Softening of ultra-nanocrystalline diamond at low grain sizes

Ultra-nanocrystalline diamond is a polycrystalline material with crystalline diamond grains in the nanometer size regime. We study the structure and mechanical properties of this material as a function of the average grain size, employing atomistic simulations. From the calculated elastic constants and the estimated hardness, we observe softening of the material as the size of its grains decreases. We attribute the observed softening to the enhanced fraction of interfacial atoms as the average grain size becomes smaller. We provide a fitting formula for the scaling of the cohesive energy and bulk modulus with respect to the average grain size. We find that both these properties scale as quadratic polynomials of the inverse grain size. Our formulas yield correct values for bulk diamond in the limit of large grain sizes.