  Ultra-nanocrystalline diamond is a polycrystalline material, having
crystalline diamond grains of sizes in the nanometer 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 they both scale as quadratic polynomials of the inverse grain size.
Our formulae yield correct values for bulk diamond in the limit of large grain
sizes.
