Application of molecular interaction volume model in separation of Pb-Sn-Sb ternary alloy by vacuum distillation

Based on the molecular interaction volume model （MIVM）, the activities of components of Pb Sn Sb ternary alloy were predicted. The vapo^liquid phase equilibrium of Pb-Sn-Sb alloy system was calculated using the activity coefficients of Pb Sn-Sb alloy system in the process of vacuum distillation. The calculated results show that the content of Sn in vapor phase increases with the increasing distillation temperature and content of Sn in liquid phase. However, the content of Sn in vapor phase is only 0.45% （mass fraction） while 97% in liquid phase at 1100 ℃, which shows that the separating effect is very well. Experimental investigations on the separation of Pb-Sn-Sb ternary alloy were carried out in the distillation temperature range of 1100-1300 ℃ under vacuum condition. It is found that the Sn content in vapor phase is 0.54% while 97% in liquid phase at 1100 ℃. Finally, the predicted data were compared with the experimental results showing good agreement with each other.

Comparison of the Molecular Interaction Volume Model with the Wagner Formulae in the Zn-Pb-In and Zn-Sn-Cd-Pb Dilute Solutions

The coordination numbers in the molecular interaction volume model (MIVM) can be calculated from the commonphysical quantities of pure liquid metals. A notable feature of the model lie in its capability to predict the ther-modynamic properties of solutes in the Zn-Pb-In and Zn-Sn-Cd-Pb dilute solutions using only the binary infinitedilute activity coefficients, and the predicted values are in good agreement with the experimental data of the dilutesolutions.

PREDICTION OF THE MIXING ENTHALPIES OF BINARY LIQUID ALLOYS BY MOLECULAR INTERACTION VOLUME MODEL

The mixing enthalpies of 23 binary liquid alloys are calculated by molecular interaction volume model （MIVM）, which is a two-parameter model with the partial molar infinite dilute mixing enthalpies. The predicted values are in agreement with the experimental data and then indicate that the model is reliable and convenient.

Application of molecular interaction volume model in separation of Sn-Zn alloy by vacuum distillation

The activity of components of Sn-Zn binary alloy system was predicted based on the molecular interaction volume model （MIVM）. The calculated values are in good agreement with available experimental data of activities, which indicates that this model is of stability and reliability because the MIVM has a good physical basis. The vapor-liquid phase equilibrium of Sn-Zn alloy system in vacuum distillation was calculated as a function of the activity coefficient. The results show that the content of Sn in vapor phase is 4.2x 10-7 （mass fraction） while in liquid phase it is 90% （mass fraction） at 1 073 K, and the content of Sn in vapor phase increases with increasing the melt temperature and content of Sn in liquid phase. Vacuum distillation experiments were carried out on Sn-Zn alloy for the proper interpretation of the results of the MIVM in the temperature range of 973-1 273 K under pressures of 15-200 Pa. The experimental results show that the content of Sn in vapor phase is 5x 10 6 （mass fraction） while in liquid phase it is 90% （mass fraction） under the operational condition of 1 073 K, 100 rain and 15 Pa. The experimental results are in good agreement with the predicted values of the MIVM for Zn-Sn binary alloy system.

Comparison of the Molecular Interaction Volume Model with the Unified Interaction Parameter Formalism in the Fe-Cr-Ni Liquid Alloys at 1873 K

The molecular interaction volume model （MIVM） for a general ternary system was deduced in detail for further clarifying and understanding its general multicomponent expression. Both MIVM and the unified interaction parameter formalism （UIPF） can be used to predict the activities of solutes and solvents in the Fe-Cr-Ni liquid alloys. But the former employs only the infinite dilute activity coefficients, and the later is not applicable without the dilute binary and ternary interaction parameters. MIVM has a certain physical meaning from the viewpoint of statistical thermodynamics, so it is an alternative for the estimation of activity coefficients of the solutes and solvents in a dilute or finite concentration metal solution where the interaction parameters are absent or their accuracies are questionable.

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.

A thermodynamic model of solid solutions and its application in solid alloys

Based on the free volume theory, lattice model, the Scatchard–Hildebrand theory, novel expressions of configuration partition function and excessive Gibbs free energy and component activity coefficients of solid solutions were developed using configuration partition function and statistical thermodynamics of molecular interaction volume model (MIVM). Herein, the separation of the volume and energy parameters was achieved. The proposed model can reflect the contributions from both the molecular configuration micro-state number (entropy) and molecular interactions (enthalpy) toward excessive Gibbs free energy. The proposed equations are more consistent with the practical solid solutions. This model can use either the relevant binary infinite dilution activity coefficients or binary activity to describe and predict the thermodynamic properties of the multi-component solid solutions. Applications of the proposed model in some typical binary and ternary solid solution alloys revealed that the thermodynamic properties predicted by the proposed model were consistent with the experimental data and the proposed model was found to be superior to MIVM in terms of the prediction performance. Hence, it can be concluded that the proposed model exhibits good physical basis, applicability, stability and reliability.

An Estimation of Component Activity of Vanadium-bearing Liquid Iron and Transition Temperature of Vanadium Oxidization Using MIVM

The component activity of Mn in Fe-C-Mn system as well as the component activities of C and Si in Fe-C-Si system was predicted by applying the pseudo-multicomponent approach of the molecular interaction volume model （MIVM） and the Wagner interaction parameter formalism （WIPF） respectively. The average relative errors between the predicted values of MIVM and the experimental data for the three components were 4.5 0%, 17.0% and 13.0 %, respectively, and those between the calculation results of the WIPF and the experimental data were 18.0K for Mn, 9.0% for C and 27.0% for Si. The results indicated that the MIVM method could better predict the component activity of carbonaceous iron-based solution. Based on the data in an actual blowing process, the MIVM method was applied to predict the component activities of C and V as well as the transition temperature of vanadium oxidization （TTVO） in Fe-C-V-Si quaternary iron-based solution, and a comparative analysis of the predictions against the ex- perimental data was carried out, with their average relative errors being 24.0% for C, 7.3% for V and 1.0% for TTVO respectively. On that basis, the TTVO at Panzhihua Iron and Steel （Group） Co. , Ltd. was estimated by the MIVM method and an expression that the TTVO changed with composition and temperature of iron solutions was obtained by multiple linear regression method. The research results showed that the estimated values were in good agree- ment with the practical data.