  The free energy of a crystalline domain coexisting with a liquid phase on a
spherical vesicle may be approximated by an elastic or stretching energy and a
line tension term. The stretching energy generally grows as the area of the
domain, while the line tension term grows with its perimeter. We show that if
the crystalline domain contains defect arrays consisting of finite length grain
boundaries of dislocations (scars) the stretching energy grows linearly with a
characteristic length of the crystalline domain. We show that this result is
critical to understand the existence of solid domains in lipid-bilayers in the
strongly segregated two phase region even for small relative area coverages.
The domains evolve from caps to stripes that become thinner as the line tension
is decreased. We also discuss the implications of the results for other
experimental systems and for the general problem that consists in finding the
ground state of a very large number of particles constrained to move on a fixed
geometry and interacting with an isotropic potential.
