High-Temperature Equilibrium Isotope Fractionation of Non-Traditional Stable Isotopes: Experiments, Theory, and Applications (Invited)

Experiments are crucial for validating our understanding of stable isotope fractionation at high temperatures. The three-isotope method has been applied with success in the Si, Mg, Fe, and Ni isotope systems to date. The results of these experiments can be compared with expectations from theory and measurements of natural samples. Qualitative insights into the partitioning of heavy and light isotopes between mineral phases are gained by treating the force constant for relevant bonds, K_{f j}, as electrostatic in origin. The ionic model, based on the mean bond strength as defined by Pauling, has obvious limitations but is useful for rationalizing structures and site occupancies in silicates and oxide minerals and is equally useful in formulating expectations for isotope fractionation between phases. In some cases, as in Fe isotopes in spinels, the expectations are contrary to predictions based on modeling but similar to observations in natural samples. Experimental verification is required. The force constant for a bond between cation i (Mg, Fe, etc.) and anion j (e.g., O) can be written in terms of mean bond strengths s_i and s_j (as defined by Pauling) as K_f,ij = s_is_j e² (1-n)/(4 π ɛ_ο r³_ij ) where ɛ_o is the electric constant (vacuum permittivity for simplicity), e is the charge of an electron, n is the exponent in the Born-Mayer formulation for ion repulsion (Born and Mayer 1932), and r_ij is the interatomic spacing. This equation shows explicitly that larger values for the force constant K_f correspond to smaller coordination numbers (via s_i and s_j). We therefore expect an inverse relationship between isotope ratios (heavy/light) and coordination of its oxygen bond partners in silicate and oxides minerals and this is verified in mantle minerals. Our work with Fe isotope partitioning in mantle spinels suggests that coordination may be equally important as oxidation state, recognizing that these distinctions are not orthogonal. Recent work on the Mg isotopic compositions of mantle minerals underscores the utility and complexity of inter-mineral partitioning of ²⁵Mg/²⁴Mg and ²⁶Mg/²⁴Mg and tests our understanding of the crystal chemical controls on isotope partitioning of the major rock-forming elements. In our initial work on mantle minerals we pointed out that the largest inter-mineral fractionation in the Mg isotopic system in many mantle xenoliths is between spinel and olivine owing to the presence of tetrahedral Mg in the former. The observation that δ²⁵Mg spinel > δ²⁵Mg pyroxene > δ²⁵Mg olivine is consistent with our understanding of the bonding environment of Mg in these minerals and our data matched expectations from theory. This expectation from theory and measurements of natural samples has now been verified experimentally using the three-isotope method. Complexity arises with substitution of Cr and Fe in the spinel structure, again warranting further experimental calibration. Stable isotope ratios of the rock-forming elements provide not only new ways of estimating temperatures of formation and resetting, but also provide an independent method for identifying mineral parageneses. For example, we have found consistent evidence for isotopic disequilibrium between pyroxene and other phases in mantle xenoliths. The full potential of these isotope systems will only be realized with exhaustive exploration of the crystal chemical influences on inter-mineral fractionations.