target="_blank" rel="nofollow" href="#fb3_img_img_bb4ef3a5-ceca-50cf-a71b-491e96e7fb98.png" alt="StartFraction upper D Subscript i Baseline Over upper D Subscript j Baseline EndFraction equals left-parenthesis StartFraction m Subscript j Baseline Over m Subscript i Baseline EndFraction right-parenthesis Superscript beta"/> . Table 1.1 gives a summary of β values for different isotope pairs in different silicate melts and minerals. The experiments by Watkins et al. (2009 and 2011) are noteworthy in showing that the kinetic isotope fractionation exponents β in silicate liquids for calcium are very different depending on the composition of the liquid. Watkins et al. (2014) also showed that β can depend on the direction of diffusion in composition space. This evidence of the complexity of kinetic isotope fractionation in silicate liquids reinforces the importance of carrying out diffusion experiments with materials from a natural setting to determine effective diffusion coefficients for modeling the elemental and isotopic fractionations measured in rocks from the natural setting. Chopra et al. (2012) exemplify this approach in their study of isotopic fractionation across contacts between silicic and mafic rock from the Vinalhaven igneous complex in Maine. There are several other studies of kinetic isotope fractionation by diffusion in condensed systems that are not listed in Table 1.1, but which might be of interest to some readers. These include experiments documenting isotope fractionation of ions diffusing in water (Bourg et al., 2010; Richter et al., 2006b) and isotopic fractionation of iron and nickel isotopes by diffusion in Fe–Ni alloys (Watson et al., 2016).
Table 1.1 Summary of the exponents β from laboratory diffusion experiments with silicate melts and minerals.
| Silicate Melts | Isotopes | β | Reference |
|---|---|---|---|
| CaO‐Al2O3‐SiO2 | 48Ca – 40Ca | 0.05, 0.1 | Richter et al., 1999 |
| CaO‐Al2O3‐SiO2 | 76Ge – 70Ge | < 0.025 | Richter et al., 1999 |
| Rhyolite‐basalt | 44Ca – 40Ca | 0.05 | Richter et al., 2003 |
| Rhyolite‐basalt | 7Li – 6Li | 0.215 | Richter et al., 2003 |
| Rhyolite‐basalt | 26Mg – 24Mg | 0.05 | Richter et al., 2008 |
| Rhyolite‐basalt | 56Fe – 54Fe | 0.03 | Richter et al., 2009b |
| Rhyolite‐basalt | 44Ca – 40Ca | 0.035 | Watkins et al., 2009 |
| Rhyolite‐Ugandite | 44Ca – 40Ca | 0.035 | Watkins et al., 2009 |
| Albite‐anorthite | 44Ca – 40Ca | 0.021 | Watkins et al., 2011 |
| Albite‐diopside | 44Ca – 40Ca | 0.165 | Watkins et al., 2011 |
| Albite‐diopside | 26Mg – 24Mg | 0.10 | Watkins et al., 2011 |
| Granite‐Basalt | 26Mg – 24Mg | 0.040, 0.045 | Chopra et al., 2012 |
| Wet rhyolite | 7Li – 6Li | 0.228 | Holycross et al., 2018 |
| Silicate Minerals | |||
| Augite | 7Li – 6Li | 0.35±0.1 | Richter et al., 2014b |
| Olivine | 7Li – 6Li | 0.04±0.1 | Richter et al., 2016 |
| Olivine | 56Fe – 54Fe | 0.09±0.05 | Sio et al., 2018 |
Note: Uncertainties are listed for β Li in augite and olivine because they are much larger than in the case of liquids, reflecting the complexity of multiple‐site lithium diffusion in these minerals. The uncertainty of β Fe was given by Sio et al. (2018).
The section on thermal isotope fractionation by Soret diffusion in molten basalt showed that even small differences of a few tens of degree, if sustained for a sufficient length of time, will produce easily measured isotopic fractionations of all the major elements of basalt and also of potassium and lithium. Fig. 1.9 in Section 1.4 gives a summary of the thermal isotope fractionations in terms of a parameter Ω with units of per mil fractionation per unit atomic mass difference of the isotopes per 100°C. The Ω values range from greater than 6 for lithium, to 3.5 for magnesium, and to a low of 0.5 for silicon.
Vacuum evaporation experiments illustrated yet another type of kinetic isotope fractionation that affected refractory inclusion in meteorites called CAIs that are the oldest dated materials in our solar system. The evaporation experiments are used to determine evaporation rate as a function of temperature and the isotopic fractionation of the evaporation flux compared to the isotopic composition of the evaporating condensed phase. The evidence that some CAIs did indeed evaporate a significant amount of their initial magnesium and silicon come from their correlated magnesium and silicon isotopic fractionation that displays a trend very much like what is found in laboratory evaporation resides (see Fig. 1.18). The amount of magnesium and silicon lost by a particular CAI can be determined using the experimentally determined kinetic fractionation parameter α Mg (or α Si) in the Rayleigh isotope fractionation equation (equation 1.15) to translate the measured isotopic fractionation of Mg (or Si) into the fraction of the initial amount of Mg (or Si) volatilized. This approach can be used to restore the bulk composition
