Why Are Alkali Halide Solid Surfaces Not Wetted By Their Own Melt?

Alkali halide (100) crystal surfaces are anomalous, being very poorly wetted by their own melt at the triple point. We present extensive simulations for NaCl, followed by calculations of the solid-vapor, solid-liquid, and liquid-vapor free energies showing that solid NaCl(100) is a nonmelting surface, and that its full behavior can quantitatively be accounted for within a simple Born-Meyer-Huggins-Fumi-Tosi model potential. The incomplete wetting is traced to the conspiracy of three factors: surface anharmonicities stabilizing the solid surface; a large density jump causing bad liquid-solid adhesion; incipient NaCl molecular correlations destabilizing the liquid surface. The latter is pursued in detail, and it is shown that surface short-range charge order acts to raise the surface tension because incipient NaCl molecular formation anomalously reduces the surface entropy of liquid NaCl much below that of solid NaCl(100).Comment: 4 pages, 3 figure

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

Electromigration of Single-Layer Clusters

Single-layer atom or vacancy clusters in the presence of electromigration are studied theoretically assuming an isotropic medium. A variety of distinctive behaviors distinguish the response in the three standard limiting cases of periphery diffusion (PD), terrace diffusion (TD), and evaporation-condensation (EC). A general model provides power laws describing the size dependence of the drift velocity in these limits, consistent with established results in the case of PD. The validity of the widely used quasistatic limit is calculated. Atom and vacancy clusters drift in opposite directions in the PD limit but in the same direction otherwise. In absence of PD, linear stability analysis reveals a new type of morphological instability, not leading to island break-down. For strong electromigration, Monte Carlo simulations show that clusters then destabilize into slits, in contrast to splitting in the PD limit. Electromigration affects the diffusion coefficient of the cluster and morphological fluctuations, the latter diverging at the instability threshold. An instrinsic attachment-detachment bias displays the same scaling signature as PD in the drift velocity.Comment: 11 pages, 4 figure

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

Changing shapes in the nanoworld

What are the mechanisms leading to the shape relaxation of three dimensional crystallites ? Kinetic Monte Carlo simulations of fcc clusters show that the usual theories of equilibration, via atomic surface diffusion driven by curvature, are verified only at high temperatures. Below the roughening temperature, the relaxation is much slower, kinetics being governed by the nucleation of a critical germ on a facet. We show that the energy barrier for this step linearly increases with the size of the crystallite, leading to an exponential dependence of the relaxation time.Comment: 4 pages, 5 figures. Accepted by Phys Rev Let

Equilibrium crystal shapes in the Potts model

The three-dimensional $q$-state Potts model, forced into coexistence by fixing the density of one state, is studied for $q=2$, 3, 4, and 6. As a function of temperature and number of states, we studied the resulting equilibrium droplet shapes. A theoretical discussion is given of the interface properties at large values of $q$. We found a roughening transition for each of the numbers of states we studied, at temperatures that decrease with increasing $q$, but increase when measured as a fraction of the melting temperature. We also found equilibrium shapes closely approaching a sphere near the melting point, even though the three-dimensional Potts model with three or more states does not have a phase transition with a diverging length scale at the melting point.Comment: 6 pages, 3 figures, submitted to PR

A contiuum model for low temperature relaxation of crystal steps

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.Comment: Submitted to Phys.Rev.Let

Statistical Mechanical Calculation of Anisotropic Step Stiffness of a Two-Dimensional Hexagonal Lattice Gas Model with Next-Nearest-Neighbor Interactions: Application to Si(111) Surface

We study a two-dimensional honeycomb lattice gas model with both nearest- and next-nearest-neighbor interactions in a staggered field, which describes the surface of stoichiometrically binary crystal. We calculate anisotropic step tension, step stiffness, and equilibrium island shape, by an extended random walk method. We apply the results to Si(111) 7$\times$7 reconstructed surface and high-temperature Si(111) 1$\times$1 surface. We also calculate inter-step interaction coefficient.Comment: revised on May 29 1999: RevTeX v3.1, 10 pages with 9 figures (one figure added

Measuring the surface stress polar dependence

While measurements of the polar dependence of the surface free energy are easily available, measurements of the whole polar dependence of the surface stress of a crystal do not exist. In this paper is presented a new procedure that allows, for the first time, the experimental determination of the surface stress polar dependence of a crystal. For this purpose (1) electromigration is used to control the kinetic faceting of surface orientations that belong to the equilibrium shape of the crystal and (2) for each destabilised surface, the period of faceting as well as the crystallographic angles of the appearing facets are measured by AFM. The so-obtained data lead to a set of equations whose mathematical solution, compatible with physical constraints, gives access to the surface stress polar dependence of the whole crystal and thus to a better understanding of surface stress properties.Comment: 8 pages, 6 Figure