PHILOSOPHICAL MAGAZINE LETTERS, 2000, VOL. 80, NO. 10, 675±682 The Peierls±Nabarro model revisited GANG LU, N ICHOLAS K IOUSSISy Department of Physics, California State University Northridge, Northridge, California 91330-8268, USA V ASILY V . BULATOV Lawrence Livermore National Laboratory, Livermore, California 94551, USA and EFTHIMIOS K AXIRAS Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA [ Received 3 March 2000 and accepted in revised form 16 June 2000 ] ABSTRACT We re-examine two important issues within the Peierls±Nabarro model, which are critical in obtaining accurate values for the Peierls stress. The ®rst is related to the sampling scheme (double versus single counting) of the mis®t energy across the glide plane and the second is the eect of atomic relaxation on the Peierls stress. We argue that the double-counting scheme is physically more appropriate. An analytical formula is derived for the Peierls stress of dislocations in alternating lattices. The atomic relaxation is shown to play an important role on the Peierls stress for narrow dislocations. } 1. I NTRODUCTION The Peierls stress ¼ P is the minimum external stress required to move a stationary dislocation irreversibly, without the assistance from lattice vibrations. This funda- mental quantity for a dislocation was ®rst estimated by Peierls (1940) and Nabarro (1947) using essentially a continuum model, the so-called Peierls±Nabarro (P±N) model. Owing to the unrealistic sinusoidal force law adopted in the model, the original P±N framework has served more as a conceptual tool for a qualitative understanding of dislocation core properties, rather than providing quantitative estimates of these properties. Recently, there has been renewed interest in applying the P±N model to study the dislocation properties (Joo Âs et al. 1994, Juan and Kaxiras 1996, Bulatov and Kaxiras 1997, Joo  s and Duesbery 1997, Hartford et al. 1998, Lu et al . 2000). This is motivated by the advance of reliable ab initio methods, which allow the accurate determination of the generalized stacking-fault energy (® energy), that is the interplanar potential energy for sliding one half of the crystal over the other half along the glide plane. To date, the P±N model has come to serve as a link between atomistic and continuum approaches, by providing a means to incorporate information obtained from atomistic ( ab initio or empirical) calculations directly into continuum models. The resultant approach can then be applied to Philosophical Magazine L etters ISSN 0950±0839 print/ISSN 1362±3036 online # 2000 Taylor & Francis Ltd http://www.tandf.co.uk /journals y Email: nick.kioussis@csun.edu.