Liquidus equations

Third, the basic liquidus equations used here are not equivalent to... 

The chemical potentials of the solid solution components can be eliminated from the liquidus equations given by Eqs. (8) and (9) using Eqs. (6) and... 

Finally there are four additional equations that we call auxiliary conditions that supplement the liquidus equations given by Eqs. (12) and (13). These follow immediately from the zero change of Gibbs energy upon the congruent melting of AC(s) and BC(s). For AC(s) these are... 

Finally the interaction coefficients used for the Ga-In-Sb system are collected in Table VI where the lj coefficients of Eq. (83)—(85) have been replaced by the original ay coefficients of Eq. (68). Using Eq. (109), which is the liquidus equation at the maximum melting point of GaSb(s), and its analog for... 

The liquidus, which is consistent with Eq. (21) and the two parts of the oxygen-potential model, may be represented by the following equation for 2416 < T < 2701 K ... 

Analytical equations for the solidus and liquidus lines can now be obtained from these equations by noting that xAq + x[ q =1 and xA + XgS =1, giving... 

These two simultaneous equations can then be solved numerically to calculate the solidus and liquidus lines. 

The mathematical treatment can be further simplified in one particular case, that corresponding to Figure 4.10(a). As we saw in the previous section, in some binary systems the two terminal solid solution phases have very different physical properties and the solid solubility may be neglected for simplicity. If we assume no solid solubility (i.e. as =a =1) and in addition neglect the effect of the heat capacity difference between the solid and liquid components, eqs. (4.29) and (4.30) can be transformed to two equations describing the two liquidus branches ... 

Flood s equation physchem A relation used to determine the liquidus temperature in a binary fused salt system. fladz i.kwa zhan flores CHEM A form of a chemical compound made by the process of sublimation. flor ez 1... 

Again, providing the various H and S terms are temperature-independent, the solution remains exact and provides a rapid method of calculating the liquidus temperature. Equation (9.10) is generally applicable to any phase boundary between a solution phase and stoichiometric compound, so could equally well be used for solid-state solvus lines. 

General solutions. In the case of a solution phase and stoichiometric compound which have temperature-dependent enthalpies and entropies, an iterative process by which T is varied can be utilised to find the liquidus by using the following equation... 

For solidification described by the lever rule and assuming linear liquidus and solidus lines, the composition of the solid C, as a function of the fraction solid transformed (/,) is given by the equation... 

The three most important factors in the equation are the viscosity and the thermodynamic parameters G and Gm- The viscosity can be approximated between the liquidus temperature, Tuq, and the liquid-+glass transition temperature, Tg, by a Doolittle expression involving the relative free volume (Ramachandrarao et al. 1977) while G can be calculated using the relationship... 

Figure 1.12 Influence of pressure on the liquidus curve of [CjCjIm][CjS04] (1) + 1-hexanol (2) up to 360 MPa (Adapted from Domariska, U. and Morawski, R, Green Chem., 9, 361, 2007.) experimental points (O), solid line, description with the Yang equation. (Adapted from Yang, M. et al.. Fluid Phase Equilib., 204, 55, 2003.)...

We wish here to obtain the thermodynamic equations defining the liquidus surface of a solid solution, (At BB)2, ). It is assumed that the A and atoms occupy the sites of one sublattice of the structure and the C atoms the sites of a second sublattice. For the specific systems considered here Sb and play the role of C in the general formula above. It is also assumed that the composition variable is confined to values near unity so that the site fractions of atomic point defects is always small compared to unity. This apparently is the case for the solid solutions in the two systems considered. Then it can be shown theoretically (Brebrick, 1979), as well as experimentally for (Hgj CdJ2-yTe)l(s) (Schwartz et al, 1981 Tung et al., 1981b), that the sum of the chemical potentials of A and C and that of and C in the solid are independent of the composition variable y ... 

Inserting Eq. (91) into Eq. (93) for the liquidus line of AC(s) gives the liquidus temperature at x =. The experimental value TAc is treated as special and it is required that the resulting equation be satisfied for T=TAC. The equation then becomes a restriction on the interaction coefficients. We use it to provide a relation between cos and vs in terms of the other coefficients and a new model parameter z, the value of z at x = and T = TAC. The relation is... 

In equation 18, is the slope of the liquidus curve for species i, that is,... 

In equation 33, the superscript I refers to the use of method I, a T) is the activity of component i in the stoichiometric liquid (si) at the temperature of interest, AHj is the molar enthalpy of fusion of the compound ij, and ACp[ij] is the difference between the molar heat capacities of the stoichiometric liquid and the compound ij. This representation requires values of the Gibbs energy of mixing and heat capacity for the stoichiometric liquid mixture as a function of temperature in a range for which the mixture is not stable and thus generally not observable. When equation 33 is combined with equations 23 and 24 in the limit of the AC binary system, it is termed the fusion equation for the liquidus (107-111). 

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