NONLINEAR CAPILLARY SHAPE EVOLUTION OF ROD MORPHOLOGIES VIA INTERFACIAL DIFFUSION

The non-linear capillary shape evolution of an infinite rod perturbed with a smooth periodic wave via interfacial diffusion is analysed in a ccordance with the chemical potential distribution of the atoms on the rod-matrix interface. Four evolution nodes ale identified, namely, (1 ) pure growth, where the trough and crest of the perturbation always g row simultaneously: (2) pur: decay, where the crest and trough of the perturbation always decay simultaneously; (3) irregular growth, where the crest of the perturbation first decays and then grows while the tr ough of the perturbation grows; (4) irregular decay, where the trough of the perturbation first grows and then decays while the crest of the perturbation decays. Thus the radius at the crest or trough of the pe rturbed cylindrical surface can first shrink and then swell. Thermodyn amic criteria governing each of these four evolution modes are derived with respect to an initial sinusoidal perturbation. The analytical re sults are presented in the form of a rod evolution map through two dim ensionless variables lambda/(2 pi R) and delta/R (lambda is the wavele ngth of the perturbation, delta the initial amplitude, and R the avera ge radius of the perturbed rod). All of the theoretical analyses are c onfirmed using a well-accepted numerical model. Comparisons are also m ade with prior studies. The reasons for choosing a sinusoidal perturba tion to mathematically formulate the rod instability problem are also discussed. (C) 1998 Acta Metallurgica Inc.