  In order to clarify thermodynamic stability of Mg-based long-period stacking
ordered (LPSO) structure, we systematically study energetic preference for
alloys on multiple stacking with different composition for random mixing of
constituent elements, Mg, Y, and Zn based on special quasirandom structure
(SQS). Through calculation of formation free energy of SQS, Mg-Y-Zn alloy
exhibits phase separation into Mg- and Y-Zn rich phase, which is consistent
with previous theoretical studies. Bulk modulus of SQSs for multiple
compositions, stacking sequences, and atomic configuratons ranges around 35
GPa, i.e., they do not show significant dependence of Mg concentration, which
therefore means that the effects of phonon do not play significant role on LPSO
phase stability. Introducing stacking fault to hcp stacking gains "negative"
energy, which indicates profound relationship between introducing stacking
faults and the formation of long-period stacking ordering.
