Analysis of non-equilibrium dendrite growth in a bulk undercooled alloy melt: Model and application

Abstract

A steady-state dendrite growth model in a bulk undercooled melt was developed for a binary alloy assuming nonlinear liquidus and solidus. As an extension of Galenko and Danilov’s model [Galenko PK, Danilov DA. Phys Lett A 1997;235:271], the present model considered the non-equilibrium interface kinetics, the relaxation effect, i.e. non-equilibrium liquid diffusion and the curved phase boundary. In the current analysis of marginal stability, the kinetic effect played an important role. The model’s validity was reinforced in terms of thermodynamic calculations of the phase diagram, as fewer fitting parameters were used in the model predictions. Adopting three characteristic velocities, i.e. the critical velocity of the absolute solute stability V C ∗ , the velocity of the maximal tip radius V R m and the velocity of bulk liquid diffusion V D, a quantitative agreement was obtained between the model predictions and the experimental results of an undercooled Ni–0.7 at.% B alloy. A plateau observed in the velocity versus undercooling stage, i.e. Δ T ( V C ∗ ) → Δ T ( V R m ) , for intermediate undercoolings implied a transition from a mainly solute-controlled to a mainly thermal-controlled process. If the dendrite growth velocity equaled V D, an abrupt change of growth mode from the power law to linear growth proceeded, which could be ascribed to a transition from mainly thermal-controlled growth to purely thermal-controlled growth.