  Characterizing the complex spectrum of topological defects in ground states
of curved crystals is a long-standing problem with wide implications, from the
mathematical Thomson problem to diverse physical realizations, including
fullerenes and particle-coated droplets. While the excess number of
"topologically-charged" 5-fold disclinations in a closed, spherical crystal is
fixed, here, we study the elementary transition from defect-free, flat crystals
to curved-crystals possessing an excess of "charged" disclinations in their
bulk. Specifically, we consider the impact of topologically-neutral patterns of
defects -- in the form of multi-dislocation chains or "scars" stable for small
lattice spacing -- on the transition from neutral to charged ground-state
patterns of a crystalline cap bound to a spherical surface. Based on the
asymptotic theory of caps in continuum limit of vanishing lattice spacing, we
derive the morphological phase diagram of ground state defect patterns, spanned
by surface coverage of the sphere and forces at the cap edge. For the singular
limit of zero edge forces, we find that scars reduce (by half) the threshold
surface coverage for excess disclinations. Even more significant, scars flatten
the geometric dependence of excess disinclination number on Gaussian curvature,
leading to a transition between stable "charged" and "neutral" patterns that
is, instead, critically sensitive to the compressive vs. tensile nature of
boundary forces on the cap.
