  Using large scale numerical simulations, we examine the ordering of colloidal
particles on square periodic two-dimensional muffin-tin substrates consisting
of a flat surface with localized pinning sites. We show that when there are
four particles per pinning site, the particles adopt a hexagonal ordering,
while for five particles per pinning site, a square ordering appears. For
fillings between four and five particles per pinning site, we identify a rich
variety of distinct ordering regimes, including disordered grain boundaries,
crystalline stripe structures, superlattice orderings, and disordered patchy
arrangements. We characterize the different regimes using Voronoi analysis,
energy dispersion, and ordering of the domains. We show that many of the
boundary formation features we observe occur for a wide range of other
fillings. Our results demonstrate that grain boundary tailoring can be achieved
with muffin-tin periodic pinning substrates.
