Coupled surface and grain boundary motion: A travelling wave solution

Nonlinear Analysis, Theory, Methods and Applications

Volumn 59, Issue 8, 2004, Pages 1267-1292

  Kanel, Jacob ^a   Novick Cohen, Amy ^a   Vilenkin, Arkady ^b  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Grain boundary motion; Motion by mean curvature; Surface diffusion; Third order ODEs; Travelling waves

Indexed keywords

ABSORPTION; BOUNDARY CONDITIONS; DIFFUSION; NONLINEAR EQUATIONS; PROBLEM SOLVING; SURFACE PHENOMENA;

GRAIN BOUNDARY MOTION; MOTION BY MEAN CURVATURE (MMC); SURFACE DIFFUSION; THIRD ORDER ODES; TRAVELLING WAVES;

GRAIN BOUNDARIES;

EID: 9344257337     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.08.014     Document Type: Article

References (25)

1. M.E. Akveld, J. Hulshof, Travelling wave solutions of a fourth-order semilinear diffusion equation, Appl. Math. Lett. 11 (3) (1998) 115-120.
2. V.Y. Aristov, V.E. Fradkov, L.S. Shvindlerman, Detachment of the migration grain-boundary half-loop from an absorbed impurity cloud, Sov. Phys. Solid State 22 (1980) 1055-1059.
3. A. Brokman, R. Kris, W. Mullins, A. Vilenkin, Analysis of boundary motion in thin films, Scripta Mater. 32 (1995) 1341-1346.
4. E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw Hill, New York, 1955.
5. B. Coleman, R. Falk, M. Moakher, Stability of cylindrical bodies in the theory of surface diffusion, Physica 089 (1995) 123-135.
6. B. Coleman, R. Falk, M. Moakher, Space-time finite element methods for surface diffusion with application to the theory of the stability of cylinders, SIAM J. Sci. Comput. 17 (1996) 1434-1448.
7. C.L. Di Prinzio, O.B. Nasello, Studies of grain boundary motion in ice bicrystals, J. Phys. Chem. B 101 (1997) 7687-7690.
8. C.G. Dunn, F.W. Daniels, M.J. Bolton, Trans. Am. Inst. Min. Eng. 185 (1949) 708.
9. M. Furtkamp, G. Gottstein, D.A. Molodov, V.N. Semenov, L.S. Shvindlerman, Grain boundary migration in Fe-3.5% Si bicrystals with [001] tilt boundaries, Acta Mater. 46 (1998) 4103-4110.
10. G. Gottstein, U. Czubayko, D.A. Molodov, L.S. Shvindlerman, W. Wunderlich, In situ observations of grain boundary migration, Mater. Sci. Forum 204-206 (1996) 99-108.
11. G. Gottstein, L.S. Shvindlerman, Grain boundary migration in metals: thermodynamics, kinetics, applications, CRC Press, Boca Raton, FL, 1999.
12. J. Kanel, A. Novick-Cohen, A. Vilenkin, A traveling wave solution for coupled surface and grain boundary motion, Acta Mater. 51 (2003) 1981-1989.
13. J. Kanel, A. Novick-Cohen, A. Vilenkin, Coupled surface and grain boundary motion: nonclassical traveling wave solutions, Adv. Differential Equations 9 (2004) 299-327.
14. J. Kanel, A. Novick-Cohen, A. Vilenkin, A numerical study for grain boundary motion in bicrystals, Acta Mater., accepted for publication.
15. J. Kanel, A. Novick-Cohen, A. Vilenkin, Stability of traveling wave solutions for grain boundary motion, in preparation
16. W.W. Mullins, Two-dimensional motion of ideal grain boundaries, J. Appl. Phys. 27 (1956) 900-904.
17. W.W. Mullins, Theory of thermal grooving, J. Appl. Phys. 28 (1957) 333-339.
18. W.W. Mullins, The effect of thermal grooving on grain boundary motion, Acta Metall. 6 (1958) 414-427.
19. A. Novick-Cohen, Triple-junction motion for an Allen-Cahn/Cahn-Hilliard system, Physica D 137 (2000) 1-24.
20. A. Novick-Cohen, L. Peres Hari, Geometric motion for a degenerate Allen-Cahn/Cahn-Hilliard system: the partial wetting case, Physica D, submitted for publication.
21. E. Rabkin, V. Semenov, T. Izyumova, Jerky motion of grain boundaries in NiAl: an atomic force microscopy study, Scripta Mater. 42 (2000) 359-365.
22. V.N. Semenov, B.B. Straumal, V.G. Glebovsky, W.J. Gust, J. Cryst. Growth 151 (1995) 180-186.
23. G. Solorzano, M. El-Boragy, W. Gust, B. Predel, In situ study of discontinuous precipitation in AI-15 at% Zn, Scripta Mater. 34 (1996) 1431.
24. A.J. Vilenkin, R. Kris, A. Brokman, Breakup and grain growth in thin-film array, J. Appl. Phys. 81 (1997) 238-245.
25. A. Vilenkin, A. Novick-Cohen, J. Kanel, A numerical study of stability of grain boundary motion in a bicrystal, in preparation.