Theory of linear facet growth during thermal etching

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Abstract
Under certain conditions, a planar metal surface will develop linear facets, or planar strips inclined to the original surface and meeting it along sharp cusp lines (e.g. Ag heated in air). A discussion is given; in terms of the Wulff plot, of the energetic conditions under which linear facts form. A theory is then developed, subject to certain simplifying assumptions, of the progressive widening of the facets under the separate action of evaporation-condensation and of surface diffusion. Order of magnitude calculations are also given for the case of volume diffusion. Facet profiles and their characteristic time laws of growth are calculated. In the case of surface diffusion, the theoretical results depend upon a parameter equal to the ratio of the surface diffusion coefficient on the facet plane to that on the general complex surface. Comparison with experiment should permit determination of this parameter as well as other interesting information.

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