Non-linear capillary shape evolution of rod morphologies via interfacial diffusion

Abstract

The non-linear capillary shape evolution of an infinite rod perturbed with a smooth periodic wave via interfacial diffusion is analysed in accordance with the chemical potential distribution of the atoms on the rod-matrix interface. Four evolution nodes are identified, namely, (1) pure growth, where the trough and crest of the perturbation always grow simultaneously; (2) pure 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 trough 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 perturbed cylindrical surface can first shrink and then swell. Thermodynamic criteria governing each of these four evolution modes are derived with respect to an initial sinusoidal perturbation. The analytical results are presented in the form of a rod evolution map through two dimensionless variables λ/(2πR) and δ/R (λ is the wavelength of the perturbation, δ the initial amplitude, and R the average radius of the perturbed rod). All of the theoretical analyses are confirmed using a well-accepted numerical model. Comparisons are also made with prior studies. The reasons for choosing a sinusoidal perturbation to mathematically formulate the rod instability problem are also discussed. © 1998 Acta Metallurgica Inc.