Solid miscibility

In solid solutions, part of the molecules A, in a crystal, are substituted by molecules B. If the two kinds of molecules are not very similar, the introduction of molecules B in the crystal A will lead to a distortion of the latter, by which the energy is increased. Unless, therefore, the molecules are very similar, the solid miscibility will be restricted at low temperature, becoming appreciable only at high temperature. 

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 temperatures of thermal arrests are plotted as a function of composition in Figure 1. The lines have been drawn to suggest the location of equilibrium phase boundaries, and the best interpretation of the thermal analysis data. The resulting diagram is characteristic of a system exhibiting solid solubility with a minimum melting point and a solid-miscibility gap. 

Comparison of Solid-Solubilities. The limit of solid miscibility has been related to the energy of distortion of the crystal lattice when atoms of a second component are introduced into the lattice Scott (6) and Lawson (11) have expressed the distortion energy as a function of the molal volumes of the two components. Both authors recognized that the solubility of small atoms in a lattice of large atoms is greater than the... 

With liquids, the degree of order being much lower, conformity of size is of far less importance. The solubility of A in B is mainly a question of the mutual attractions AA, BB, and AB. If AA and BB very much exceed AB, then the liquids remain as separate phases. If the AB attractions prevail strongly, solubility is complete. In intermediate cases limited miscibility is possible, because the tendency of A to separate from B as a distinct phase depends not only upon the AA attractions but upon the frequency of encounter. The treatment of the phase equilibria is very similar to that of solid miscibility discussed on p. 75. 

The phase boundaries involving (7Fe)-(aFe) transformations are uneertain at very low temperatures because of the strong hysteresis effects. A comparison with the aeeepted binary system Fe-Ni indicates that the (aFe) region shown in the isothermal section at 20°C available in the literature [1935Koe, 1941Bra] should extend to only about 1 at.% Ni. Due to the laek of data at this temperature regarding all the accepted binaries, no definitive isotherm can be drawn at 20°C. A metastable solid miscibility gap exists in the a phase [2004Wanl] and the computed curves are shown in Fig. 7. 

The pseudoquaternary Y(0)-Sr(0)-Ba(0)-Cu(0) system has been investigated to some extent in conjunction with effects of Sr substitution in the RBaiCusOe + v, phase, particularly for R=Y (Roth et al. 1989b, Karen et al. 1991b) and R=La (Skakle and West 1995b). In the system with R = Y, mutual solid miscibility ranges are observed for Sr and Ba (see fig. 50) ... 

Similarly, there is high mutual solid solubility between U, Np, and Pu when they occur in their complex crystalline forms at low temperatures. Solid miscibility gaps of only a few atomic percent separate a-Np and /J-Np from a-Pu and /3-Pu, although the terminal solid solutions have different crystal structures. The same may be said of the extent of solid solubility between the low-temperature forms in the systems U-Np and U-Pu, provided that the broadly stable intermediate phases that occur are considered to be transitional extensions of the terminal solid solution phases. Fig. 19.S shows schematically that regions of single-phase solid solution exist over virtually the entire compositional region at low temperatures in the ndghboring binary systems U-Np and Np-Pu [31]. ... 

This fractional power dependence of <(c) has shown to be a unique flexible polymer effect by experiments with PS samples of low molar mass ° and PS in solid miscible blends." When the molar mass of PS is less than 2 kD the concentration dependence <(c) showed a linear dependence without a region of fractional power dependence as shown in (Fig. 4). For small molecules in solution <(c) has been found to be proportional to the concentration in all cases and the value of < starts from zero. For low molar mass polymer PS because of the intrachain excimers existing in solution <(c) extrapolates to some finite value at zero concentration. A demarkation of the behavior of (c) for PS-DCE solutions of different molar mass samples has been found to lie between 1.7-4.2 kD. 

We next treat the case of solid-liquid equilibria (SLE), solid-solid equilibria (SSE), and solid-solid-liquid equilibria (SSLE). Solids that are in equilibrium with liquids can take two forms (1) pure solids that are immiscible with other species and (2) solid solutions that, like liquid solutions, contain more than one species. Ciystalhne solids are formed within a well-defined geometrical lattice structure. While partial miscibility in liquid systems is due solely to the relative strength of like intermolecular interactions compared to unlike intermolecular interactions, the ability of solids to mix depends primarily on how well one atom fits to the lattice structure of the other species. Thus, complete solid miscibility occurs only when species are nearly the same size, have the same crystal structure, and have similar electronegativities and valences. We treat pure solids first and then address solid solutions. 

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