  We present atomistic simulations for the mechanical response of ultra
nanocrystalline diamond, a polycrystalline form of diamond with grain diameters
of the order of a few nm. We consider fully three-dimensional model structures,
having several grains of random sizes and orientations, and employ
state-of-the-art Monte Carlo simulations. We calculate structural properties,
elastic constants and the hardness of the material; our results compare well
with experimental observations for this material. Moreover, we verify that this
material becomes softer at small grain sizes, in analogy to the observed
reversal of the Hall-Petch effect in various nanocrystalline metals. The effect
is attributed to the large concentration of grain boundary atoms at smaller
grain sizes. Our analysis yields scaling relations for the elastic constants as
a function of the average grain size.
