which includes the vacancy formation enthalpy for all kMC transitions adjusted

Which includes the vacancy formation enthalpy for all

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, which includes the vacancy formation enthalpy, for all kMC transitions, adjusted so that the proper ratio of reverse and forward transition rates is maintained. Specifically, the transition rate of Mg from site i to neighbouring site j is Γ i j = ν 0 e β( H b W ij / 2 ) = Γ b e β W ij / 2 , where W ij = W ( x i ) W ( x j ) is the binding-energy di ff erence for Mg between sites i and j (see Fig. 1). The Mg site energies, precomputed by molecular statics, include full relaxation of the atomistic system. The corresponding bulk continuum di ff usion coe cient is D b = 2 b 2 Γ b . Received 24 April 2006; accepted 15 September 2006; published 22 October 2006. References 1. Hirth, J. P. & Lothe, J. Theory of Dislocations 2nd edn (Wiley, New York, 1982). 2. Robinson, J. M. & Shaw, M. P. Microstructural and mechanical influences on dynamic strain aging phenomena. Int. Mater. Rev. 39, 113–122 (1994). 3. Cottrell, A. H. & Bilby, B. A. Dislocation theory of yielding and strain ageing of iron. Proc. R. Soc. A 62, 49–62 (1949). 4. Cottrell, A. H. Theory of brittle fracture in steel and similar metals. Trans. Met. Soc. AIME 212, 192–203 (1958). 5. Friedel, J. Dislocations (Addison-Wesley, New York, 1964). 6. Louat, N. On the theory of the Portevin-Le Chˆatelier e ff ect. Scripta Metall. 15, 1167–1170 (1981). 7. McCormick, P. G. A model for the Portevin-Le Chˆatelier e ff ect in substitutional alloys. Acta Metall. 20, 351–354 (1972). 8. van den Beukel, A. Theory of the e ff ect of dynamic strain aging on mechanical properties. Phys. Status Solidi A 30, 197–206 (1975). nature materials VOL 5 NOVEMBER 2006 879 Nature PublishingGroup ©200 6
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ARTICLES 9. Estrin, Y. & Kubin, L. P. Collective dislocation behaviour in dilute alloys and the Portevin-Le Chˆatelier e ff ect. J. Mech. Behav. Mater. 2, 255–292 (1989). 10. Kubin, L. P. & Estrin, Y. Evolution of dislocation densities and the critical conditions for the Portevin-Le Chˆatelier e ff ect. Acta Metall. Mater. 38, 697–708 (1990). 11. Kubin, L. P. & Estrin, Y. The critical conditions for jerky flow: discussion and application to Cu-Mn solid solutions. Phys. Status Solidi B 172, 173–185 (1992). 12. Estrin, Y. & Kubin, L. P. in Continuum Models for Materials with Microstructure (ed. M¨uhlhaus, H. B.) 395–450 (Wiley, Chichester, 1995). 13. Lebyodkin, M., Dunin-Barkovskii, L., Br´echet, Y., Kubin, L. & Estrin, Y. Kinetics and statistics of jerky flow: experiments and computer simulations. Mater. Sci. Eng. A 234–236, 115–118 (1997). 14. Lebyodkin, M., Dunin-Barkovskii, L., Br´echet, Y., Estrin, Y. & Kubin, L. P. Spatio-temporal dynamics of the Portevin-Le Chˆatelier e ff ect: experiment and modelling. Acta Mater. 48, 2529–2541 (2000). 15. Zhang, S., Estrin, Y. & McCormick, P. G. The morphology of Portevin-Le Chˆatelier bands: finite element simulation for Al-Mg-Si. Acta Mater. 49, 1087–1094 (2001). 16. Kok, S. et al . Spatial coupling in jerky flow using polycrystal plasticity. Acta Mater. 51, 3651–3662 (2003). 17. Penning, P. Mathematics of the Portevin-Le Chˆatelier e ff ect. Acta Metall. 20, 1169–1175 (1972).
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