We examine the formation of long-period stacking ordered (LPSO) structure for Mg-RE-Zn (RE = La, Tb, Dy, Ho, Er) ternary alloys based on the short-range order (SRO) tendency of energetically competitive disordered phases. While we see that SRO does not show effective correlation with atomic radius, we find that anisotropic SRO tendencies for structures with stacking faults cannot be simply interpreted by arithmetic average of SRO for constituent fcc and hcp stackings, indicating that the SRO should be significantly affected by periodically-introduced stacking faults. We also find that SRO for neighboring RE-Zn pair, which should have positive sign to form specific L12 type cluster found in LPSO, is strongly affected by the distance between stacking faults: e.g., five atomic layer distance does not prefer in-plane RE-Zn pair, while seven atomic layer distance prefer both in- and inter-plane RE-Zn pair. These facts strongly indicate that ordering tendency for the Mg-RE-Zn alloy is significantly dominated by the stacking faults as well as their periodicity, precursor to form L12 cluster in LPSO structure.
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