Peierls-Nabarro modeling of dislocations in high-entropy alloys

The Peierls-Nabarro (PN) framework for modeling of dislocations is adapted and evaluated for application to high-entropy alloys. Solute-dislocation interactions in the complex alloys are introduced rigorously within elasticity theory. Detailed studies are performed on model 1/2⟨111⟩{110} edge dislocations in the BCC NbTaV high-entropy alloy. Key findings are that: (i) solute misfit stresses dominate the strengthening while fluctuations in the generalized stacking fault energy (GSFE) are negligible; (ii) the misfit stresses cannot be accurately measured using the atomic virial stress; (iii) the core spreading influences the alloy strength; (iv) the PN model using the atomistically-measured GSFE predicts a core narrower than measured atomistically; (v) correlations in atomic stresses have moderate influences on the distribution and spacing of energy barriers at the critical length scale but a small effect on the yield stress, and (vi) with increasing dislocation line length the yield stress using uncorrelated stresses converges quickly but to a value much lower than that found in direct atomistic stresses at 1100Å. Specifically, for segments at the theoretical characteristic length ζc ≈ 24Å, the PN model captures the energy landscape encountered by a gliding dislocation in good agreement with atomistic Nudged Elastic Band (NEB) calculations on the same atomistic realizations when the atomistic GSFE is used. Comparisons of the energy barrier distribution and barrier spacing across many simulations show reasonable agreement with NEB. Using a GSFE fitted to match the atomistic core spreading, however, the PN energy landscape is smoother. Using the atomistic GSFE, direct simulations of the T=0K stress to achieve dislocation glide are also in good overall agreement with NEB results. Lower strengths are found using the fitted GSFE due to the larger barrier spacing. Strengths with and without the true spatial correlations in the misfit stresses are slightly different. PN predictions of strength of longer dislocation lines show a decrease in strength but saturating at a length of ≈ 100Å to a value notably lower than atomistic simulations. This very detailed study of the computationally-efficient PN model for HEAs shows that it is viable for the studying dislocations in random alloys but remains imperfect. Nonetheless, the PN model provides significant flexibility to quantitatively and parametrically investigate the role of many different material parameters on many features of alloy strengthening, and enables future incorporation of additional complex metallurgical features such as short-range-order, clustering, and precipitation.