Using estimated thermodynamic properties to model accessory phases: the case of tourmaline

Accessory phases and minor components in minerals are commonly ignored in thermodynamic modelling. Such an approach seems unwarranted, as accessory phases can represent a significant element reservoir and minor components can substantially change their host mineral's stability field. However, a lack of thermodynamic data prohibits assessment of these effects. In this contribution, the polyhedron method is used to estimate the thermodynamic properties of tourmaline, a common and widespread accessory phase, stable over a range of P–T–X conditions. The polyhedron method allows Δ H , S , V , C _P and V _m ( T , P ) properties to be estimated from a linear stoichiometric summation over the fractional properties of its polyhedron constituents. To allow for estimates of tourmaline, fractional thermodynamic properties for B^III and B^IV polyhedra were derived. Mixing contributions to molar volume were evaluated and symmetrical mixing parameters derived for Al-Mg, Al-Fe and Al-Li interaction on tourmaline's Y-site and T-site Al-Si interaction. Evaluation of the estimated properties using experimental and natural equilibria between tourmaline and melts, minerals and hydrothermal fluids, shows that reliable semi-quantitative results are obtained. The boron contents in fluids coexisting with tourmaline are calculated to within an order of magnitude of measured content, and where anchor-points are available, agreement improves to within a factor of 2. Including tourmaline in petrogenetic modelling of metamorphic rocks indicates that its presence leads to disappearance of staurolite and garnet, among others, and modifies the X _Mg of coexisting phases, in line with observations on natural rocks.