| Abstract: | Melting in two dimensions is characterized by the thermal excitation
and proliferation of free topological defects, disclinations and
dislocations which destroy the rigidity of the crystal. This
freezing/melting process has been well established for flat systems
especially for dipolar, U(r) ~1/r3 potentials, with control
parameter, Γ = U(a)/kBT, where a is an interparticle spacing. The flat spacing
freezing occurs at Γ ~ 70. On a sphere topology requires that there
must be a net 12 pentagons (1/2 disclinations) i.e. the 12 pentagons
on a soccer ball, and energetically it is favorable to screen the
pentagons with strings of dislocations (pentagon-heptagon pairs)
known as “scars”. Our system consists of charged colloidal particles
in an oil droplet in water bound to the inner surface by image charges.
We study particle mean square displacement, hexagonal order, defect
structure, and scar-scar correlations by confocal microscopy for
droplets of different Γ and number of particles. Freezing on a
sphere proceeds by the formation of a single, encompassing, crystalline
“continent” that forces the defects into 12 isolated “seas”
with icosahedral symmetry at the flat space value of Γ ~ 70.
Long-range order is revealed only by projecting the “continent”
on an icosahedral net, unpeeling and flattening it.) |
