Isotopic Constraints on Earth System Processes. Группа авторов

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 of CAIs back to that of their pre‐evaporation precursor, which can then be compared to the results of thermodynamic calculations that predict the bulk composition of materials that would have condensed from solar composition gas as the solar nebula cooled. The evaporation experiments also provide information on the evaporation rates of magnesium and silicon as a function of temperature and surrounding gas pressure (mostly hydrogen). The evaporation rates were used to estimate that even the most isotopically fractionated CAIs were partially molten for only a few hours, implying a transient heating event, quite possibly a nebular shockwave.

      The importance of the laboratory experiments that quantified kinetic isotope fractionation by either diffusion or evaporation is that they provide a unique isotopic “fingerprint” with which to constrain the nature and extent of mass transfer processes in natural settings. To simply assert that an instance of zoning or bulk isotopic fractionation of a silicate material was due to diffusion or evaporation without the sort of supporting evidence that isotopes provide can lead to totally spurious estimates of its thermal history.

1.8. THOUGHTS ON FURTHER RESEARCH

      Experiments documenting kinetic isotope fractionation in silicate materials are relatively recent and have only covered a limited range of the parameter space of interest to geochemistry and cosmochemistry. Expanding the parameter space with new experiments will be an important future research direction. Recent experiments by Watkins et al. (2009; 2011; 2014) have already shown that the kinetic fractionation of major elements in silicate liquids is surprisingly dependent on the composition of the liquid and that it increases as the binary diffusion coefficient of an element increases relative to that of silicon. On the other hand, it appears that the kinetic isotope fractionation of lithium during diffusion in wet rhyolite melt (Holycross et al., 2018) is not much different than in molten rhyolite‐basalt melt. Expanding investigations to include isotopic fractionation of different elements in different silicate liquid compositions will put applications of kinetic isotope effects in geochemical studies on an increasingly sound footing.

      The present state of understanding of diffusion and associated isotopic fractionation in silicate systems is mostly empirical, but there have been efforts to develop a more theoretical understanding. Liang and coworkers combined the results of self‐diffusion experiments, chemical diffusion experiments, and new thermodynamic data to develop a mathematical model for calculating the diffusion matrix of molten CaO‐Al₂O₃‐SiO₂ from the self‐diffusion and thermodynamic properties of the individual components (Liang et al., 1997). Extending this approach to complex natural composition systems of interest to geochemistry is an important next step, but will require many experiments to document the self‐diffusion of the expanded number of components and the full diffusion matrix of the systems. The work by Guo and Zhang (2018) shows how many experiments were needed just to determine the diffusion matrix of an 8‐component basaltic liquid at a single temperature. Guo and Zhang (2018) also showed how the diffusion matrix is used to predict diffusion profiles during mineral dissolution in basaltic melts. The goal of validating a mathematical method for calculating the diffusion matrix of a silicate liquid given the self‐diffusion of the components and their chemical activity would significantly reduce the number of experiments needed to calculate the diffusion matrix of a system of interest.

Another approach that can provide a deeper understanding of the mass transport process in a condensed system involves molecular dynamics calculations. An example of this is the calculations by Bourg and coworkers that reproduce measured diffusion rates and isotopic fractionation of ionic species in water (see Bourg et al., 2010; Richter et al., 2006). These calculations showed that the rate of diffusion of the dissolved species is significantly reduced by the size and stability of their hydration spheres, adding the new insight that the degree of kinetic isotope fractionation is correlated with the residence time of individual water molecules in the hydration sphere (i.e., the shorter the residence time the greater the isotopic fractionation). Molecular dynamics calculations of kinetic isotope fractionation in condensed systems includes the work by Tsuchiyama et al. (1994), who determined a fractionation exponent β = 0.1 for magnesium diffusing in molten MgO. Goel et al. (2012) reported the results of molecular dynamics calculations to