A thermodynamic model for di-trioctahedral chlorite from experimental and natural data in the system MgO-FeO-Al2O3-SiO2-H2O. Applications to P-T sections and geothermometry

We present a new thermodynamic activity-composition model for di-trioctahedral chlorite in the system FeO–MgO–Al2O3–SiO2–H2O that is based on the Holland–Powell internally consistent thermodynamic data set. The model is formulated in terms of four linearly independent end-members, which are amesite, clinochlore, daphnite and sudoite. These account for the most important crystal-chemical substitutions in chlorite, the Fe–Mg, Tschermak and di-trioctahedral substitution. The ideal part of end-member activities is modeled with a mixing-on-site formalism, and non-ideality is described by a macroscopic symmetric (regular) formalism. The symmetric interaction parameters were calibrated using a set of 271 published chlorite analyses for which robust independent temperature estimates are available. In addition, adjustment of the standard state thermodynamic properties of sudoite was required to accurately reproduce experimental brackets involving sudoite. This new model was tested by calculating representative P–T sections for metasediments at low temperatures (<400 °C), in particular sudoite and chlorite bearing metapelites from Crete. Comparison between the calculated mineral assemblages and field data shows that the new model is able to predict the coexistence of chlorite and sudoite at low metamorphic temperatures. The predicted lower limit of the chloritoid stability field is also in better agreement with petrological observations. For practical applications to metamorphic and hydrothermal environments, two new semi-empirical chlorite geothermometers named Chl(1) and Chl(2) were calibrated based on the chlorite + quartz + water equilibrium (2 clinochlore + 3 sudoite = 4 amesite + 4 H2O + 7 quartz). The Chl(1) thermometer requires knowledge of the (Fe3+/ΣFe) ratio in chlorite and predicts correct temperatures for a range of redox conditions. The Chl(2) geothermometer which assumes that all iron in chlorite is ferrous has been applied to partially recrystallized detrital chlorite from the Zone houillère in the French Western Alps.

The calculation of Afρ and mass loss rate for comets

Ab initio calculations of Afρ are presented using Mie scattering theory and a Direct Simulation Monte Carlo (DSMC) dust outflow model in support of the Rosetta mission and its target 67P/Churyumov-Gerasimenko (CG). These calculations are performed for particle sizes ranging from 0.010 μm to 1.0 cm. The present status of our knowledge of various differential particle size distributions is reviewed and a variety of particle size distributions is used to explore their effect on Afρ , and the dust mass production View the MathML sourcem˙. A new simple two parameter particle size distribution that curtails the effect of particles below 1 μm is developed. The contributions of all particle sizes are summed to get a resulting overall Afρ. The resultant Afρ could not easily be predicted a priori and turned out to be considerably more constraining regarding the mass loss rate than expected. It is found that a proper calculation of Afρ combined with a good Afρ measurement can constrain the dust/gas ratio in the coma of comets as well as other methods presently available. Phase curves of Afρ versus scattering angle are calculated and produce good agreement with observational data. The major conclusions of our calculations are: – The original definition of A in Afρ is problematical and Afρ should be: qsca(n,λ)×p(g)×f×ρqsca(n,λ)×p(g)×f×ρ. Nevertheless, we keep the present nomenclature of Afρ as a measured quantity for an ensemble of coma particles.– The ratio between Afρ and the dust mass loss rate View the MathML sourcem˙ is dominated by the particle size distribution. – For most particle size distributions presently in use, small particles in the range from 0.10 to 1.0 μm contribute a large fraction to Afρ. – Simplifying the calculation of Afρ by considering only large particles and approximating qsca does not represent a realistic model. Mie scattering theory or if necessary, more complex scattering calculations must be used. – For the commonly used particle size distribution, dn/da ∼ a−3.5 to a−4, there is a natural cut off in Afρ contribution for both small and large particles. – The scattering phase function must be taken into account for each particle size; otherwise the contribution of large particles can be over-estimated by a factor of 10. – Using an imaginary index of refraction of i = 0.10 does not produce sufficient backscattering to match observational data. – A mixture of dark particles with i ⩾ 0.10 and brighter silicate particles with i ⩽ 0.04 matches the observed phase curves quite well. – Using current observational constraints, we find the dust/gas mass-production ratio of CG at 1.3 AU is confined to a range of 0.03–0.5 with a reasonably likely value around 0.1.