Improved Peierls-Nabarro model for asymmetric nonplanar 1/2

Abstract

The 1/2 < 11_0]{111} ordinary dislocations play an important role in the mechanical behaviors of L10 alloys. The core of this kind of dislocations has asymmetric four-fold nonplanar structure spreading onto two equivalent {111} planes, which makes the traditional planar core structure based Peierls-Nabarro (P–N) model inappropriate to describe the dislocation properties. Under this context, an improved Peierls-Nabarro (P–N) model is developed in the present work to investigate the dislocation width, stress field and Peierls stress of the ordinary 1/2 < 11_0]{111} screw dislocation in L10 alloys (TiAl, TiGa and CuAu). This extended P–N model considers the nonplanar core structure with physical information obtained by the density functional theory (DFT) simulations. By the variational method, the corresponding dislocation equation is solved. It is found that the dislocation width of the ordinary 1/2 < 11_0]{111} screw dislocation is as narrow as 0.5b. Compared to the results predicted for the planar core structure or the assumed Volterra dislocation, the long-range stress field induced by the real asymmetric four-fold core presents a clear rotation. When increasing the applied stress, the distribution of the Burgers vector along the four different core folds differs more and more from each other. When the applied stress attains a critical value (i.e., the Peierls stress), the dislocation core turns to be a planar structure and a fully discrete method is used to calculate the Peierls stress. Different from the original P–N model that underestimates the Peierls stress by several orders of magnitude, the Peierls stress predicted by the improved P–N model is well consistent with the previous DFT simulations. Apparently, when the long-range interaction between dislocations is taken into account for discrete dislocation simulations or theoretical analysis and when the Peierls stress is calculated for L10 alloys, the consideration of the asymmetric nonplanar core structure by the improved P–N model is necessary to have more accurate results.