  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.
