Solid solutions strain versus electron transfer

3 Solution energetics trends and rationalization schemes Solid solutions strain versus electron transfer 

The factors that affect the energetics of solid solutions and indirectly solid solubility are to a large extent the same as those that control the enthalpy of formation of compounds. Most often the differences between the atomic radii of the participating elements, in electronegativity and in valence electron density are considered for solutions of elements. For solid solutions of binary compounds, similar factors are used, but some measure of the volume of the compounds is often used instead of atomic radii. 

Two elements or compounds that do not adopt the same crystal structure cannot exhibit complete solid solubility except when one of the space groups is a subgroup of the other. The energetics of solid solutions of compounds with different structures are obviously difficult to treat systematically and trends may be impossible to obtain, since the energetics is largely related to structural short-range order. We will thus confine our discussion of solid solutions to systems where the two end-members take the same crystal structure. 

For ionic solutions the strain energy seem to be relatively more important than for the metallic alloy systems [38-40] and the size difference between the two components being mixed dominates the energetics, although other factors are also of importance. In cases where the the covalency or ionicity of the components being mixed are largely different a limited solid solubility also must be expected, even 

the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74)  

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