Solid-liquid phase diagrams with compounds

The solubility is defined with respect to a second precipitated phase. The solubility of an impurity is the maximum concentration, which can be incorporated in the liquid or solid phase without precipitating a second phase. For most impurities in solid silicon at high-temperatures, equilibrium is achieved with the liquid phase governed by the liquidus in the phase diagram. Solid solubility is temperature-dependent as represented by the solidus or solvent curves in the phase diagram. At lower temperatures, the reference phase is usually a compound or an impurity-rich alloy. When the impurity is volatile, the saturated crystal is in equilibrium with the vapor, and the impurity solubility also depends on its vapor pressure. 

A first look at figs. 1-7 indicates that rare earths and actinides behave like early transition metals. When alloyed with elements of columns IB to VB the phase diagrams exhibit many intermetallic compounds. The exceptions are of interest uranium possesses a miscibility gap in the liquid state when alloyed with Cu, Ag, Au, Zn, Cd, Pb and Bi even if intermetallic compounds are found in the solid state (except in the Ag-U system) plutonium also has a miscibility gap in the liquid state when alloyed with Ag and Cd. 

Figure A 1.52 shows the Ti-Al phase diagram (important for the standard commercial alloy Ti-6% Al-4% V. It shows two peritectic reactions, at each of which liquid reacts with a solid phase to give an intermetallic compound, (a) Ring the peritectics and give the (approximate) chemical formula for the two compounds, (b) Shade all... 

The phase diagram for aluminum/silicon (Fig. 4.5) is a typical example of a system of two components that form neither solid solutions (except for very low concentrations) nor a compound with one another, but are miscible in the liquid state. As a special feature an acute minimum is observed in the diagram, the eutectic point. It marks the melting point of the eutectic mixture, which is the mixture which has a lower melting point than either of the pure components or any other mixture. The eutectic line is the horizontal line that passes through the eutectic point. The area underneath is a region in which both components coexist as solids, i.e. in two phases. 

The above series of calculations helps demonstrate that all types of topology of phase diagrams involving simple liquid and solid solutions can be calculated within the same simple framework, and diagrams with increasing complexity, i.e., increasing number of phases, compounds, allotropic changes in the elements, etc., can also be routinely handled. 

Solid-Solution Models. Compared with the liquid phase, very few direct experimental determinations of the thermochemical properties of compound-semiconductor solid solutions have been reported. Rather, procedures for calculating phase diagrams have relied on two methods for estimating solid-solution model parameters. The first method uses semiem-pirical relationships to describe the enthalpy of mixing on the basis of the known physical properties of the binary compounds (202,203). This approach does not provide an estimate for the excess entropy of mixing and thus... 

Figure 14.23 gives the (solid + liquid) phase diagram for (tetrachloromethane + 1,4-dimethylbenzene).19 The maximum in the (solid + liquid) equilibrium curve at X2 = 0.5 results from the formation of a solid addition compound with the formula CCl4-l,4-C6H4(CH3)2 that melts at the temperature corresponding... 

Partial Miscibility in the Solid State So far, we have described (solid + liquid) phase equilibrium systems in which the solid phase that crystallizes is a pure compound, either as one of the original components or as a molecular addition compound. Sometimes solid solutions crystallize from solution instead of pure substances, and, depending on the system, the solubility can vary from small to complete miscibility over the entire range of concentration. Figure 14.26 shows the phase diagram for the (silver + copper) system.22 It is one in which limited solubility occurs in the solid state. Line AE is the (solid -I- liquid) equilibrium line for Ag, but the solid that crystallizes from solution is not pure Ag. Instead it is a solid solution with composition given by line AC. If a liquid with composition and temperature given by point a is... 

Figure 14.29 shows the (solid + liquid) phase diagram for (benzene + hexafluoro-benzene). A congruently melting solid molecular addition compound with the formula QFU-CeFe ) is evident in this system.26 The rounded top of the freezing curve (solid line) for the addition compound results from almost complete dissociation of the addition compound in the liquid mixture. In other words, benzene and hexafluorobenzene act as independent molecular species in the liquid state and combine together as the addition compound only in the solid state. 

Carbon dioxide plays a central role in the CNG process both as a pure component and in mixture with other compounds. The triple point of carbon dioxide is referred to frequently in the following discussion it is the unique temperature and pressure at which solid, liquid, and vapor phases of carbon dioxide can exist at equilibrium (-56.6°C, 5.1 atm). The carbon dioxide triple point is shown in Figure 2, a phase diagram for carbon dioxide. 

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