Framework for a Volume Model for Monoclinic Amphibole

We developed a framework for a volume model for monoclinic amphiboles that can be applied to a new amphibole solution model compatible with the MELTS algorithm. The model is designed to allow the incorporation of minor components that are not present in the existing MELTS-compatible amphibole models. These minor components help stabilize amphibole through their configurational contribution to the Gibbs energy. The calibrated model permits estimation of amphibole volumes for compositions in the oxide space SiO2-TiO2-Al2O3-Cr2O3-FeO-Fe2O3-MnO-MgO-Na2O-K2O-H2O-F, expressed as linear combinations of the end-member components tremolite [□Ca2Mg5Si8O22(OH)2], cummingtonite [□Mg7Si8O22(OH)2], grunerite [□Fe2+7Si8O22(OH)2], clino-mangano-suenoite [□Mn7Si8O22(OH)2], pargasite [NaCa2(Mg4Al)(Si6Al2)O22(OH)2], magnesiohastingsite [NaCa2(Mg4Fe3+)(Si6Al2)O22(OH)2], tschermakite [□Ca2(Mg3Al2)(Si6Al2)O22(OH)2], chromio-pargasite [NaCa2(Mg4Cr3+)(Si6Al2)O22(OH)2], potassic-richterite [K(NaCa)Mg5Si8O22(OH)2], glaucophane [□Na2(Mg3Al2)Si8O22(OH)2], kaersutite [NaCa2(Mg3Ti4+Al)(Si6Al2)O22(O)2], oxo-magnesio-hastingsite [NaCa2(Mg2Fe3+3)(Si6Al2)O22(O)2] and fluoro-tremolite [□Ca2Mg5Si8O22(F)2]. This framework accounts for some ordering of cations among A- and B-sites, as well as between B- and C-sites and C and T-sites in the amphibole crystal structure, although the end members were selected so that each has a fixed ordering state. We used this framework to fit a preliminary volume model for clino-amphiboles using site occupancy data sourced from X-ray refinements from the American Mineralogist Crystal Structure Database and the crystal-chemical database for amphiboles at the CNR-Istituto di Geoscienze e Georisorse (Pavia, Italy), plus additional refinements from peer-reviewed journals. We initially fit a linear model and then used volume residuals and χ2 statistics to select second-order parameters that capture nonlinear mixing behavior. We test the quality of the fit parameters using χ2 statistics and by a Monte Carlo scheme aimed at gauging the quality of the model parameters, given measured and estimated uncertainties in the data. Interrogation of the available X-ray refinement data uncovers regions in the amphibole compositional space that are still insufficiently characterized to be confidently described by our model (particularly the rare Mn-amphiboles). We further address regions where X-ray refinement data is lacking in high pressure and high temperature regimes, which will be a limiting factor in terms of extending the calibration to account for compressibility and thermal expansion.