Binary phase diagrams calculation

Figure 10.10 Fe-Cr binary phase diagram calculated by FactSage and FSstel data base [39].

Although fractional crystallization has always been the most common method for the separation of diastereomers. When it can be used, binary-phase diagrams for the diastereomeric salts have been used to calculate the efficiency of optical resolution. However, its tediousness and the fact that it is limited to solids prompted a search for other methods. Fractional distillation has given only limited separation, but gas chromatography and preparative liquid chromatography have proved more useful and, in many cases, have supplanted fraetional crystallization, especially where the quantities to be resolved are small. 

A significant review of several aspects of the phase diagram computation (phase diagram calculations in teaching, research and industry) has been published by Chang (2006). The relationship between the characteristic features of a phase diagram and the relative thermodynamic stabilities of the phases involved has been there underlined and exemplified. Representative examples of binary, ternary and high-order alloy systems have been presented. Moreover a number of applications have... 

A major complication in the analysis of convection and segregation in melt crystal growth is the need for simultaneous calculation of the melt-crystal interface shape with the temperature, velocity, and pressure fields. For low growth rates, for which the assumption of local thermal equilibrium is valid, the shape of the solidification interface dDbI is given by the shape of the liquidus curve Tm(c) for the binary phase diagram ... 

Liquid-Solution Models. The simple-solution model has been used most extensively to describe the dependence of the excess integral molar Gibbs energy, Gxs, on temperature and composition in binary (142-144, 149-155), quasi binary (156-160), ternary (156, 160-174), and quaternary (175-181) compound-semiconductor phase diagram calculations. For a simple multicomponent system, the excess integral molar Gibbs energy of solution is expressed by... 

The main difference between the carbon and low alloy steels, shown in figures 6.1 and 6.2, was the lowering of the solidus lines by alloying elements. The liquidus temperatures were also decreased somewhat. It has not been possible to calculate the factors for the temperature depression by, for example, nickel and chromium, as the levels of other elements were not held constant in the present work. However, at the low contents present, the influence of minor changes in composition can be estimated from the binary phase diagrams. 

Equation 5.7 [10], where do, d[, 62 and d3 are fitting parameters, and d>B is the volume fraction of Component B, can produce all of the binary phase diagram types shown in Figure 5.1, when used either to lit experimental data in the context of the Flory-Huggins theory of thermodynamics or to express interaction energies calculated by atomistic simulations in a convenient manner as a function of the temperature and the component volume fractions. 

A number of other models have been used in conjunction with Equation 7 to calculate the binary phase diagrams. Among these are the quasichemical equation (35,44), a truncated Margules equation (45,46), Darken s formalism (47,48), and various forms of the chemical theory, in which associated liquid species are postulated and some assumptions are made about the physical interactions between the species (49-51). Several of these studies have considered the liquid phase properties as well as the liquidus in the parameter estimation (45,46,51). 

Thus, to calculate the composition of the azeotrope point and the difference in the regular solution parameters, only and pure component transition temperatures and enthalpies are required. That so much can be accomplished with only knowledge of T n is very convenient, since the commonly used contact method for determining binary phase diagrams of mesogenic mixtures will only provide temperature information. 

Regular solution theory has been successfully applied to the calculation of binary phase diagrams of mesomorphic materials. Correlation of the parameters required by the theory with simple physical properties of the mixture s components, may offer an empirical way to predict the phase diagrams for mixtures involving members of homologous series. 

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