Peierls-Nabarro landscape for martensitic phase transitions

Physical Review B - Condensed Matter and Materials Physics

Volumn 67, Issue 17, 2003, Pages

  Vainchtein, Anna ^b  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALLOY; ALUMINUM; COPPER; NICKEL;

ARTICLE; CRYSTAL STRUCTURE; ENERGY; FORCE; HYSTERESIS; MICROSCOPY; MODEL; PHASE TRANSITION;

EID: 0038237007     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.67.172103     Document Type: Article

References (30)

1. R. Krishnan, Mater. Sci. Forum3, 387 (1985).
2. M W. Burkart and T A. Read, Trans. AIME197, 1516 (1953).
3. T W. Shield, J. Mech. Phys. Solids43, 869 (1995).
4. K. Otsuka, H. Sakamoto, and K. Shimizu, Acta Metall.27, 585 (1979).
5. J A. Shaw and S. Kyriakides, Acta Mater.45, 683 (1997).
6. P H. Leo, T W. Shield, and O P. Bruno, Acta Metall. Mater.41, 2477 (1993).
7. Shape Memory Materials, edited by K. Otsuka, K. Shimizu, M. Doyama, S. Somiya, and R.P.H. Chang (Materials Research Society, Pittsburgh, 1989).
8. Proceedings of the Workshop on First-Order Displacive Phase Transformations, edited by L.E. Tanner and M. Wuttig [Mater. Sci. Eng., A 127, 137 (1990)].
9. J P. Sethna, et al., Phys. Rev. Lett.70, 3347 (1993).
10. R. Abeyaratne, C. Chu, and R D. James, Philos. Mag. A73, 457 (1996).
11. L. Truskinovsky and G. Zanzotto, J. Mech. Phys. Solids44, 1371 (1996).
12. L. Truskinovsky and A. Vainchtein (unpublished).
13. F.R.N. Nabarro, Theory of Crystal Dislocations (Dover, New York, 1987).
14. R N. Peierls, Proc. Phys. Soc. London52, 34 (1940).
15. O. Kresse and L. Truskinovsky, J. Mech. Phys. Solids51, 1305 (2003).
16. I. Müller and P. Villaggio, Arch. Ration. Mech. Anal.65, 25 (1977).
17. B. Fedelich and G. Zanzotto, J. Nonlinear Sci.2, 319 (1992).
18. G. Puglisi and L. Truskinovsky, J. Mech. Phys. Solids50, 165 (2002).
19. G. Puglisi and L. Truskinovsky, Continuum Mech. Thermodyn.14, 437 (2002).
20. Y Y. Ye, C T. Chan, and K M. Ho, Phys. Rev. Lett.66, 2018 (1991).
21. N. Triantafyllidis and S. Bardenhagen, J. Elast.33, 259 (1993).
22. S. Pagano and S. Paroni, Q. Appl. Math.61, 89 (2003).
23. A. Braides and M S. Gelli, J. Convex Anal.9, 363 (2002).
24. O. Braun and Y. Kivshar, Phys. Rep.306, 1 (1998).
25. M. Charlotte and L. Truskinovsky, J. Mech. Phys. Solids50, 217 (2002).
26. J H. Weiner and W T. Sanders, Phys. Rev.134, A1007 (1964).
27. J. Kratovchil and V I. Indenbom, Czech. J. Phys., Sect. B13, 814 (1963).
28. Observe that as a result of nonsmoothness of our energy, the ith and (formula presented)th particles are not in equilibrium at a saddle point; instead, they are subjected to forces of equal magnitude (formula presented) and opposite directions. For an analogous result in the FK model, see R. Hobart, J. Appl. Phys.36, 1944 (1965).
29. L. Truskinovsky, J. Appl. Math. Mech. (PMM)51, 777 (1987).
30. R. Abeyaratne and J K. Knowles, Acta Mater.45, 1671 (1997).