Isotope Fractionation during Condensation and Evaporation during Planet Formation Processes

During the early stages of a protoplanetary disk, it is expected that the temperatures reached in the disk will lead to total or partial vaporization of dust, followed by condensation upon cooling. Similarly, chondrule forming events or giant impacts followed by magma oceans can also produce partial evaporation. Thus, moderately volatile elements can be mobilized during these thermal events, thereby leading to characteristic isotope signatures that can be used to decipher the conditions of elemental fractionation. Indeed, the magnitude of isotope fractionation of moderately volatile elements is directly modulated by the partial pressure of the element of interest. Thus, the isotope fractionation pattern for a given level of elemental depletion can be used to infer the pressure conditions during condensation or evaporation, thus providing strong constraints on astrophysical settings. The observations made on moderately volatile elements or on some major elements such as Mg, Si, or Fe isotopes demonstrate that the isotope signature is most generally more subdued than that of vacuum evaporation producing the maximum isotope fractionation. Thus, experimental studies showing the existence of kinetic isotope fractionation associated with evaporation experiments are not sufficient to interpret cosmochemical data. In this study, we show that the evaporation or condensation coefficients may play a key role in controlling isotope fractionation. The possible role of composition and temperature on the values of evaporation/condensation coefficients are emphasized. Similarly, the role of diffusion in the gas phase leading to a back reaction of condensation during evaporation (or vice versa) is addressed. In addition, we demonstrate that a new expression linking elemental depletion and isotope fractionation needs to be used in the case of evaporation or condensation in a closed system. Specifically, for condensation in a closed system, one needs to take into account the effect of decreasing oversaturation to model isotope fractionation. We also explored the effect of having a population of grains rather than a single grain on isotope fractionation associated with evaporation on the isotope trajectories. Last, the case of evaporation with multiple species produces a situation where the isotope fractionation pattern is modified. Overall, this study demonstrates a wealth of behaviors in isotope tracers associated with volatile loss that needs to be carefully investigated to fully exploit the information carried by them.