href="#ulink_24f1c428-53bf-53a2-9f30-807d1636c12d">equation 1.10 and the isotopic fractionation coefficients α Mg and α Si for calculating the isotopic fractionation of evaporation residues using equation 1.15. When calculating the bulk composition of evaporation residues, one assumes CaO and Al2O3 are effectively conserved, being much too refractory to significantly evaporate while there is still any MgO left in the melt.
The evaporation coefficients γ Mg and γ Si are determined by the amount of initial magnesium and silicon lost by evaporation from a molten bead of a given surface area as a function of temperature and run duration. The evaporation coefficients of magnesium and silicon are very similar to each other and decrease with temperature from about 0.2 at 1900°C to about 0.05 at 1500°C (see Fig. 3 in Richter et al., 2007). The kinetic isotope fractionation factors α Mg and α Si are determined by fitting the isotopic fractionation of evaporation residues as a function of the fraction of the initial amount of the parent element remaining in the residue with calculations using the Rayleigh fractionation equation (equation 1.15). Fig. 1.17 shows the isotopic fractionation of magnesium and silicon of evaporation residues of a CAI‐like melt from vacuum evaporation experiments run for different lengths of time by Richter et al. (2007) and Knight (2009). The curved profiles are fits to the data calculated assuming perfect Rayleigh fractionation (equation 1.15) with α Mg = 0.9855 for 25Mg/24Mg and α Si = 0.0990 for 29Si/30Si. The fits are sufficiently good to confirm not only that the vacuum evaporation was a Rayleigh process but also that α Mg and are α Si do not significantly change as the composition of the evaporating material evolves by evaporation of its volatile components MgO and SiO2. The experimentally determined value α Mg = 0.9855 is significantly larger (i.e., significantly less fractionation) than the inverse square root of the atomic mass of 24Mg/25Mg (0.9797). In the case of silicon, α Si = 0.9901 is only slightly larger than the inverse square root the mass ratio 29Si16O/30Si16O (0.9890). A more detailed analysis of the magnesium isotope fractionation data in Fig. 1.17 showed that when the data from experiments run at different temperatures are fit separately with Rayleigh fractionation curves, the α Mg increased (i.e., became less fractionating) as the temperature declined from 1900°C to 1600°C (see figure 10 in Richter et al., 2007). This temperature dependence of α Mg must be extrapolated from the high temperature of the evaporation experiments down to temperatures in the range of 1450°C to 1300°C, at which the Type B CAIs were molten. If one were to use α Mg as given by the inverse square root law in the Rayleigh fractionation equation to invert the isotopic fractionation of a CAI for the amount of the parent element evaporated, it would result in an estimate of about a factor of two more magnesium evaporated compared to that calculated with α Mg derived by extrapolating the experimental values down to 1400°C. Using the experimentally determined α Mg and α Si is particularly important when using the magnesium isotopic fractionation of a CAI to determine the bulk composition of its pre‐evaporation precursor.
Figure 1.17 The unfilled circles and squares are the isotopic fractionation of magnesium and silicon in vacuum evaporation residues of a CAI‐like melt from experiments by Richter et al. (2007) for magnesium and Knight et al. (2009) for silicon. The black curved lines through the data are Rayleigh fractionation trajectories calculated as described in the text.
1.6.4. Evidence of Evaporation in Natural CAIs from Chondritic Meteorites
The correlated isotopic fractionation of magnesium and silicon in CAIs led to the suggestion that their precursors were melted by a transient heating event during which their more volatile components, MgO and SiO2, were partially lost by evaporation (see discussion in Grossman et al., 2000; Richter et al. 2002). The best evidence for this comes from comparing the correlation between the magnesium and silicon isotopic fractionation of laboratory evaporation residues with that of actual CAIs (see Fig. 1.18). The δ29Si versus δ25Mg data from the natural CAIs are somewhat scattered but there is a definite trend of larger silicon isotope fractionation being associated with larger magnesium isotope fractionation. The scatter can, for the most part, be explained by the precursor of each CAI having a somewhat different Mg/Si composition. The more silicon‐rich the precursor the faster silicon evaporates initially compared to magnesium and as a result the δ29Si versus δ25Mg trajectory will be somewhat more δ29Si‐rich than for the evaporation residue of a less silicon‐rich precursor. The same applies to the magnesium isotopic fractionation of precursors with more or less MgO compared to SiO2. Overall the comparison of the isotopic fractionation of silicon versus magnesium of evaporation residues from experiments with the trend of the natural CAI fractionations is persuasive evidence that many CAIs did indeed evaporate some fraction of their initial silicon and magnesium. Once one is persuaded that CAIs with correlate silicon and magnesium isotopic fractionation are evaporation residues, their isotopic fractionation, together with experimental values for α Mg and α Si in the Rayleigh fractionation equation, can be used calculate the fraction of silicon and magnesium that evaporated. Knight et al. (2009) used this approach to estimate of how much MgO and SiO2 had evaporated from particular CAIs to calculate the bulk composition of their precursors and make a more detailed comparison with the predictions of the bulk composition of condensates from a solar composition gas. Richter et al. (2006a) gives several examples of how the experimentally determined evaporation kinetics and associated isotopic evolution of evaporation residues can be used to calculate detailed trajectories of CAIs in time‐temperature‐bulk composition space. These trajectories show that the precursors of CAIs were reheated and partially molten for at most a few hours. A nebular shockwave was a plausible process responsible for the short‐duration heating event (see Fig. 9 in Richter et al., 2006a)
Figure 1.18 This figure compares the correlation of the silicon and magnesium isotopic fractionation of vacuum evaporation residues using data from Richter et al. (2007) and Knight et al. (2009) with isotope fractionation data from natural CAIs listed in Table 2 of Clayton et al. (1988).
1.7. SUMMARY
Sections 1.3 and 1.5 discussed experimental evidence of isotope fractionations associated with chemical diffusion at high temperature in both silicate liquids and silicate minerals, along with examples of analogous kinetic isotope fractionations in materials from natural settings. The purpose of the chemical diffusion experiments was to determine the relative magnitude of the effective diffusion coefficients Di and Dj of isotopes of atomic mass mi and mj
