A new activity model for biotite and its application

Abstract

A new activity model for biotite is formulated in the system K2O-FeO-MgO-Al2O3-SiO2-H2O-TiO2-O2 (KFMASHTO), which extends that for the KFMASH system by introducing a titanium-biotite and a ferric-biotite end-member (tbio: K(TiMg2)[(O)2(AlSi3)O10] and fbio: K(Fe3+Mg2)[(OH)2(Al2Si2)O10]), as well as a pyrophyllite end-member (pyp: Al2[(OH)2Si4O10]) that accounts for the presence of octahedral excess-Al in natural biotites. Phonon calculations applying density functional theory (DFT) using the software Castep yielded the standard entropies of tbio and fbio as Sotbio = 328.06 J/(mol·K) and Sofbio = 301.69 J/(mol·K), and their heat capacity functions. From experimental phase-equilibrium data, the enthalpy of formation value of tbio was constrained as ΔHf,tbioo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {H}_{f,tbio}^{o}$$\\end{document} = −6124.68 ± 3.33 kJ/mol. Natural data were used to derive ΔHf,fbioo\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta {H}_{f,fbio}^{o}$$\\end{document}= −5935.3 ± 6.6 kJ/mol. The single-defect DFT method was applied to parameterize important macroscopic mixing properties (macro-W’s) involving tbio and pyp end-members in the model (fbio was treated ideal). Castep-derived microscopic interaction energies (micro-w’s) are presented herein for KFMASH-biotite. The octahedral same-site (M1) Mg–Al mixing micro-w (wMgAl(M1)), the same-site tetrahedral Si-Al mixing parameter (wSiAl(T1)) and the related cross-site term are: wMgAl(M1) = 82.5 kJ/mol, wSiAl(T1) = 95.6 kJ/mol (two T1-sites) and wMgAlAlSi(M1T1)=\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${w}_{MgAlAlSi(M1T1)}=$$\\end{document} 175.1 kJ/mol. The linear combination of these micro-w’s gives a macroscopic Wphleas = 18.8 kJ/mol, that is not transferable to other mineral groups. Micro w’s for Mg-Fe mixing in biotite (wMgFe(M1), wMgFe(M2),wMgMgFeFe(M1M2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${w}_{MgMgFeFe(M1M2)}$$\\end{document}), 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-w’s and reassembled macro-W’s for petrological calculations. Test calculations on 5 samples from low- to high-grade metamorphic environments covering metapelite to greywacke bulk-compositions using Perple_X 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.