Linear instability signals the initiation of motion of a twin plane under load

This letter presents a study of the atomic mechanism of the initiation of motion of a static twin plane under applied mechanical load in a model shape-memory material. By tracking the deformation under load and using linear stability analysis, we find that the eigenvalues of the Hessian matrix provide an indicator of the initiation of motion of the twin plane. The initiation of motion is signaled by a linear instability and a drop in the lowest eigenvalue to zero as well as a sharp drop in higher eigenvalues. Additionally, by comparing with direct molecular dynamics, we see that the eigenmode associated with the zero eigenvalue is found to accurately predict the initial mode of motion. We also find that the initial motion occurs through the formation of a stacking fault just ahead of the existing twin plane and the broadening of the stacking fault drives further transformation.