  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.
