Geometry and relevant activation barriers for the model used here for a stepped surface. In the direction across the steps, there is an additional barrier at the step edge position known as the Ehrlich-Schwoebel barrier . The denotes an additional binding energy at the lower step edge, and characterizes the diffusion barrier of a single adatom in the dilute limit on a flat surface. The diffusion tensor for adatoms has its principal axes in the direction across the steps and in the direction along the steps.
Equilibrium (solid line) and BM (dotted) results for for diffusion across the steps, using and . For comparison, the dashed line represents for diffusion along the steps. The case along the steps is qualitatively similar to the equilibrium results for a flat surface (Ref. 39) Vertical lines indicate the positions of phase boundaries in equilibrium for a flat surface (see text for details).
(a) Equilibrium mobility across (solid line) and along (dotted line) the steps. Here stands for diffusion across (parallel to) the steps. (b) Thermodynamic factor as determined through equilibrium simulations. The results are for and . Vertical lines indicate the positions of phase boundaries in equilibrium for a flat surface.
Snapshot of the system after 300 000 MCS for and . Note that only part of the system is shown here in the direction. The density profile vs is also shown by the continuous line across the system (see the right panel for the coverage scale).
Results for the collective diffusion coefficient across steps, , for different terrace widths , 10, 20, and 50. The additional binding energy at the lower step edge has been chosen as . on a flat surface (solid line) is shown for reference. Vertical dashed lines denote the phase boundaries of the and phases for a system without steps.
Example of the system configuration after 300 000 MCS for and . Only part of the system is shown in the direction. The density profile is also shown by the continuous line.
Collective diffusion coefficients across the steps, , for odd and even terrace widths. The result for a flat surface is also given for comparison. For the even terrace width , the data demonstrate the effect of two different binding energies at the lower step edge position ( and ). Also shown is the case of a wide terrace with a strong binding energy . In the case of the odd terrace width , we only show the results for strong binding . The for with a small binding energy is essentially identical to the flat surface behavior and is hence not plotted here. Vertical dashed lines denote the locations of phase boundaries for a flat system without steps.
Schematic structures for occupied (filled circles) and vacant (open circles) sites on the W(110) surface, where the first rows of adsorption sites under the step edge are shown as dashed boxes. (a) The ordered phase has a periodicity of 2 and hence matches the periodicity of a vicinal surface with even (here ). (b) In the case of an odd (here ), the periodicity of the phase does not match the periodicity of the vicinal surface. (c) Consequently, for odd (here ), the orientation perpendicular to steps is also possible and may emerge spontaneously.
Snapshot of the system configuration after 300 000 MCS for a case with and . Only part of the system is shown in the direction. Continuous line indicates the density profile.
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