  The local structure of disordered jammed packings of monodisperse spheres
without friction, generated by the Lubachevsky-Stillinger algorithm, is studied
for packing fractions above and below 64%. The structural similarity of the
particle environments to fcc or hcp crystalline packings (local crystallinity)
is quantified by order metrics based on rank-four Minkowski tensors. We find a
critical packing fraction \phi_c \approx 0.649, distinctly higher than
previously reported values for the contested random close packing limit. At
\phi_c, the probability of finding local crystalline configurations first
becomes finite and, for larger packing fractions, increases by several orders
of magnitude. This provides quantitative evidence of an abrupt onset of local
crystallinity at \phi_c. We demonstrate that the identification of local
crystallinity by the frequently used local bond-orientational order metric q_6
produces false positives, and thus conceals the abrupt onset of local
crystallinity. Since the critical packing fraction is significantly above
results from mean-field analysis of the mechanical contacts for frictionless
spheres, it is suggested that dynamic arrest due to isostaticity and the
alleged geometric phase transition in the Edwards framework may be disconnected
phenomena.
