Epitaxial growth of ordered and disordered granular sphere packings

We demonstrate that epitaxy can be used to obtain a wide range of ordered to disordered granular packings by simply changing the deposition flux. We show that a defect-free face-centered-cubic (fcc) monocrystal can be obtained by depositing athermal granular spheres randomly into a container with a templated surface in a gravitational field without direct manipulation. This packing corresponds to the maximum sphere packing fraction and is obtained when the substrate is templated corresponding to the (100) plane of a fcc crystal and the container side is an integer multiple of the sphere diameter. We find that the maximum sphere packing is obtained when the deposited grains come to rest, one at a time, without damaging the substrate. A transition to a disordered packing is observed when the flux is increased. Using micro x-ray computed tomography, we find that defects nucleate at the boundaries of the container in which the packing is grown as grains cooperatively come to rest above their local potential minimum. This leads to a transition from ordered to disordered loose packings that grow in the form of an inverted cone, with the apex located at the defect nucleation site. We capture the observed decrease in order using a minimal model in which a defect leads to growth of further defects in the neighboring sites in the layer above with a probability that increases with the deposition flux.