Eutectic Growth in Two-Phase Multicomponent Alloys

A theory of two-phase eutectic growth for a multicomponent alloy is presented. This theory employs the thermodynamic equilibrium at the solid/liquid interface and thus makes it possible to use standard CALPHAD databases to determine the effects of multicomponent phase equilibrium on eutectic growth. Using the same hypotheses as the Jackson Hunt theory, we find that the growth law determined for binary alloys in the Jackson Hunt theory can be generalized to systems with N elements. In particular, a new model is derived from this theory for ternary two-phase eutectics. The use of this model to predict the eutectic microstructure of systems is discussed

A quantitative variational phase field framework

The finite solid-liquid interface width in phase field models results in non-equilibrium effects, including solute trapping. Prior phase field modeling has shown that this extra degree of freedom, when compared to sharp-interface models, results in solute trapping that is well captured when realistic parameters, such as interface width, are employed. However, increasing the interface width, which is desirable for computational reasons, leads to artificially enhanced trapping thus making it difficult to model departure from equilibrium quantitatively. In the present work, we develop a variational phase field model with independent kinetic equations for the solid and liquid phases. Separate kinetic equations for the phase concentrations obviate the assumption of point wise equality of diffusion potentials, as is done in previous works. Non-equilibrium effects such as solute trapping, drag and interface kinetics can be introduced in a controlled manner in the present model. In addition, the model parameters can be tuned to obtain ``experimentally-relevant" trapping while using significantly larger interface widths than prior efforts. A comparison with these other phase field models suggests that interface width of about three to twenty-five times larger than current best-in-class models can be employed depending upon the material system at hand leading to a speed-up by a factor of $W^{(d+2)}$, where $W$ and $d$ denote the interface width and spatial dimension, respectively. Finally the capacity to model non-equilibrium phenomena is demonstrated by simulating oscillatory instability leading to the formation of solute bands.Comment: 51 pages, 9 figures, supplemental material

Twin plane re-entrant mechanism for catalytic nanowire growth.

A twin-plane based nanowire growth mechanism is established using Au catalyzed Ge nanowire growth as a model system. Video-rate lattice-resolved environmental transmission electron microscopy shows a convex, V-shaped liquid catalyst-nanowire growth interface for a ⟨112⟩ growth direction that is composed of two Ge {111} planes that meet at a twin boundary. Unlike bulk crystals, the nanowire geometry allows steady-state growth with a single twin boundary at the nanowire center. We suggest that the nucleation barrier at the twin-plane re-entrant groove is effectively reduced by the line energy, and hence the twin acts as a preferential nucleation site that dictates the lateral step flow cycle which constitutes nanowire growth.S. H. acknowledges funding from ERC grant InsituNANO (project number 279342). A. D. G. acknowledges funding from the Marshall Aid Commemoration Commission and the National Science Foundation. C. D. acknowledge funding from the Royal Society. P.V. acknowledges the support of ONR grant N00014-12-1-0198. We gratefully acknowledge the use of facilities within the LeRoy Eyring Center for Solid State Science at Arizona State University.This document is the Accepted Manuscript version of a Published Work that appeared in final form in Nano Letters, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://pubs.acs.org/doi/abs/10.1021/nl404244u. (AD Gamalski, PW Voorhees, C Ducati, R Sharma, S Hofmann, Nano Letters 2014, 14, 1288–1292