  We study numerically the equilibrium shapes, shape transitions and
dislocation nucleation of small strained epitaxial islands with a
two-dimensional atomistic model, using simple interatomic pair potentials. We
first map out the phase diagram for the equilibrium island shapes as a function
of island size (up to N = 105 atoms) and lattice misfit with the substrate and
show that nanoscopic islands have four generic equilibrium shapes, in contrast
with predictions from the continuum theory of elasticity. For increasing
substrate-adsorbate attraction, we find islands that form on top of a finite
wetting layer as observed in Stranski-Krastanow growth. We also investigate
energy barriers and transition paths for transitions between different shapes
of the islands and for dislocation nucleation in initially coherent islands. In
particular, we find that dislocations nucleate spontaneously at the edges of
the adsorbate-substrate interface above a critical size or lattice misfit.
