Solid Solutions and Structure Elements

The modeling of solid solutions, when the solvent and the solute exhibit major behavioral differences, is not easy. The required models quickly become complex. The intervention of structure elements enables us to model such solutions using quasi-chemical equilibria. 

In this chapter, we will examine two cases where that modeling enables us to correetly represent the behavior of the poly-constituent solid phase. We will look, in turn, at the study of ionic solid solutions and the fixation of water molecules in the lattices of salts. 

Ionic solids, unlike metal alloys and molecular solids, exhibit crystalline sites whieh are very different from each other. Generally speaking, there tends to be a very clear division into aitioitic sites (which receive anions) and cationic sites (which receive cations). The crystal has two distinct sublattices. In view of this arrangement, the probability of exehange of an ion between a site of one type and site of the opposite type is practically none. 

solid solutions are the solutions of ions which are placed in an interstitial position or in substitution on the sublattice which corresponds to their charge. 

Thermodynamic Modeling of Solid Phases, First Edition. Michel Soustelle. ISTE Ltd 2015. Published by ISTE Ltd and John Wiley Sons, Inc. 

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For ions in a solution and structure elements in a solid, the derivation of relation [3.4] presents a difficulty. Indeed, in the case of ions, it is inqjossible to keep the amounts of ions of all the components in an ionic solution constant while varying the amount of only one of them because then the electric neutrality is not respected. The same condition applies to stmcture elements for which we caimot carry out derivation because we would modify the ratio of sites related to the crystal. 

The materials for solid solutions of transition elements in j3-rh boron are prepared by arc melting the component elements or by solid-state diffusion of the metal into /3-rhombohedral (/3-rh) boron. Compositions as determined by erystal structure and electron microprobe analyses together with the unit cell dimensions are given in Table 1. The volume of the unit cell (V ) increases when the solid solution is formed. As illustrated in Fig. 1, V increases nearly linearly with metal content for the solid solution of Cu in /3-rh boron. In addition to the elements listed in Table 1, the expansion of the unit cell exceeds 7.0 X 10 pm for saturated solid solutions " of Ti, V, (2o, Ni, As, Se and Hf in /3-rh boron, whereas the increase is smaller for the remaining elements. The solubility of these elements does not exceed a few tenths at %. The microhardness of the solid solution increases with V . Boron is a brittle material, indicating the accommodation of transition-element atoms in the -rh boron structure is associated with an increase in the cohesion energy of the solid. 

Thus, studies on the chemical structure of alkali aluminosilica gels utilized in zeolite synthesis reveal a complicated dependence in the distribution of components between the solid and liquid phases. At the same time, in the case of gels prepared from the homogenous solutions, the structural elements of disordered (Si,Al,0)-network in the gel skeleton and those of the regular (Si,Al,0) -frameworks in zeolites probably are... 

At x 0.429( the Region B particles corresponding to the cubic phase dominate the structures as seen by S.E.M. As before, for both composite and coprecipitated samples, this phase appears (by EDX) to consist primarily of Y, B1 and Ba, with traces of Ca and Cu. The remainder of the copper Is mostly present as small, smooth chunks, which. In the composite material, contain only traces of the other elements, and In the coprecipitated sample, contain large concentrations of both strontium and calcium. It seems likely that both phases In these complex systems exist as solid solutions, and that the exact partition of the elements between the phases Is a klnetlcally controlled phenomenon, determined by the starting materials from which they were synthesized. 

Complete structural characterization of a material involves not only the elemental composition for major components and a study of the crystal structure, but also the impurity content (impurities in solid solution and/or additional phases) and stoichiometry. Noncrystalline materials can display unique behavior, and noncrystalline second phases can alter properties. Both the long-range order and crystal imperfection or defects must be defined. For example, the structural details which influence properties of oxides include the impurity and dopant content, nonstoichiometry, and the oxidation states of cations and anions. These variables also influence the point-defect structure, which in turn influences chemical reactivity, and electrical, magnetic, catalytic, and optical properties. 

The constant compositions of ternary compounds and the absence of solid solutions on the basis of binary compounds are other characteristic features of scandiiun systems (with the exception of the systems Sc-M-Ga with M = rare earth or 4A element). However, in some systems solid solutions of phases with narrow homogeneity regions occur. Sometimes a substitution of Sc and M atoms occurs and sometimes the M and the X atoms are mutually substituted. There is no doubt that the atomic size factor has a dominating influence on the formation of solid solutions and their nature (solid solutions of substitution, of inclusion or of subtraction of atoms). Examples of solid solutions of substitution are presented in table 31. It is interesting to note that all ternary compounds which form such solid solutions crystallize in structures characteristic for binary compoimds. 

Usually, a solid is generated starting from a solution that can be either fluid (mi rture of gas or liquid solution) or solid (real solid with point defects and thus re rded as a solution of structure elements). The thermodynamics of such heterogenous systems is not basically different from what we have already considered, but the concept of supersaturation is usually used. 

Solid sodium nitrite (0.97 g) was added at room temperature with stirring over a period of one hour to a solution of 2-chloro-9-(2-hydroxyethoxymethyl)adenine (0.5 g) in glacial acetic acid (10 ml). The reaction mixture was stirred for an additional A A hours. The white solid was removed by filtration, washed with cold acetic acid and then well triturated with cold water to remove the sodium acetate present. The solid product was retained. The combined acetic acid filtrate and wash was evaporated at reduced pressure and 40°C bath temperature and the residual oil triturated with cold water. The resulting solid material was combined with the previously isolated solid and the combined solids dried and recrystallized from ethanol to give 2chloro-9-(2-hydroxyethoxymethyl)+iypoxanthine (0.25 g), MP>310°C. Elemental analysis and NMR spectrum were consistent with this structure. 

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