On parameterizing thermodynamic descriptions of minerals for petrological calculations

A new regularization approach, termed micro-ϕ, is outlined for parameterizing activity–composition (a–x) relations and other aspects of the thermodynamic descriptions of minerals for petrological calculations. In the context of the symmetric formalism, a formulation of a–x relations that is easily generalizable to multi-component minerals, parameterization with micro-ϕ extends from where there are good data available to constrain, for example, interaction energies, to where there are little or no data. This involves decomposing the interaction energies, which are macroscopic between end-members, into their microscopic components involving interactions between elements on sites. Micro-ϕ involves heuristics to simplify and approximate these microscopic interaction energies prior to their reassembly as macroscopic interaction energies. Micro-ϕ also allows parameterization of Fe2+–Mg order–disorder between the sites of minerals. Application of micro-ϕ is illustrated by making a thermodynamic description of chlorite in FeO–MgO–Al2O3–SiO2–H2O–O, FMASHO. Micro-ϕ has been developed for use with the significant upgrade of the Holland & Powell internally consistent thermodynamic data set which required the re-evaluation of a–x relations of several common rock-forming minerals