Monte carlo simulation of the concentration dependence of segregation at vicinal grain boundaries

Interface Science

Volumn 6, Issue 4, 1998, Pages 259-265

  Udler, D ^a   Seidman, D N ^a  

^a Northwestern University   (United States)

Author keywords

Fowler Guggenheim segregation models; Grain boundaries; Langmuir McLean; Metropolis Monte Carlo; Nickel platinum alloys; Simulation; Solute atom segregation; Twist and tilt boundaries

Indexed keywords

ALGORITHMS; GRAIN BOUNDARIES; MATHEMATICAL MODELS; MONTE CARLO METHODS; NICKEL ALLOYS; PLATINUM;

LANGMUIR-MCLEAN AND FOWLER-GUGGENHEIM SEGREGATION MODELS; METROPOLIS MONTE CARLO; NICKEL-PLATINUM ALLOYS; SOLUTE-ATOM SEGREGATION; TWIST AND TILT BOUNDARIES;

SEGREGATION (METALLOGRAPHY);

EID: 0003018220     PISSN: 09277056     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008697503079     Document Type: Article

References (41)

1. E.D. Hondros, M.P. Seah, S. Hofmann, and P. Lejcek, in Physical Metallurgy, 4th edition, edited by R.W. Cahn and P. Haasen (North Holland, Amsterdam, 1996), Vol. II, p. 856.
2. R.W. Balluffi, in Interfacial Segregation, edited by W.C. Johnson and J.M. Blakely (ASM, Metals Park, Ohio, 1979), p. 193.
3. J.W. Cahn, J. Phys. (Paris) 43, C6-192 (1982).
4. D.N. Seidman, in Materials Interfaces: Atomic-Level Structure and Properties, edited by D. Wolf and S. Yip (Chapman & Hall, London, 1992), p. 58.
5. A.P. Sutton and R.W. Balluffi, Interfaces in Crystalline Solids (Oxford University Press, New York, 1995), chap. 4.
6. A.P. Sutton and R.W. Balluffi, Interfaces in Crystalline Solids (Oxford University Press, New York, 1995), chap. 7.
7. 2. That this assumption is inappropriate for GBs was realized by C.L. White and W.A. Coglan, Metall. Trans. 8A, 1363 (1977). They suggested applying it to individual sites with due allowance for the frequency of occurrence of a given type of site.
8. 2. That this assumption is inappropriate for GBs was realized by C.L. White and W.A. Coglan, Metall. Trans. 8A, 1363 (1977). They suggested applying it to individual sites with due allowance for the frequency of occurrence of a given type of site.
9. 2,bulk) at finite solute concentrations.
10. S.M. Foiles, in Surface Segregation and Related Phenomena, edited by P.A. Dowben and A. Miller (CRC Press, Boca Raton, Florida, 1990), p. 79.
11. A. Seki, D.N. Seidman, Y. Oh, and S.M. Foiles, Acta Metall. Mater. 39, 3167 (1991).
12. D. Udler and D.N. Seidman, Physica Status Solidi (B) 172, 267 (1992).
13. S.M. Kuo, A. Seki, Y. Oh, and D.N. Seidman, Phys. Rev. Lett. 65, 199 (1990).
14. D. Udler and D.N. Seidman, Acta Metall. Mater. 42, 1959 (1992).
15. D.N. Seidman, B.W. Krakauer, and D. Udler, J. Phys. Chem. Sol. 55, 1035 (1994).
16. J.D. Rittner, D. Udler, D.N. Seidman, and Y. Oh, Phys. Rev. Lett. 74, 1115 (1995).
17. D. Udler and D.N. Seidman, Interface Sci. 3, 41 (1995).
18. D. Udler and D.N. Seidman, J. Mater. Res. 10, 1933 (1995).
19. D. Udler and D.N. Seidman, Phys. Rev. Lett. 77, 3379 (1996).
20. J.D. Rittner, D. Udler, and D.N. Seidman, Interf. Sci. 4, 65 (1996).
21. J.D. Rittner, Ph.D. Thesis, Northwestern University, Evanston, Illinois, 1996.
22. J.D. Rittner and D.N. Seidman, Acta Mater. 45, 3191 (1997).
23. S.M. Foiles, M.I. Baskes, and M.S. Daw, Phys. Rev. B 33, 7983 (1986); M.S. Daw, S.M. Foiles, and M.I. Baskes, Mater. Sci. Repts. 9, 251 (1993).
24. S.M. Foiles, M.I. Baskes, and M.S. Daw, Phys. Rev. B 33, 7983 (1986); M.S. Daw, S.M. Foiles, and M.I. Baskes, Mater. Sci. Repts. 9, 251 (1993).
25. P.D. Bristowe and A.G. Crocker, Phil. Mag. A 38, 487 (1978); D. Schwartz and V. Vitek, Philos. Mag. A 51, 499 (1985); D. Schwartz, P.D. Bristowe, and V. Vitek, Acta Metall. 36, 675 (1988).
26. P.D. Bristowe and A.G. Crocker, Phil. Mag. A 38, 487 (1978); D. Schwartz and V. Vitek, Philos. Mag. A 51, 499 (1985); D. Schwartz, P.D. Bristowe, and V. Vitek, Acta Metall. 36, 675 (1988).
27. P.D. Bristowe and A.G. Crocker, Phil. Mag. A 38, 487 (1978); D. Schwartz and V. Vitek, Philos. Mag. A 51, 499 (1985); D. Schwartz, P.D. Bristowe, and V. Vitek, Acta Metall. 36, 675 (1988).
28. D.A. Smith, V. Vitek, and R.C. Pond, Acta Metall. 25, 475 (1977); A.P. Sutton and V. Vitek, Phil. Trans. R. Soc. Lond. A 309, 1 (1983).
29. D.A. Smith, V. Vitek, and R.C. Pond, Acta Metall. 25, 475 (1977); A.P. Sutton and V. Vitek, Phil. Trans. R. Soc. Lond. A 309, 1 (1983).
30. The structure of the ∑ = 5/(002) twist boundary in gold has been studied experimentally in detail by X-ray diffraction at room temperature and was found to have a CSL structure. M.S. Taylor, I. Majid, P.D. Bristowe, and R.W. Balluffi, Phys. Rev. B 40, 2772 (1989); I. Majid, P.D. Bristowe, and R.W. Balluffi, Phys. Rev. 840, 2779 (1989).
31. The structure of the ∑ = 5/(002) twist boundary in gold has been studied experimentally in detail by X-ray diffraction at room temperature and was found to have a CSL structure. M.S. Taylor, I. Majid, P.D. Bristowe, and R.W. Balluffi, Phys. Rev. B 40, 2772 (1989); I. Majid, P.D. Bristowe, and R.W. Balluffi, Phys. Rev. 840, 2779 (1989).
32. C.E. Dahmani, M.S. Cadeville, J.M. Sanchez, and J.L. Moran-Lopez, Phys. Rev. Lett. 55, 1208 (1985).
33. In the literature one can often observe straight lines drawn through experimental data points that do not pass through the origin. This implies that the recorded points are most probably beyond the dilute-solution limit and therefore the Langmuir-McLean analysis is not applicable.
34. R.H. Fowler and E.A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, Cambridge, 1939); M. Guttmann, Surface Sci. 53, 213 (1975); R. Kirchheim, Prog. Mater. Sci. 22, 261 (1988); P. Lejcek and S. Hofmann, Critical Revs. Solid State Mater. Science 20, 1 (1995).
35. R.H. Fowler and E.A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, Cambridge, 1939); M. Guttmann, Surface Sci. 53, 213 (1975); R. Kirchheim, Prog. Mater. Sci. 22, 261 (1988); P. Lejcek and S. Hofmann, Critical Revs. Solid State Mater. Science 20, 1 (1995).
36. R.H. Fowler and E.A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, Cambridge, 1939); M. Guttmann, Surface Sci. 53, 213 (1975); R. Kirchheim, Prog. Mater. Sci. 22, 261 (1988); P. Lejcek and S. Hofmann, Critical Revs. Solid State Mater. Science 20, 1 (1995).
37. R.H. Fowler and E.A. Guggenheim, Statistical Thermodynamics (Cambridge University Press, Cambridge, 1939); M. Guttmann, Surface Sci. 53, 213 (1975); R. Kirchheim, Prog. Mater. Sci. 22, 261 (1988); P. Lejcek and S. Hofmann, Critical Revs. Solid State Mater. Science 20, 1 (1995).
38. D. Wolf, Acta Metall. 37, 1983 (1989).
39. D. Udler and D.N. Seidman, Phys. Rev. B 54, 11133 (1996).
40. Unless we assume that the interactions occur only between solute atoms sitting at GB sites of one type. Such sites are never first-nearest neighbors, so this assumption is physically unreasonable.
41. D. Udler and D.N. Seidman, Acta Mater. 46, 1221 (1998).