The nucleation rates were calculated by using a 2-dimensional Frenkel-Kontorova model, combined with transition-state theory. A method for determining effective Frenkel-Kontorova adatom pair potentials was tested by using embedded atom method potentials. It was found that the calculated pre-factors and activation energies for dislocation nucleation were in excellent agreement with the results of a full embedded-atom method molecular dynamics simulation. The results indicated that dislocation nucleation could occur extremely rapidly in the case of islands on close-packed surfaces. It was expected that the theory would also be useful for predicting the nucleation rates of other types of dislocation at surfaces and in bulk materials. A method was also presented for systematically calculating effective Frenkel-Kontorova adatom pair potentials for dislocations in hetero-epitaxial layers. This was considered to be important because the periodicities of surface dislocation networks could be very large, and vary markedly during growth. Such systems could not be treated by using first-principles calculations alone. It was concluded that the Frenkel-Kontorova model would provide a useful bridge between atomistic calculations and dislocation phenomena in systems with large numbers of atoms. Also, transition-state theory would provide a bridge between the short time intervals that could be treated using molecular dynamics simulations, and the time-scales which were pertinent to practical situations.

Dislocation Nucleation and Sub-Monolayer Growth of Hetero-Epitaxial Thin Films. J.C.Hamilton: Physical Review B, 1997, 55[12], R7402-5