Critical conditions for defect formation and melting in 2D periodic systems

When periodic systems are exposed to external stresses, defects such as dislocations and vortices can spontaneously form through nucleation to relieve local strains. Additionally, if the system is conserved and near a phase boundary, the external forces may induce local melting of the lattice. In this work, the stability of periodic structures are studied using linear stability analysis of the amplitude phase field crystal model (APFC). By varying factors such as conserved versus non-conserved dynamics, average density, effective temperature, and magnitudes of applied strains, the critical conditions for instability in both one- and two-dimensional systems are derived.