Inelastic neutron scattering: a novel approach towards determination of equilibrium isotopic fractionation factors. Size effects on heat capacity and beta-factor of diamond.

A new experimental method for the determination of equilibrium isotopic properties of substances based on inelastic neutron scattering (INS) is proposed. We present a mathematical formalism, which allows the calculation of the beta-factor of single-element solids based on INS-derived Phonon Density of States (PDOS). PDOS data for nanodiamonds of widely different sizes and of macroscopic diamond were determined from inelastic neutron scattering experiments. This allowed the determination of heat capacities and, for the first time, ß-factors of the diamond nanoparticles. We demonstrate a considerable size-dependent increase of the heat capacities and decrease of the beta-factors for nanodiamonds relative to bulk diamond. Contributions of surface impurities/phases and phonon confinement to the size effects are evaluated. Applications in the formation of diamond nanoparticles in nature are briefly discussed.

Carbon-bearing iron phases and the carbon isotope composition of the deep Earth.

The carbon budget and dynamics of the Earth's interior, including the core, are currently very poorly understood. Diamond-bearing, mantle-derived rocks show a very well defined peak at δ(13)C ≈ -5 ± 3‰ with a very broad distribution to lower values (∼-40‰). The processes that have produced the wide δ(13)C distributions to the observed low δ(13)C values in the deep Earth have been extensively debated, but few viable models have been proposed. Here, we present a model for understanding carbon isotope distributions within the deep Earth, involving Fe-C phases (Fe carbides and C dissolved in Fe-Ni metal). Our theoretical calculations show that Fe and Si carbides can be significantly depleted in (13)C relative to other C-bearing materials even at mantle temperatures. Thus, the redox freezing and melting cycles of lithosphere via subduction upwelling in the deep Earth that involve the Fe-C phases can readily produce diamond with the observed low δ(13)C values. The sharp contrast in the δ(13)C distributions of peridotitic and eclogitic diamonds may reflect differences in their carbon cycles, controlled by the evolution of geodynamical processes around 2.5-3 Ga. Our model also predicts that the core contains C with low δ(13)C values and that an average δ(13)C value of the bulk Earth could be much lower than ∼-5‰, consistent with those of chondrites and other planetary body. The heterogeneous and depleted δ(13)C values of the deep Earth have implications, not only for its accretion-differentiation history but also for carbon isotope biosignatures for early life on the Earth.

Equilibrium iron isotope fractionation at core-mantle boundary conditions.

The equilibrium iron isotope fractionation between lower mantle minerals and metallic iron at core-mantle boundary conditions can be evaluated from the high-pressure 57Fe partial vibrational density of states determined by synchrotron inelastic nuclear resonant x-ray scattering spectroscopy using a diamond anvil. Ferropericlase [(Mg,Fe)O] and (Fe,Mg)SiO3- post-perovskite are enriched in heavy iron isotopes relative to metallic iron at ultrahigh pressures, as opposed to the equilibrium iron isotope fractionation between these compounds at low pressure. The enrichment of Earth and Moon basalts in heavy iron isotopes relative to those from Mars and asteroid Vesta can be explained by the equilibrium iron isotope fractionation during the segregation of Earth's core and the assumption that Earth was already differentiated before the Moon-forming "giant impact."