Theoretical calculation of Gibbs free energy of mixing of biotite: Phlogopite-annite-eastonite-siderophyllite system

초록

The Gibbs free energy of mixing (ΔG<inf>mix</inf>) can be represented as the sum of the ideal mixing energy (ΔG<inf>id</inf>) and the excess energy (G<inf>ex</inf>). For biotite in phlogopite (Ph)-annite (An)-eastonite (Es)-siderophyllite (Sd) system, ΔG<inf>id</inf> is estimated based on MOS (mixing on site) model and G<inf>ex</inf> is obtained from the theoretically calculated binding energies of biotite. Previous experimental works suggested that Ph-An and possibly Ph-Es pairs form ideal solutions. In this study, however, G<inf>ex</inf> shows that none of the binary solutions among Ph-An-Es-Sd end-members are ideal. The calculated ΔG<inf>mix</inf> indicates that Ph-An and Es-Sd pairs form complete solutions, but Ph-Es and An-Sd pairs both mixed by Tschermak's substitution show miscibility gaps. The limit of Tschermak's substitution in biotite is a function of the mole fraction of Fe in the trioctahedral site, X(Fe), and temperature. A comparison of the solvus and spinodal points obtained from the calculated ΔG<inf>mix</inf> with the chemical compositions of the synthesized and natural biotites implies that Es and Sd are metastable and the limits of Tschermak's substitution are determined not by solvus curves but by spinodal ones. Most chemical compositions of natural biotite fall fairly well within the range defined by the estimated spinodal curves at 800°C, although there are some out-lying biotites especially when their X(Fe) is between 0.5 and 0.7. The general good agreement in limits of Tschermak's substitution between what natural biotite shows and what this study predicts suggests that the theoretical function of thermodynamic mixing of this study seems promising to be applied for understanding the behavior of not only biotite but also other similar solid solutions, particulary when experimental approach is difficult.

키워드