K. Reuther

Simulating dendritic solidification using an anisotropy-free meshless front-tracking method

Dendritic morphologies are by far the most frequently observed structures during solidification of metals and alloys. The simulation of dendritic solidification, however, places strong requirements on the applied models, as the formation of the complex morphology is the result of the weakly anisotropic interfacial energy of the solid–liquid interface. The difference in equilibrium solute concentration along the interface is usually much smaller than the difference between the concentration at the interface and the liquid bulk. This results in small differences in the solute fluxes to or from the interface, which need to be accounted for with a sufficiently high accuracy to reproduce dendritic structures by a spatially resolved simulation method. Common simulation models for dendritic solidification (e.g. Cellular Automaton or Phase Field models) usually operate on Cartesian grids which may affect the simulation results by introducing an anisotropic error. In Phase Field models it is attempted to reduce this error by choosing fine grids, whereas in Cellular Automata special modifications for the reduction of the anisotropy error are usually incorporated into the model (e.g. [1–4]). Another approach (as demonstrated by Schönfisch for Cellular Automata [5]) is the adoption of stochastic, quasi-isotropic grids that can be expected to introduce no direction-dependent error at all. This approach has been taken up in a recent publication [6] by the present authors in the form of a Meshless Front Tracking (MFT) method. In the MFT method the spatial domain is discretized by nodes on random positions throughout the domain, with the constraint of a minimum pairwise distance between all nodes. These nodes do not have any connectivity as would be required for e.g. FEM methods. The diffusion equation is instead discretized by the meshless Diffuse Approximation Method (DAM) [7,8], with additional stability handling [9] for the reduction of numerical noise that is introduced by the use of an irregular grid. The DAM represents the solute concentration field by a weighted Least Squares fit of the nodes’ concentration

Micron-sized gold-nickel alloy wire integrated silica optical fibers

Hybrid fibers containing metallic micro- and nanowires are an emerging class of optical devices thanks to their electro-optic functionality and applicability in plasmonics. However, pure metals suffer from poor mechanical and chemical properties, which is why alloys displaying synergistic properties of their metallic constituents are becoming popular. Here, we use pressure assisted melt filling to produce micron sized gold-nickel alloy wires with aspect ratios of 105 and diameters of 1.3 μm in silica optical fibers. We show that the alloy remains stable within the highly confined wire state despite exhibiting a miscibility gap in the bulk state at room temperature. Measurements show that the loss of the alloy in the confined state is comparable to that predicted by the bulk alloy permittivity. The presented fabrication and characterization procedure represent a first step towards integration of high aspect ratio micron sized gold-nickel alloy wires in optical fibers and may be extended to a wide range of other alloys.

Kinetic transition in the order–disorder transformation at a solid/liquid interface

Phase-field analysis for the kinetic transition in an ordered crystal structure growing from an undercooled liquid is carried out. The results are interpreted on the basis of analytical and numerical solutions of equations describing the dynamics of the phase field, the long-range order parameter as well as the atomic diffusion within the crystal/liquid interface and in the bulk crystal. As an example, the growth of a binary A50B50 crystal is described, and critical undercoolings at characteristic changes of growth velocity and the long-range order parameter are defined. For rapidly growing crystals, analogies and qualitative differences are found in comparison with known non-equilibrium effects, particularly solute trapping and disorder trapping. The results and model predictions are compared qualitatively with results of the theory of kinetic phase transitions (Chernov 1968 Sov. Phys. JETP 26, 1182–1190) and with experimental data obtained for rapid dendritic solidification of congruently melting alloy with order–disorder transition (Hartmann et al. 2009 Europhys. Lett. 87, 40007 (doi:10.1209/0295-5075/87/40007)). This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

Effect of convective transport on dendritic crystal growth from pure and alloy melts

We report on the comparative influence of convective transport due to flow in the melt on dendrites growing in one-component (pure) and two-component (alloy) melts. We perform an analysis using a sharp interface model of slow and rapid dendritic growth under the influence of convective transport. As examples, solidification of melts of Ti and binary TiAl, respectively, is investigated. The observed principal differences in the effect of convective transport in melt on the growth of one-component and binary dendrites are discussed in the frame of a scaling analysis.