Dislocation core properties of β-tin: A first-principles study

Dislocation core properties of tin (β-Sn) were investigated using the semi-discrete variational Peierls-Nabarro (SVPN) model. The SVPN model, which connects the continuum elasticity treatment of the long-range strain field around a dislocation with an approximate treatment of the dislocation core, was employed to calculate various core properties, including the core energetics, widths, and Peierls stresses for different dislocation structures. The role of core energetics and properties on dislocation character and subsequent slip behavior in β-Sn was investigated. For instance, this work shows that a widely spread dislocation core on the {110} plane as compared to dislocations on the {100} and {101} planes. Physically, the narrowing or widening of the core will significantly affect the mobility of dislocations as the Peierls stress is exponentially related to the dislocation core width in β-Sn. In general, the Peierls stress for the screw dislocation was found to be orders of magnitude higher than the edge dislocation, i.e., the more the edge component of a mixed dislocation, the greater the dislocation mobility (lower the Peierls stress). The largest Peierls stress observed was 365 MPa for the dislocation on the {101} plane. Furthermore, from the density plot, we see a double peak for the 0° (screw) and 30° dislocations which suggests the dissociation of dislocations along these planes. Thus, for the {101} 〈101〉 slip system, we observed dislocation dissociation into three partials with metastable states. Overall, this work provides qualitative insights that aid in understanding the plastic deformation in β-Sn.