The LPSO Structure with an Extra Order beyond Stacking Periodicity

Abstract

We have investigated a novel long-period stacking/order (LPSO) structure in a Mg₇₅Al₁₀Y₁₅ alloy, based on electron diffraction, scanning transmission electron microscopy (STEM) observations and first-principles calculations. Fundamental lattice of the present LPSO structure is identified as one of the stacking polytypes of 10H-type, and the in-plane 6×(1210)_hcp superlattice order is well developed as represented by the L1₂-type Al₆Y₈ cluster arrangement. We find that, across the stacking direction, the inter-cluster order tends to be further developed beyond its periodicity, showing an extra order which doubles the 10H-stacking periodicity. We have constructed the LPSO variant models including such extra inter-cluster order, and their formation energy comparison has confirmed that the extra order becomes indeed stable when the L1₂-Al₆Y₈ cluster contains interstitial atoms. The interstitial effects turn out to be prominent in favor of Y atom, as being consistent with the STEM observations.

Fig. 4 (a): The LPSO variant structures formed by the A₃-type and the A₁-type shifts, shown together with the corresponding in-plane positions (a, b, c, d) of the L1₂-Al₆Y₈ clusters. abcb (C2/c) and abcd (Cc) inter-cluster correlations are responsible for the extra order that doubles the 10H-stacking periodicity. (b): Formation energy of the LPSO variant models based on first-principles calculations. Shapes and colors denote the inter-cluster configurations and the element species at the interstitial site, respectively. For computations, the cut-off energy is chosen as 360 eV, with a 3 × 3 × 1 k-mesh. The electronic iterations convergence is 1.00 × 10⁻⁵ eV using the blocked Davidson algorithm and real space projection operators. Calculations are performed by non-fixed conditions both for atomic positions and a unit-cell volume.