Precise geothermometry on fluid inclusion populations that trapped mixtures of immiscible fluids

A population of fluid inclusions that sampled boiling, condensing, effervescing, or otherwise immiscible fluids (aqueous, carbonic, or silicate melt) is potentially the most sensitive of geothermobarometers for diagenetic, hydrothermal, metamorphic, and igneous environments. This paper introduces a new, simple procedure for high-precision (to tenths of a degree usually) retrieval of crystal growth temperatures, which extends applications of fluid-inclusion studies for gradient-reconstructive hydrothermal fluid dynamics and physico-chemical modelling, and for extracting stable-isotopic fractionation factors and precise thermochemical data for end-member components of minerals by analysis of natural assemblages. In contrast to traditional estimates of the entrapment temperature (T_trap) as equivalent to the frequency mode of a homogenization temperature (T_h) histogram, or the lowest Th in the measured range, the new data-reduction prc cedure uses the frequency distribution in the entire collection of measurements spanning a large T_h range, in order to determine by regression analysis the average T_trap. In theory, a population of coeval fluid inclusions that sampled immiscible fluids should have an exponential frequency distribution of the fluid-phase proportions that were trapped as heterogeneous mixtures. Thermodynamic analysis of the energy budget for nucleation and growth of an immiscible fluid phase on a growing crystal surface provides a quantitative description of how the statistical moments of the exponential frequency distribution vary with crystal/liquid/gas interfacial energies, latent heat of crystal growth, and latent heat of the fluid immiscibility reaction. Tests of the physical theory on inclusion populations in natural quartz crystals that trapped boiling hydrothermal fluids reveal well developed exponential frequency distributions with statistical properties that agree closely with thermodynamic predictions. Near the end of the paper, a practical example shows how the method is quick and easy to use, and widely applicable in metamorphic, hydrothermal and diagenetic contexts. Mg-Ca-Sr-Ba carbonates and sulfates, fluorite, apatite, and scheelite precipitating from low-salinity boiling hydrothermal fluids are minerals that can only trap the aqueous liquid, not steam, in primary inclusions. They cannot provide a fluid inclusion record of hydrothermal boiling. The thermodynamic basis and examples are given. Variable T_h can have other causes than isothermal entrapment of immiscible fluids. Based on differences in physical mechanisms and energy budgets of the processes, statistical discriminants are derived to distinguish dispersion of T_h that is due to (1) heterogeneous entrapment, (2) analytical imprecision, (3) inelastic stretching of the inclusion cavity during prior heating in nature or in the laboratory, (4) post-entrapment necking, and (5) real variation in entrapment temperature of immiscible fluids in an analyzed inclusion population.