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A new experimental method of determination of equilibrium isotopic propertiesof substances based on Inelastic Neutron Scattering (INS) is proposed. Wepresent mathematical formalism allowing calculation of beta-factor ofsingle-element solids based on INS-derived Phonon Density of States (PDOS).PDOS data for nanodiamonds of widely different sizes and of macroscopic diamondwere determined from Inelastic Neutron Scattering experiment. This alloweddetermination of heat capacities and, for the first time, \b{eta}-factors forthe diamond nanoparticles. We demonstrate considerable size-dependent increaseof the heat capacities and decrease of the beta-factors for nanodiamondsrelative to bulk diamond. Contributions of surface impurities/phases and phononconfinement to the size effects are evaluated. Applications to formation ofdiamond nanoparticles in nature are briefly discussed.

physical chemistry chemical physics/pccp. physical chemistry chemical physics

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