Timescales determining the degree of kinetic isotope fractionation by evaporation and condensation

A first order characteristic of the relative abundance of the elements in solar system materials ranging in size from inclusions in primitive meteorites to planetary sized objects such as the Earth and the Moon is that they are very much like that of the Sun for the more refractory elements but systematically depleted to varying degrees in the more volatile elements. This is taken as evidence that evaporation and and/or condensation were important processes in determining the distinctive chemical properties of solar system materials. In some instances there is also isotopic evidence suggesting evaporation in that certain materials are found enriched in the heavy isotopes of their more volatile elements. Here model calculations are used to explore how the relative rates of various key processes determine the relationship between elemental and isotopic fractionation during partial evaporation and partial condensation. The natural measure of time for the systems considered here is the evaporation or condensation timescale defined as the time it would take under the prevailing conditions for evaporation or condensation to completely transfer the element of interest between the two phases of the system. The other timescales considered involve the rate of change of temperature, the rate at which gas is removed from further interaction with the condensed phase, and the rates of diffusion in the condensed and gas phases. The results show that a key determinant of whether or not elemental fractionations have associated isotopic effects is the ratio of the partial pressure of a volatile element (Pi) to its saturation vapor pressure (Pi,sat) over the condensed phase. Systems in which the rate of temperature change or of gas removal are slow compared to the evaporation or condensation timescale will be in the limit Pi ∼ Pi,sat and thus will have little or no isotopic fractionation because at the high temperatures considered here there is negligible equilibrium fractionation of isotopes. If on the other hand the temperature changes are relatively fast, then Pi ≠ Pi,sat and there will be both elemental and isotopic fractionation during partial evaporation or partial condensation. Rapid removal of evolved gas results in Pi ≪ Pi,sat which will produce isotopically heavy evaporation residues. Diffusion-limited regimes, where transports within a phase are not sufficiently fast to maintain chemical and or isotopic homogeneity, will typically produce less isotopic fractionation than had the phases remained well mixed. The model results are used to suggest a likely explanation for the heavy silicon and magnesium isotopic composition of Type B CAIs (as due to rapid partial melting and subsequent cooling at rates of a few °C per hour), for the uniformity of the potassium isotopic composition of chondrules despite large differences in potassium depletions (as due to volatilization of potassium by reheating in regions of large but variable chondrules per unit volume), and that the remarkable uniformity of the potassium isotopic composition of solar system materials is not a measure of the relative importance of evaporation and condensation but rather due to the solar nebula having evolved sufficiently slowly that materials did not significantly depart from chemical equilibrium.