The thermodynamics of iron and magnesium partitioning between olivine and liquid: criteria for assessing and predicting equilibrium in natural and experimental systems

摘要: The equations for the chemical potentials of fayalite and forsterite components in olivine liquid may be used to derive a thermodynamic expression exchange coefficient \( K^{{\;\;\;{\text{Mg - Fe}}}}_{{D{\text{Ol Liq}}}} \) (defined as molar Mg/Fe2+ divided by Mg/Fe coexisting olivine). This expression, well known literature, shows that is function temperature, pressure, compositions liquid. Quantitative application this equation requires knowledge free energies volumes crystalline forsterite, description non-ideality Fe–Mg mixing olivine. Independent measurements these parameters reported literature have been constrain influence pressure composition on iron–magnesium partitioning. other requirement calculation ratio activity coefficients Fe2+ Mg phase (γFe2+/γMg), but no independent predictive model exists. To assess predict variation γFe2+/γMg composition, database almost 400 olivine–liquid pairs at 1 bar 200 experiments pressures upper stability limit has considered. Measured values data base vary from 0.17 0.45, were chosen cover wide ranges temperature addition composition. Within framework equation, found silica content alkali Water also inferred direct high pressure. A K_{D} {\kern 1pt} ^{{{\text{Mg}} {\text{Fe}}}}_{{{\text{Ol}} {\text{Liq}}}} proposed which recovers all input 1σ level uncertainty. It equilibrium published experimental studies mantle melting illustrate individual such Application field melt inclusions discussed.