O.Braun: surface science studies

Some topics from surface science studies

Chemical adsorption with image forces: the local polaronic model
Interaction between adsorbed atoms
Energy exchange on the surface
Surface diffusion

Chemical adsorption with image forces: the local polaronic model

Chemical adsorption

Gurney 1935

Anderson 1961

H_And = ε_An_A + Un_A↑n_A↓+

∑

ε_k n_k
s

∑

(

V_Ak c_As^*c_ks+ h.c.

)

See also the review paper by O.M. Braun, Ukr. Fiz. Zh. 23 (1978) 1233 "Theoretical models of chemisorption on metals" (pdf files may be found here)

Screening (image forces)

adatom charge: Q = Z_A – ‹n_A›, where ‹n_A› = _∫^εF dE ρ_ad(E)

screening radius: r_scr ≈

ì
í
î

r_Debay =

(

ε₀k_BT /8πe²n

)

^1/2

for semiconductor

r_TF =

(

ε_F /6πe²n

)

^1/2

for metal

H = H_And + ω_sb^*b + g(n_A– 1)(b+b^*), where g = (φω_s)^1/2

Local polaronic model: ε_k→ε_B

Local polaronic model has the exact solution !

For details see the following papers (pdf files may be found here):

O.M. Braun and A.I. Volokitin, Surface Sci. 131 (1983) 148 "On the role of image forces in chemisorption theory"
O.M. Braun and A.I. Volokitin, Fiz. Tverd. Tela 25 (1983) 309 [Sov. Phys.- Solid State (USA) 25 (1983) 177] "Exact solution of the local polaron model"
O.M. Braun and A.I. Volokitin, Fiz. Tverd. Tela 23 (1981) 3530 [Sov. Phys.- Solid State (USA) 23 (1981) 2052] "Contribution of the image potential to the chemisorption energy"
O.M. Braun, L.G. Il'chenko, and E.A. Pashitsky, Fiz. Tverd. Tela 22 (1980) 1649 [Sov. Phys.- Solid State (USA) 22 (1980) 963] "Adsorption of alkali metal atoms on transition metal surfaces with allowance for the image potential"

Interaction between adsorbed atoms

Mechanisms of interaction

A. Electrostatic interaction: exchange by photons & (surface) plasmons

E_int(R) ≈

ì
í
î

2Q²/R(ε₀+1)	if	R << r_scr
2p²/R³	if	R >> r_scr

where p = Q (d + r_scr) is the dipole moment

B. Direct interaction: direct exchange by electrons of two adatoms

E_int(R) ~ exp(-γR), where γ ~ |‹ψ_A|H|ψ_B›|

C. Indirect interaction: exchange by electrons through the substrate

E_int(R) ≈ V²ρ(ε_F) sin(2k_FR+ψ)/R^m, where m = 1 to 5
(the exponent m depends of the shape of Fermi surface)

near-lying region (R << R_A): E_int(R) ~ R ^{–(m– 1)}
asymptotic (R >> R_A): E_int(R) ~ R ^–m, where R_A≈ [Δ² + 4(ε_A– ε_F)²]^{– 1}

Asymptotic of the indirect interaction

	spherical Fermi surface: E_int(R) ~ R ^–5 (recall: in bulk E_int(R) ~ R^–3)
	cylinder Fermi surface, axis is parallel to the crystal surface: E_int(x) ~ x ^–4 in the direction perpendicular to the cylinder axes E_int(y) ~ exp(–cy) in the direction of open parts of the Fermi surface
	cylinder Fermi surface, axis is perpendicular to the crystal surface: E_int(R) ~ R^–2
	flat Fermi surface: E_int(x) ~ x ^–1 and E_int(y) ~ exp(–cy)

More details and the references may be found in the survey by O.M. Braun and V.K. Medvedev, Usp. Fiz. Nauk 157 (1989) 631 [Sov. Phys. Usp. 32 (1989) 328] "Interaction between particles adsorbed on metal surfaces" and in the papers (pdf files may be found here):

O.M. Braun, Fiz. Tverd. Tela 23 (1981) 2779 [Sov. Phys.- Solid State (USA) 23 (1981) 1626] "Special properties of indirect interaction of atoms adsorbed on metal surfaces"
O.M. Braun, Fiz. Tverd. Tela 22 (1980) 2079 [Sov. Phys.- Solid State (USA) 22 (1980) 1212] "Indirect interaction of hydrogen atoms adsorbed on the (110) face of tungsten"

Energy exchange on the surface

The results of these studies are summarized in the survey by O.M. Braun, A.I. Volokitin, and V.P. Zhdanov, Usp. Fiz. Nauk 158 (1989) 421 [Sov. Phys. Usp. 32 (1989) 605] "Vibration spectroscopy of adsorbates"; see also the following papers (pdf files may be found here):

O.M. Braun, Surface Sci. 213 (1989) 336 "Energy exchange in adsorbed layers"
O.M. Braun, Radiofizika 30 (1987) 788 "Evolution of vibrational excitation of an adsorbed atom"
O.M. Braun, Poverkhn (USSR) No.11 (1987) 5 "Interaction between vibrational modes of an adsorbed atom"
O.M. Braun and A.I. Volokitin, Fiz. Tverd. Tela 28 (1986) 1008 [Sov. Phys.- Solid State (USA) 28 (1986) 564] "Electron-hole friction mechanism in the vibration of chemisorbed atoms"
O.M. Braun and E.A. Pashitsky, Fiz. Tverd. Tela 24 (1982) 1973 [Sov. Phys.- Solid State (USA) 24 (1982) 1127] "Vibrations of a chemisorbed atom"

Surface diffusion

The results of these studies have been published in the following papers (pdf files may be found here):

Diffusion of a single adatom
- O.M. Braun and R. Ferrando, Phys. Rev. E 65 (2002) 061107 "Role of long jumps in surface diffusion"
- O.M. Braun, In: Atomic Aspects of Epitaxial Growth, Eds. M. Kotrla et al. (Kluwer, 2002) p.31 "Surface diffusion with a realistic damping coefficient"
- O.M. Braun, Phys. Rev. E 63 (2001) 011102 "Role of entropy barriers for diffusion in the periodic potential"
- O.M. Braun and C.A. Sholl, Phys. Rev. B 58 (1998) 14870-14879 "Diffusion in generalized lattice-gas models"
Collective diffusion (mainly based on the FK model)
- O.M. Braun, Thierry Dauxois, M.V. Paliy, and M. Peyrard, Phys. Rev. B 54 (1996) 321 "Mobility and diffusivity in a generalized Frenkel-Kontorova model"
- O.M. Braun, Thierry Dauxois, and M. Peyrard, Phys. Rev. B 54 (1996) 313 "Solitonic-exchange mechanism of surface diffusion"
- O.M. Braun and Yu.S. Kivshar, Phys. Rev. B 50 (1994) 13388 "Concentration dependence of conductivity and diffusivity in one-dimensional anharmonic lattices"
- O.M. Braun, Surface Sci. 230 (1990) 262 "Adiabatic motion of an atomic chain in periodic potential"
- O.M. Braun and Yu.S. Kivshar, J. Phys.: Condensed Matter 2 (1990) 5961 "Kinks in a system of adatomic chains"
Stimulated diffusion
- O.M. Braun, R. Ferrando, and G.E. Tommei, Phys. Rev. E 68 (2003) 051101 "Stimulated diffusion of an adsorbed dimer"
Crystal growth
- O.M. Braun, M.V. Paliy, and M. Peyrard, Phys. Rev. B 55 (1997) 4797 "Growth of ordered domains in a highly anisotropic two-dimensional system"
- O.M. Braun and M.V. Paliy, Phys. Rev. Lett. 73 (1994) 2091 "Growth kinetics in a lattice-gas model with anisotropic jump probabilities"

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Last updated on September 26, 2008 by Oleg Braun. Copyright © by O.Braun