The effects of surface roughness and stress on lattice gas models using kinetic Monte Carlo modeling

Abstract

This thesis reports kinetic Monte Carlo computer simulations using a lattice gas model conducted on a variety of systems. These studies may be divided into two main categories: rod eutectics and related surface roughening, and surface morphology changes due to local stresses. The first grouping is a study of irregular rod eutectic systems. Simulations of directional solidification of rod eutectic systems were conducted using a model similar to the spin one Ising model. Growth of the rods was initiated from columns of pure A atoms embedded in a matrix of B atoms. The growth characteristics of the eutectic depend on the location of the surface roughening transition for the two phases. The surface roughening transition was determined using fluctuation dissipation theory, where the kinetic behavior of the interface is related to a characteristic time of fluctuations about an equilibrium position. These times were determined by time correlations. Results show a sharp transition in the kinetic behavior of the interface as a function of Jackson's alpha factor. This is the first time this method has been used to locate the surface roughening transition. An applied temperature gradient supplied the restoring force for the interface. The roughening behavior of binary alloys was also examined and compared to pure component systems. The second set of simulations reported here examine the effects of local stress on surface morphology. The weakening of bonds due to the dislocation stress field was studied as the origin of the formation of etch-pits at dislocations. Atoms from a diamond cubic lattice were irreversibly removed with a probability which depends on an local surface configuration as well as on the local stress developed from its physical location with respect to a dislocation in the lattice. In accordance with experimental observations, both faceted and non-faceted dislocation etch-pits have been observed. Simulations of crystal surfaces near equilibrium have reproduced direct experimental results using atomic force microscopy (AFM). The probe tip interacts with the shape and the motion of step edges, and the motion of a step is retarded in the vicinity of the tip.