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We investigate the formation of long-period stacking ordered (LPSO) structure for Mg-Y-Zn ternary alloys based on the short-range order (SRO) tendency of energetically competitive disordered phases. We find that unisotropic 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 Y-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 Y-Zn pair, while seven atomic layer distance prefer both in- and inter-plane Y-Zn pair. These facts strongly indicate that ordering tendency for the Mg-Y-Zn alloy is significantly dominated by the stacking faults as well as their periodicity. We also systematically investigate correlation between SRO for other Mg-RE-Zn (RE = La, Tb, Dy, Ho, Er) alloys and the physical property of RE elements. We find that while SRO for RE-Zn pair does not show effective correlation with atomic radius, it has strong quadratic correlation with atomic radius considering unisotoropy along in- and inter-plane directions.

First-principles Study on Formation of LPSO Structures for Ternary Alloys Revisited from Short-range Order