A new activity model for Mg-Al biotites determined through an integrated approach.

A new activity model for Mg-Al biotites was formulated through an integrated approach combining various experimental results (calorimetry, line-broadening in infrared (IR) spectra, analysis of existing phase-equilibrium data) with density functional theory (DFT) calculations. The resulting model has a sound physical-experimental basis. It considers the three end-members phlogopite (Phl, KMg3[(OH)2AlSi3O10]), ordered eastonite (Eas, KMg2Al[(OH)2Al2Si2O10]), and disordered eastonite (dEas) and, thus, includes Mg-Al order-disorder. The DFT-derived disordering enthalpy, ΔH dis, associated with the disordering of Mg and Al on the M sites of Eas amounts to 34.5 ± 3 kJ/mol. Various biotite compositions along the Phl-Eas join were synthesised hydrothermally at 700 °C and 4 kbar. The most Al-rich biotite synthesized had the composition X Eas = 0.77. The samples were characterised by X-ray diffraction (XRD), microprobe analysis and IR spectroscopy. The samples were studied further using relaxation calorimetry to measure their heat capacities (C p) at temperatures from 2 to 300 K and by differential scanning calorimetry between 282 and 760 K. The calorimetric (vibrational) entropy of Phl at 298.15 K, determined from the low-T C p measurements on a pure synthetic sample, is S cal = 319.4 ± 2.2 J/(mol K). The standard entropy, S o, for Phl is 330.9 ± 2.2 J/(mol K), which is obtained by adding a configurational entropy term, S cfg, of 11.53 J/(mol K) due to tetrahedral Al-Si disorder. This value is ~1% larger than those in different data bases, which rely on older calorimetrical data measured on a natural near-Phl mica. Re-analysing phase-equilibrium data on Phl + quartz (Qz) stability with this new S o, gives a standard enthalpy of formation of Phl, Δ H f o , Phl = - 6209.83 ± 1.10 kJ/mol, which is 7-8 kJ/mol less negative than published values. The superambient C p of Phl is given by the polynomial [J/(mol K)] as follows: C p = 667.37 ± 7 - 3914.50 ± 258 · T - 0.5 - 1.52396 ± 0.15 × 10 7 · T - 2 + 2.17269 ± 0.25 × 10 9 · T - 3 . Calorimetric entropies at 298.15 K vary linearly with composition along the Phl-Eas join, indicating ideal vibrational entropies of mixing in this binary. The linear extrapolation of these results to Eas composition gives S o = 294.5 ± 3.0 J/(mol K) for this end-member. This value is in excellent agreement with its DFT-derived S o, but ~ 8% smaller than values as appearing in thermodynamic data bases. The DFT-computed superambient C p of Eas is given by the polynomial [in J/(mol K)] as follows: C p = 656.91 ± 14 - 3622.01 ± 503 · T - 0.5 - 1.70983 ± 0.33 × 10 7 · T - 2 + 2.31802 ± 0.59 × 10 9 · T - 3 . A maximum excess enthalpy of mixing, ΔH ex , of ~6 kJ/mol was derived for the Phl-Eas binary using line-broadening from IR spectra (wavenumber region 400-600 cm-1), which is in accordance with ΔH ex determined from published solution-calorimetry data. The mixing behaviour can be described by a symmetric interaction parameter W Phl , Eas H = 25.4 kJ/mol. Applying this value to published phase-equilibrium data that were undertaken to experimentally determine the Al-saturation level of biotite in the assemblage (Mg-Al)-biotite-sillimanite-sanidine-Qz, gives a Δ H f , Eas o = - 6358.5 ± 1.4 kJ/mol in good agreement with the independently DFT-derived value of Δ H f , Eas o DFT = - 6360.5 kJ/mol. Application examples demonstrate the effect of the new activity model and thermodynamic standard state data, among others, on the stability of Mg-Al biotite + Qz.