Morphological Changes of a Surface of Revolution due to Capillarity-Induced Surface Diffusion

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Abstract
The partial differential equation describing morphological changes of a surface of revolution due to capillarity‐induced surface diffusion has been derived under the assumption of isotropy of surface tension and surface self‐diffusion coefficient. A stable, convergent finite‐difference method has been developed for the general case of an arbitrary surface of revolution and solutions have been obtained for the specific problems of the blunting of field‐emission tips and the sintering of spheres. Spheroidization of cylindrical rods, as well as field‐emission tips with taper below a certain critical value, is predicted; for tapers above the critical value, steady‐state shapes are predicted and equations describing the blunting and recession of the tips are presented. If the sintering results for spheres are represented by a plot of log x/a vs log t, it is found that the inverse slope varies from approximately 5.5 to approximately 6.5 for the range 0.05≤x/a≤0.3, in contrast with the constant value of 7 found by Kuczynski from an order‐of‐magnitude analysis. At higher values of x/a, n increases steadily and without bound.

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