Heterogeneous nucleation of solid Al from the melt by ${\text{TiB}}_2$ and ${\text{Al}}_3\text{Ti}$: An ab initio molecular dynamics study

The nucleation of solid Al from the melt by ${\text{TiB}}_2$ is well established and is believed to involve the formation of ${\text{Al}}_3\text{Ti}$. Since the atomic-scale mechanisms involved are not fully understood, we look to computer simulation to provide insight. As there is an absence of suitable potentials for all of this complex system we have performed large-scale density-functional-theory molecular dynamics simulations of the nucleation of solid Al from the melt on ${\text{TiB}}_2$ and ${\text{Al}}_3\text{Ti}$ substrates at undercoolings of around 2 K. Using periodic boundary conditions, we find limited ordering and no signs of incipient growth in the liquid Al close to the B-terminated surface of ${\text{TiB}}_2$. By contrast, we see fcc-like ordering near the Ti-terminated surface, with growth being frustrated by the lattice mismatch between bulk Al and the ${\text{TiB}}_2$ substrate. The Al interatomic distances at the Ti-terminated surface are similar to distances found in ${\text{Al}}_3\text{Ti}$; we suggest that the layer encasing ${\text{TiB}}_2$ observed experimentally may be strained Al on a Ti-terminated surface rather than ${\text{Al}}_3\text{Ti}$. For the ${\text{Al}}_3\text{Ti}$ substrate, fcc-like structures are observed on both sides which extend rapidly into the melt. Periodic boundaries introduce unphysical stresses which we removed by introducing a vacuum region to separate the liquid from the solid at one of the interfaces. We see ordering in the Al on both the B-terminated (0001) surface of ${\text{TiB}}_2$, and on ${\text{Al}}_3\text{Ti}\left(112\right)$, with the ordering able to be stronger on the ${\text{Al}}_3\text{Ti}$ substrate. However, we cannot draw strong conclusions as these simulations need more time to allow long-ranged fluctuations in the liquid Al to dampen out. The huge computational cost restricted the range and duration of simulations that was possible.

Figure 1

(Color online) The simulation time for single step of ionic relaxation of ${\text{TiB}}_2\text{AlP}$ system as a function of number of cores used on IBM Blue Gene, KSL, KAUST.

Figure 2

(Color online) Sequential images and calculated density profile of solid Al nucleation from the melt on top of ${\text{TiB}}_2$ substrate at $T=910\text{K}$ using periodic boundary condition. (a) $t_s=0.05\text{ps}$; (b) $t_s=1.42\text{ps}$; (c) $t_s=2.85\text{ps}$.

Figure 3

(Color online) $d$ spacing as a function of atomic position. A bin size of $0.11\text{Å}$ was used to build the histogram from which the peak positions were found. The error bars are found from the half width at half maximum of the peaks.

Figure 4

(Color online) Two-dimensional structure factor and corresponding ordering layers on the Ti side [(a1) and (a2)] and B side [(a3) and (a4)] of TiB2. [(a1) and (a2)] Ti layer; [(a3) and (a4)] B layer, [(b1)–(b4)] first layer in the liquid Al; [(c1)–(c4)] second layer in the liquid Al; [(d1)–(d4)] third layer in the liquid Al. Computed at $t=2.85\text{ps}$

Figure 5

(Color online) (a) The RDF of Ti-Ti, Ti-B, B-B in the solid substrate and Al-Al in the solidlike films on both sides of ${\text{TiB}}_2$ and the bulk liquid which are calculated from the last 100 MD steps at 910 K. (b) The RDF of Al-Al and Ti-Al around the Ti atoms in the liquid with insert images (I and II) showing different ordering behaviors of atoms around Ti atoms.

Figure 6

(Color online) (a) The atoms colorized by their averaged centro symmetry parameter $\left(\alpha \right)$ over the last 200 fs showing the ordering of Al atoms on the Ti-terminated surface $\left({\text{Al}}_{\text{a}}\right)$, disordered liquid Al $\left({\text{Al}}_{\text{b}}\right)$, three different positions of Ti atoms including a single Ti atom on the B-terminated surface $\left({\text{Ti}}_1\right)$, in bulk liquid $\left({\text{Ti}}_2\right)$, at the surface of the ${\text{TiB}}_2$ substrate $\left({\text{Ti}}_3\right)$, and in the middle of the ${\text{TiB}}_2$ substrate $\left({\text{Ti}}_4\right)$. (b) The distribution of $\alpha$ for each atom type.

Figure 7

(Color online) Calculated density profile of solid Al nucleation from the melt on top of the ${\text{Al}}_3\text{Ti}$ substrate at $T=910\text{K}$ using periodic boundary condition. (a) $t_s=0.05\text{ps}$; (b) $t_s=1\text{ps}$; (c) $t_s=2\text{ps}$.

Figure 8

(Color online) Structural ordering at the beginning of continuous growth on ${\text{Al}}_3\text{Ti}$ (112) surface at 910 K. (a) a snapshot at $t_s=2\text{ps}$, and projections of the outer four layers [(a1)–(d1)] and the corresponding time-averaged structure factors for 50 MD steps [(a2)–(d2)]. Ti and Al atoms in ${\text{Al}}_3\text{Ti}$ structure are in red (gray) and blue (dark), respectively. Liquid Al atoms are in green (light gray).

Figure 9

(Color online) Sequential images and calculated density profile of solid Al nucleation from the melt on top of ${\text{TiB}}_2$ and ${\text{Al}}_3\text{Ti}$ substrates at $T=910\text{K}$ using the free surface condition. (a) ${\text{TiB}}_2$ substrate, $t_s=0.05\text{ps}$; (b) ${\text{TiB}}_2$ substrate, $t_s=1\text{ps}$ (c) ${\text{TiB}}_2$ substrate, $t_s=2\text{ps}$, (d) ${\text{Al}}_3\text{Ti}$ substrate, $t_s=0.05\text{ps}$; (e) ${\text{Al}}_3\text{Ti}$ substrate, $t_s=1\text{ps}$; (f) ${\text{Al}}_3\text{Ti}$ substrate, $t_s=2\text{ps}$.