Atomistic Underpinnings for Orientation Selection in Alloy Dendritic Growth

In dendritic solidification, growth morphologies often display a pronounced sensitivity to small changes in composition. To gain insight into the origins of this phenomenon, we undertake an atomistic calculation of the magnitude and anisotropy of the crystal-melt interfacial free energy in a model alloy system featuring no atomic size mismatch and relatively ideal solution thermodynamics. By comparing the results of these calculations with predictions from recent phase-field calculations, we demonstrate that alloying gives rise to changes in free-energy anisotropies that are substantial on the scale required to induce changes in growth orientations.

Figure 1

Temperature-composition phase diagram calculated for the Lennard-Jones alloy characterized by $\sigma =1.0$ and $ϵ=0.75$.

Figure 2

${\gamma }_0$ (upper panel) and free-energy anisotropies (lower panel) vs $T$ for the LJ alloy characterized by $ϵ=0.75$ and $\sigma =1.0$. The dotted line in the top figure represents a linear interpolation between the pure species values.

Figure 3

Anisotropy coefficients (${ϵ}_1$ vs $-{ϵ}_2$) for the Lennard-Jones alloy with $ϵ=0.75$ and $\sigma =1.0$ (definition in text) are plotted with filled symbols, where error bars denote 95% confidence intervals. The solid lines represent the borders between $⟨100⟩$, hyperbranched, and $⟨110⟩$ dendrites, as derived from phase-field simulations [5].