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Beginning in the 1920’s, crystal chemical and thermodynamic studies produced well-known and widely used empirical rules and structural systematics for solid solutions or isomorphous mixtures (mixed crystals). Subsequently, from the 1940’s to the present day attempts to calculate structural relaxation and energetic properties of solid solutions have been undertaken using different approaches. It has been shown by theoreticians, as well as experimentalists, that a treatment of local structure relaxation in a solid solution is critical if one is to understand the bulk or macroscopic properties. Presently there is a number of different theoretical approaches available to describe and calculate the mixing properties of solid solutions: e.g. mixing energy, mixing volume, configurational and vibrational entropies, excess free energy and stability (i.e. solubility limits as a function of temperature and pressure). They can be classified into three main types:

  1. Semi-empirical phenomenological models.

  2. Semi-classical atomistic approaches.

  3. First-principle or ab initio calculations.

This chapter presents a discussion, analysis and further development of semi-empirical phenomenological models [atomistic potential simulations and first-principle calculations are discussed by Dove (2001) and Heine (2001), respectively]. It is emphasised that this approach to structural relaxation and energetic properties of solid solutions retains its validity, because it provides insight into the physical nature of the mixing properties and enables one to describe them in analytical terms. Binary oxide solid solutions, MO–M′O, with the NaCl-type structure are given special consideration because they have been subjected to extensive theoretical and experimental investigation.

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