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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.
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We carried out a study of the pressure dependence of the solidification temperature in nine pressure transmitting media that are liquid at ambient temperature, under pressures up to 2.3 GPa. These fluids are: 1:1 isopentane/n-pentane, 4:6 light mineral oil/n-pentane, 1:1 isoamyl alcohol/n-pentane, 4:1 methanol/ethanol, 1:1 FC72/FC84 (Fluorinert), Daphne 7373, isopentane, and Dow Corning PMX silicone oils 200 and 60,000 cst. We relied on the sensitivity of the electrical resistivity of Ba(Fe1-xRux)2As2 single crystals to the freezing of the pressure media, and cross-checked with corresponding anomalies observed in the resistance of the manganin coil that served as the ambient temperature resistive manometer. In addition to establishing the Temperature-Pressure line separating the liquid (hydrostatic) and frozen (non-hydrostatic) phases, these data permit rough estimates of the freezing pressure of these media at ambient temperature. This pressure establishes the extreme limit for the medium to be considered hydrostatic. For higher applied pressures the medium has to be treated as non-hydrostatic.
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.
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 $V = V_D$.
Molecular dynamics simulation study based on the EAM potential is carried out to investigate the effect of pressure on the rapid solidification of Aluminum. The radial distribution function is used to characterize the structure of the Al solidified under different pressures. It is indicated that a high pressure leads to strong crystallization tendency during cooling.
Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Granasy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Granasy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystal-line solidification obtained using an atomistic phase-field model.
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