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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 D_i and D_j of isotopes of atomic mass m_i and m_j with the results parameterized by an exponent β in relationship . 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 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.