Solubility in the Solid State

Solid solutions of the impurity and the target compound can be formed via two different mechanisms that are regarded as limiting cases. Either the impurity molecules occupy sites in-between host molecules, forming so-called interstitial mixed crystals, or the impurity (guest) molecules replace the molecules of the target compound (host) forming so-called substitutional mixed crystals. 

The incorporation of similarly shaped guest components into the lattice of a host component can be quantified by a distribution coefficient, keq, equal to the ratio of the impurity content in the solid phase, Ximp.s. to that in the liquid phase, Ximp.i (with % in mol fractions), supposing both phases are in equilibrium at a given temperature. The so-defined coefficient is called thermodynamic distribution (or segregation) coefficient (Equation 7.2)  

The thermodynamic distribution coefficient is only a constant in the region close to the target component, that is, at ideal dilution with respect to the impurity (solidus and liquidus lines are linear). For values of keq equal to unity, no purification is achieved for keq less than unity, a purification can be obtained with highest purity for keq close to zero. 

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The phase diagrams we have shown are based upon the fact that A and B form solid mutually soluble solid state solutions. If they do not, i.e.- they are not mutually soluble in the solid state, then the phase diagram becomes more complicated. As an example, consider the following, which is the case of limited solid solubility between A and B. (N.B.- study the following diagrams carefully)"... 

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 similar behaviour (complete mutual solubility in the liquid state and partial solubility in the solid state) is presented also by the Pt-Au and Ba-Ca systems (Fig. 2.9(b) and (c)). Notice in the Pt-Au diagram the closeness (mainly for compositions near 40 at.% Au) between the melting and the de-mixing equilibria. 

Figure 2.10. Examples of binary systems characterized by complete mutual solubility in the liquid state and, depending on temperature and/or composition, partial solubility in the solid state and presenting (in certain composition ranges) an invariant (three-phase) reaction (eutectic in the Cu-Ag, peritectic in the Ru-Ni and Re-Co and eutectoidal in Ti-W (one) and in Th-Zr (two)).

Figure 2.11. The Au-Si diagram is an example of a simple eutectic system with complete mutual solubility in the liquid state and no (or negligible) solubility in the solid state at a temperature of 363°C the liquid having the composition of 18.6 at.% Si solidifies with the simultaneous crystallization of the practically pure gold and silicon mechanically mixed. In the Cr-U system a slightly more complex situation due to the solid-state transformations of uranium is shown.

Extreme cases of solid solubility are shown in Fig. 2.11. In particular notice the system Au-Si for which, owing to a negligible solubility in the solid state, the terminal phases are practically coincident with the pure elements. 

The diagrams of Fig. 2.16 maybe considered examples of systems showing not only small (or very small) solubility in the solid state, but also a degree of insolubility in the liquid state (existence of miscibility gaps in the liquid state). 

In Fig. 5.18 on the other hand, binary systems of Ti, Zr, Hf are indicated in which complete mutual solubility in the solid state is observed (even if only in a limited range of temperature). Notice the peculiar behaviour of titanium which exhibits... 

Using specific metal combinations, electrodeposited alloys can be made to exhibit hardening as a result of heat treatment subsequent to deposition. This, it should be noted, causes solid precipitation. When alloys such as Cu-Ag, Cu-Pb, and Cu-Ni are coelectrodeposited within the limits of diffusion currents, equilibrium solutions or supersaturated solid solutions are in evidence, as observed by x-rays. The actual type of deposit can, for instance, be determined by the work value of nucleus formation under the overpotential conditions of the more electronegative metal. When the metals are codeposited at low polarization values, formation of solid solutions or of supersaturated solid solutions results. This is so even when the metals are not mutually soluble in the solid state according to the phase diagram. Codeposition at high polarization values, on the other hand, results, as a rule, in two-phase alloys even with systems capable of forming a continuous series of solid solutions. 

In the case of limited solubility in the solid state, the hardness of crystals as solid solutions depending on the composition of the alloy, should grow in the homogeneity region up to the point of saturation at a given temperature, but should remain invariable on passing into the two-phase region. 

A and B have negligible mutual solid solubilities in the solid state and their phase diagram shows a eutectic transformation. The liquid phase at 1 atm is represented by die equation... 

Microstructures like those in Figs 3.8 and 3.9 are often employed to set off massive specimens with multiple compound layers against thin-film ones with one or two compound layers. For binary systems without any considerable solubility in the solid state, however, the dimensions of reaction couples play no role, if of course not of the order of lattice... 

Although for temperatures below 1627 K, there is no reciprocal solubility in the solid state, a metastable, homogeneous oxynitride phase could have potential applications in many areas because, e.g.,... 

Assume, for example, that two metals A and B are completely soluble in the solid state, as illustrated by the phase diagram of Fig. 12-1. The solid phase a, called a continuous solid solution, is of the substitutional type it varies in composition, but not in crystal structure, from pure A to pure B, which must necessarily have the same structure. The lattice parameter of a also varies continuously from that of pure A to that of pure B. Since all alloys in a system of this kind consist of the same single phase, their powder patterns appear quite similar, the only effect of a change in composition being to shift the diffraction-line positions in accordance with the change in lattice parameter. 

More commonly, the two metals A and B are only partially soluble in the solid state. The first additions of B to A go into solid solution in the A lattice, which may expand or contract as a result, depending on the relative sizes of the A and B atoms and the type of solid solution formed (substitutional or interstitial). Ultimately the solubility limit of B in A is reached, and further additions of B cause the precipitation of a second phase. This second phase may be a B-rich solid solution with the same structure as B, as in the alloy system illustrated by Fig. 12-2(a). Here the solid solutions a and P are called primary solid solutions or terminal solid solutions. Or the second phase which appears may have no connection with the B-rich solid solution, as in the system shown in Fig. 12-2(b). Here the effect of supersaturating a with metal B is to precipitate the phase designated y. This phase is called an intermediate solid solution or intermediate phase. It usually has a crystal structure entirely different from that of either a or P, and it is separated from each of these terminal solid solutions, on the phase diagram, by at least one two-phase region. 

The Cu-Fe system, accepted from [1994Swa] has been critically evaluated by [1995Che]. It presents a total solubility in the liquid state and a limited solubility in the solid state. No stable intermetallic compound is known. 

Pet] Pettersson, H., Investigations of the Solubility in the Solid State in the Binary Systems of the Oxides CaO, MnO, MgO and FeO (in Sweedish), Jemkontorets Ann., 130(12), 653-663 (1946) (Crys. Stmcture, Experimental, Phase Diagram, Phase Relations, 19) [1947Cir] Cirilli, V, Reduction of Calcium Ferrites with Carbon Oxide at High Temperature (in Italian), Ricerca Sci, 17(6), 942-945 (1947) (Experimental, 5)... 

It has been suggested that this high creep resistance might be related to the low density and the low mobility of dislocations present in YAG single crystals [105]. Further, YAG is stable In contact with alumina up to about 1700°C. Both materials display similar CTEs they do not react with each other and their mutual solubility in the solid state is negligible. Hence, YAG... 

E, mutual solubility in the solid state <1 at.% (simple eutectic, no binary cmnpound occurs) ... 

Aqueous H2[S406] is the most stable thionic acid but has not been isolated. Its dilute solution can be boiled without decomposition. A concentrated solution decomposes into S, SO2 and H2SO4. Its acidity is as great as that of H2[S206]. The salts of H2[S406] are generally soluble. In the solid state they may be kept for a month or more, but they readily decompose in solution, especially when warmed. The alkali salts are more stable than those of Ba Cu etc. 

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