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Lunar rocks are severely depleted in moderately volatile elements such as Rb, K, and Zn relative to Earth. Identifying the cause of this depletion is important for understanding how the Earth-Moon system evolved in the aftermath of the Moonforming giant impact. We measured the Rb isotopic compositions of lunar and terrestrial rocks to understand why moderately volatile elements are depleted in the Moon. Combining our new measurements with previous data reveals that the Moon has an 87 Rb/ 85 Rb ratio higher than Earth by +0.16±0.04 ‰. This isotopic composition is consistent with evaporation of Rb into a vapor medium that was ~99% saturated. Evaporation under this saturation can also explain the previously documented isotopic fractionations of K, Ga, Cu and Zn of lunar rocks relative to Earth. We show that a possible setting for achieving the same saturation upon evaporation of elements with such diverse volatilities is through viscous drainage of a partially vaporized protolunar disk onto Earth. In the framework of an a-disk model, the a-viscosity needed to explain the ~99% saturation calculated here is 10 −3 to 10 −2 , which is consistent with a vapor disk where viscosity is controlled by magnetorotational instability.

We used first-principle approaches to calculate the equilibrium isotopic fractionation factors of potassium (K) and rubidium (Rb) in a variety of minerals of geological relevance (orthoclase, albite, muscovite, illite, sylvite, and phlogopite). We also used molecular dynamics simulations to calculate the equilibrium isotopic fractionation factors of K in water. Our results indicate that K and Rb form bonds of similar strengths and that the ratio between the equilibrium fractionations of K and Rb is approximately 3–4. Under low-temperature conditions relevant to weathering of continents or alteration of seafloor basalts (∼25 °C), the K isotopic fractionation between solvated K+ and illite (a proxy for K-bearing clays) is +0.24‰, exceeding the current analytical precision, so equilibrium isotopic fractionation can induce measurable isotopic fractionations for this system at low temperature. These findings, however, cannot easily explain why the δ41K value of seawater is shifted by +0.6‰ relative to igneous rocks. Our results indicate that part of the observed fractionation is most likely due to kinetic effects. The narrow range of mean force constants for K and Rb in silicate minerals suggests that phase equilibrium is unlikely to create large K and Rb isotopic fractionations at magmatic temperatures (at least in silicate systems). Kinetic effects associated with diffusion can, however, produce large K and Rb isotopic fractionations in igneous rocks.

SciPhon is a software for the reduction of nuclear resonant inelastic X-ray scattering data. Tests and examples of applications to Fe, Kr, Sn, Eu and Dy data are presented.

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We use density functional theory to calculate the equilibrium isotopic fractionation factors of zirconium (Zr) in a variety of minerals including zircon, baddeleyite, Ca-catapleiite, ilmenite, geikielite, magnetite, apatite, K-feldspar, quartz, olivine, clinopyroxene, orthopyroxene, amphibole, and garnet. We also report equilibrium isotopic fractionation factors for Hf in zircons, Ca-catapleiite, and ilmenite. These calculations show that coordination environment is an important control on Zr and Hf isotopic fractionation, with minerals with Zr and Hf in low coordinations predicted to be enriched in the heavy isotopes of Zr and Hf, relative to those with Zr and Hf in high coordinations. At equilibrium, zircon, which hosts Zr and Hf in 8fold coordination, is predicted to have low 94 Zr/ 90 Zr and 179 Hf/ 177 Hf ratios compared to silicate melt, which hosts Zr and Hf in 6-fold coordination. However, our modeling results indicate that little equilibrium isotopic fractionation for Zr is expected during magmatic differentiation and zircon crystallization. We show through isotopic transport modeling that the Zr isotopic variations that were documented in igneous rocks are likely due to diffusion-driven kinetic isotopic fractionation. The two settings where this could take place are (i) diffusion-limited crystallization of zircon (DLC model) and (ii) diffusion-triggered crystallization of zircon (DTC model) in the boundary layer created by the growth of Zr-poor minerals. Fractional crystallization of zircons enriched in light Zr isotopes by diffusion can drive residual magmas toward heavy Zr isotopic compositions. Our diffusive transport model gives the framework to interpret Zr isotope data and gain new insights into the cooling history of igneous rocks and the setting of zircon crystallization.

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