Measuring kinetic coefficients by molecular dynamics simulation of zone melting

Molecular dynamics simulations are performed to measure the kinetic coefficient at the solid-liquid interface in pure gold. Results are obtained for the (111), (100) and (110) orientations. Both Au(100) and Au(110) are in reasonable agreement with the law proposed for collision-limited growth. For Au(111), stacking fault domains form, as first reported by Burke, Broughton and Gilmer [J. Chem. Phys. {\bf 89}, 1030 (1988)]. The consequence on the kinetics of this interface is dramatic: the measured kinetic coefficient is three times smaller than that predicted by collision-limited growth. Finally, crystallization and melting are found to be always asymmetrical but here again the effect is much more pronounced for the (111) orientation.Comment: 8 pages, 9 figures (for fig. 8 : [email protected]). Accepted for publication in Phys. Rev.

Theoretical and numerical investigation of diffusive instabilities in multi-component alloys

Mechanical properties of engineering alloys are strongly correlated to their microstructural length scale. Diffusive insta- bilities of the Mullins-Sekerka type is one of the principal mechanisms through which the scale of the microstructural features are determined during solidification. In contrast to binary systems, in multicomponent alloys with arbitrary interdiffusivities, the growth rate as well as the maximally growing wavelengths characterizing these instabilities depend on the the dynamically selected equilibrium tie-lines and the steady state growth velocity. In this study, we derive analytical expressions to characterize the dispersion behavior in isothermally solidified multicomponent (quaternary) alloys for different choices of the inter-diffusivity matrices and confirm our calculations using phase-field simulations. Thereafter, we perform controlled studies to capture and isolate the dependence of instability length scales on solute diffusivities and steady state planar front velocities, which leads to an understanding of the process of length scale selection during the onset of instability for any alloy composition with arbitrary diffusivities, comprising of both independent and coupled diffusion of solutes.Comment: 17 pages, 9 figure

Phase-field investigation on the non-equilibrium interface dynamics of rapid alloy solidification

The departure from the equilibrium solid concentration at the solid-liquid interface was often observed during rapid solidification. The energetic associated non-equilibrium solute partitioning has been treated in detail, providing possible ranges of interface concentrations for a given growth condition. For analytical description of specific single-phase dendritic and cellular operating point selection, analytical models for solute partitioning under a given set of growth conditions have been developed and widely utilized in most of the theoretical investigations of rapid solidification. However, these solute trapping models are not rigorously verified due to the difficulty in experimentally measuring under rapid growth conditions. Moreover, since these solute trapping models include kinetic parameters which are difficult to directly measure from experiments, application of the solute trapping models or the associated analytic rapid solidification model is limited. These theoretical models for steady state rapid solidification which incorporate the solute trapping models do not describe the interdependency of solute diffusion, interface kinetics, and alloy thermodynamics. This research program is focused on critical issues that represent conspicuous gaps in current understanding of rapid solidification, limiting our ability to predict and control microstructural evolution at high undercooling, where conditions depart significantly from local equilibrium. Through careful application of phase-field modeling, using appropriate thin-interface and anti-trapping corrections and addressing important details such as transient effects and a velocity-dependent numerics, the current analysis provides a reasonable simulation-based picture of non-equilibrium solute partitioning and the corresponding oscillatory dynamics associated with single-phase rapid solidification and show that this method is a suitable means for a self-consistent simulation of transient behavior and operating point selection under rapid growth conditions. Moving beyond the limitations of conventional theoretical/analytical treatments of non-equilibrium solute partitioning, these results serve to substantiate recent experimental findings and analytical treatments for single-phase rapid solidification. In addition, the simulations carried out here predict, for the first time, the full scope of behavior, from the initial transient to the steady-state conditions, where departure from equilibrium partitioning may lead to oscillations in composition, velocity, and interface temperature or may lead to a far-from-equilibrium steady-state. Such predictive capability is a necessary prerequisite to more comprehensive modeling of morphological evolution and, therefore, of significant importance

Eutectic colony formation: A phase field study

Eutectic two-phase cells, also known as eutectic colonies, are commonly observed during the solidification of ternary alloys when the composition is close to a binary eutectic valley. In analogy with the solidification cells formed in dilute binary alloys, colony formation is triggered by a morphological instability of a macroscopically planar eutectic solidification front due to the rejection by both solid phases of a ternary impurity that diffuses in the liquid. Here we develop a phase-field model of a binary eutectic with a dilute ternary impurity and we investigate by dynamical simulations both the initial linear regime of this instability, and the subsequent highly nonlinear evolution of the interface that leads to fully developed two-phase cells with a spacing much larger than the lamellar spacing. We find a good overall agreement with our recent linear stability analysis [M. Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a destabilization of the front by long-wavelength modes that may be stationary or oscillatory. A fine comparison, however, reveals that the assumption commonly attributed to Cahn that lamella grow perpendicular to the envelope of the solidification front is weakly violated in the phase-field simulations. We show that, even though weak, this violation has an important quantitative effect on the stability properties of the eutectic front. We also investigate the dynamics of fully developed colonies and find that the large-scale envelope of the composite eutectic front does not converge to a steady state, but exhibits cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.