Systems that Form Solid Solutions

The thermodynamic relationships for equilibrium between a binary solid solution and a binary liquid solution are given by 

If the solid undergoes polymorphic transitions, then one or more terms involving the transition enthalpies and temperatures must be added. Thus 

In Equation (6), A Vis the difference in volume between the liquid and solid phases, and the integration is carried out from the triple point pressure to the pressure of the system. 

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Figure 4 (a) Ternary systems that form solid solutions, (b) Ternary systems in which the three constituent binaries exhibit eutectic behavior, (c) Projection ofliquidus curves in (b). (d) Ternary system in which two of the constituent binaries form eutectics, (e) Ternary system in which A and B combine to form AB... 

A second type of solubility behavior is exhibited by mixtures that form solid solutions. Consider, for example, a hypothetical system containing R and S whose... 

When any likely impurities in the system readily form solid solutions in the crystals, they may be very difficult to remove by conventional methods. Effects of such foreign molecules in the crystal lattice can profoundly modify barriers to molecular rotation, and can thereby enhance premelting. In favourable cases, this can be tested by the direct addition of the appropriate impurity, whose structure must be so close to that of the primary molecules that the foreign species can easily be accommodated in the crystals. Some experimental examples have been investigated by Ubbelohde, Oldham and Ubbelohde, and Thompson and Ubbelohde (cf. Reference 27). 

Binary systems are known that form solid solutions over the entire range of composition and which exhibit either a maximum or a minimum in the melting point. The Uquidus-solidus curves have an appearance similar to that of the liquid-vapor curves in systems which f orm azeotropes. The mixture having the composition at the maximum or minimum of the curve melts sharply and simulates a pure substance in this respect just as an azeotrope boils at a definite temperature and distills unchanged. Mixtures having a maximum in the melting-point curve are comparatively rare. 

Szczepanik and Skalmowski (Szczepanik et al, 1963 Szczepanik and Ryszard, 1%3) studied the phase behavior of over 60 PAH binary mixture systems, and demonstrate that PAH mixture systems also form solid solution, as shown by naphthalene + 1-methynaphthanlene, naphthalene + anthracene, phenanthrene + anthracene, phenanthrene + carbazole, anthracene + acridine, anthracene + fluoranthene, and chrysene + 1,2-benzanthracene systems. It is not known whether the the Hume-Rothery rules still work for PAH mixtures. However, it is worth noting that the number of such systems is small, comp>ared with the number of eutectic-forming systems. 

Niobium-Tantalum Niobium and tantalum form solid-solution alloys which are resistant to many corrosive media and possess all the valuable properties of the pure metals. This could have great practical value since in a number of branches of technology it might permit the replacement of pure tantalum by a cheaper alloy of niobium and tantalum. Miller" and Argent" reported data on the resistance of the niobium-tantalum system, but the tests were only carried out under mild conditions and the data have only limited significance. However, Gulyaev and Georgieva and Kieffer, Bach and Slempkowski carried out tests at elevated temperatures and their work indicated that the corrosion rates of the alloys are substantially that of tantalum provided the niobium content does not exceed 50%. 

Solubility equilibria are described quantitatively by the equilibrium constant for solid dissolution, Ksp (the solubility product). Formally, this equilibrium constant should be written as the activity of the products divided by that of the reactants, including the solid. However, since the activity of any pure solid is defined as 1.0, the solid is commonly left out of the equilibrium constant expression. The activity of the solid is important in natural systems where the solids are frequently not pure, but are mixtures. In such a case, the activity of a solid component that forms part of an "ideal" solid solution is defined as its mole fraction in the solid phase. Empirically, it appears that most solid solutions are far from ideal, with the dilute component having an activity considerably greater than its mole fraction. Nevertheless, the point remains that not all solid components found in an aquatic system have unit activity, and thus their solubility will be less than that defined by the solubility constant in its conventional form. 

Protons are not the sole species that can be incorporated into the lattices of different host materials. At the beginning of the 1960s, Boris N. Kabanov showed that during cathodic polarization of different metals in alkaline solutions, intercalation of atoms of the corresponding alkali metal is possible. As a result of such an electrochemical intercalation, either homogeneous alloys are formed (solid solutions) or heterogeneous polyphase systems, or even intermetallic compounds, are formed. 

Typically, binary Laves compounds AM2 are formed in several systems of A metals such as alkaline earths, rare earths, actinides, Ti, Zr, Hf, etc., with M = Al, Mg, VIII group metals, etc. Laves phases are formed also in several ternary systems either as solid solution fields extending from one binary phase (or possibly connecting the binary phases of two boundary systems) or as true ternary phases, that is forming homogeneity fields not connected with the boundary systems. 

Solid solutions will only form between ions with similar radii ( 15 %). Table 3.15 shows the radii in crystal lattices of divalent cations that might form solid solutions in soils. Hence, for example Mn +,Fe + and Cd + might be expected to form solid solutions in CaCOs, but Cu + and Zn + would not. However, soils do not necessarily behave the same as pure systems. Thus there is little evidence for strong association of Cd + or Pb + with calcite (CaCOs) in soil systems, despite having similar radii to Ca + (McBride, 1994). However Cd + and Pb + are both commonly associated with hydroxyapatite (Caio(P04)6(OH)2),... 

Solid mixtures of CdS and HgS have been shown to form solid solutions after treatment with certain solutions, such as concentrated ammonium sulphide [16]. This may be due partly to the very similar ionic radii of the two cations and (maybe more important) the ability of Hg to diffuse readily in solids. Therefore it is probable that solid solutions can readily form in this system. 

In Section 24 it was shown that, under favorable conditions, two oxides of the same metal, in different states of valency, may form solid solutions which have been described as compounds with variable composition. The stabilizing factor in this case is the increase in entropy, due to the random distribution of the two positive ions these systems, strictly speaking, are stable only at elevated temperature. The conditions may be such that two oxides form a real compound, because this process is connected with a decrease in energy. The compounds formed in this way have a stoichiometric composition, with two kinds of positive ions in fixed positions, so arranged that the energy of the system is minimal. A good example of a compound of this type is Fe304. 

Figure 7.3 shows the free energy versus composition curves for a system that forms a simple eutectic. At the lowest temperature, T, there is equilibrium between two solid solutions, a and fi. At the eutectic temperature, T2, there is a common tangent between a, liquid, and ji. At Tj, equilibrium corresponds to Ga, the tangent between Ga and Gl,Gb, the tangent between Gl and Gp, and Gp. Finally, at 7), the lowest free energy corresponds to liquid for all compositions. 

However, the general form of the curve on the left-hand side of Fig. 10 is followed even in nonideal systems. Looking at the right-hand side of Fig. 10, we see that as A is added to pure B, the freezing point of the solution is also lowered. (We have also assumed that B does not form solid solutions.) Alternatively, this can be described as reducing the solubility of B in the solution as the temperature of the solution is lowered below the freezing point of pure B. At an intermediate concentration, the two solubility curves in Fig. 10 meet at point e and a solution with the lowest freezing point is obtained. This solution is known as the eutectic and the concentration and temperature at point e, is known as the eutectic concentration and temperature. 

An additional interesting property of cubic oxides is their ability to form solid solutions (25) that maintain the original cubic structure. In these solids the cation sites can be shared between the two competitive cations over a wide range of compositions. This is the case for the NiO-MgO system, for which the Mg Nii O solid solution can be prepared with 0 < x < 1 because of the very similar ionic radii of the cations jr(Mg2+) = 0.72 A and r(Ni2+) = 0.69 A], Another relevant case is CoO-MgO. 

The temperature-composition phase diagram constructed from thermal arrests observed in the MoFe-UFa system is characteristic of a binary system forming solid solutions, a minimum-melting mixture (22 mole % UFe at 13.7°C.), and a solid-miscibility gap. The maximum solid solubility of MoFq in the UFe lattice is about 30 mole % MoFe, whereas the maximum solid solubility of UFe in the MoFe lattice is 12 to 18 mole % UFe- The temperature of the solid-state transformation of MoFe increases from ——lO C. in pure MoFe to 5°C. in mixtures with UFe, indicating that the solid solubility of UFe is greater in the low temperature form of MoFe than in the high temperature form of MoFe- This solid-solubility relationship is consistent with the crystal structures of the pure components The low temperature form of MoFe has an orthorhombic structure similar to that of UFe. 

The phase diagram of a ternary system in which the three species do not form solid solutions with each other and the constituent binary systems form eutectics, is shown in Figure 4(b). The temperatures A B and Tc correspond to the melting points of A, B, and C, respectively. The vertical faces of the prism represent the temperature-concentration behavior of the three binaries. Note that the behavior of each binary system is that shown in Figure 2d. The solidus lines are not shown for the sake of clarity. Points E g, E j. are the eutectic points of the three binary... 

Other systems that form eutectic mixmres are chloramphenicol-urea, sulfathiazole-urea, and niacinamide-ascorbic acid. The solid solution of chloramphenicol in urea was found to dissolve twice as rapidly as a physical mixmre of the same composition and about four times as rapidly as the pure dmg. In vivo, however, the system failed to display improved bioavailability. On the other hand, the eutectic mixmre of sulfathiazole-urea did give higher blood levels than pure sulfonamide. 

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