1. A new activity model for biotite and its application.
- Author
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Dachs, Edgar and Benisek, Artur
- Abstract
A new activity model for biotite is formulated in the system K
2 O-FeO-MgO-Al2 O3 -SiO2 -H2 O-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 (Al2 Si2 )O10 ]), as well as a pyrophyllite end-member (pyp: Al2 [(OH)2 Si4 O10 ]) 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 So tbio = 328.06 J/(mol·K) and So fbio = 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 Δ H f , t b i o o = −6124.68 ± 3.33 kJ/mol. Natural data were used to derive Δ H f , f b i o o = −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 w M g A l A l S i (M 1 T 1) = 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), w M g M g F e F e (M 1 M 2) ), 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. [ABSTRACT FROM AUTHOR]- Published
- 2024
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