Ab initio molecular dynamics simulations of molten Al${}_{1-x}$Si${}_x$ alloys

Recent increases in computational efficiency have enabled large-scale ab initio molecular dynamics simulations to be performed on molten eutectic Al${}_{1-\mathrm{x}}$Si${}_{\mathrm{x}}$ alloys ($x$ $=$ 0.12). Atomic forces were calculated using real-space pseudopotential density-functional theory, and the pair correlation, structure factor, coordination number, velocity autocorrelation, and mean-square displacement were computed at temperatures 973 K, 1223 K, and 1473 K. The calculated structure factor agrees very well with data from neutron-diffraction experiments. In addition an analysis of partial coordination numbers suggests that Si and Al are well mixed. This finding does not support an earlier conjecture attributing anomalous density variations to Si-aggregation phenomena. For dynamical properties the velocity autocorrelation function calculated for Al atoms demonstrates a “cage effect” similar to that found in pure liquid Al. In addition, the diffusion constants of Al are consistently lower than that of Si over the temperature range we have studied.

Figure 1

(a) $G\left(r\right)=r\left(g\left(r\right)-1\right)$ derived from the partial and total pair correlation functions for liquid Al${}_{0.88}$Si${}_{0.12}$ calculated at 973 K, 1223 K, and 1473 K from 500 atom simulations. (b) Comparison of the total pair correlation function calculated from 200 atom (dashed lines) and 500 atom (solid lines) simulations for several target temperatures.

Figure 2

(a) Simulated total structure factor for Al${}_{0.88}$Si${}_{0.12}$ at 973 K, 1223 K, and 1473 K. (b) Structure factor at 973 K from simulations and neutron-diffraction data.[5] (c) Simulated structure factor at 973 K and results from XRD at 948 K.[3, 6]

Figure 3

(a) Distribution of Al (black) and Si (red) atoms by number of nearest neighbor atoms. (b) Fraction of Al atoms having specific Al and Si coordination numbers. (c) Same as in (b) but for Si atoms.

Figure 4

(a) Velocity autocorrelation function for Al atoms at 973 K, 1223 K, and 1473 K. (b) Velocity autocorrelation for Si atoms at the same temperatures.

Figure 5

Mean-squared displacement for (a) Al and (b) Si atoms as a function of time. (c) Diffusion constants as function of temperature obtained from Eqs. (6) and (7).