Journal Article10.1063/1.1714360
Morphological Changes of a Surface of Revolution due to Capillarity‐Induced Surface Diffusion
F. A. Nichols,W. W. Mullins +1 more
652
TL;DR: In this article, a 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 blunting of field-emission tips and the sintering of spheres.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Structural properties of nanoclusters: Energetic, thermodynamic, and kinetic effects
TL;DR: In this paper, a review of the experimental methods for the production of free nanoclusters is presented, along with theoretical and simulation issues, always discussed in close connection with the experimental results.
Materials design for the next generation thermal barrier coatings
David R. Clarke,Carlos G. Levi +1 more
TL;DR: In this article, the materials issues involved in the development of present thermal barrier coatings and the advances necessary for the next generation, higher temperature capability coatings are described and discussed.
1.2K
Solid-State Dewetting of Thin Films
TL;DR: In this article, the authors use dewetting to make arrays of nanoscale particles for electronic and photonic devices and for catalyzing growth of nanotubes and nanowires.
1.1K
New Method of Obtaining Volume, Grain‐Boundary, and Surface Diffusion Coefficients from Sintering Data
TL;DR: In this paper, a sintering model is proposed by which all of the significant mechanisms of material transport may be identified, even though more than one mechanism may be operating simultaneously, and it is possible to calculate both the volume and the grain-boundary diffusion coefficients from measurements of neck size, shrinkage, and shrinkage rate.
457
Capillary instabilities in thin films. I. Energetics
TL;DR: In this paper, a stability theory is presented which describes the conditions under which thin films rupture, and it is found that holes in the film will either grow or shrink, depending on whether their initial radius is larger or smaller than a critical value.
335
References
Theory of Thermal Grooving
TL;DR: In this paper, the Gibbs-Thompson formula is used to describe the development of surface grooves at the grain boundaries of a heated polycrystal and the mechanisms of evaporation-condensation and surface diffusion are discussed with the use of the Gibbs•Thompson formula.
2.6K
Finite-difference methods for partial differential equations
George E. Forsythe,Wolfgang R. Wasow +1 more
- 01 Jan 1960
1.3K
Effect of Change of Scale on Sintering Phenomena
TL;DR: In this paper, it is shown that when certain plausible assumptions are fulfilled simple scaling laws govern the times required to produce, by sintering at a given temperature, geometrically similar changes in two or more systems of solid particles.
1K
Flattening of a Nearly Plane Solid Surface due to Capillarity
TL;DR: In this article, a general solution is obtained for the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion.
913