Dirichlet extremum problem associated with the asymmetric grain-boundary thermal grooving under the Dirac δ -type anisotropic surface stiffness in bicrystal thin solid films

Journal of Applied Physics

Volumn 102, Issue 6, 2007, Pages

  Ogurtani, Tarik Omer ^a  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC FORCE MICROSCOPY; CRYSTAL SYMMETRY; GRAIN BOUNDARIES; OPTICAL ANISOTROPY; SURFACE TOPOGRAPHY;

ANISOTROPIC SURFACE STIFFNESS; BICRYSTAL THIN SOLID FILMS; DIRICHLET BOUNDARY; THERMAL GROOVING;

THIN FILMS;

EID: 34848851904     PISSN: 00218979     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2781574     Document Type: Article

References (48)

1. A. Ramasubramaniam and V. B. Shenoy, J. Appl. Phys. 95, 7813 (2004).
2. T. O. Ogurtani, J. Chem. Phys. 0021-9606 10.1063/1.2185625 124, 144706 (2006).
3. T. O. Ogurtani, Phys. Rev. B 0163-1829 10.1103/PhysRevB.73.235408 73, 235408 (2006).
4. T. O. Ogurtani, Phys. Rev. B 0163-1829 10.1103/PhysRevB.74.155422 74, 155422 (2006).
5. W. Lu and Z. Suo, Phys. Rev. B 0163-1829 10.1103/PhysRevB.65.085401 65, 085401 (2002).
6. C. Herring, in The Physics of Powder Metallurgy, edited by, W. E. Kinston, (McGraw-Hill, New York, 1951), p. 143.
7. J. von-Neumann, Metal Interfaces (ASM, Cleveland, 1952), p. 108.
8. W. W. Mullins, J. Appl. Phys. 0021-8979 10.1063/1.1722742 28, 333 (1957).
9. W. Gibbs, The Collected Works of J. Willard Gibbs, Vol. I Thermodynamics (Yale University Press, New Haven, 1948), p. 226.
10. T. Young, Philos. Trans. R. Soc. London 0370-2316 10.1098/rstl.1805.0005 95, 65 (1805).
11. E. Rabkin, L. Klinger, and V. Semenov, Acta Mater. 1359-6454 10.1016/S1359-6454(99)00432-2 48, 1533 (2000).
12. L. Klinger and E. Rabkin, Interface Sci. 0927-7056 10.1023/A: 1011270830969 9, 55 (2001).
13. W. Zhang, P. Sachenko, and I. Gladwell, Acta Mater. 107, 16 (2004). 1359-6454
14. T. Xin and H. Wong, Acta Mater. 51, 2305 (2003). 1359-6454
15. T. O. Ogurtani and O. Akyildiz, J. Appl. Phys. 0021-8979 10.1063/1.1883305 97, 093520 (2005).
16. T. O. Ogurtani and O. Akyildiz, in Materials, Technology, and Reliability of Low- k Dielectrics and Copper Interconnects, edited by T. Y. Tsui, Y-C. Joo, A. A. Volinsky, M. Lane, and L. Michaelson, MRS Symposium Proceedings No. 914 (Materials Research Society, Warrendale, PA, 2006), p. 0914-F09-22.
17. T. O. Ogurtani and E. E. Oren, Int. J. Solids Struct. 0020-7683 10.1016/j.ijsolstr.2004.11.013 42, 3918 (2005).
18. E. E. Oren and T. O. Ogurtani, in Thin Films: Stresses and Mechanical Properties IX, edited by C. S. Ozkan, R. C. Cammaratai, L. B. Freund, and H. Gao, MRS Symposia Proceedings No. 695 (Materials Research Society, Pittsburgh, 2002), p. L.5.51.
19. A. Averbuch, M. Israeli, M. Nathan, and I. Ravve, J. Comput. Phys. 0021-9991 10.1016/S0021-9991(03)00199-2 188, 640 (2003).
20. M. Nathan, A. Averbuch, and M. Israel, Thin Solid Films 0040-6090 10.1016/j.tsf.2004.03.019 466, 347 (2004).
21. D. Min and H. Wong, J. Appl. Phys. 0021-8979 10.1063/1.2159082 99, 023515 (2006).
22. D. Min and H. Wong, J. Appl. Phys. 0021-8979 10.1063/1.2336980 100, 053523 (2006).
23. A. Ramasubramaniam and V. B. Shenoy, Acta Mater. 53, 2943 (2005). 1359-6454
24. Z. Suo, Adv. Appl. Mech. 33, 193 (1997). 0065-2156
25. M. Jin, E. Shimada, and Y. Ikuma, J. Mater. Res. 14, 2548 (1999). 0884-2914
26. T. O. Ogurtani and E. E. Oren, J. Appl. Phys. 0021-8979 10.1063/1.1382835 90, 1564 (2001).
27. A. D. Myskis, Advanced Mathematics for Engineers (MIR Publications, Moscow, 1975), p. 357.
28. F. B. Hildebrand, Methods of Applied Mathematics (Prentice-Hall, Englewood Cliffs, NJ, 1961), p. 127.
29. R. Haase, Thermodynamics of Irreversible Processes (Addison-Wesley, Massachusetts, 1969), p. 245.
30. T. O. Ogurtani and A. K. Seeger, J. Chem. Phys. 0021-9606 10.1063/1.445599 79, 5041 (1983).
31. S. R. De Groot, Thermodynamics of Irreversible Processes (North-Holland, Amsterdam, 1961), p. 59.
32. L. Onsager, Phys. Rev. 0031-899X 10.1103/PhysRev.37.405 37, 405 (1931); L. Onsager, Phys. Rev. 0031-899X 10.1103/PhysRev.38.2265 38, 2265 (1931).
33. L. Onsager, Phys. Rev. 0031-899X 10.1103/PhysRev.37.405 37, 405 (1931); L. Onsager, Phys. Rev. 0031-899X 10.1103/PhysRev.38.2265 38, 2265 (1931).
34. A. Needleman and J. R. Rice, Acta Metall. 0001-6160 10.1016/0001-6160(80) 90001-2 28, 1315 (1980).
35. G. E. M. Karniadakis and S. J. Shervin, Spectral/hp Element Methods for CFD (Oxford University Press, Oxford, 1999), p. 21.
36. L. F. Lösch and J. E. Lösch, Tables of Higher Functions (McGraw-Hill, New York, 1960), p. 101.
37. C. W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, New Jersey, 1971), p. 109.
38. G. Dahlquist, Proc. Symp. Appl. Math. 15, 147 (1963); G. Dahlquist, BIT 3, 27 (1963).
39. G. Dahlquist, Proc. Symp. Appl. Math. 15, 147 (1963); G. Dahlquist, BIT 3, 27 (1963).
40. T. O. Ogurtani and E. E. Oren, J. Appl. Phys. 0021-8979 10.1063/1.1815389 96, 7246 (2004).
41. K. N. Tu, J. Appl. Phys. 0021-8979 10.1063/1.1611263 94, 5451 (2003).
42. L. E. Murr, Interfacial Phenomena in Metals and Alloys (Addison-Wesley, Reading, MA, 1975).
43. W. M. Robertson, J. Appl. Phys. 0021-8979 10.1063/1.1659625 42, 463 (1971).
44. W. Zhang and J. H. Schneibel, Comput. Mater. Sci. 0927-0256 10.1016/0927-0256(94)00073-L 3, 347 (1995).
45. T. Xin and H. Wong, Surf. Sci. Lett. 0167-2584 10.1016/S0039-6028(01) 01158-X 487, L529 (2001).
46. T. Xin and H. Wong, Mater. Sci. Eng., A 0921-5093 10.1016/j.msea.2003.08. 042 364, 287 (2004).
47. P. Du and F. Wong, Scr. Mater. 55, 1171 (2006).
48. H. Wong, M. J. Miksis, P. W. Voorhees, and S. H. Davis, Acta Mater. 1359-6454 10.1016/S1359-6454(96)00351-5 45, 2477 (1997).