Partial miscibility in the solid state

It is usual to find that two substances are neither completely miscible nor immiscible in the solid state, but rather each substance has a limited solubility in the other. For this case, the most common type of phase diagram is shown in Fig. 15.17. The points in region a describe solid solutions of B in A, while those in p describe solid solutions of A in B. The points in region a + jS describe states in which the two saturated solid solutions, two phases, a and P, coexist in equilibrium. If we cool a system described by point a, then at point b crystals of solid solution a having the composition c appear. As the temperature drops, the compositions of solid and liquid shift at d compositions/and g are in equilibrium. At h the liquid has the eutectic composition e solid p appears, a, p, and liquid coexist, and the system is invariant. On cooling to i, two solid solutions coexist a of composition j, p of composition k. 

A different type of system in which solid solutions appear is shown in Fig. 15.18. This system has a transition point rather than a eutectic point. Any point on the line abc describes an invariant system in which a, p, and melt of composition c coexist. The temperature of abc is the transition temperature. If the point lies between a and b, cooling 

An interesting example of a system in which many solid solutions occur is the Cu-Zn diagram (brass diagram) in Fig. 15.19. The symbols a, jS, 7, 5, , rj refer to homogeneous solid solutions, while regions labeled a + jS, jS + y indicate regions in which two solid solutions coexist. Note that there is a whole series of transition temperatures and no eutectic temperatures in this diagram. 

It is usual for phase diagrams to contain several features solid solutions, compound formation, eutectic points, transition points, and the like. Once the interpretation of the individual features is understood, the interpretation of complex diagrams poses no difficulty. 

In describing the equilibria between solids and liquids, we assumed implicitly that the pressure on the system was high enough to prevent the appearance of vapor in the system. At lower pressures, if one or more of the components of the system is volatile, vapor may be present at equilibrium. A common and important example of the equilibrium between solid and vapor is the equilibrium between salt hydrates and water vapor. 

---

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... 

Fig. 10 Thermodynamic and kinetic basis for solute depletion in the case of a binary alloy consisting of solvent A and solute B. (a) Binary equilibrium phase diagram with complete miscibility in the liquid state, partial miscibility in the solid state given by existence of a terminal solid solution. Cs is the composition along the solvus line. is the overall composition of the alloy, (b) Time-temperature-transformation diagram for precipitation of in an a matrix for the alloy shown in (a) with overall composition,...

Type III MiscibiUty in the liquid state, partial miscibility in the solid state, melting point diagram shows eutectic point and mixed crystal region. 

System in which the solid phases consist of the pure components and the components are only partially miscible in the liquid state... 

When lattice integration due to a partial or complete miscibility in the solid state is the dominant mechanism of impurity incorporation, the impurity content in the crystalline product increases with the yield. This can be easily verified on the basis of the phase diagram (Figure 7.5a). Assuming equilibrium conditions (i.e., slow crystallization), the concentration of the impurity incorporated in the target compound steadily increases with progressing crystallization (arrow at the solidus line) and reaches a maximum value close to the eutectic temperature. Simultaneously, the... 

The enthalpy of mixture for this system is not available in the literature. Only the phase diagram is given [14, 15]. The phase diagram presents a eutectic point at x(NdF3) = 0.69 and T = 1488 K (Figure 3.5.1). This figure shows a partial miscibility in a solid state and an azeotrope at x(NdF3) = 0.21 and T = 1688 K. 

If PAANa and POE were miscible, single ion conduction would be possible because anions would be fixed to the polymer matrix. Since PAANa and POE, however, were not miscible in the solid state, acrylic acid moieties were introduced to PAANa for the purpose of the partial complexation through hydrogen bonding. In the experiment, the glass transition temperature and ionic conductivity were studied for PAANa-PAA-POE composite films having different neutralization of PAA and different incorporation of POE. 

Partial mutual solubility in the solid state. Fig. 2.9 shows different examples of binary systems for which there is still a complete miscibility in the liquid state, but only a limited mutual solubility in the solid state, depending on the temperature. The Ni-Au system, for instance, still has complete mutual solid solubility but only at high temperature, that is, by decreasing the temperature, de-mixing... 

A summary of all the metal pairs showing partial or complete immiscibility in the liquid state is presented in the map of Fig. 2.17. In the same figure metal pairs giving solid-gas equilibria are also shown. The solid-gas equilibria are especially observed in systems in which there is a large difference in the boiling points of the components (see for instance the systems formed by the alkali metals with refractory metals such as Cr, Mo, V etc.). Several groups of systems forming miscibility... 

---