Local analysis of structural instability in stressed lattices: Crack nucleation in a covalent solid

For the local analysis of structural instability, a site-dependent measure of local contribution to a global mode is introduced which is decomposed into contributions from individual interatomic bonds. Since this measure incorporates both spatial and dynamical information, the method provides insight into the temporal evolution of the lattice instability. Using this method to study lattice decohesion under pure dilation, we find the crack nucleation process to consist of the onset of instabilities at several distinct sites, followed by coalescence of local instabilities which triggers the bond rupturing along a plane.