Self-organized Sr leads to solid state twinning in nano-scaled eutectic Si phase

Abstract

A new mechanism for twin nucleation in the eutectic Al-Si alloy with trace Sr impurities is proposed. Observations made by sub-angstrom resolution scanning transmission electron microscopy and X-ray probing proved the presence of <110> Sr columns located preferentially at twin boundaries. Density functional theory simulations indicate that Sr atoms bind in the Si lattice only along the <110> direction, with preferential positions at first and second nearest neighbors for interstitial and substitutional Sr, respectively. Density functional theory total energy calculations confirm that twin nucleation at Sr columns is energetically favorable. Hence, twins may nucleate in Si precipitates after solidification, which provides a different perspective to the currently accepted mechanism which suggests twin formation during precipitate growth.

Figure 1

(a) HAADF STEM high resolution image (300 kV) of an eutectic Si particle tilted in the [110] zone axis. Yellow arrows indicate first order twins in {111} <112> direction associated with Sr columns. (b) Shows a qualitative representation of the Si and Sr columns intensities within the yellow square in Fig. 1(a) (Si - full contrast in red, Si - lower contrast in orange, Si - lowermost contrast in yellow-orange, and the Sr columns in green). (c) HAADF STEM image of the X-ray Spectrum Image (60 kV) from a “star-like” region in Fig. 1(a); (d) extracted spectrum from EDX –SI; the Sr atom column is marked with an yellow dashed square in Fig. 1(c). Strontium signal is about 100 times smaller than the silicon signal. The copper signal is from the TEM holder and the faint aluminum signal is more likely due to the fact that the signal is averaged through the thickness of the sample, and some Al matrix remained in the depth of the investigated area.

Figure 2

(a) Variation of the system energy with the distance between Sr atoms in the directions indicated in the legend. The vertical axis represents the excess energy above the pure Si lattice energy. This excess energy has been scaled by the long distance limit for each of the defects, which is 2.296 ± 0.072 eV for the interstitial case and 1.203 ± 0.100 eV for the substitutional case (with the error bounds resulting from differing k-point grids). Open and filled symbols correspond to substitutional and interstitial Sr, respectively. (b) Atomic configurations of the interstitial and substitutional <110> Sr columns, respectively, corresponding to the lowest energy states indicated by (I) and (S) in (a).

Figure 3

Charge density difference plot for the Si-Sr (a) and Si-Sr-Al (b) systems, with Si atoms (blue) and a <110> interstitial Sr column (marked by a red dot in the center of the image) in the {110} projection (yellow - regions of and cyan - regions of ). The simulation cell size is 2×3 Si unit cells (18.9 Å × 20.1 Å) in the plane of the image. Superimposed on these images is the vector displacement field (shown by red arrows) of the Si atoms relative to the pure Si case (the tails of the arrows correspond to the location of the atoms in a perfect Si crystal). The charge perturbation is aligned with the <1–12> direction, while atomic displacements indicate incipient twinning. The position of the Al atom is shown in (b) with a black arrow. The displacement field and the charge density difference in (b) correspond to the {110} atomic plane containing the Al atom.