Thermodynamic Solution Models: Non-electrolytes
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Thermodynamic Solution and Mixing Models: Non-electrolytes
Solution properties of minerals and melts form the link between laboratory experimental data in simplified model systems and complex natural and other systems which motivate the experimental investigations. The solution properties need to be expressed as a function of composition, temperature and pressure using forms that are able to represent the data over a sufficiently large range of conditions, and can also be extrapolated well beyond the range of experimental data. The purpose of thermodynamic solution and mixing models is the analytical development of these forms. The solution models provide useful rational expressions of the activity of a component in different types of solutions, whereas the mixing models deal with the excess thermodynamic functions. In this chapter we would deal with a variety of thermodynamic solution and mixing models that have been developed over many years, using both theoretical and empirical approaches, and have been applied to model geologically important solutions with different degrees of success1 .
9.1 Ionic Solutions An ionic solution is the one in which individual ions or specific ionic complexes constitute the mixing units. As an example, consider a binary olivine solid solution (Fe,Mg)2 SiO4 . In this the mixing units are Fe2+ and Mg, while the complex (SiO4 )4constitutes an inert framework. This is an example of a single-site ionic solid solution. A solid solution such as garnet, VIII (Fe,Mg,Ca,Mn)3 VI (Al,Cr,Fe3+ )2 Si3 O12 , is an example of two-site ionic solution (the left-hand superscripts indicate the oxygen coordination numbers of the cations). Similarly, there can be multi-site ionic solutions involving substitutions in several sites which are internally charged balanced. When there are substitutions in more than one site, the solution also has a reciprocal property arising from interactions between individual sites. Thus, solid
1 Much
of the material in this section was previously published in EMU notes in Mineralogy, v. 3 (Ganguly, 2001)
J. Ganguly, Thermodynamics in Earth and Planetary Sciences, C Springer-Verlag Berlin Heidelberg 2008 DOI 10.1007/978-3-540-77306-1 9,
249
250
9 Thermodynamic Solution and Mixing Models: Non-electrolytes
solutions involving internally charge-balanced substitutions within more than one site are commonly referred to as reciprocal solutions. It should be noted at the outset that all expressions for the activity of a component are equivalent as long as these are based on the same standard state of the component. But explicit expression of the activity coefficient of a component depends on the form of the activity expression. The ionic solution model provides a rational approach towards the development of such expressions.
9.1.1 Single Site, Sublattice and Reciprocal Solution Models From a microscopic point of view, ideality of mixing implies random distribution of the mixing units. Thus, in general the activity of an end-member component in a solution should be expr
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