Tip shape evolution: Capillarity-induced matter transport by surface diffusion. I

From basic equations describing physical phenomena occuring at different temperatures, we have calculated numerically the matter transport by surface diffusion alone or by simultaneous action of surface diffusion and evaporation. Tip morphological evolution is then obtained by computer simulation for different cone angles and for different temperatures. Theoretical results show a critical cone angle. For tips with cone angles below this critical value a solid drop formation and detachment is observed at the tip end. For angles greater than this critical value two cases must be considered. First, for matter transport by surface diffusion only, steady-state profile evolution is predicted; such an evolution follows the Herring scaling law t ^{1}/{4}. Second, in the case of simultaneous action of surface diffusion and evaporation and for these high angles, calculations show tip evolution toward pseudo-stationary profiles; these profiles are characteristic of each cone angle, but their geometrical dimensions are function of the heating conditions (i.e. surface diffusion and evaporation values). Equations for the variations of the tip apex radius as function of surface diffusion coefficient and evaporation rate are deduced for these two cases, as well as variations of geometrical constants as a function of tip half-cone angles.