Capture numbers in the presence of repulsive adsorbate interactions

Physical Review B - Condensed Matter and Materials Physics

Volumn 66, Issue 19, 2002, Pages 1954041-19540416

  Venables, J A ^a   Brune, H ^b  

^a UNIVERSITY OF SUSSEX   (United Kingdom)

^b EPFL   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

METAL;

ADSORPTION; ARTICLE; ATOM; CALCULATION; CHEMICAL BINDING; DENSITY; DIFFUSION; ENERGY; HEAT TREATMENT; KINETICS; LOW TEMPERATURE; MODEL; MOLECULAR INTERACTION; MONTE CARLO METHOD; SCANNING TUNNELING MICROSCOPY; SURFACE PROPERTY; THEORY;

EID: 0037113719     PISSN: 01631829     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (47)

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21. M. J. Stowell, Philos. Mag. 26, 349 (1972); 26, 361 (1972). Most calculations use one radial variable to define the "lattice" as a Wigner-Seitz "circle." An extensive numerical discussion is given by B. Lewis and G. J. Rees, ibid. 20, 1253 (1974) and by B. Lewis and J. C. Anderson, Nucleation and Growth of Thin Films (Academic, London, 1978), pp. 238-246.
22. M. J. Stowell, Philos. Mag. 26, 349 (1972); 26, 361 (1972). Most calculations use one radial variable to define the "lattice" as a Wigner-Seitz "circle." An extensive numerical discussion is given by B. Lewis and G. J. Rees, ibid. 20, 1253 (1974) and by B. Lewis and J. C. Anderson, Nucleation and Growth of Thin Films (Academic, London, 1978), pp. 238-246.
23. M. J. Stowell, Philos. Mag. 26, 349 (1972); 26, 361 (1972). Most calculations use one radial variable to define the "lattice" as a Wigner-Seitz "circle." An extensive numerical discussion is given by B. Lewis and G. J. Rees, ibid. 20, 1253 (1974) and by B. Lewis and J. C. Anderson, Nucleation and Growth of Thin Films (Academic, London, 1978), pp. 238-246.
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25. See Ref. 1, or J. A. Venables, Phys. Rev. B 36, 4153 (1987) for explicit expressions.
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27. J. G. Amar and F. Family, Phys. Rev. Lett. 74, 2066 (1995); M. C. Bartelt, C. R. Stoldt, C. J. Jenks, P. A. Thiel, and J. W. Evans, Phys. Rev. B 59, 3125 (1999); P. A. Mulheran and D. A. Robbie, Europhys. Lett. 49, 617 (2000); D. A. Robbie and P. A. Mulheran, Philos. Mag. B 80, 1299 (2000); J. G. Amar, M. N. Popescu, and F. Family, Phys. Rev. Lett. 86, 3092 (2001), and references therein.
28. J. G. Amar and F. Family, Phys. Rev. Lett. 74, 2066 (1995); M. C. Bartelt, C. R. Stoldt, C. J. Jenks, P. A. Thiel, and J. W. Evans, Phys. Rev. B 59, 3125 (1999); P. A. Mulheran and D. A. Robbie, Europhys. Lett. 49, 617 (2000); D. A. Robbie and P. A. Mulheran, Philos. Mag. B 80, 1299 (2000); J. G. Amar, M. N. Popescu, and F. Family, Phys. Rev. Lett. 86, 3092 (2001), and references therein.
29. J. G. Amar and F. Family, Phys. Rev. Lett. 74, 2066 (1995); M. C. Bartelt, C. R. Stoldt, C. J. Jenks, P. A. Thiel, and J. W. Evans, Phys. Rev. B 59, 3125 (1999); P. A. Mulheran and D. A. Robbie, Europhys. Lett. 49, 617 (2000); D. A. Robbie and P. A. Mulheran, Philos. Mag. B 80, 1299 (2000); J. G. Amar, M. N. Popescu, and F. Family, Phys. Rev. Lett. 86, 3092 (2001), and references therein.
30. J. G. Amar and F. Family, Phys. Rev. Lett. 74, 2066 (1995); M. C. Bartelt, C. R. Stoldt, C. J. Jenks, P. A. Thiel, and J. W. Evans, Phys. Rev. B 59, 3125 (1999); P. A. Mulheran and D. A. Robbie, Europhys. Lett. 49, 617 (2000); D. A. Robbie and P. A. Mulheran, Philos. Mag. B 80, 1299 (2000); J. G. Amar, M. N. Popescu, and F. Family, Phys. Rev. Lett. 86, 3092 (2001), and references therein.
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32. x approximates to 4π/[-1n(Z)+0.116]. But this is just the low-Z limit of the full Bessel function solution, given in Ref. 10 and repeated here in Appendix A.
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37. K. H. Lau and W. Kohn, Surf. Sci. 75, 69 (1978). There are other effects with similar r dependence, but for close-packed metals the surface-state effect appears to be the largest (see Refs. 7-9 for a discussion).
38. This formulation is given, with different notation and different amounts of detail, in many places, See, for example, P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963), Secs. 1.5 and 4.4; R. Gomer, in Surface Mobilities on Solid Materials, Vol. 86 of NATO Advanced Studies Institute, Series B: Physics, edited by V. T. Binh (Plenum, New York, 1982), pp. 7-12; R. Gomer, Rep. Prog. Phys. 53, 917 (1990); A. R. Allnatt and A. B. Lidiard, Atomic Transport in Solids (Cambridge University, Cambridge, England, 1993), Secs. 5.2, 6.5, and 8.2.2.
39. This formulation is given, with different notation and different amounts of detail, in many places, See, for example, P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963), Secs. 1.5 and 4.4; R. Gomer, in Surface Mobilities on Solid Materials, Vol. 86 of NATO Advanced Studies Institute, Series B: Physics, edited by V. T. Binh (Plenum, New York, 1982), pp. 7-12; R. Gomer, Rep. Prog. Phys. 53, 917 (1990); A. R. Allnatt and A. B. Lidiard, Atomic Transport in Solids (Cambridge University, Cambridge, England, 1993), Secs. 5.2, 6.5, and 8.2.2.
40. This formulation is given, with different notation and different amounts of detail, in many places, See, for example, P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963), Secs. 1.5 and 4.4; R. Gomer, in Surface Mobilities on Solid Materials, Vol. 86 of NATO Advanced Studies Institute, Series B: Physics, edited by V. T. Binh (Plenum, New York, 1982), pp. 7-12; R. Gomer, Rep. Prog. Phys. 53, 917 (1990); A. R. Allnatt and A. B. Lidiard, Atomic Transport in Solids (Cambridge University, Cambridge, England, 1993), Secs. 5.2, 6.5, and 8.2.2.
41. This formulation is given, with different notation and different amounts of detail, in many places, See, for example, P. G. Shewmon, Diffusion in Solids (McGraw-Hill, New York, 1963), Secs. 1.5 and 4.4; R. Gomer, in Surface Mobilities on Solid Materials, Vol. 86 of NATO Advanced Studies Institute, Series B: Physics, edited by V. T. Binh (Plenum, New York, 1982), pp. 7-12; R. Gomer, Rep. Prog. Phys. 53, 917 (1990); A. R. Allnatt and A. B. Lidiard, Atomic Transport in Solids (Cambridge University, Cambridge, England, 1993), Secs. 5.2, 6.5, and 8.2.2.
42. 1(r) due to V(r) itself.
43. 2 compared to conventional expressions. We have also noted in Appendices B and D, and in relation to Fig. 2, that there are uncertainties or order 0.5a in the position of the zero in our continuum diffusion model. This is a rediscovery of the point published by C. Ratsch, M. Kang, and R. E. Caflisch, Phys. Rev. B 64, 020601 (2001) in the context of their level set models.
44. 1/F) values, which is also a transient nucleation phenomenon, is thoroughly discussed in Ref. 16.
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