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 determine a similar value of β ~ 0.1 for the isotopic fractionation of magnesium in molten MgSiO3 and β ~ 0.05 for the isotopic fractionation of silicon in both molten MgSiO3and SiO2. In future it will be especially revealing if one were to combine the results from well‐resolved kinetic isotopic fractionation laboratory experiments in a specific medium with molecular calculations of the same system. Something will be learned even when the molecular dynamics calculations fail to reproduce the data from the analogous laboratory experiments.
An important topic that has not yet been explored by experiments involves kinetic isotope fractionation by diffusion in grain boundaries. Diffusion along grain boundaries in unsaturated rocks is commonly many orders of magnitude larger than in the minerals themselves and thus it is the dominant mass transport process in such rocks. There is evidence from natural settings that significant isotopic fractionation of lithium is associated with diffusion along grain boundaries in coarse‐grained metamorphic rocks (see the classic study by Teng et al., 2006) but as yet no complementary laboratory experiments have reported. The experimental design developed by Thomas and Watson (2014) to monitor the transport of magnesium along grand boundaries in quartzite would a good way of producing samples with which to measure the isotope fractionation of elements that diffused along grain boundaries.
Some recent diffusion experiments showed results that still are quite surprising and raise issues that could eventually be understood by further laboratory experiment and theoretical methods including molecular dynamics calculations. For example, recent experiments raise the question of why diffusion in igneous minerals such as clinopyroxene and olivine is more effective at fractionating isotopes of a major element (e.g., Mg) and of a trace element (e.g., Li) than diffusion in a silicate melt? Another question whose answer might illuminate fundamental thermodynamic properties of silicate melts is why Soret diffusion in a basalt liquid is so effective at fractionating isotopes, or put another way, why is the isotopic fractionation associated with the mass flux driven by a thermal gradient so much larger than that of the flux driven differences in concentration?
The situation with regard to experiments that determine high‐temperature kinetic isotope fractionation of silicate liquids by evaporation is similar to that of diffusion in that only a limited parameter range has so far been thoroughly explored. For the most part these experiments involve evaporation into vacuum whereas evaporation in the early solar system involved evaporation of molten precursors to the CAIs now found in chondritic meteorites in a finite gas pressure of hydrogen and more oxidizing conditions later on when chondrules were melted. Richter et al. (2002) did report the results of the chemical and isotopic fractionation of a set of experiments in which a CAI‐like liquid was evaporated at 1500°C and PH2 = 2×10‐4 bars. They found that despite the evaporation rates in these low‐PH2 experiments being about two orders of magnitude faster than in vacuum, the magnesium isotopic fractionation of the evaporation residues as a function of the amount of magnesium lost was not measurably different than in vacuum. The isotopic composition of the evaporation residues from these experiments were measured with much less precision compared to what can be done with a modern ion probe, so there now could well be a resolvable difference between evaporation in vacuum and in low pressure hydrogen. The reason why one should consider repeating these earlier evaporation experiments in hydrogen is that the more precisely one can determine the amount of Mg and Si volatilized based on the isotopic fractionation of individual CAIs, the more precisely one can determine the composition of their precursor. More accurate estimates of the composition of CAI precursors will allow for more compelling validation or refutation of a fundamental proposition in cosmochemistry: that the precursors of the CAIs were condensates from a common well‐mixed solar compositions gas.
Expanding the laboratory evaporation experiments to higher pressures and more oxidizing gas mixtures will be challenging. The design of the furnaces that are now used to determine the isotopic fractionation of evaporation residues are limited to low gas pressures
