Phase Transitions in Surface Films 2 pp 247-267 | Cite as

# Interplay between Surface Roughening, Preroughening, and Reconstruction

## Abstract

Solid-on-solid models provide a comprehensive description of surface roughening, preroughening, and reconstruction. The origin and properties of the preroughening transition and disordered flat (DOF) phase are reviewed. The present experimental evidence for realizations of DOF phases in (110) facets of face-centered cubic (FCC) metals and in (111) facets of noble gas crystals is discussed. A chiral 4-state clock-step model is introduced to describe the deconstruction and roughening of missing row reconstructed (110) facets of FCC crystals. It is shown that a reconstructed rough phase is not possible. Instead roughening induces a simultaneous deconstruction transition, with central charge c=1.5 and both Ising and conventional roughening critical exponents. This, together with the experimental evidence suggests that at deconstruction Pt(110) becomes rough and simultaneously undergoes an incommensurate melting transition with respect to its reconstruction degrees of freedom.

## Keywords

Ising Model Step Height Reconstructed State Bloch Wall Reconstruction Order## Preview

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## References

- 1.K. Rommelse and M. den Nijs, Phys. Rev. Lett.
**59**, 2578 (1987).ADSCrossRefGoogle Scholar - 2.M. den Nijs and K. Rommelse, Phys. Rev.
**B 40**, 4709 (1989).Google Scholar - 3.M. den Nijs, Phys. Rev. Lett..
**64**, 435 (1990).ADSCrossRefGoogle Scholar - 4.
- H. Derks
*et al*., Surf. Sci.**188**, L685 (1987); E. C. Sowa*et al*., Surf. Sci.**199**, 174 (1988).Google Scholar - 5.I. K. Robinson, E. Vlieg, and K. Kern, Phys. Rev. Lett.
**63**, 2578 (1989).ADSCrossRefGoogle Scholar - 6.Modify the RSOS model as follows: Choose
*K*directional dependent,*K*_{n}*K*_{m}. Let only*K*_{n}change sign. Choose the next nearest neighbour interaction*L*between sites (*n*,*m*) and (*n*+ 2,*m*). The transfer matrix leads to the same spin-1 quantum chain Hamiltonian as the RSOS model, eq.(2.1), in the so-called “time continuum limit” and therefore to the same phase diagram; see also ref.[2].Google Scholar - 7.S. M. Foiles, Surf. Sci.
**191**, L779 (1987).ADSCrossRefGoogle Scholar - 8.B. M. Ocko and S. G. J. Monchrie, Phys. Rev. B
**38**, 7378 (1988).ADSCrossRefGoogle Scholar - 9.P. Zeppenfeld, K. Kern, R. David, and G. Comsa, Phys. Rev. Lett.
**62**, 63 (1989).ADSCrossRefGoogle Scholar - 10.Y. Cao and E. Conrad, Phys. Rev. Lett.
**64**, 447 (1990).ADSCrossRefGoogle Scholar - 11.
- 12.
- 13.For a review see M. den Nijs, in
*Phase Transitions and Critical Phenomena*, edited by C. Domb and J. Lebowitz (Academic, London, 1987), Vol. 12.Google Scholar - 14.H. van Beijeren, Phys. Rev. Lett.
**38**, 993 (1977).ADSCrossRefGoogle Scholar - 15.For a review see J.D. Weeks, in
*Ordering in Strongly Fluctuating Condensed Matter Systems*, T. Riste, ed, p. 293. Plenum Press, New. York (1980).Google Scholar - 16.M. den Nijs, Phys. Rev. B
**27**, (1983) 1674.MathSciNetADSCrossRefGoogle Scholar - 17.For a review see B. Nienhuis, in
*Phase Transitions and Critical Phenomena*, edited by C. Domb and J. Lebowitz (Academic, London, 1987), Vol. 11.Google Scholar - 18.
- 19.F. S. Rys, Phys. Rev. Lett.
**56**, 624 (1986).ADSCrossRefGoogle Scholar - 20.J. Villain, D.R. Grempel and J. Lapujoulade, J. Phys. F
**15**, 809 (1985).ADSCrossRefGoogle Scholar - 21.M.P.M. den Nijs, E.K. Riedel, E.H. Conrad and T. Engel, Phys. Rev. Lett.
**55**, 1689 (1985)ADSCrossRefGoogle Scholar - M.P.M. den Nijs, E.K. Riedel, E.H. Conrad and T. Engel, Phys. Rev. Lett.
**57**, 1279 (1986).ADSCrossRefGoogle Scholar - 22.The BCSOS model is equivalent to the spin-
_{z}quantum spin chain. As explained in section VI of ref.[2] this model has a DOF phase with the same type of properties as the RSOS model. The PR transition belongs to the same universality class.Google Scholar - 23.J. Villain and I. Vilfan, Surf. Sci.
**199**, L165 (1988).ADSCrossRefGoogle Scholar - 24.see e.g. O. Foda, Nucl. Phys.
**B 300**, 611 (1988).Google Scholar - 25.H.S. Youn and G.B. Hess, Phys. Rev. Lett.
**64**, 918 (1990).ADSCrossRefGoogle Scholar - 26.J.Z. Larese and Q.M. Zhang private communication.Google Scholar
- 27.Da-ming Zhu and J.G. Dash, Phys. Rev. Lett.
**57**, 2959 (1986).ADSCrossRefGoogle Scholar - 28.It is possible, but less likely that the intermediate phase is reconstructed instead of DOF, i.e., to enter the reconstructed phase via a first-order transition (the phase boundary to the right of point N in Fig. 1) and from there to follow a path of type 3.Google Scholar
- 29.Fig. 5 is the simplest theoretical phase diagram. The Ising critical points could just as well be triple points with first-order boundaries between them; and even more elaborate phase diagram diagrams with e.g. critical endpoints are theoretically allowed too. However, the second-order nature of the PR transition and also the experimentally observed complete wash-out of the steps in the isotherms make Fig. 5 more likely.Google Scholar
- 30.