A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra I: enthalpy, entropy and molar volume

The thermodynamic properties of silicate minerals can be described as a linear combination of the fractional properties of their constituent polyhedra. In contrast, given the thermodynamic properties of these polyhedra, the thermodynamic properties of minerals can be estimated, where only the crystallography of the mineral needs to be known. Such estimates are especially powerful for hypothetical mineral end‐members or for minerals where experimental determination of their thermodynamic properties is difficult. In this contribution the fractional enthalpy, entropy and molar volume for 35 polyhedra have been determined using weighted multiple linear regression analysis on a data set of published mineral thermodynamic properties. The large number of polyhedra determined, allows calculation of a much larger variety of phases than was previously possible and the larger set of minerals used provides more confident fractional properties. The OH‐bearing minerals have been described by partial and total hydroxide coordinated components, which gives better results than previous models and precludes the need of a S–V term to improve estimates of entropy. However, the fractional thermodynamic properties only give adequate results for silicate minerals and double oxides, and should therefore not be used to estimate the properties of other minerals. The thermodynamic properties of ‘new’ minerals are calculated from a linear stoichiometric combination of their constituent polyhedra, resulting in estimates generally with associated uncertainty of <5%. The quality of such data appears to be of sufficient accuracy for thermodynamic modelling as shown for meta‐bauxites from the Alps and the Aegean, where the effect of Zn on the P–T stability of staurolite can be both qualitatively and quantitatively reproduced.