Klaus Kassner
Institut für Theoretische Physik
Computerorientierte Theoretische Physik
Otto-von-Guericke-Universität Magdeburg

Phase-field simulations of 3D crystal growth in a channel

Abstract: Quite generally, solidication patterns of an undercooled melt result from a competition between connement eects and directional properties of the material or imposed experimental conditions. In particular, constant-velocity patterns grow in an originally homogeneously undercooled environment with a velocity that is governed by the anisotropy of the interfacial material properties or by the conning geometry, and possibly by a compromise between them.
There are good analytical theories describing free growth of dendritic structures in two and three dimensions; for other structures such as double ngers or for crystal growth in channel geometries, only the two-dimensional theory has been developed substantially. The talk will report on phase-eld simulations of solidication in three-dimensional channels of dierently shaped cross section. Results from these simulations may serve as input for the development of an analytic description aimed at a detailed understanding of connement eects, which become the more important, the smaller the channel diameter (nanotubes).
As it turns out, the three-dimensional situation diers from the two-dimensional one not only in allowing a richer variety of patterns. Our simulations suggest that the value Δ= 1/2 of the nondimensional undercooling loses the signicance for the case of isotropic surface tension that it has in 2D. The in uence of the energy conservation law on the ratio of the cross section of stationary patterns to that of the channel is subtly dierent in the 3D situation from the 2D case. We nd bifurcations from symmetric to asymmetric ngers to be always continuous, whereas analogous bifurcations in 2D have been claimed to be discontinous, and the bifurcation leading from the dendrite to the doublon most certainly is discontinuous. On the other hand, we observe coexistence of chaotic patterns with steady-state ngers in a certain parameter range.

The seminar takes place at 4 p.m. in the ICAMS seminar room UHW 11/1102, Stiepeler Straße 129, 44801 Bochum.