Surface Evolution of Crystalline Tubes

Fuqian Yang
Department of Chemical and Materials Engineering
University of Kentucky
Lexington, KY 40506-0046, USA

Wei Song, and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA


The surface evolution of an annular tube has been established on the basis of lattice diffusion and linear stability analysis. Without surface disturbance the annular tube will shrink to reduce the surface energy while the cross-sectional area of the tube remains constant. For an annular tube having infinitesimal thickness, the time dependence of the tube radius follows a linear law. When surface energy is significant, a new dispersion relation describing the morphological stability of crystalline tubes due to longitudinal surface perturbation has been formulated. A criterion has been obtained on the dependence of perturbation frequency is less than the critical frequency. The perturbation will grow when the perturbation frequency is less than the critical frequency, which is equal to the inverse of the inner surface radius. To our surprise, the critical frequency for an annular tube of infinitesimal thickness is the same as that given by Nichols and Mullins [Trans. Metall. Soc. AIME 233 (1965) 1840] for an infinitely cylindrical rod. A finite spatial frequency for maximum growth rate was also obtained, which depends on the ratio of the inner surface radius to the outer surface radius. The surface stability will lead to the formation of closed end of crystalline tubes.

Key words: crystalline tube, critical frequency.

Mathematics Subject Classification:

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This paper has been accepted for publication in International Journal of Thin Solid Films.

Technical Report 362-02, Department of Computer Science, University of Kentucky, Lexington, KY, 2002.

This research work supported in part by the U.S. National Science Foundation under the grant CCR-9902022, CCR-9988165, CCR-0092532, and ACI-0202934, in part by the U.S. Department of Energy Office of Sceince under grant DE-FG02-02ER45961, in part by the Japanese Research Organization for Information Science & Technology, and in part by the University of Kentucky Research Committee.