A new activity model for biotite and its application.

Unlabelled: A new activity model for biotite is formulated in the system KO-FeO-MgO-AlO-SiO-HO-TiO-O (KFMASHTO), which extends that for the KFMASH system by introducing a titanium-biotite and a ferric-biotite end-member (: K(TiMg)[(O)(AlSi)O] and : K(FeMg)[(OH)(AlSi)O]), as well as a pyrophyllite end-member (: Al[(OH)SiO]) that accounts for the presence of octahedral excess-Al in natural biotites. Phonon calculations applying density functional theory (DFT) using the software yielded the standard entropies of and as  = 328.06 J/(mol·K) and  = 301.69 J/(mol·K), and their heat capacity functions. From experimental phase-equilibrium data, the enthalpy of formation value of was constrained as = -6124.68 ± 3.33 kJ/mol. Natural data were used to derive = -5935.3 ± 6.6 kJ/mol. The single-defect DFT method was applied to parameterize important macroscopic mixing properties (macro-'s) involving and end-members in the model ( was treated ideal). -derived microscopic interaction energies (micro-'s) are presented herein for KFMASH-biotite. The octahedral same-site (M1) Mg-Al mixing micro- ( ), the same-site tetrahedral Si-Al mixing parameter ( ) and the related cross-site term are:  = 82.5 kJ/mol,  = 95.6 kJ/mol (two T1-sites) and 175.1 kJ/mol. The linear combination of these micro-'s gives a macroscopic  = 18.8 kJ/mol, that is not transferable to other mineral groups. Micro 's for Mg-Fe mixing in biotite ( , ), are all close to ideality. The biotite activity model of this study is thus a first example of next-generation activity models that use DFT- and thus physically based micro-'s and reassembled macro-'s for petrological calculations. Test calculations on 5 samples from low- to high-grade metamorphic environments covering metapelite to greywacke bulk-compositions using suite of programs illustrate the performance of the new biotite activity model. Computed mineral-chemistries are in all cases in better agreement with measured compositions than resulting from published activity models of biotite.

Supplementary Information: The online version contains supplementary material available at 10.1007/s00410-024-02173-6.