Solidus equation

Figure 15. Variation in Dxh for garnet versns reciprocal temperature for experimental data sources listed in Table lb at a variety of pressures n = 33). A distinction is made between mantle solidus partition coefficients (Salters and Longhi 1999 Salters et al. 2002 McDade et al. 2003a,b) and the rest. Note the strong temperatnre dependence, which is qnalitatively similar to that incorporated in Equation (25b). The scatter is due to additional compositional controls.

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. 

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... 

Figure 9 Calculated (from Equation (17)) M2 site radius for experimentally produced clinopyroxenes in peridotite close to the solidus. Note that, despite scatter due to differences in bulk composition, the trend to lower radius with increasing pressure is clear and reproduced in all of the polybaric data sets. This leads to crossover from less than 1.0 at low pressure to...

There are only a few systems, where the two components are closely similar in nature, in which the liquidus and solidus curves are given by the simple equations (23.3). As examples we may mention the systems chlorobenzene+ bromobenzene, silvers gold, copper + nickel, and certain pairs of optical isomers. The data for the system copper +nickel ... 

For the equilibrium solidus-liquidus of the component i in a simple eutectic system in which no compounds are formed and the solubility of the components in the solid state does not exist, the differential form of the Le Chatelier-Shreder s equation holds... 

Extrapolation of Equation 1 to Vni=100 corresponds to T=1360°C for the liquidus. Extrapolation of Equation 3 to Vm=0 yields T=1119°C for the disappearance of liquid, the solidus temperature. This is a complex system for which complete phase diagrams are not available pseudoternary diagrams such as those presented by Grove et a l. (2) for similar compositions are generally applicable to this composition. 

So these nonlinear equations must be solved simultaneously for the liquidus and solidus lines, together with the equations for the second component, and that the sum of the mole fractions in each phase must be unity. 

Equation (6.84) may be arranged to give the phase boundaries of the solidus and liquidus curves as... 

The energy of mixing is essentially the only parameter that characterizes the nonideality of the system, that is, the difference in the interactions between similar and dissimilar atoms. Using the indices and " to designate the liquid and solid phases, respectively, one can write the following equations for the solidus and the liquidus ... 

Coriell et al. [92] solved the transient one-dimensional heat and solute diffusion equation without considering convective effect. The situation considered was similar to a diffusion-controlled problem of Coates and Kirkaldy [93] and Maugis et al. [90], which has multiple similarity solutions. Assuming local equilibrium at the solid/metal interface Coriell et al. [92] obtained the equation for the parabolic growth rate which was solved numerically. Using a lead-tin alloy as an example to examine phase stability, it was found that the diffusion path begins at the composition and temperature of one phase, crosses the two-phase region between the liquidus and solidus lines, and terminates at the composition and temperature of the other phase. 

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