Surface dynamics dominated by bulk thermal defects: The case of NiAl(110)

Physical Review B - Condensed Matter and Materials Physics

Volumn 71, Issue 8, 2005, Pages

  McCarty, K F ^a   Nobel, J A ^a   Bartelt, N C ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALUMINUM DERIVATIVE; NICKEL COMPLEX;

ARTICLE; ENERGY; MATERIALS; MODEL; MOLECULAR DYNAMICS; MOTION; SURFACE PROPERTY; TEMPERATURE DEPENDENCE; THERMAL EXPOSURE;

EID: 16344390026     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.71.085421     Document Type: Article

References (87)

1. C. P. Flynn, Point Defects and Diffusion (Clarendon Press, Oxford, 1972).
2. C. Wagner and W. Schottky, Z. Phys. Chem. Abt. B 11, 163 (1930).
3. C. Herring, in Structure and Properties of Solid Surfaces, edited by R. Gomer and C. S. Smith (University of Chicago Press, Chicago, 1952).
4. W. W. Mullins, J. Appl. Phys. 30, 77 (1959).
5. J. M. Blakely, Trans. Faraday Soc. 57, 1164 (1961).
6. J. M. Blakely and H. Mykura, Acta Metall. 10, 565 (1962).
7. P. S. Maiya and J. M. Blakely, J. Appl. Phys. 38, 698 (1966).
8. K. Hoehne and R. Sizmann, Phys. Status Solidi A 5, 577 (1971).
9. P. Nozieres, J. Phys. (Paris) 48, 1605 (1987).
10. A. Rettori and J. Villain, J. Phys. (Paris) 49, 257 (1988).
11. M. Uwaha, J. Phys. Soc. Jpn. 57, 1681 (1988).
12. M. Ozdemir and A. Zangwill, Phys. Rev. B 42, 5013 (1990).
13. J. W. Cahn and J. E. Taylor, Acta Metall. Mater. 42, 1045 (1994).
14. H. P. Bonzel and W. W. Mullins, Surf. Sci. 350, 285 (1996).
15. N. C. Bartelt, W. Theis, and R. M. Tromp, Phys. Rev. B 54, 11 741 (1996).
16. A. J. Vilenkin and A. Brokman, Phys. Rev. B 56, 9871 (1997).
17. J. G. McLean, B. Krishnamachari, D. R. Peale, E. Chason, J. P. Sethna, and B. H. Cooper, Phys. Rev. B 55, 1811 (1997).
18. E. Adam, A. Chame, F. Lancon, and J. Villain, J. Phys. I 7, 1455 (1997).
19. N. Israeli and D. Kandel, Phys. Rev. Lett. 80, 3300 (1998).
20. M. Iwamatsu and Y. Okabe, J. Appl. Phys. 86, 5541 (1999).
21. H. C. Jeong and E. D. Williams, Surf. Sci. Rep. 34, 175 (1999):
22. M. Giesen, Prog. Surf. Sci. 68, 1 (2001).
23. J. M. Wen, J. W. Evans, M. C. Bartelt, J. W. Burnett, and P. A. Thiel, Phys. Rev. Lett. 76, 652 (1996).
24. S. J. Chey, J. E. Van Nostrand, and D. G. Cahill, Phys. Rev. Lett. 76, 3995 (1996).
25. A. Ichimiya, Y. Tanaka, and K. Ishiyama, Phys. Rev. Lett. 76, 4721 (1996).
26. W. W. Pai, A. K. Swan, Z. Y. Zhang, and J. F. Wendelken, Phys. Rev. Lett. 79, 3210 (1997).
27. J. B. Hannon, C. Klunker, M. Giesen, H. Ibach, N. C. Bartelt, and J. C. Hamilton, Phys. Rev. Lett. 79, 2506 (1997).
28. S. Tanaka, N. C. Bartelt C. C. Umbach, R. M. Tromp, and J. M. Blakely, Phys. Rev. Lett. 78, 3342 (1997).
29. G. R. Carlow, D. D. Perovic, and M. Zinke-Allmang, Appl. Surf. Sci. 130, 704 (1998).
30. K. Morgenstern, G. Rosenfeld, E. Laegsgaard, F. Besenbacher, and G. Comsa, Phys. Rev. Lett. 80, 556 (1998).
31. G. S. Icking-Konert, M. Giesen, and H. Ibach, Surf. Sci. 398, 1 (1998).
32. D. M. Kolb, R. Ullmann, and J. C. Ziegler, Electrochim. Acta 43, 2751 (1998).
33. M. Giesen and H. Ibach, Surf. Sci. 431, 109 (1999).
34. G. Rosenfeld, K. Morgenstern, M. Esser, and G. Comsa, Appl. Phys. A: Mater. Sci. Process. 69, 489 (1999).
35. K. Morgenstern, E. Laegsgaard, I. Stensgaard, and F. Besenbacher, Phys. Rev. Lett. 83, 1613 (1999).
36. M. Giesen, Surf. Sci. 441, 2 (1999).
37. P. Broekmann, M. Wilms, M. Kruft, C. Stuhlmann, and K. Wandelt, J. Electroanal. Chem. 467, 307 (1999).
38. S. Kodambaka, V. Petrova, A. Vailionis, P. Desjardins, D. G. Cahill, I. Petrov, and J. E. Greene, Surf. Rev. Lett. 7, 5 (2000).
39. A. Ichimiya, K. Hayashi, E. D. Williams, T. L. Einstein, M. Uwaha, and K. Watanabe, Phys. Rev. Lett. 84, 3662 (2000).
40. K. Hayashi and A. Ichimiya, Appl. Surf. Sci. 162, 37 (2000).
41. M. Z. Li, J. F. Wendelken, B. G. Liu, E. G. Wang, and Z. Y. Zhang, Phys. Rev. Lett. 86, 2345 (2001).
42. S. Kodambaka, V. Petrova, A. Vailionis, P. Desjardins, D. G. Cahill, I. Petrov, and J. E. Greene, Thin Solid Films 392, 164 (2001).
43. A. R. Layson, J. W. Evans, and P. A. Thiel, Phys. Rev. B 65, 193409 (2002).
44. E. Bauer, Rep. Prog. Phys. 57, 895 (1994).
45. D. B. Miracle, Acta Metall. Mater. 41, 649 (1993).
46. H. L. Davis and J. R. Noonan, Phys. Rev. Lett. 54, 566 (1985).
47. K. F. McCarty, J. A. Nobel, and N. C. Bartelt, Nature (London) 412, 622 (2001).
48. K. F. McCarty and N. C. Bartelt, Phys. Rev. Lett. 90, 046104 (2003).
49. K. F. McCarty and N. C. Bartelt, Surf. Sci. 540, 157 (2003).
50. K. F. McCarty and N. C. Bartelt, Surf. Sci. 527, L203 (2003).
51. B. Poelsema, J. B. Hannon, N. C. Bartelt, and G. L. Kellogg, Appl. Phys. Lett. 84, 2551 (2004).
52. M. Ondrejcek, W. Swiech, G. Yang, and C. P. Flynn, Philos. Mag. Lett. 84, 69 (2004).
53. S. Kodambaka, S. V. Khare, W. Swiech, K. Ohmori, I. Petrov, and J. E. Greene, Nature (London) 429, 49 (2004).
54. W. F. Chung and M. S. Altman, Ultramicroscopy 74, 237 (1998).
55. Since the thermal smoothing discussed below is slow on the time scale of the cooling, nearly all the mass removed from the surface in Fig. 3 results from the temperature change, not thermal smoothing.
56. Even during a rapid temperature increase, we do not observe the nucleation of new islands. However, if the crystal is greatly put out of equilibrium by quenching from high temperature and then warmed somewhat, monatomic pits ("vacancy islands") will nucleate in regions of low step density.
57. Y. Mishin and D. Farkas, Philos. Mag. A 75, 169 (1997).
58. M. Hagen and M. W. Finnis, Philos. Mag. A 77, 447 (1998).
59. B. Meyer and M. Fahnle, Phys. Rev. B 59, 6072 (1999).
60. B. Meyer and M. Fahnle, Phys. Rev. B 60, 717 (1999).
61. P. A. Korzhavyi, A. V. Ruban, A. Y. Lozovoi, Y. K. Vekilov, I. A. Abrikosov, and B. Johansson, Phys. Rev. B 61, 6003 (2000).
62. A. Y. Lozovoi and Y. Mishin, Phys. Rev. B 68, 184113 (2003).
63. A. J. Bradley and A. Taylor, Proc. R. Soc. London, Ser. A 159, 56 (1937).
64. R. J. Wasilewski, J. Phys. Chem. Solids 29, 39 (1968).
65. A. A. Smirnov, Sov. Phys. Dokl. 36, 479 (1991).
66. M. C. Bartelt, A. K. Schmid, J. W. Evans, and R. Q. Hwang, Phys. Rev. Lett. 81, 1901 (1998).
67. A. J. Ångström, Philos. Mag. 25, 130 (1863).
68. S. K. Evnochides and E. J. Henley, J. Polym. Sci., Part A-2 8, 1987 (1970).
69. If the size of the temperature, oscillations are sufficiently large, the temperature dependence of D will cause a nonsinusoidal response in the mass flux. This effect was negligible for the temperature oscillations analyzed in this paper; for example, Fourier transforming the mass flux in Fig. 6 shows negligible higher harmonics. In principle, however, measuring the size of the higher harmonics offers a method of probing the temperature dependence of D.
70. S. Frank, S. V. Divinski, U. Södervall, and C. Herzig, Acta Mater. 49, 1399 (2001).
71. The diffusion model implies that these oscillation rates are slow enough to ensure that >95% of the defects that would be produced by a fully equilibrated temperature change are swept to the surface.
72. Y. Mishin, A. Y. Lozovoi, and A. Alavi, Phys. Rev. B 67, 014201 (2003).
73. B. Bai and G. S. Collins, in High-Temperature Ordered Intermetallic Alloys V11, MRS Symposia Proceedings No. 552, edited by E. P. George, M. Yamaguchi, and M. J. Mills (Materials Research Society, Pittsburgh, 1999), p. KK8.7.1.
74. H. J. Ko, K. T. Hong, M. J. Kaufmann, and K. S. Lee, J. Mater. Sci. 37, 1915 (2002).
75. R. Kozubski, D. Kmiec, E. Partyka, and M. Danielewski, Intermetallics 11, 897 (2003).
76. R. Nakamura, K. Takasawa, Y. Yamazaki, and Y Iijima, Intermetallics 10, 195 (2002).
77. R. Nakamura, K. Fujita, Y. Iijima, and M. Okada, Acta Mater. 51, 3861 (2003).
78. Y. Mishin and D. Farkas, Philos. Mag. A 75, 187 (1997).
79. C. R. Kao and Y. A. Chang, Intermetallics 1, 237 (1993).
80. G. F. Hancock and B. R. McDonnel, Phys. Status Solidi A 4, 143 (1971).
81. The scatter in the decay rates of the pits results from the fact that the pits were made by quenching the sample. Thus there was only a limited time available to equilibrate the sample at the measurement temperature before the decay rates were measured.
82. The decay rates of noncircular islands generally decrease somewhat as the islands shrink. We believe that this effect results from anisotropy in the step velocity as a function of step orientation. In contrast, if islands remain nearly circular, their decay rates remain linear. [see Figs. 5(b) and 8].
83. As the island vanishes at the lowest temperature in Fig. 10(a), its area decreases nonlinearly, suggesting that diffusion is becoming important.
84. We note that during isothermal surface smoothing only the surface is out of equilibrium. In contrast, after a temperature change, the entire sample is not equilibrated. How fast the bulk then equilibrates is controlled by the rate defects diffuse through the bulk, as described by the diffusion model.
85. M. Zinke-Allmang, L. C. Feldman, and M. H. Grabow, Surf. Sci. Rep. 16, 377 (1992).
86. bulk. For this case, the bulk defect concentration will not have time to respond to the oscillations and will be time independent. The flux is then determined by the time-dependent state of the surface: F ∝cos(ωt). Therefore, the phase shift δ between the temperature and the flux will be essentially zero, much smaller then the -π/4 limit of Eq. (2). As the frequency decreases, the concentration near the surface has time to come into equilibrium with the surface and the analysis of Eqs. (1)-(4) becomes correct. The fact that the smallest phase shift we observe is -π/4, not zero, indicates that we are in the frequency regime where the step-attachment barrier is not important to temperature-change-driven mass flow between the bulk and the surface.
87. See, for example, N. Israeli and D. Kandel, Phys. Rev. Lett. 88, 1 (2002) and references therein.