Europhys. Lett.
Volume 65, Number 2, January 2004
Page(s) 276 - 282
Section Interdisciplinary physics and related areas of science and technology
Published online 01 January 2004
Europhys. Lett., 65 (2) , pp. 276-282 (2004)
DOI: 10.1209/epl/i2003-10078-2

Stability of hexagonal solidification patterns

M. Plapp and M. Dejmek

Laboratoire de Physique de la Matière Condensée CNRS/Ecole Polytechnique - 91128 Palaiseau, France

(Received 8 August 2003; accepted in final form 17 November 2003)

We investigate the dynamics of cellular solidification patterns using three-dimensional phase-field simulations. The cells can organize into stable hexagonal patterns or exhibit unsteady evolutions. We identify the relevant secondary instabilities of regular hexagonal arrays and find that the stability boundaries depend significantly on the strength of crystalline anisotropy. We also find multiplet states that can be reached by applying well-defined perturbations to a pre-existing hexagonal array.

81.30.Fb - Solidification.
05.70.Ln - Nonequilibrium and irreversible thermodynamics.
64.70.Dv - Solid-liquid transitions.

© EDP Sciences 2004