New Model for the Brittle-to-Ductile Transition Based on a Collective Dislocation Generation Instability: Theory and Experiment

摘要

This final report summarizes the results of our research on the Brittle-To-Ductile Transition (BDT) using a new approach based on a cooperative dislocation generation instability. We developed a two dimensional model of the instability, extending the well-known Kosterlitz-Thouless model into the combined regime of temperature and stress. Using this model we were able to calculate the minimum temperature at which the dislocation generation instability occurs, which we identify to be the BDTT. Monte Carlo simulations were also carried out on a crystal of finite size to check the model predictions and to examine how various parameters evolve close to the instability. Experiments were performed employing a homogeneous stress field in dislocation-free Si crystals (to avoid the complexities associated with Frank-Read dislocation sources). Most experiments were performed on coherent Si/Ge overlayers on Si substrates. The sample was heated while measuring the radius of curvature to determine the temperature at which interfacial dislocations are produced in the sample. It was found that, consistent with the model, there is a massive dislocation instability at about 500 deg C, depending upon the Ge content (which determines the stress). Similar results were obtained for three point bending experiments.