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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 of determination of equilibrium isotopic properties of substances based on Inelastic Neutron Scattering (INS) is proposed. We present mathematical formalism allowing calculation of 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 experiment. This allowed determination of heat capacities and, for the first time, \b{eta}-factors for the diamond nanoparticles. We demonstrate 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 to formation of diamond nanoparticles in nature are briefly discussed.