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Register a new userCrossover Scaling of Wavelength Selection in Directional Solidification of Binary Alloys
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Added by
Nikolas Provatas Dr.
Publication date
2004
fields
Physics
and research's language is
English
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We simulate dendritic growth in directional solidification in dilute binary alloys using a phase-field model solved with an adaptive-mesh refinement. The spacing of primary branches is examined for a range of thermal gradients and alloy compositions and is found to undergo a maximum as a function of pulling velocity, in agreement with experimental observations. We demonstrate that wavelength selection is unambiguously described by a non-trivial crossover scaling function from the emergence of cellular growth to the onset of dendritic fingers, a result validated using published experimental data.
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On the basis of local nonequilibrium approach, the one-dimensional model of the solute diffusion during rapid solidification of the binary alloy in the semi-infinite volume is considered. Within the scope of the model it is supposed that mass transport is described by the telegrapher equation. The basic assumption concerns the behavior of the diffusion flux and the solute concentration at the interface. Under the condition that these quantities are given by the superposition of the exponential functions the solutions of the telegrapher equation determining the flux and the solute distributions in the melt have been found. On the basis of these solutions different regimes of the solidification in the near surface region and the behavior of the partition coefficient have been investigated. The concentration profiles in the solid after complete solidification are analyzed depending on the model parameters.
Inelastic x-ray scattering (IXS) measurements of the dynamic structure factor in liquid Na57K43, sensitive to the atomic-scale coarse graining, reveal a sound velocity value exceeding the long wavelength, continuum value and indicate the coexistence of two phonon-like modes. Applying Generalized Collective Mode (GCM) analysis scheme, we show that the positive dispersion of the sound velocity occurs in a wavelength region below the crossover from hydrodynamic to atom-type excitations and, therefore, it can not be explained as sound propagation over the light specie (Na) network. The present result experimentally proves the existence of positive dispersion in a binary mixture due to a relaxation process, as opposed to fast sound phenomena.
We simulate solidification in a narrow channel through the use of a phase-field model with an adaptive grid. In different regimes, we find that the solid can grow in fingerlike steady-state shapes, or become unstable, exhibiting unsteady growth. At low melt undercoolings, we find good agreement between our results, theoretical predictions, and experiment. For high undercoolings, we report evidence for a new stable steady-state finger shape which exists in experimentally accessible ranges for typical materials.
We examine scaling in two-dimensional simulations of dendritic growth at low undercooling, as well as in three-dimensional pivalic acid dendrites grown on NASAs USMP-4 Isothermal Dendritic Growth Experiment. We report new results on self-similar evolution in both the experiments and simulations. We find that the time dependent scaling of our low undercooling simulations displays a cross-over scaling from a regime different than that characterizing Laplacian growth to steady-state growth.
The rapid solidification of a binary mixture in the region of the interface velocities $V$ close to the diffusion speed in the bulk of the liquid phase $V_D$ is considered within the framework of the local nonequilibrium approach. In this high-speed region the derivation of the analytical expression for the response function temperature-velocity representing kinetic phase diagram is given without using the concept of the equilibrium phase diagram. The modes of movement of the interface both without and with the drag effect are analyzed. It is shown that the drag effect can be accompanied by a local interface temperature maximum at $V = V_D$.
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