A new method to calculate end-member thermodynamic properties of minerals from their constituent polyhedra II: Heat capacity, compressibility and thermal expansion

Abstract

Thermodynamic calculations in petrology are generally performed at pressures and temperatures beyond the standard state conditions. Accurate prediction of mineral equilibria therefore requires knowledge of the heat capacity, thermal expansion and compressibility for the minerals involved. Unfortunately, such data are not always available. In this contribution we present a data set to estimate the heat capacity, thermal expansion and compressibility of mineral end-members from their constituent polyhedra, based on the premise that the thermodynamic properties of minerals can be described by a linear combination of the fractional properties of their constituents. As such, only the crystallography of the phase of interest needs to be known. This approach is especially powerful for hypothetical mineral end-members and for minerals, for which the experimental determination of their thermodynamic properties is difficult. The data set consists of the properties for 35 polyhedra in the system K-Na-Ca-Li-Be-Mg-Mn-Fe-Co-Ni-Zn-Al-Ti-Si-H, determined by multiple linear regression analysis on a data set of 111 published end-member thermodynamic properties. The large number of polyhedra determined allows calculation of a much larger variety of phases than was previously possible, and the choice of constituents together with the large number of thermodynamic input data results in estimates with associated uncertainty of generally <5%. The quality of the data appears to be sufficiently accurate for thermodynamic modelling as demonstrated by modelling the stability of margarite in the CASH system and the position of the talc-staurolite-chloritoid-pyrope absent invariant point in the KMASH system. In both cases, our results overlap within error with published equivalents. © 2005 Blackwell Publishing Ltd.