A new activity model for Mg\u2013Al biotites determined through an integrated approach

Abstract

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, ΔHdis, 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 XEas = 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 (Cp) 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 Cp measurements on a pure synthetic sample, is Scal = 319.4 ± 2.2 J/(mol K). The standard entropy, So, for Phl is 330.9 ± 2.2 J/(mol K), which is obtained by adding a configurational entropy term, Scfg, 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 So, gives a standard enthalpy of formation of Phl, Delta H^{text{o}}_{text{f}} ,_{text{Phl}} = − 6209.83 ± 1.10 kJ/mol, which is 7–8 kJ/mol less negative than published values. The superambient Cp of Phl is given by the polynomial [J/(mol K)] as follows: C_{text{p}} = 667.37left( { pm 7} right) - 3914.50left( { pm 258} right) cdot T^{ - 0.5} - 1.52396left( { pm 0.15} right) times 10^{7} cdot T^{ - 2} + , 2.17269left( { pm 0.25} right) times 10^{9} cdot 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 So = 294.5 ± 3.0 J/(mol K) for this end-member. This value is in excellent agreement with its DFT-derived So, but ~ 8% smaller than values as appearing in thermodynamic data bases. The DFT-computed superambient Cp of Eas is given by the polynomial [in J/(mol K)] as follows: C_{text{p}} = 656.91left( { pm 14} right) - 3622.01left( { pm 503} right) cdot T^{ - 0.5} - 1.70983left( { pm 0.33} right) times 10^{7} cdot T^{ - 2} + , 2.31802left( { pm 0.59} right) times 10^{9} cdot T^{ - 3}. A maximum excess enthalpy of mixing, ΔHex, 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 ΔHex determined from published solution-calorimetry data. The mixing behaviour can be described by a symmetric interaction parameter W^{text{H}}_{{{text{Phl}},{text{Eas}}}} = 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 Delta H^{text{o}}_{{{text{f}},{text{Eas}}}} = − 6358.5 ± 1.4 kJ/mol in good agreement with the independently DFT-derived value of {Delta H^{rm o}_{rm f,Eas}}^{rm 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.