particles introduced into the system. For binary systems, the thermodynamic interaction parameters χ₂₃ have been determined and increasing thermodynamic stability of the mixture in the presence of the solid phase has been discovered. The complicated dependences of the interaction parameters on mixture composition are connected with differences in selectivity of adsorption for various compositions. It is supposed that increased thermodynamic stability of a mixture of two incompatible polymers in the presence of solid is due to the transition of both polymers into adsorption and border layers.     

Ternary complexes of palladium(II) and selected amines

Summary The formation and equilibria of the binary and ternary palladium(II) complexes of diethylenetriamine (dien) with other selected amines have been investigated. The results of pH titration measurements allowed the calculation of equilibrium constants, characteristic for the binary and ternary complexes formed. The concentration distribution of various complex species was evaluated and the chelation mode ascertained by conductivity measurements.     

Phase equilibria of the ternary system vinyl acetate/(R,S)-1-phenylethanol/carbon dioxide at high pressure conditions

Phase equilibrium measurements, correlations and predictions are presented for the binary systems (R,S)-1-phenylethanol/CO₂ and vinyl acetate/CO₂ and for the ternary system vinyl acetate/(R,S)-1-phenylethanol/CO₂. Experiments for the ternary system were performed in the temperature range of 323–343 K and in the pressure range of 7–12 MPa, using a high pressure phase equilibrium apparatus with a high pressure visual variable volume cell. Phase compositions were determined by taking samples of each phase and analysing them by gas chromatography. Equilibrium data were correlated with the Peng–Robinson equation of state combined with the Mathias–Klotz–Prausnitz mixing rule. A good correlation of both phases behaviour was obtained with an average absolute deviation (AAD) of 6.80%. Predictions for the binary sub-systems and for the ternary system were performed using the Peng–Robinson and the Soave–Redlich–Kwong equation of state, with the predictive mixing rule MHV1.