Neglected adsorbate interactions behind diffusion prefactor anomalies on metals

Physical Review B - Condensed Matter and Materials Physics

Volumn 64, Issue 12, 2001, Pages

  Ovesson, S ^a   Wahnstrom G ^a   Lundqvist, B I ^a   Bogicevic, A ^b  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b FORD MOTOR COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; DIFFUSION; ENTROPY; MATHEMATICAL ANALYSIS; MOLECULAR MODEL; SCANNING TUNNELING MICROSCOPY; SURFACE PROPERTY; SYSTEM ANALYSIS;

EID: 0035883524     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.64.125423     Document Type: Article

References (83)

1. H. Eyring, J. Chem. Phys.3, 107 (1935);
2. S. Glasstone, K J. Laidler, and H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941).
3. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys.62, 251 (1990).
4. G. Wahnström, in Interaction of Molecules with Solid Surfaces, edited by V. Bortaloni, N. M. March, and M. P. Tosi (Plenum Press, New York, 1990).
5. V P. Zhdanov, Surf. Sci. Rep.12, 183 (1991).
6. R. Gomer, Rep. Prog. Phys.53, 917 (1990).
7. H. Brune, Surf. Sci. Rep.31, 121 (1998).
8. J V. Barth, H. Brune, B. Fischer, J. Weckesser, and K. Kern, Phys. Rev. Lett.84, 1732 (2000).
9. H. Brune, K. Bromann, H. Röder, K. Kern, J. Jacobsen, P. Stoltze, K. Jacobsen, and J. Nørskov, Phys. Rev. B52, 14 380 (1995).
10. B. Fischer, H. Brune, J V. Barth, A. Fricke, and K. Kern, Phys. Rev. Lett.82, 1732 (1999).
11. J.-R. Chen and R. Gomer, Surf. Sci.94, 456 (1980).
12. J R. Banavar, M H. Cohen, and R. Gomer, Surf. Sci.107, 113 (1981).
13. B G. Briner, M. Doering, H.-P. Rust, and M. Bradshaw, Science278, 257 (1997).
14. E. Nabighian and X D. Zhu, Chem. Phys. Lett.316, 177 (2000).
15. G L. Kellogg, Surf. Sci. Ref.21, 1 (1994).
16. K A. Fichthorn and M. Scheffler, Phys. Rev. Lett.84, 5371 (2000).
17. A. Bogicevic, S. Ovesson, P. Hyldgaard, B I. Lundqvist, H. Brune, and D R. Jennison, Phys. Rev. Lett.85, 1910 (2000).
18. J A. Venables, G D T. Spiller, and M. Hanbücken, Rep. Prog. Phys.47, 399 (1984);
19. J A. Venables, Phys. Rev. B36, 4153 (1987).
20. In Ref. 12, the diffusion of CO on Cu(110) is monitored directly with the STM and found to have a preexponential factor of (formula presented). It is not clear, however, whether the diffusion of CO on Cu(110) is a simple one-step, one-channel process or a more complex motion.
21. T. Michely, W. Langenkamp, H. Hansen, and C. Busse, Phys. Rev. Lett.86, 2695 (2001).
22. G H. Vineyard, J. Phys. Chem. Solids3, 121 (1957).
23. Quantum corrections to this formula can be invoked [see P G. Wolynes, Phys. Rev. Lett.47, 968 (1981) and
24. E. Pollak, Chem. Phys. Lett.127, 178 (1986)], but with the exception of hydrogen, those corrections are always quite small.
25. U. Kürpick, A. Kara, and T S. Rahman, Phys. Rev. Lett.78, 1086 (1997);
26. U. Kürpick and T S. Rahman, Phys. Rev. B57, 2482 (1998).
27. W. Meyer and H. Neldel, Z. Tech. Phys. (Leipzig)12, 588 (1937).
28. G. Boisvert and L J. Lewis, Phys. Rev. B54, 2880 (1996).
29. A F. Voter and J D. Doll, J. Chem. Phys.80, 5832 (1984).
30. C. Ratsch and M. Scheffler, Phys. Rev. B58, 13 163 (1998).
31. R. Stumpf and M. Scheffler, Phys. Rev. B53, 4958 (1996).
32. D C. Senft and G. Ehrlich, Phys. Rev. Lett.74, 294 (1994).
33. J. Jacobsen, K W. Jacobsen, and J P. Sethna, Phys. Rev. Lett.79, 2843 (1997).
34. A F. Voter, Phys. Rev. B34, 6819 (1986).
35. Molecular-dynamics simulations of adatom diffusion for systems with low activation energies are reported in G C. Kallinteris, G A. Evangelakis, and N I. Papanicolaou, Surf. Sci.369, 185 (1996), but that study does not discuss the accuracy of TST.
36. H A. Kramers, Physica (Amsterdam)7, 284 (1940).
37. H. Brune, G S. Bales, J. Jacobsen, C. Boragno, and K. Kern, Phys. Rev. B60, 5991 (1999).
38. S. Liu, L. Bönig, and H. Metiu, Phys. Rev. B52, 2907 (1995).
39. M C. Bartelt, S. Günther, E. Kopatzki, R J. Behm, and J W. Evans, Phys. Rev. B53, 4099 (1996).
40. See Table 2 in Ref. 6.
41. R. Stumpf and M. Scheffler, Phys. Rev. Lett.72, 254 (1994).
42. S C. Wang and G. Ehrlich, Phys. Rev. Lett.70, 41 (1993);
43. F. Watanabe and G. Ehrlich, J. Phys. Chem.95, 6075 (1991);
44. J. Phys. Chem.F. WatanabeG. Ehrlich96, 3191 (1992).
45. S. Horch, H T. Lorensen, S. Helveg, E. Lægsgaard, I. Steensgaard, K W. Jacobsen, J K. Nørskov, and F. Besenbacher, Nature (London)398, 134 (1999).
46. T B. Grimley, Proc. Phys. Soc. London90, 751 (1967);
47. Proc. Phys. Soc. LondonT B. Grimley92, 776 (1967).
48. T L. Einstein and J R. Schrieffer, Phys. Rev. B7, 3629 (1973);
49. T L. Einstein, Surf. Sci. Lett.75, 161 (1978);
50. Handbook of Surface Science, edited by W. N. Unertl (Elsevier, Amsterdam, 1996), Vol. 1, p. 577.
51. K H. Lau and W. Kohn, Surf. Sci.75, 69 (1978).
52. P. Hyldgaard and M. Persson, J. Phys.: Condens. Matter12, L13 (2000).
53. A. Bogicevic, Phys. Rev. Lett.82, 5301 (1999).
54. K H. Lau and W. Kohn, Surf. Sci.65, 607 (1977).
55. P. Hohenberg and W. Kohn, Phys. Rev.136, B864 (1964).
56. W. Kohn and L J. Sham, Phys. Rev.140, A1133 (1965).
57. G. Kresse and J. Hafner, Phys. Rev. B47, 558 (1993);
58. Phys. Rev. BG. KresseJ. Hafner49, 14 251 (1994);
59. Phys. Rev. BG. KresseJ. Hafner54, 11 169 (1996).
60. B. Hammer and L. Bengtsson, computer code DACAPO-1.30, (Denmark Technical University, Lyngby, Denmark, 1999).
61. J P. Perdew and A. Zunger, Phys. Rev. B23, 5048 (1981).
62. J P. Perdew, Phys. Rev. B46, 6671 (1992).
63. The different energy cutoffs for Al(111) and Al(100) merely reflect the use of different pseudopotentials.
64. D. Vanderbilt, Phys. Rev. B32, 8412 (1985).
65. The artificial electric field induced by one-sided adsorption is very weak; when compensated by a dipole layer in the vacuum, energy differences change by (formula presented) meV, and (more importantly), by the same energy amount for different adsorption sites.
66. E. Wahlström, I. Ekvall, H. Olin, and L. Wallden, Appl. Phys. A: Mater. Sci. Process.A66, S1107 (1998).
67. J. Repp, F. Moresco, G. Meyer, K. Rieder, P. Hyldgaard, and M. Persson, Phys. Rev. Lett.85, 2981 (2000).
68. M F. Crommie, C P. Lutz, and D M. Eigler, Nature (London)363, 524 (1993).
69. A. Bogicevic and K C. Hass (unpublished).
70. S. Renisch, R. Schuster, J. Wintterlin, and G. Ertl, Phys. Rev. Lett.82, 3839 (1999).
71. The calculations for Al/Al(100) have been repeated without adsorbate relaxation in order to confirm the division of the total energy into electronic and elastic contributions, as described in the text. A single adatom is placed on the frozen substrate and allowed to relax. The calculations depicted in Fig. 22 are then carried out with both adatoms fixed in the positions that correspond to the one attained by the isolated adatom. Imposing these constraints, however, does not change the qualitative features of the binding curve in comparison with the case of frozen substrate with adsorbate relaxation.
72. L. Österlund, M. Ø. Pedersen, I. Stensgaard, E. Lægsgaard, and F. Besenbacher, Phys. Rev. Lett.83, 4812 (1999).
73. A. Bogicevic, P. Hyldgaard, G. Wahnström, and B I. Lundqvist, Phys. Rev. Lett.81, 172 (1998).
74. A. Bogicevic, S. Ovesson, B I. Lundqvist, and D R. Jennison, Phys. Rev. B61, 2456 (2000).
75. (formula presented) refers to a hopping diffusion process, i.e., diffusion via exchange with the substrate is not considered.
76. A. Bogicevic, J. Strömquist, and B I. Lundqvist, Phys. Rev. Lett.81, 637 (1998).
77. P. Ruggerone, C. Ratsch, and M. Scheffler, in Growth and Properties of Ultrathin Epitaxial Layers, edited by D. A. King and D. P. Woodruff (Elsevier Science, Amsterdam, 1997).
78. S. Ovesson, A. Bogicevic, and B I. Lundqvist, Phys. Rev. Lett.83, 2608 (1999).
79. For this reason the KMC simulations with interactions become very expensive: a single run with a (formula presented) lattice can involve up to (formula presented) atomic jumps, which is more than 100 times more than without interactions.
80. H. Brune (private communication).
81. B. Fischer, J V. Barth, A. Fricke, L. Nedermann, and K. Kern, Surf. Sci.389, 366 (1997).
82. J V. Barth, H. Brune, G. Ertl, and R J. Behm, Phys. Rev. B42, 9307 (1990).
83. A R. Sandy, S G J. Mochrie, D M. Zehner, K G. Huang, and D. Gibbs, Phys. Rev. B43, 4667 (1991).