The phase diagram of the lattice Calogero-Sutherland model

We introduce a {\it lattice} version of the Calogero Sutherland model adapted to describe $1/d^2$ pairwise interacting steps with discrete positions on a vicinal surface. The configurational free energy is obtained within a transfer matrix method. The full phase diagram for attractive and for repulsive interaction is deduced. For attraction, critical temperatures of faceting transitions are found to depend on step density.Comment: latex PRBCalogSuth.tex, 6 files, 4 pages [SPEC-S00/900

Vicinal silicon surfaces: from step density wave to faceting

This paper investigates faceting mechanisms induced by electromigration in the regime where atomic steps are transparent. For this purpose we study several vicinal orientations by means of in-situ (optical diffraction, electronic microscopy) as well as ex-situ (AFM, microprofilometry) visualization techniques. The data show that faceting proceeds in two stages. The first stage is short and leads to the appearance of a step density wave, with a wavelength roughly independent of the surface orientation. The second stage is much slower, and leads to the formation of a hill-and-valley structure, the period of which depends on the initial surface orientation. A simple continuum model enables us to point out why the wavelength of the step density wave does not depend on the microscale details of the surface. The final wavelength is controlled by the competition between elastic step-step interaction and facet edge energy cost. Finally, the surface stress angular dependence is shown to emerge as a coarsed-grained picture from the step model.Comment: 26 pages, 9 figure

Ne diffraction from Cu(110)

Experimental results of diffraction of thermal energy (64 meV) Ne atoms from the (110) face of copper are presented Diffraction is observed up to fifth order and strong selective adsorption features were measured. The bound state energy levels are fitted using the shifted Morse hybrid potential. Diffraction intensities extrapolated to zero kelvin are fitted using the so called modified corrugated Morse potential (MCMP) which is a realistic soft potential. The potential is found to be more corrugated and steeper in its repulsive part than in the Cu(110)/He case. This shows that attractive forces play an important rôle in the corrugation of the potential.On présente les résultats expérimentaux de la rétrodiffusion d'atomes de néon d'énergie thermique (64 meV) sur la face (110) du cuivre. La diffraction est observée jusqu'au cinquième ordre, ainsi que le phénomène de résonance avec les états liés. On ajuste les niveaux d'énergie des états liés à l'aide du potentiel de Morse hybride déplacé. Les intensités diffractées extrapolées à zéro kelvin sont reproduites en utilisant le potentiel de Morse corrugué modifié (MCMP) qui est un potentiel non abrupt réaliste. On trouve que, dans sa partie répulsive, le potentiel est plus modulé que dans le cas de la diffraction de l'hélium par Cu(110). Ceci montre que les forces attractives influencent de manière importante la modulation du potentiel total

Observation of surface roughening on Cu(1, 1, 5)

We present a detailed analysis of the topography of the Cu(1,1, 5) surface in the temperature range 70 K < T < 670 K. The line-shape analysis of the specular helium beam diffraction peak as a function of temperature is found to be in agreement with a model of roughening previously proposed by Villain et al. The roughening temperature is found to be T R = 380 K. From the anisotropy of peak profiles, the step repulsive energy is deduced and found to be Wn = 120 K per lattice spacing. The experimental procedure is carefully examined and its consequences are discussed. The connection between roughness at small and large scale is indicated.Nous présentons une analyse détaillée de la topographie de la face de cuivre Cu(1, 1, 5) pour des températures T ; 70 K < T < 670 K. L'analyse de la forme du pic spéculaire de diffraction d'hélium en fonction de la température est en accord avec le modèle de transition rugueuse proposé par Villain et al. La température de transition rugueuse est TR = 380 K. A partir de l'anisotropie de la forme des pics, on en déduit l'énergie de répulsion entre marches qui vaut Wn = 120 K par maille élémentaire. La procédure expérimentale est détaillée avec soin et ses conséquences sont discutées. La liaison entre rugosité à petite et grande échelle est indiquée

Temperature dependence of the atomic relaxations and vibrations on a stepped surface: a molecular dynamics study of Cu(1,1,19)

We have studied the relaxations and vibrations of atoms near the surface of a (1,1,19) copper crystal. For this purpose, we have performed molecular dynamics simulations using a semi-empirical many-body potential derived from tight binding models. The total displacement field can be described as the sum of a mean surface relaxation and a specific contribution of the steps, which is maximal for step edge atoms (0.08 Å) and corner atoms (0.06 Å). Whereas step edge atoms relax towards the inner terrace and towards the bulk, corner atoms relax in the opposite direction, leading to vortex-like structures in the displacement field. We demonstrate that, as predicted by continuous elasticity, the displacement field induced by steps is equivalent to the one created by a line of dipoles on a flat surface. In the particular case studied here, the equivalent dipole density is 3.3×10−10 N. The specific relaxations of kink atoms have been calculated. We have also studied the variation of the relaxations as a function of temperature (T). A strong effect is predicted for inner terrace atoms: when increasing T, the contraction of the first interplanar distance, with respect to the bulk value, progressively cancels and turns to an expansion at high T. This is not the case for the specific contraction of step edge atoms that is nearly temperature independent. This latter behaviour is related to very strong longitudinal correlation between vibrations of the step edge atom and of its nearest neighbour inside the terrace. In the same time, whereas the vibrations of inner terrace atoms are found to be isotropic, the ones of step edge atoms are anisotropic, with a larger component along the direction parallel to the terrace plane and perpendicular to the step edge, the other components being the same as for inner terrace atoms