Metastability in 2D self-assembling systems

We show that 2D self-assembled domains can remain trapped in a large variety of long-lived and metastable shapes that arise from an interplay of crystalline anisotropy and relaxation of elastic strain. On commonly used cubic (111) substrates, these shapes include extended or stacked structures made up of triangular domains connected at their corners, compact shapes with both convex and concave curvatures and others with narrow and elongated arms. We show that all of these distinct experimentally observed shapes can be explained within a unified framework and present a phase diagram that systematically classifies the metastable shapes as a function of their size.