Chemical Geology 395 (2015) 176–195 Contents lists available at ScienceDirect Chemical Geology journal homepage: www.elsevier.com/locate/chemgeo High-temperature equilibrium isotope fractionation of non-traditional stable isotopes: Experiments, theory, and applications Edward D. Young a,⁎, Craig E. Manning a,EdwinA.Schaublea, Anat Shahar b,CatherineA.Macrisc, Codi Lazar b, Michelle Jordan a a Department of Earth, Planetary, and Space Sciences, UCLA, United States b Geophysical Laboratory, Carnegie Institution of Washington, United States c California Institute of Technology, United States article info abstract Article history: High-temperature partitioning of the stable isotopes of rock-forming elements like Mg, Si, Fe, Ni and others are Received 14 August 2014 useful new tools in geochemistry and cosmochemistry. Understanding the fundamental driving forces for Received in revised form 15 December 2014 equilibrium inter-mineral fractionation comes from basic crystal chemistry and is invaluable for interpreting Accepted 17 December 2014 data from natural systems. Both charge and coordination number are key factors affecting bond length and Available online 26 December 2014 bond stiffness and therefore the relative proclivity of a mineral phase for concentrating heavy or light isotopes. fi Editor: K. Mezger Quantitative interpretation of the plethora of new data relies on re nements of equilibrium fractionation factors through a feedback between crystal chemical reasoning, ab initio predictions, experiments, and analyses of Keywords: well-characterized natural samples. This multifaceted approach is leading to a rapid rate of discovery using non- Stable isotopes traditional stable isotopes in high temperature systems. For example, open-system mass transfer in the mantle is Magnesium becoming increasingly evident from departures from equilibrium Mg and Fe isotope ratio partitioning between min- Silicon erals, and differences in isotope ratios between bulk silicate Earth and meteorites are elucidating the conditions for Iron Earth's core formation quantitatively. These applications rely critically on accurate equilibrium fractionation factors. Core formation © 2014 Elsevier B.V. All rights reserved. Contents 1. Introduction.............................................................. 176 2. Factors influencingisotopefractionation................................................. 177 2.1. Thefoundations......................................................... 177 2.2. Crystalchemicalcontrolsonfractionation............................................. 180 2.3. Examples............................................................ 181 2.4. Pressure............................................................ 184 3. Three-isotopemethodfordeterminingfractionationfactors........................................ 184 4. Earth'smantleandcrust........................................................ 186 4.1. Ironisotopes.......................................................... 186 4.2. Magnesiumisotopes....................................................... 188 5. Isotopefractionationandcoreformation................................................. 190 5.1. Siliconinthecore........................................................ 190 5.2. Feisotopefractionationwithcoreformation............................................ 192 5.3. Otherisotopicconsequencesofcoreformation........................................... 193 6. Concludingremarks.......................................................... 193 Acknowledgments.............................................................. 193 References................................................................. 193 1. Introduction Ratios of the so-called non-traditional stable isotopes (stable ⁎ Corresponding author. isotopes of elements other than the more traditional H, C, N, O, and E-mail address: [email protected] (E.D. Young). S) can be used in a variety of ways in the study of rocks formed at http://dx.doi.org/10.1016/j.chemgeo.2014.12.013 0009-2541/© 2014 Elsevier B.V. All rights reserved. E.D. Young et al. / Chemical Geology 395 (2015) 176–195 177 high temperatures. Two of the most common are thermometry, an anion) with quantum number n (withvalues0,1,2,…0) can be meaning the calculation of temperatures from the distribution of written as isotopes between phases, and the sorting of parageneses, i.e., the identification of equilibrium (or disequilibrium) mineral assemblages ðÞ¼; ν þ 1 ν −η þ 1 ð Þ En i n h i 1 n 1 by virtue of their degree of isotopic equilibration (or lack of equilibra- 2 2 tion) (e.g., Young et al., 2009; Pogge von Strandmann et al., 2011). On a planetary scale, isotope partitioning can be used to infer the presence where h is the Planck constant and η quantifies departures from of unseen reservoirs, light elements in the core being a prominent harmonicity in the vibrations (a finite value for η related to the energy recent example (Georg et al., 2007; Shahar et al., 2009; Ziegler et al., well depth results in the familiar Morse potential describing potential 2010; Fitoussi and Bourdon, 2012). energy versus inter-atomic separation for a diatomic molecule). For Equilibrium isotope fractionation factors between phases are a pre- isotope work, it is often assumed that η = 0 (i.e., it is assumed that requisite for all of these applications, whether they are being applied the vibration is harmonic). In this case to interpret data under the assumption of isotopic equilibrium or as 1 foils for exposing disequilibrium. Even in studies where the aim is to EnðÞ¼; ν hν þ nhν ð2Þ i 2 i i use non-traditional stable isotope ratios as tracers of geochemical reser- voirs, as in the mantle for example, where fractionation between phases where the first term on the right-hand side is the zero-point energy is not the primary focus, equilibrium isotope fractionation factors are (where n = 0). The total energy associated with vibrational frequency nonetheless indispensible for interpretations of whole-rock data νi is partitioned among the different energy states prescribed by (e.g., Williams and Bizimis, 2014). Determining reliable equilibrium quantum numbers n. The probability for the occurrence of a vibrational fractionation factors requires feedbacks between computational predic- energy level corresponding to quantum number n and frequency tions and experiments. Our experience in the last decade has shown νi, P(E(n, νi)), as a function of temperature is calculable from the that experiments are required to assess the veracity of computational Boltzmann factor for that energy level: predictions for the non-traditional stable isotopes. Nonetheless, it is also true that these systems have proven surprisingly amenable to ðÞn þ 1 hν ðÞ¼ðÞ; ν − 2 i ð Þ PEn i exp 3 predictions by ab initio calculations. In some cases, natural samples kbT can be used to calibrate fractionation factors where theory is uncertain and experiments are lacking. where kb is the Boltzmann constant. Eq. (3) can be rewritten using the A sound appreciation for the sources of inter-mineral isotope substitution partitioning comes from basic crystal chemical principles. Bond fi ν strength, or more speci cally, bond stiffness, controls vibrational ¼ h i ð Þ ui 4 frequencies that in turn influence the propensity for heavier or lighter kbT isotopes to occupy a given crystallographic site. Measurements of mineral isotope fractionations for a variety of major rock-forming in to obtain the laboratory and in the field over the last decade have shown that −ðÞnþ1 u ðÞ¼ðÞ; 2 i : ð Þ simple crystal chemical considerations can be used to predict the signs PEnui e 5 and rough magnitudes of inter-mineral isotope fractionation. In this review we focus on advances in our understanding of high- Because the probabilities in Eq. (5) are exclusive, the total probability for temperature stable isotope fractionation in the Mg, Si, Fe, and Ni all n, Pν , is the sum of the Boltzmann factors over all n: i systems with applications in geochemistry and planetary science. fi Xn∞ This is a rapidly growing eld, and by necessity we emphasize those −ðÞþ = n 1 2 ui Pν ¼ e : ð6Þ contributions for which we have first-hand knowledge from studies i ¼ carried out at UCLA and the Geophysical Laboratory. n 0 The approximate symbol in front of the infinity symbol in Eq. (6) 2. Factors influencing isotope fractionation reminds us that in principle, only in the case of perfectly harmonic vibrations can n go to infinity. Eq. (6) is a geometric series and is 2.1. The foundations evaluated using the general formula for such a series: ÀÁ ÀÁ Isotope substitution affects the bulk thermodynamic properties of ¼∞ − = − ∞ − = Xn ÀÁ ui 1 2 ui ui 2 − ðÞþ1 e − e e ui n 2 crystalline materials by altering the energy associated with the ever- Pν ¼ e ¼ − ¼ − : ð7Þ i 1−e ui 1−e ui present vibrational motions of constituent atoms. Equilibrium inter- n¼0 mineral stable isotope fractionation arises from differences in the effects of atomic mass on vibrational energies in crystals (Bigeleisen and Thus far we have focused on vibrations with a particular frequency Mayer, 1947; Urey, 1947). Appreciation for the factors controlling frac- corresponding to a particular type of motion. However, there are a tionation comes from the underlying principles. A complete description multitude of interatomic vibrational motions with different vibrational of the theory behind stable isotope fractionation can be found in frequencies in a crystalline material all occurring simultaneously. The previous reviews (e.g.,