Summary
Surface melting is strongly influenced by the interaction between the solid-liquid interface and the liquid-vapour interface. Unretarded electromagnetic dispersion forces yield a potential of the formH/l 2, wherel is the distance between the interfaces (thickness of the quasi-liquid film) andH is the appropriate Hamaker constant. We have adopted the well-known treatment of dispersion forces of Lifshitzet al., where the frequency-dependent conductivities of solid and liquid are the primary quantities for the calculation of this Hamaker constant. Using the dielectric functions obtained from experimental data, numerical values forH are obtained for Al, Pb, Au, Bi and Ge. The Hamaker constant of the metals is found to be positive and is discussed in connection with recent experimental data on surface melting, particularly of Pb(110) and Al(110). The Hamaker constants of Bi (semimetal) and Ge (semiconductor) are negative, allowing at most blocked surface melting.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
E. M. Lifshitz andL. P. Pitaevskii:Statistical Physics, Part 1, p. 529.
E. Brézin, B. I. Halperin andS. Leibler:J. Phys.,44, 775 (1983).
R. Lipowsky:Phys. Rev. B,32, 1731 (1985).
Actually,A=12πH is usually called the Hamaker constant. SeeJ. N. Israelachvili:Intermolecular and Surface Forces (Academic Press, San Diego, Cal., 1985).
For a review of recent experiments, seeJ. G. Dash:Contemp. Phys.,30, 6961 (1988);J. G. Dash: inSolvay Conference on Surface Science, edited byF. W. de Wette (Springer-Verlag, Berlin, 1988), p. 142.
B. Pluis, T. N. Taylor, D. Frenkel andJ. F. van der Veen:Phys. Rev. B,40, 1353 (1989).
A. W. Denier van der Gon, R. J. Smith, J. M. Gay, D. J. O'Connor andJ. F. van der Veen:Surf. Sci.,227, 143 (1990).
In particular, one should avoid the quite common mistake of believing that metallic screening is sufficient to cancel them.
I. E. Dzyaloshinsky, E. M. Lifshitz andL. P. Pitaevskii:Soviet Phys. JETP,10, 161 (1960).
A. C. Levi andE. Tosatti:Surf. Sci.,189/190, 641 (1987).
J. Visser: inSurface and Colloid Science, Vol.6, edited byE. Matejavec (Wiley, 1976).
H. Krupp:Adv. Colloid Interface Sci.,1, 79 (1967).
For a review, seeE. Tosatti: inThe Structure of Surfaces-II, edited byJ. F. van der Veen andM. A. van Hove (Springer-Verlag, Berlin, 1988), p. 535.
X. J. Chen, A. C. Levi andE. Tosatti: to be published inProceedings of the 11th European Conference on Surface Science, Surf. Sci. (1991).
N. G. van Kampen, B. R. A. Nijboer andK. Schram:Phys. Lett. A,26, 307 (1968).
See, for example,F. Wooten:Optical Properties of Solids (Academic Press, 1972).
More generally, for arbitrary wave, vectorq, ɛ-1 (q, ω) is generally a sum of simple poles.
P. O. Nilsson:Solid State Physics, Vol.29 (1974).
P. H. Dederichs, H. Schober, D. J. Sellmyer: inMetals: Phonon States, Electron States and Fermi surfaces, Landolt-Börnstein, Vol. III/13a, edited byK.-H. Hellwege andJ. L. Olsen (1981).
T. E. Faber: inOptical Properties and Electronic Structures of Metals and Alloys, edited byF. Abelès (North-Holland, Amsterdam, 1966).
D.Y. Smith, E. Shiles andMitio Inokuti: inHandbook of Optical Constants of Solids, edited byD. Palik (Academic Press, 1985).
A. G. Mathewson andH. P. Myers:J. Phys. F,2, 403 (1972).
H. G. Liljenvall, A. G. Mathewson andH. P. Myers:Philos. Mag.,22, 243 (1970).
J. Bass andK. H. Fischer: inMetals: Electronic Transport Phenomena, Landolt-Börnstein, Vol. III/15a, edited byK.-H. Hellwege andJ. L. Olsen (1982).
A. I. Golovashkin andG. P. Motulevich:Sov. Phys. JETP,19, 310 (1964);20, 44 (1965).
J. C. Lemonnier, M. Priol andS. Robin:Phys. Rev. B,8, 5452 (1972).
A. G. Mathewson, H. P. Myers andP. O. Nilsson:Phys. Status Solidi B,57, k31 (1973).
Jane C. Miller:Philos. Mag.,20, 1115 (1969).
D. Beaglehole:Proc. Phys. Soc. London,85, 1007 (1965);87, 461 (1966).
N. V. Smith:Philos. Mag.,16, 629 (1967).
D. W. Lynch andW. R. Hunter: inHandbook of Optical Constants of Solids, edited byD. Palik (Academic Press, New York, 1985).
H.-J. Hagemann, W. Gudat andC. Kunz:Optical constants from the far infrared to the X-ray region, DESY, May 1974.
N. W. Ashcroft andN. David Mermin:Solid State Physics (Holt-Saunders, 1976).
M. S. Skolnick andR. Blachnikm: inPhysics of Group IV Elements and III–V Compounds, Landolt-Börnstein, Vol. III/17a, edited byO. Madelung (1982).
Roy F. Potter: inHandbook of Optical Constants of Solids, edited byD. Palik (Academic Press, 1985).
Smithells Metal Reference Book, edited byE. A. Brandes (Butterworth, 1983).
J. Bass, J. S. Dugdale, C. L. Foiles, A. Myers: inMetals: Electronic Transport Phenomena, Landolt-Börnstein, Vol. III/15b, edited byK.-H. Hellwege andJ. L. Olsen (1982).
Note added in proof.— Nonmelting of Bi has been very recently observed byE. Bauer and collaborators (private communication).
E. G. McRae andR. A. Malic:Phys. Rev. Lett.,58, 1473 (1987).
A. W. Denier van der Gon, J. M. Gay, J. W. M. Frenken andJ. F. van der Veen: preprint.
A. A. Chernov andL. V. Mikheev:Physica A,157, 1052 (1989).
X. J. Chen, F. Ercolessi, A. C. Levi andE. Tosatti: to be published.
X. J. Chen: Ph. D. Thesis, International School for Advanced Studies, Trieste (1990).
R. Lipowsky andM. E. Fisher:Phys. Rev. B,36, 2126 (1987).
F. Ercolessi, S. Iarlori, O. Tomagnini andE. Tosatti: to be published.
Note added in proof.— A discussion of dispersion forces has very recently been applied byElbaum andSchick to the surface melting of Bi ice (Phys. Rev. Lett.,66, 1713 (1991)) using a similar approach.
Author information
Authors and Affiliations
Additional information
Due to the relevance of its scientific content, this paper has been given priority by the Journal Direction.
Rights and permissions
About this article
Cite this article
Chen, X.J., Levi, A.C. & Tosatti, E. Hamaker-constant calculations and surface melting of metals, semimetals and semiconductors. Il Nuovo Cimento D 13, 919–937 (1991). https://doi.org/10.1007/BF02457179
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF02457179