Phase-Field Approach for Faceted Solidification

We extend the phase-field approach to model the solidification of faceted materials. Our approach consists of using an approximate gamma-plot with rounded cusps that can approach arbitrarily closely the true gamma-plot with sharp cusps that correspond to faceted orientations. The phase-field equations are solved in the thin-interface limit with local equilibrium at the solid-liquid interface [A. Karma and W.-J. Rappel, Phys. Rev. E53, R3017 (1996)]. The convergence of our approach is first demonstrated for equilibrium shapes. The growth of faceted needle crystals in an undercooled melt is then studied as a function of undercooling and the cusp amplitude delta for a gamma-plot of the form 1+delta(|sin(theta)|+|cos(theta)|). The phase-field results are consistent with the scaling law "Lambda inversely proportional to the square root of V" observed experimentally, where Lambda is the facet length and V is the growth rate. In addition, the variation of V and Lambda with delta is found to be reasonably well predicted by an approximate sharp-interface analytical theory that includes capillary effects and assumes circular and parabolic forms for the front and trailing rough parts of the needle crystal, respectively.Comment: 1O pages, 2 tables, 17 figure

The kinetics of primary alpha plate growth in titanium alloys

The kinetics of primary α-Ti colony/Widmanstätten plate growth from the β are examined in Ti-6246, comparing a simple quasi-analytic model to experiment. The plate growth velocity depends sensitively both on the diffusivity D(T) of the rate-limiting species and on the supersaturation around the growing plate. These result in a maxima in growth velocity around 40 K below the transus, once sufficient supersaturation is available to drive the plate growth. In Ti-6246, the plate growth velocity was found to be around 0.32 μm min−1 at 850 °C, which was in good agreement with the model prediction of 0.36 μm min−1. The solute field around the growing plates, and the plate thickness, was found to be quite variable, due to the intergrowth of plates and soft impingement. This solute field was found to extend to up to 30 nm, and the interface concentration in the β was found to be around 6.4 at. pct Mo. It was found that the increasing O content from 500 to 1500 wppm will have minimal effect on the plate lengths expected during continuous cooling; in contrast, Mo approximately doubles the plate lengths obtained for every 2 wt pct Mo reduction. Alloys using V as the β stabilizer instead of Mo are expected to have much faster plate growth kinetics at nominally equivalent V contents. These findings will provide a useful tool for the integrated design of alloys and process routes to achieve tailored microstructures