Dynamics of dislocations and surface instabilities in misfitting heteroepitaxial films

We introduce a continuum model of elasticity in a nonequilibrium multiphase system—including smooth and singular strains, as well as their coupling to free surfaces—and apply it to the dynamics of misfitting heteroepitaxial films. Above a critical thickness, defects relieve strain, competing with an instability at the interface. Depending on their mobility, defects can screen stress by building up at large-curvature groove tips, leading to high ductility, or be “outrun” by the tips, leading to brittleness. Hence we find a nonequilibrium brittle to ductile transition.