Phase equilibria

First-principles phase equilibria calculations often overestimate an order-disorder transition temperature due to the neglect of local lattice distortion effects originated from the mixture of elements of different atomic sizes. The lattice vibration effects introduced through the Debye-Grü neisen theory within the quasi-harmonic approximation has proven to be quite effective in circumventing the inconveniences. With the preferential enhancement of the stability of a disordered phase by introducing the lattice vibration effects, the transition temperature was reduced considerably. In order to gain further insight into the lattice vibration effects, a systematic investigation of the vibrational free energy of the Debye-Grü neisen theory is attempted on the two-dimensional square lattice which constitutes a prototype study prior to the firstprinciples calculations on realistic alloy systems. A particular focus of the present study is placed on the effects of Debye temperatures of constituent phases on the transition temperature. It is shown that lattice softening by lattice vibration stabilizes the disordered phase by reducing the energy expended to accommodate atoms of different sizes, which is manifested by the reduction of the curvature of the atomic potentials. It is, however, predicted that an opposite case can also take place. When the Debye temperature of an ordered phase is lower than that of the pure metals, the ordered phase is more stabilized and the inclusion of the lattice vibration effects in the free energy raises the resultant transition temperature.

Microstructural changes in a metallic oxidation protection coating (Ni-Co-Cr-Al-Y) applied on a nickel base superalloy were investigated by means of scanning and transmission electron microscopy. The changes are due either to thermal mechanical fatigue testing under high thermal gradients or to defined isothermal heat treatments. The coated specimens were quenched from temperatures between 840 and 1100 • C to ambient temperature. The resultant phases, their local distribution and compositions were determined by energy dispersive X-ray (EDX) spectroscopy and electron diffraction. Phase equilibria at respective temperatures were determined by thermodynamic calculations based on the CALPHAD method. The calculated and experimentally determined phase distributions were compared. A particular microstructural feature, namely the existence and spatial distribution of spherical ␥ Ni 3 Al precipitates in the coating and the diffusion zone between substrate and coating, was used as a postmortem indicator for the maximum temperature experienced by the specimen during testing. This paper gives a road map for developing a microstructural-based temperature calibration for complex metallic materials using thermodynamic simulations.

... K–Ar dating has placed a lower limit of 0.6 Ma on the age of Soufriere [35 ... Crustal contamination is also well documented from some of the central Lesser Antilles islands such as Martinique [30] and [40]where the lavas define a good positive array on diagrams of SiO 2 versus 87 ...

The isothermal ternary phase diagram for the 1-dodecylpyridinium bromide/dodecane/water system was determined at 40°C by 2 H NMR and polarizing microscopy methods. Two liquid crystalline phases, a large cubic area and a normal hexagonal phase, and one isotropic normal micellar solution phase were characterized, and their ranges of existence were determined. The micelles were found to be probably small and spherical at lower concentrations of surfactant, and were found to grow at higher concentrations and on addition of oil. The two-phase areas, L 1 ؉ H I and H I ؉ I, are both very narrow. The comparatively large cubic area, containing 43-63 wt% surfactant and 3-10 wt% dodecane, is probably consistent of more than one structure. SAXS experiments indicate two different structures built of discrete micellar aggregates.

The effect of tin content in the equilibrium phases of the Cu-Zn-based alloys, within the range of chemical compositions with interest to brass producers is described. For this purpose, ternary alloys with copper contents between 55.4 and 67.5 wt.% and tin contents up to 5.30 wt.% have been studied. The chemical composition of each alloy has been determined by X-ray fluorescence spectrometry (XRF). Isothermal homogenization, followed by rapid cooling, has been employed to determine the equilibrium phases at different temperatures. The homogenized alloys have been observed by scanning electron microscopy and the respective chemical analysis of the phases determined by electron probe microanalysis (EPMA). The statistical analysis of the obtained results enable to correlate the chemical composition of equilibrium phases with temperature. The chemical composition of the three-phase field, for the studied temperatures, has also been determined.

We study the liquid structure and solvation forces of dense monovalent electrolytes (LiCl, NaCl, CsCl, and NaI) in a nanometer slab-confinement by explicit-water molecular dynamics (MD) simulations, implicit-water Monte Carlo (MC) simulations, and modified Poisson-Boltzmann (PB) theories. In order to consistently coarse-grain and to account for specific hydration effects in the implicit methods, realistic ion-ion and ion-surface pair potentials have been derived from infinite-dilution MD simulations. The electrolyte structure calculated from MC simulations is in good agreement with the corresponding MD simulations, thereby validating the coarse-graining approach. The agreement improves if a realistic, MD-derived dielectric constant is employed, which partially corrects for (water-mediated) many-body effects. Further analysis of the ionic structure and solvation pressure demonstrates that nonlocal extensions to PB (NPB) perform well for a wide parameter range when compared to MC simulations, whereas all local extensions mostly fail. A Barker-Henderson mapping of the ions onto a charged, asymmetric, and nonadditive binary hard-sphere mixture shows that the strength of structural correlations is strongly related to the magnitude and sign of the salt-specific nonadditivity. Furthermore, a grand canonical NPB analysis shows that the Donnan effect is dominated by steric correlations, whereas solvation forces and overcharging effects are mainly governed by ion-surface interactions. However, steric corrections to solvation forces are strongly repulsive for high concentrations and low surface charges, while overcharging can also be triggered by steric interactions in strongly correlated systems. Generally, we find that ion-surface and ion-ion correlations are strongly coupled and that coarse-grained methods should include both, the latter nonlocally and nonadditive (as given by our specific ionic diameters), when studying electrolytes in highly inhomogeneous situations.

The cloud point curve, tie-lines and interfacial tensions were measured for solutions of 50 mol-Yo neutralized (counter-ion Na@) poly(ary1ic acid) (mass-average molar mass M , = 9700 g/mol; polydispersity index a,/M, = 2,O) in the mixed solvent water/2-propanol at 30 "C.

We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarsegrained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.

Complex equilibria and phase transformations involving diffusion can now be calculated quickly and efficiently. Detailed examples are given for cases which involve varying degrees of non-equilibrium and therefore time-dependence. Despite very good agreement between such calculations and experimental results, many potential end-users are still not convinced that such techniques could be usefully applied to their own specific problems. Friendly graphic interface versions of calculating software are now generally available, so the authors conclude that the most likely source of the reluctance to use such tools lies in the formulation of relevant questions and the interpretation of the results. Although the potential impact of such tools was foreseen many years ago [M. Hillert, Calculation of phase equilibria, in: Conference on Phase Transformations, 1968], few changes in the relevant teaching curricula have taken into account the availability and power of such techniques. This paper has therefore been designed not only as a collection of interesting problems, but also highlights the critical steps needed to achieve a solution. Each example includes a presentation of the "real" problem, any simplifications that are needed for its solution, the adopted thermodynamic formulation, and a critical evaluation of the results. The availability of such examples should facilitate changes in subject matter that will both make it easier for the next generation of students to use these tools, and at the same time reduce the time and effort currently needed to solve such problems by less efficient methods. The first set of detailed examples includes the deoxidation of steel by aluminum; heat balance calculations associated with ladle additions to steel; the determination of conditions that avoid undesirable inclusions; the role of methane in sintering atmospheres; interface control during the physical vapour deposition of cemented carbide; oxidation of γ-TiAl materials; and simulation of the thermolysis of metallorganic precursors for Si-C-N ceramics and interface reaction of yttrium silicates with SiC-coated C/C-SiC composites for heat shield applications. A second set of examples, more dependent on competitive nucleation and growth, includes segregation and carburization in multicomponent steels and features a series of sophisticated simulatons using DICTRA software. Interfacial and strain energies become increasingly important in defining phase nucleation and morphology in such problems, but relatively little information is available compared to free energy and diffusion databases. The final section therefore demonstrates how computational thermodynamics, semi-empirical atomistic approaches and first-principles calculations are being used to aid filling this gap in our knowledge.

The pseudopotential method and the thermodynamic perturbation theory are applied to construct the phase diagram of the eutectic system Cd-Zn. The Einstein model approximation in the solid phase and the hard sphere approximation in the liquid phase are chosen as reference systems. Satisfactory agreement of the calculated phase separation curves with experimental data is observed. A correlation between the position of the phase separation curves and the thermodynamic characteristics of the components is found. An analysis of the contributions to the mixing energy is made, and the correlation between the mixing energy and the mixing volume is established.

ray diffraction data show that these carboxylates reflect all the cases from localization of the electron on one atom to complete delocalization of the electron over the three sites. These results are in good accord with the Moessbauer spectral data for these compounds. Study of the temperature dependence of the Moessbauer spectra permits an independent conclusion concerning the state of the iron atoms .

A computer algorithm has been developed to determine the cloud and shadow point curves of polydisperse polymer/solvent systems using continuous thermodynamics to represent the polymer. The algorithm is based upon the work of Michelsen [M.L. Michelsen, Fluid Phase Equilibria, 4 (1980), pp. 1–10] and Koak [N. Koak, Polymer Solution Phase Behaviour, PhD Thesis, University of Calgary, Calgary, 1997] where a Newton–Raphson procedure is used to solve the equations defining phase equilibrium for fixed phase segment fractions between 0 and 1. The equations have been developed with the Sanchez–Lacombe equation of state which allows the continuous system to be defined by a set of five equations in five unknowns. Numerical integration is used to determine the values of the indefinite integrals involved. The cloud and shadow curves for a polydisperse polyethylene/n-hexane system were found at 6 bar using both a log-normal distribution and a Schulz–Flory distribution to represent the polyethylene. Compositions of the cloud point curve covered the entire composition range showing the model's behavior in high temperature regions, a hypothetical liquid–vapour critical point and a three-phase point when the log-normal distribution was used. The cloud and shadow point curves of a polyethylene/ethylene system were also found and indicated a high pressure critical point.

Cryovolcanism is among the foremost processes responsible for modifying the surfaces of icy satellites. Volcanic brine petrogenesis in ammonia-deficient satellites should mainly involve eutectic melting in relevant salt-water systems. Carbonaceous chondrites provide useful insights into the compositions of salts and aqueously altered rock in icy satellites and asteroids. C l chondrites contain about one-fifth by mass of salts in various states of hydration. Many aspects of the petrogenesis and physical volcanology of icy satellite brines should be well described in the system H20-MgSO4-NazSO4. Minor components include sulfates of K, Ni, Mn, and Ca. Chondrites also contain abundant carbonates, but these are probably not very important in brine magmatism due to their low solubilities under expected conditions. Chlorides are also unimportant under most circumstances because of the low cosmic abundance ratio of CI/S. Soluble salts may have profound effects on the geology and structure of icy satellites and asteroids. In some models late episodes of water volcanism are facilitated by high buoyant forces due to the relatively high densities of sulfate-rich mantle and crustal layers. In other models early hypersaline brine volcanism quickly yields to plutonic magmatism due to low crustal densities. Europa probably has a layered crust composed of anhydrous Mg-Na sulfates near the base and a frozen or partially molten eutectic mixture of ice and hydrated Mg and Na sulfates near the surface. Ganymede may have a crust about 300 km thick composed of a I0:1 ratio of ice:mirabilite, and a mantle 500 km thick composed of 50% ice phases plus 50% hydrated Mg and Na sulfates. :,

In Part I, various models for the prediction of the occurrence and stability of Laves phases have been discussed. In the present Part II paper, an overview is given on the various types of manifestation of Laves phases in intermetallic alloy systems with emphasis on transition metal systems. Temperature-and composition-dependent as well as stress-induced phase transformations between the cubic C15 and the hexagonal C14 and C36 structural polytypes of Laves phases were observed in various binary and ternary systems. The phase fields of the different polytypes are generally separated by small two-phase fields. Some general rules for the occurrence of the different Laves phase polytypes are derived from a study of the results of experimental phase diagram investigations of various binary and ternary systems. The solubilities and site occupancies of ternary additions in the different Laves phase polytypes and the mutual miscibility of different binary Laves phases are discussed. The need for careful experimental investigations of phase equilibria is demonstrated. Existing models discussed in the preceding Part I paper are shown to fail to predict the structure and stability of the presented Laves phases in many cases. q

Low temperature adiabatic calorimetry and high temperature differential scanning calorimetry have been used to measure the heat-capacity of ilmenite (FeTiO 3) from 5 to 1000 K. These measurements yield S2980 = 108.9 J/( mol · K). Calculations from published experimental data on the reduction of ilmenite yield Δ2980( I1) = -1153.9 kJ/( mol · K). These new data, combined with available experimental and thermodynamic data for other phases, have been used to calculate phase equilibria in the system Fe-Ti-O. Calculations for the subsystem Ti-O show that extremely low values of ƒO 2 are necessary to stabilize TiO, the mineral hongquiite reported from the Tao district in China. This mineral may not be TiO, and it should be re-examined for substitution of other elements such as N or C. Consideration of solid-solution models for phases in the system Fe-Ti-O allows derivation of a new thermometer/oxybarometer for assemblages of ferropseudobrookite-pseudobrookite ss and hematite-ilmenite ss. Preliminary application of this new thermometer/oxybarometer to lunar and terrestrial lavas gives reasonable estimates of oxygen fugacities, but generally yields subsolidus temperatures, suggesting re-equilibration of one or more phases during cooling.

The solid + liquid phase equilibria between α-Al and β-AlLi were determined using differential thermal analysis (DTA), metallography, and chemical analysis. Boron nitride (BN), which was found to be inert to these alloys, was used as the container. These measurements were carried out in order to resolve the discrepancies reported in the literature. The α-Al+β-AlLi eutectic temperature and composition were

The low-temperature heat capacity and thermodynamic properties of the solid-to-solid transition and fusion of di-isobutyl ether (DIBE) were determined by adiabatic calorimetry in the temperature range from (8 to 373) K. The saturation vapor pressure of DIBE was determined by a comparative ebulliometry over the moderate pressure range from (10.8 to 99.6) kPa. A density of liquid DIBE was measured in the temperature interval from (298 to 313) K using a quartz pycnometer. The normal boiling temperature, T n.b. , the enthalpy of vaporization at T ) 298.15 K and T n.b. , and the ideal gas thermodynamic functions (changes of the entropy, enthalpy, and Gibbs energy) at T ) 298.15 K were derived. Appropriate thermodynamic functions over a wide temperature range from (150 to 1000) K and the standard enthalpy of formation at T ) 298.15 K were computed by the methods of statistical thermodynamics (ST) and the density functional theory (DFT) on the level B3LYP/6-31G(d,p). The experimental data on the vapor pressure of DIBE were extended to the entire range of liquid phase from the triple to the critical temperatures by the corresponding states law and combined treatment of the pT-parameters and the low-temperature differences between the heat capacities of the ideal gas and liquid. The data on thermodynamic properties of some branched ethers, C 5 to C 9 , studied earlier and in this work were critically analyzed for verification of their reliability and mutual consistency.

Experlmental studles of vapor-tlquld, vapor-IJquWIqukl, and llquld-llqukl equllibrla In the system dlmethyl ether/water (DME/H20) have been carded out at 14 temperatures In the range 50-220 OC and pressures up to 50.9 m a . The data have been obtained by uslng a vapor-rechculatlng apparatus operatlng at Isothermal condltlons. The phase dlagram for thls system exhlblts a three-phase region of vapor-llquld-llquid equllbrlum, endlng at an upper crltlcal end polnt where the vapor phase and the M E -r k h UquM phase become Identical.

An algorithm for the construction of phase diagram sections is formulated that is well suited for geodynamic problems in which it is necessary to assess the influence of phase transitions on rock properties or the evolution and migration of fluids. The basis of the algorithm is the representation of the continuous compositional variations of solution phases by series of discrete compositions. As a consequence of this approximation the classical non-linear free energy minimization problem is trivially solved by linear programming. Phase relations are then mapped as a function of the variables of interest using bisection to locate phase boundaries. Treatment of isentropic and isothermal phase relations involving felsic and mafic silicate melts by this method is illustrated. To demonstrate the tractability of more complex problems involving mass transfer, a model for infiltration driven-decarbonation in subduction zones is evaluated. As concluded from earlier closed system models, the open-system model indicates that carbonates are likely to persist in the subducted oceanic crust beyond sub-arc depths even if the upper section of the oceanic mantle is extensively hydrated. However, in contrast to more simplistic models of slab devolatilization, the open-system model suggests slab fluid production is heterogeneous and ephemeral. Computed seismic velocity profiles, together with thermodynamic constraints, imply that for typical geothermal conditions serpentinization of the subducted mantle is unlikely to extend to N 25 km depth and that the average water-content of the serpentinized mantle is b 2 wt.%.

General properties of aluminium alloys of the rare earth metals are briefly summarised. Their phase equilibria and the crystal structures of the different intermediate phases are presented and discussed. The results obtained in the experimental investigation of the Y-Al and Sm-Al systems are reported. The formation enthalpies of YA12 and SmAlz have been re-measured, resulting in-50.5kJ/(mol at) and-55.0kJ/(mol at) at room temperature, in a good agreement with literature data. Phase equilibria investigation in the Sm-Al system has been carried out and the results obtained via thermal analysis, micrographic examination, microprobe and X-ray diffraction analyses described and discussed in the framework of the general behaviour of the rare earth alloys. The experimental Sm-Al phase diagram, collated with previous literature data, is compared with the results of a thermodynamic optimisation. The following inter-metallic compounds exist: Sm2Al (peritectic decomposition, at 860°C) SmAl (per.dec.960"Q SmAl2 (melting point 148O"Q SmAls (peritectoidal decomposition at 113o"C), SmsAlr , (melting point-1380°C). The following eutectic equilibria have also been determined or confirmed: 20 at% Al and 760°C 75 at% Al and 134O"C, 97.0 at%Al and 635°C. A eutectoidal equilibrium occurs at 10 at% Al and 700°C.

A thermodynamic description of the Al-Ca-Sr system is carried out using the modified quasichemical model. The three binary systems Al-Ca, Al-Sr, and Ca-Sr have been re-optimised based on the experimental phase equilibria and thermodynamic properties available in the literature. Good agreement was obtained for the calculated binary phase diagrams and their thermodynamic properties. The established database of this system predicted one saddle point, one peritectic, seven quasi-peritectics, and two ternary eutectics.

A thermodynamic description is presented for the ternary Cu-Al-Si system in its copper-rich corner. The thermodynamic parameters of the subsystems , Cu-Al, Cu-Si and Al-Si, are taken from earlier SGTE-based assessments and those of the ternary system are optimized in this study by using the experimental mixing enthalpy and phase equilibrium data. The present ternary description is valid for aluminum contents up to 18 wt% and silicon contents up to 8 wt%.

An extension of the transferable potentials for phase equilibria-united atom (TraPPE-UA) force field to acrylate and methacrylate monomers is presented. New parameters were fit to the liquid density, normal boiling point, saturated vapor pressure, and (where experimentally available) critical constants of 1,3-butadiene, isoprene, methyl acrylate, and methyl methacrylate using Gibbs ensemble Monte Carlo simulations. Excellent agreement with experiment was obtained for the parametrization compounds and seven additional acrylate and methacrylate compounds, with average errors in liquid density and normal boiling point of approximately 1%. The TraPPE-UA force field also predicts accurate heats of vaporization at 298 K. In addition, Gibbs ensemble Monte Carlo simulations of binary vapor-liquid equilibria for the mixtures methyl acrylate/1butanol and methyl acrylate/n-decane show that the TraPPE-UA acrylate force field performs well in mixtures with both polar and nonpolar molecules. These simulations also indicate structural microheterogeneity in the liquid phase of these mixtures.

The precipitation of different forms of magnesium carbonate has been studied at temperatures between 25 and 120 • C and at a partial pressure of CO 2 between 1 and 100 bar. These conditions are relevant for mineral carbonation applications. Precipitation was triggered by the supersaturation created by mixing Na 2 CO 3 solutions in equilibrium with a CO 2 atmosphere with MgCl 2 solutions. Experiments were monitored using attenuated total reflection Fourier transform infrared (ATR-FTIR) and Raman spectroscopy as well as a focused beam reflectance measurement (FBRM) probe and a turbidimeter. Solubility and supersaturation were calculated using the software package EQ3/6. Solids were identified using X-ray diffraction (XRD) analysis and scanning electron microscope (SEM) images. At 25 • C and P CO 2 = 1 bar, only the hydrated carbonate nesquehonite (MgCO 3 · 3H 2 O) precipitates, as it has previously been observed. Solutions undersaturated with respect to nesquehonite did not form any precipitates in experiments lasting 16 h. Induction times increased with decreasing supersaturation with respect to nesquehonite. At 120 • C and P CO 2 = 3 bar, hydromagnesite ((MgCO 3 ) 4 · Mg(OH) 2 · 4H 2 O) was formed which transformed within 5-15 h into magnesite (MgCO 3 ). Solutions undersaturated with respect to brucite (Mg(OH) 2 ) did not form any precipitates in experiments lasting 19 h. At 120 • C and P CO 2 = 100 bar, direct formation of magnesite and, at elevated levels of supersaturation, the co-precipitation of magnesite and hydromagnesite has been observed. In the latter case, hydromagnesite transformed within a few hours into magnesite. Solutions undersaturated with respect to hydromagnesite did not form any precipitates in experiments lasting 20 h. ᭧

The cubic-plus-association equation of state (CPA EoS) has been extended to phase equilibria of industrially important binary mixtures of alcohol-hydrocarbon, alcohol/glycol-water systems and mixtures with organic acids. The ability of the model to predict different types of equilibria was tested. Very satisfactory VLE and SLE prediction is achieved for alcohol-hydrocarbon systems, while the sensitivity of the LLE to the interaction parameter is demonstrated. It has been shown that CPA can perform VLE/LLE/SLE calculations in the case of alcohol-hydrocarbon binary systems with a single interaction parameter. Satisfactory SLE correlation of alcohol/glycol-water systems is achieved using a single interaction parameter over an extended temperature range. Moreover, satisfactory prediction was achieved for the multiphase equilibria of the mixture acetic acid-water-hexane based solely on binary interaction parameters.

The text is written for undergraduate materials science students and can be utilized by materials-related graduate students who have not taken such a course in their undergraduate studies. It has been more than 40 years since I used the first edition of the text when teaching my first class in thermodynamics at Carnegie Mellon University. I also used the text in the mid-1990s in several summer school classes on thermodynamics at CMU. Experience makes me aware that it is impossible to make
it through the entire text in a one-semester course. In this edition, I have divided the book into three sections. I suggest that at least the first section (“Thermodynamic Principles”) and as much as possible of the second section (“Phase Equilibria”) be included in a one-semester undergraduate course. The third section (“Reactions and Transformations”) can make its way into other courses of the curriculum that deal with oxidation, energy, and phase transformation.

We present a thermodynamic evaluation of the yttrium-oxygen (Y-O) system by focusing on the thermodynamic properties of the Y O phases. A review of the experimental data on phase equilibria in the Y-O system and the thermodynamic properties of the Y O 2 3 2 3 phases pertinent to the evaluation is provided. The transition properties of Y O have been assessed by considering systematic trends in 2 3 the thermodynamic behaviour of rare earth sesquioxides and scandia. With the evaluated data, the phase relations and thermodynamic properties of the Y-O system can be calculated and are in good agreement with the majority of experimental measurements.

A mathematical model is developed to simulate the drying of hygroscopic porous media and, in particular, of wood. Drying rate experiments were performed using wood specimens and a nonhygroscopic porous ceramic solid and were simulated using the appropriate version of the drying model. Calculated model predictions are in very satisfactory agreement with experimental results. An examination of the relative impacts on drying of the transport mechanisms that comprise the model leads to meaningful interpretations of observed drying behavior. Controlling rate factors can be identified and different types of drying behavior specific to a given material or drying condition can be explained and understood through model simulation studies. Such capability can provide important guidance for drying process design and control.

The steady state simulators, used for on-line performance prediction and for on-line optimization in crude distillation units are often sensitive to small variations in the feed composition, which is specified in terms of a True Boiling Point (TBP) vs volume percent distilled curve. The exact feed TBP is often not available during the plant operation. Also stratification of raw crude oil into layers in the large tank farm sections cause severe operating problems in terms of the stability of the column. If feed TBP can be predicted online, necessary feedforward action can considerably reduce the operating problems. A model has been developed for backcalculation of feed TBP using measured plant parameters. A heat balance is performed around an envelope encompassing the rectifying section of the fractionator and is followed by the calculation of Equilibrium Flash Vaporization (EFV) temperatures at six different locations of the column which are correlated with corresponding feed TBP temperatures. The second part of model tuning consists of calculating model parameters in the form of point efficiencies so as to minimize the discrepancy between the simulator predicted and measured column parameters which arises out of modelling approximations such as assumption of phase equilibria at each stage and use of imperfect thermodynamics correlations. The simulator results, after tuning, were found to match the plant measurements within two percent in all the cases investigated. The simulator output was used to predict various product properties using a Property Prediction package and these were also found to match well with those of laboratory measurements. Both the backcalculation of feed TBP and the efficiency tuning need to be implemented on-line for inferential control and supervisory optimization. #

Our recently completed wide-ranging correlations for the tbermophysical properties of methane and ethane fluids have enabled us to improve the extended corresponding states calculations for the properties of the binary mixtures. The pure fluid equations are based on the analytic Schmidt-Wagner equation of state and give improved results in the general region of the critical point. We use these pure fluid equations (and a reference fluid for which an equivalent equation is known) to calculate properties and compare with experimental PVT data, isochoric heat capacities, and sound speeds of binary mixtures of methane and ethane. We also examine the properties at the vaporliquid boundary and compare the representation from the classical extended corresponding states calculations with quantities derived from a scaling theory model. The shape of the binary mixture phase boundary is improved with this model, however our new representation of the single phase properties provides only a slight improvement over models based on modified Benedict-Webb-Rubin pure fluid equations of state.

Natural gas production from a gas reservoir (Reservoir A) located in the south of Iran, presents solids deposition during processing because the condensate contains suspended and dissolved solids. Solids deposition occurs not only in the transportation lines from the wells to the separators but also in the various operating units of gas streams and condensate stream. In this study, the multisolid-phase model has been used to predict the wax precipitation from gas and gas condensate fluids. The properties of gas and liquid phases are described using the Soave-Redlich-Kwong (SRK) equation of state. The model is then used to predict the possibility of the wax formation in Reservoir A gas facilities, located at the south of Iran. Solid deposition which occurred in the various streams of that facility confirmed the calculated results. Finally, the wax appearance temperature (WAT), the weight percent of wax formation and the effects of pressure and temperature on the wax formation were also predicted.

Solvents like propane and carbon dioxide have been studied in previous works at supercritical and subcritical conditions and also as highpressure liquid solvents for the extraction of lipids and oils. Propane is completely miscible with vegetable oils at room temperature but has liquid-liquid phase equilibrium with typical vegetable oils at temperatures between the lower critical end point (LCEP) and the upper critical end point (UCEP)-around 340 K and 370 K. In this temperature range, the propane solvent power for triglycerides is drastically reduced unless higher pressures are used to recover the single phase region.

Phase equilibria in the CaO-CuO system have been determined at 1 atm pressure in oxygen over the temperature range 800" to 1300°C. CaO is the stable phase at the calcium-rich end of the system. Two intermediate crystalline phases, namely Ca,CuO, and Ca,Cu,O,,, form. Ca,CuO, is stable up to 1085" f 3"C, where it melts incongruently to CaO + liquid (peritectic liquid has -82% CuO). Ca,Cu,O,, becomes stable at 977" f 3°C by reaction between Ca,CuO, and CuO. Ca3Cu,0,, melts incongruently at 1046" % 3°C to Ca,CuO, + liquid (peritectic liquid has -83% CuO). CuO is the stable copper oxide phase up to 1061" +-3°C at the copper-rich end of the system; at higher temperatures, Cu,O is stable until the liquidus is reached at 1121°C. The binary eutectic is at 1045" f 5"C, in which a liquid with 83% CuO coexists with Ca,Cu,O,, and CuO.

The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database (+/-550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/-750 cals).

The vapor pressure of a pure liquid or of a solution is a property that has been observed since antiquity. Here, we trace the different equations that have been suggested to describe the variation of the vapor pressure with the temperature, until the time when Antoine proposed his equation, a functionality that has survived the test of time and is the one mostly widely used today.

We report a complete set of thermodynamic properties of the interface layer between liquid and vapor two-component mixtures, using molecular dynamics. The mixtures consist of particles which have identical masses and diameters and interact with a long-range Lennard-Jones spline potential. The potential depths in dimensionless units for like interactions is 1 (for component 1) and 0.8 (for component 2). The surface excess entropy decreases when the temperature increases, so the surface has a negative excess heat capacity. This is a consequence of the fact that the surface tension decreases to zero at the critical point, proportional to ðT C,i ÀTÞ 2n. The surface entropy decreases also as the excess concentration of component 2 increases, at a given temperature. The surface becomes less able to store energy as the more volatile component accumulates. We show that the more volatile component 2 has a maximum in its excess concentration in the interfacial region when the density of component 1 starts to go down. The vapor is described with the Soave-Redlich-Kwong equation of state, and the liquid activity coefficients are described by the three-suffix Margules equation. The observed densities and surface tension variations are fitted with good accuracy, with the critical exponents b ¼ 0:32 and 2n ¼ 1:26, respectively. The results for the critical temperature of mixtures can be fitted to a second order polynomial, with significant deviations from Kay's rule.

The equilibrium phase diagram of the Si-Ga system is shown in . The diagram includes a eutectic transformation at a temperature very close to the melting point of Ga (29.7741 ~ The solid solubility of Ga in (Si) is retrograde, with a maximum solubility of 0.1 at.% Ga near 1200 ~ Si exhibits no appreciable solid solubility in (Ga). The Si-Ga phase diagram was investigated by thermal analysis [48Kle] and by thermal analysis and metallography [58Sav]. [48Kle] did not specify the purity of the materials used in their experiments, and [58Sav] indicated the purity to be 99.99% Ga and 99.6% Si. Liquid solubilities were determined by a weighing technique in the temperature range 300 to 800 ~ by [53Kec] and [77Girl; [77Girl specified only the purity of Ga as 99.999%, and [53Kec] gave no information in this regard. The temperature-composition coordinates of the liquidus listed in Table 1 have been taken from [48Kle], [53Kec], and [77Girl; the data of [58Sav] seem to be questionable (the authors claimed the eutectic point to be at 20 ~ and 1.2 at.% Si).

Reservoir hydrocarbon fluids contain heavy paraffins that may form solid phases of wax at low temperatures. Problems associated with wax formation and deposition are a major concern in production and transportation of hydrocarbon fluids. The industry has directed considerable efforts towards generating reliable experimental data and developing thermodynamic models for estimating the wax phase boundary.

Phase relations in the ternary oxide system Al 2 O 3 -V 2 O 5 -MoO 3 in the solid state in air have been investigated by using the x-ray diffraction (XRD) and differential thermal analysis/thermogravimetric (DTA/TG) methods. It was confirmed that in the subsolidus area of the Al 2 O 3 -V 2 O 5 -MoO 3 system, there exist seven phases, that is Al 2 O 3 , V 2 O 5(s.s.) , MoO 3 , AlVO 4 , Al 2 (MoO 4 ) 3 , AlVMoO 7 , and V 9 Mo 6 O 40 . Seven fields, in which particular phases coexist at equilibrium, were isolated. The crystal structure of AlVO 4 has been refined from x-ray powder diffraction data. Its space group is triclinic, P " 1, Z = 6, with a = 0.65323 nm, b = 0.77498(2) nm, c = 0.91233(3) nm, a = 96.175(2)°, b = 107.234(3)°, c = 101.404(3)°, V = 0.42555 nm 3 . The crystal structure of the compound is isotypic with FeVO 4 . Infrared (IR) spectra of AlVO 4 and FeVO 4 are compared.

The Cu-O system shows complete miscibility between the metallic liquid and the oxide liquid above ~1623 K and a miscibility gap below that temperature. Because of the practical importance of the system, a wealth of experimental data exists, both on the phase diagram and on the thermodynamic properties. These data have been reviewed, and a consistent set of thermodynamic model parameters has been optimized. An ionic two-sublattice model was used to describe the liquid phase and was found to represent accurately the experimental data.

In the present paper, a general survey of the diffusion-controlled transformations (DICTRA) software is given. DICTRA is an engineering tool for diffusion simulations in multicomponent alloys. The simulations are based on multicomponent diffusion and thermodynamic data, both obtained by analyzing and assessing experimental information. This allows for many different cases to be studied as soon as the underlying data are available. DICTRA is not a complete simulation tool because only geometries that can be transformed into one space variable can be treated, but many well posed problems of practical interest may be solved. The program contains several different models, which are discussed in the present paper. Each model has its own applications and several examples from recent simulations are given in order to demonstrate the usage of the particular models.