  The structure of finite self-assembling systems depends sensitively on the
number of constituent building blocks. Recently, it was demonstrated that hard
sphere-like colloidal particles show a magic number effect when confined in
spherical emulsion droplets. Geometric construction rules permit a few dozen
magic numbers that correspond to a discrete series of completely filled
concentric icosahedral shells. Here, we investigate the free energy landscape
of these colloidal clusters as a function of the number of their constituent
building blocks for system sizes up to several thousand particles. We find that
minima in the free energy landscape, arising from the presence of filled,
concentric shells, are significantly broadened. In contrast to their atomic
analogues, colloidal clusters in spherical confinement can flexibly accommodate
excess colloids by ordering icosahedrally in the cluster center while changing
the structure near the cluster surface. In-between these magic number regions,
the building blocks cannot arrange into filled shells. Instead, we observe that
defects accumulate in a single wedge and therefore only affect a few
tetrahedral grains of the cluster. We predict the existence of this wedge by
simulation and confirm its presence in experiment using electron tomography.
The introduction of the wedge minimizes the free energy penalty by confining
defects to small regions within the cluster. In addition, the remaining ordered
tetrahedral grains can relax internal strain by breaking icosahedral symmetry.
Our findings demonstrate how multiple defect mechanisms collude to form the
complex free energy landscape of hard sphere-like colloidal clusters.
