Molecular models for the vapor-liquid equilibrium of simple binary mixtures

Simple analytical expressions are proposed for the calculation of the equilibrium pressure, as well as (for a given temperature and pressure) the mole fractions of both liquid and vapor phases at the vapor-liquid equilibrium of binary mixtures. They are based on a recently proposed molecular model for the vapor pressure of pure nonpolar fluids, which, for a given temperature, only requires as input the values of the two Lennard-Jones (LJ) molecular parameters and the acentric factor, which are parameters related to the molecular shape of each substance and whose values are readily available. The model for the equilibrium pressure of a binary mixture (which also permits one to obtain the liquid phase mole fraction) is similar to that derived from Raoult’s law, where a properly modified Lorentz-Berthelot mixing rule is used, the interaction parameters being given as simple functions of the temperature and composition with eight appropriate constants for each binary mixture. A different model is needed to calculate the vapor mole fraction in which five appropriate constants are needed for each mixture. Here, we show how the models reproduce accurately and straightforwardly the vapor liquid equilibrium properties (pressure, liquid mole fraction, and vapor mole fraction) of eight binary systems over a broad temperature range, including some data at or near the critical locus.     

Application of vacuum distillation in refining crude indium

Vacuum distillation is a technique suitable for low boiling and melting point materials,to remove the heavy and low vapor pressure impurities at low level.As indium has low melting point and high boiling point,it is suitable for refining by vacuum distillation.First,saturation vapor pressure for major elements in crude indium was calculated by the Clausius–Clay Prang equation,which could approximately predict the temperature and pressure during vacuum distillation process.Second,the activity coefficients for In–Cd,In–Zn,In–Pb,In–Tl at 1373 K,and In–Sn at 1573 K were acquired by means of molecular interaction on volume model.Vapor–liquid equilibrium composition diagrams of those above systems in crude indium were drawn based on activity coefficients.These diagrams could estimate the compositions of products in each process during the refinement of crude indium.Finally,1.2–1.6 ton crude indium was used per day when vacuum distillation experiments were carried out,and experimental results are in good agreement with the predicted values of the vapor–liquid equilibrium composition diagrams.     

Theoretical research on vacuum separation of Au−Ag alloy

To provide an accurate prediction of the product component dependence of temperature and pressure in vacuum distillation and give convenient and efficient guidance for the designing of the process parameters of industrial production, according to the molecular interaction volume model (MIVM), the separation coefficient (β) and vapor?liquid equilibrium composition of Au?Ag alloy at different temperatures are calculated. Combined with the vapor?liquid equilibrium (VLE) theory, the VLE phase diagrams, including the temperature?composition (T?x) and pressure?composition (p?x) diagrams of Au?Ag alloy in vacuum distillation are plotted. The triple points and condensation temperatures of gold and silver vapors are calculated as well. The results show that the β decreases and the contents of gold in vapor phase increase with the distillation temperature increasing. Low pressures have positive effect on the separation of Ag and Au. The difference between the condensation temperatures of gold and silver is about 450 K in the pressure range of 1?10 Pa.     

Change law of real vapor pressure of Al element in Ti-xAl （x = 25～50） melt during ISM process

A new model was established to calculate the real vapor pressure of the AI dement in the molten Ti-xAl (x=25～50, mole fraction, % ) alloy. The effects of the holding time, chamber pressure, mole fraction of AI and melting temperature on the real vapor pressure of AI element in the vacuum chamber were analyzed. Because of the impeding effect of the real vapor pressure on the evaporation loss rate, within a short time (less than 10s), the real vapor pressure tends to a constant value. When the chamber pressure is less than the saturated vapor pressure of the AI component, the real vapor pressure of Al is equal to the chamber pressure. While when the chamber pressure is larger than the saturated vapor pressure, the real vapor pressure is equal to the saturated vapor pressure of the Al element of the same condition.     

分子相互作用体积模型在真空蒸馏分离铅-锡-锑三元合金中的应用

基于分子相互作用体积模型(MIVM),计算Pb?Sn?Sb三元合金体系的活度,并使用活度系数计算真空蒸馏过程中Pb?Sn?Sb三元合金体系的气液相平衡。结果表明：随着蒸馏温度和液相中锡含量的增加,气相中锡含量也不断增加;然而,在1100°C液相中锡含量为97%(质量分数)时,气相中锡含量仅为0.45%,分离效果较好。在真空(10 Pa)条件下,在1100~1300°C蒸馏温度范围内进行真空蒸馏分离Pb?Sn?Sb三元合金实验。结果表明：在1100°C时,当液相中锡含量为97%时,气相中锡含量为0.54%。最后对比分析了实验结果和预测值,分析表明实验结果和预测值吻合较好。     

Manometric method for the study of P-T-X diagrams

A new null-manometric method has been elaborated and applied for investigations fo the systems with the low-volatile compounds. The essence of this method is in obtaining the phase diagram for low-volatile binary compounds using the temperature dependence of equilibrium nonsaturated vapor pressure, formed by a third (auxiliary) component, which is put in contact with the investigated system. The aim of applying the third component assumes its reversible chemical interaction with one of the components of a weakly volatile compound. This compound component is converted into vapor (in the form of a compound with the auxiliary component) and the composition of a condensed part of the system is changed. Controlling equilibrium with temperature adjustment makes possible control of the disappearance of some of the condensed phases and formation of the others. Changes in equilibrium when employing this process are clearly observed in the temperature dependence of the vapor pressure. From the data, it is possible to trace the correlation between the total vapor pressure and the composition of binary condensed phases, as well as the correlation between the total and partial pressures. The overall results allow determination of the phase diagram. In the present work, the phase diagrams of the Ga-Se and Ga-S systems have been investigated using iodine and chlorine as third components (in the initial form of GaHal₃). It has been shown that at temperatures up to ∼1080 K the homogeneity region for GaSe is 0.12±0.04 at.%, and it is completely shifted toward an excess of gallium. The boundary of the phase homogeneity region from selenium is close to stoichiometric composition. Gallium monosulfide is characterized by a more narrow range of homogeneity commensurable with the error of determination of the composition in the performed experiments (0.04 at.%). The temperature dependencies of equilibrium constants K _p and the values of gallium partial vapor pressure over solid gallium sulfides and selenides were calculated. For the equilibrium involving solid GaSe, solid Ga₂Se₃, and their vapor, the calculated partial vapor of gallium was shown to be independent of the nature of the third component.     

Manometric method for the study of P-T-X diagrams

A new null-manometric method has been elaborated and applied for investigations fo the systems with the low-volatile compounds. The essence of this method is in obtaining the phase diagram for low-volatile binary compounds using the temperature dependence of equilibrium nonsaturated vapor pressure, formed by a third (auxiliary) component, which is put in contact with the investigated system. The aim of applying the third component assumes its reversible chemical interaction with one of the components of a weakly volatile compound. This compound component is converted into vapor (in the form of a compound with the auxiliary component) and the composition of a condensed part of the system is changed. Controlling equilibrium with temperature adjustment makes possible control of the disappearance of some of the condensed phases and formation of the others. Changes in equilibrium when employing this process are clearly observed in the temperature dependence of the vapor pressure. From the data, it is possible to trace the correlation between the total vapor pressure and the composition of binary condensed phases, as well as the correlation between the total and partial pressures. The overall results allow determination of the phase diagram. In the present work, the phase diagrams of the Ga-Se and Ga-S systems have been investigated using iodine and chlorine as third components (in the initial form of GaHal₃). It has been shown that at temperatures up to ～1080 K the homogeneity region for GaSe is 0.12±0.04 at.%, and it is completely shifted toward an excess of gallium. The boundary of the phase homogeneity region from selenium is close to stoichiometric composition. Gallium monosulfide is characterized by a more narrow range of homogeneity commensurable with the error of determination of the composition in the performed experiments (0.04 at.%). The temperature dependencies of equilibrium constants K _p and the values of gallium partial vapor pressure over solid gallium sulfides and selenides were calculated. For the equilibrium involving solid GaSe, solid Ga₂Se₃, and their vapor, the calculated partial vapor of gallium was shown to be independent of the nature of the third component.     

多元合金耦合热力学数据非等温凝固的相场模拟

研究一种多元合金的非等温相场模型,定量地模拟工业多元合金的真实凝固过程,结合热力学和扩散迁移率的数据来预测整个系统中的相平衡、溶质扩散系数、比热容和放出的潜热。结果表明：这些参数不是常数,它们的值与成分和温度有关。没有这些参数,定量模拟多元合金的凝固几乎是不可能。在这个模型中,界面区域假设是由有同样化学势的固相和液相混合而成的,但组成不同。这个模型中同样考虑反溶质截流。一并将模型应用到工业Al?Cu?Mg合金的各向枝晶自由长大的凝固过程。     

A model for work of solid–liquid adhesion in multicomponent melts

The thermodynamic work of solid–liquid adhesion in multicomponent melts is important in many fields. Quantitative calculation of the work of solid–liquid adhesion has not, however, been well developed. A model for quantitative calculation of the work of solid–liquid adhesion in a multicomponent melt has been proposed based on the expansion of the Maclaurin infinite series in the neighborhood of each pure component of the binary alloy. The parameters used in this model are assessed through the statistical thermodynamic model of surface and interface tensions, which is based on the monolayer approximation for metal–vapor and metal–solid interfaces and Bragg–Williams statistics. According to the present model, the work of adhesion–concentration dependency over the whole concentration range for binary alloy can be theoretically determined from only the physical parameters of the pure components. The model has been successfully applied to calculate the work of adhesion for various solid–liquid systems.     

Zinc Electroplating in the Presence of Mixtures of o-Oxyazomethine Derivatives

Variations in the potential and current of zinc electroplating as functions of the nature of substituents in the molecules of mixture of o-oxyazomethine derivatives are described based on the linear of Gibbs energy relation. Polar effect of substituents is estimated from partial polar constants by taking into account the mole fraction of each component of the mixture.     

Zinc Electroplating in the Presence of Mixtures of o-Oxyazomethine Derivatives

Variations in the potential and current of zinc electroplating as functions of the nature of substituents in the molecules of mixture of o-oxyazomethine derivatives are described based on the linear of Gibbs energy relation. Polar effect of substituents is estimated from partial polar constants by taking into account the mole fraction of each component of the mixture.     

沉积参数对Mo-Re合金基体上沉积金刚石薄膜的影响

采用热丝化学气相沉积法(HFCVD),以甲烷和氢气为反应气体,在综合性能良好的Mo-40%Re(摩尔分数)合金基体上沉积金刚石薄膜.采用X射线衍射仪(XRD)、场发射扫描电子显微镜(FESEM)和显微激光拉曼光谱仪(Raman)分别对金刚石薄膜相组成、表面形貌、晶粒大小和质量等进行检测分析,研究CVD沉积参数,如基体温度(θs)、碳源浓度(R,Cn4的体积分数)和沉积压强(p),对金刚石形核、生长和金刚石成膜的影响.结果表明在合适的基体预处理条件下,当θs=750℃,R=-3%,p=3.5kPa时,薄膜平均线生长速率高达1μm/h,得到的金刚石膜完整致密,晶粒大小均匀,纯度较高,具有明显的(111)织构.     

Evaporation of multi—components in Ti—25Al—25Nb melt during induction skull melting process

Based on activity calculation model, t he activity coefficients of Ti, Al and Nb components of Ti-25Al-25Nb (mole fraction, %) melt, the vapor pressu res of correspo nding components and the evaporation loss rates were calculated. Utilizing these activity coefficients and the vapor pressures, the relative evaporation coeffic ient is used to judge the evaporation tendency of these components. The evapora tion tendency among the three components were compared and the result shows that the evaporation tendency is that: AlTi>Nb. Evaporation loss rate increases with the increase of melting temperature and decreases with the increase of chamber pressure. There exists an impeding pressure pimpe of Al element evapo ration during induction skull melting process of Ti-25Al-25Nb alloy. The impeding pressu re can be written as pimpe=8.1pe, where perepresents the equilibrium partial pressure. The calculation of evaporation loss of Al element also showed that when chamber pressure exceeds pimpe, the Al volatilization losses could be ignored. In order to prevent the evaporation loss of components, the pressure in the vacuum chamber should not below pimpe.     

Phase equilibrium in binary aqueous mixtures of interest in alcoholic distillation using a modified PSRK equation of state

Phase equilibrium in binary mixtures that are found in wine and must distillation processes have been modeled using the predictive Soave-Redlich-Kwong equation, with original and modified molecular parameters. In wine and must distillation, the presence of polar substances found in the mixture to be distilled and the many components (i.e., those different from ethanol and water), called congeners, makes it difficult to model these mixtures. Thus, the prediction and correlation of the concentration of the distilled product, which is the most interesting variable, become very complex, and some experimental data are needed. The cases studied considered nine binary water + congener mixtures. The congeners considered are acetic acid, acetaldehyde, ethyl acetate, furfural, methanol, 3-methylbutanol, 2-methyl-1-propanol, 1-pentanol, and 1-propanol. These are the substances that are considered to be legal compounds by the Chilean legislation governing the production of a spirit called Pisco. The work allows evaluation of the advantages, disadvantages, and expected accuracy of this model. Comparison with available literature data is done.     

Equilibrium Pressure Measurements Above ZnS from 680° to 825°C

The pressure of the gas in equilibrium with sphalerite has been determined in the temperature range of 680° to 825°C, using the Knudsen orifice method. A comparison of these experimental pressures with those calculated from thermal data and from other equilibrium measurements shows that the vapor above sphalerite is predominantly dissociated ZnS. Equations have been given for correctly calculating dissociation pressures using the Knudsen orifice method. It has been shown that the experimentally determined pressure is the same, whether the zinc sulphide is sphalerite or not, or a mixture of wurtzite and sphalerite.     

The effect of system volume limitation on the surface tension of a vapor–liquid interface

The effect of the system volume limitation on the thermodynamic characteristics of a vapor–liquid interface, that is, the phase states of a substance and the surface tension, is considered. The molecular theory is used based on the lattice gas model, which describes the two-phase state of a vapor–liquid system. To simplify the calculations, the molecular characteristics of the spherical interface of a drop inside a spherical region of vapor having a single dimensional parameter, namely, the radius of the system, are assessed. It is found that, when the radius of the system decreases, the critical temperature decreases, while the internal pressure, the chemical potential, and the surface tension increase.     

Fluctuation theory of microheterogeneous systems in the molecular-field approximation

Principles of the fluctuation theory of microheterogeneous systems are considered based on the example of adsorption on a heterogeneous surface of microcrystals and spherical liquid droplets in the vapor phase. Equations that describe the equilibrium distributions of molecules are derived within the lattice gas model with allowance for lateral interactions in the mean-field approximation. This approximation does not take into account the correlation effects of interacting particles. We discuss the structure of entropy and energy contributions in the derived equations and the relationship between the molecular chemical potential and the expansion pressure, which is analogous to the equation of the state, as well as the molecular interpretation of the concept of pressure in an ensemble of small particles and its relation to the mechanical interpretation of the surface tension.     

钽表面离子渗氮工艺研究

采用组合的二次回归正交设计方法,针对表面硬度、表面粗糙度,对钽表面离子渗氮工艺参数（气体压力、温度、氢气摩尔分数）进行了优化。根据回归结果和统计分析给出了回归方程。     

Static equilibrium model for the bead formation in high speed gas metal arc welding

On the basis Of the Young-Laplace Equation that describes the pressure difference betweeneach side of acurved liquid surface,a static equilibrium model is established to describe the surface shape of the weld bead.The geo-metrical model for the molten pool is included,which is essential to explain the undercut phenomenon during high speedbead-on-plate welding.The results got from an iteration algorithm show that it is the force balance on the liquid mixtureof the deposited metal and the deposited metal and the molten base metal and the molten base metal that causes the undercut.Some factors and their effects are also ana-lyzed.     

Surface tension of liquid Ag-Sn alloys: Experiment versus modeling

The maximum bubble pressure method has been used to measure the surface tension of pure tin and seven binary alloys with concentrations of 15, 30, 40, 60, 75, 87.8, and 96.2 at.% Sn. Measurements were performed at the temperature range from 500 to about 1400 K depending on the composition of the investigated alloy. Densities of the Ag-Sn alloys were measured dilatometrically. The linear dependencies of densities and surface tensions on temperature were observed, and they are described by a straight-line equation. Experimental data of the surface tensions were compared with calculations using Butler’s model, which assumes an equilibrium between the bulk phase and the monolayer surface phase. Excess Gibbs energies of silver and tin necessary in calculations were taken from the optimized thermodynamic parameters reported recently from Tohoku University. It is shown that the calculated surface tension data from the optimized thermodynamic parameters of the liquid phase of the Ag-Sn are in good agreement with the experimental results.