Front instability and pattern dynamics in the phase-field model for crystal growth

✍ Scribed by Hidetsugu Sakaguchi; Seiji Tokunaga

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 324 KB
• Volume: 205
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/j.physd.2004.12.009

✦ Synopsis

We study front instability and the pattern dynamics in the phase-field model with four-fold rotational symmetry. When the undercooling ∆ is 1 < ∆ < ∆ c , the flat interface is linearly unstable, and the deformation of the interface evolves to spatiotemporal chaos or nearly stationary cellular structures appear, depending on the growth direction. When ∆ < 1, the flat interface grows with a power law x ∼ t 1/2 and the growth rates of linear perturbations with finite wave number q decay to negative values. It implies that the flat interface is linearly stable as t → ∞, if the width of the interface is finite. However, the perturbations around the flat interface actually grow since the linear growth rates take positive values for a long time, and the flat interface changes into an array of doublons or dendrites. The competitive dynamics among many dendrites is studied more in detail.