Critical terrace width

Surface reconstruction or adsorption can often cause a vicinal surface with a single macroscopic orientation to facet into surfaces with different orientations. Generally the reconstruction occurs on a particular low-index flat face, and lowers its free energy relative to that of an unreconstructed surface with the same orientation. However the same reconstruction that produces the lower free energy for the flat face generally increases the energy of surface distortions such as steps that disturb the reconstmction. Thus reconstmction is often observed only on terraces wider than some critical terrace width Wc. When steps are uniformly distributed initially and if Wc is much greater... 

We now modify the 2D continuum equations of step motion, Eqs. (7) and (8), in order to study some aspects of the dynamics of faceting. We assume the system is in the nucleation regime where the critical width Wc is much larger than the average step spacing In the simplest approximation discussed here, we incorporate the physics of the two state critical width model into the definition of the effective interaction term V(w) in Eq. (2), which in turn modifies the step chemical potential terms in Eqs. (7) and (8). Again we set V(w) = w/ l/w) as in Eq. (4) but now we use the /from Eq. (10) that takes account of reconstruction if a terrace is sufficiently wide. Note that this use of the two state model to describe an individual terrace with width w is more accurate than is the use of Eq. (10) to describe the properties of a macroscopic surface with average slope s = Mw. 

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