  We investigate thermodynamic behaviors of dilute Mg-Zn-Y ternary alloys to
form a unique solute-enriched stacking-fault (SESF), which is an intrinsic-II
type stacking-fault (I2-SF) enriched by the Zn and Y atoms and represents the
structural-unit of the long-period stacking/order (LPSO) phase. SESF in the
hexagonal-close-packed (hcp) Mg matrix forms a local face-centered-cubic (fcc)
environment, and hence our thermodynamic analysis is based on the Gibbs energy
comparison between hcp and fcc phases over the Mg-Zn-Y ternary composition
ranges, using the calculation of phase diagrams (CALPHAD) method aided by the
first principles calculations. Segregation behaviors of solute Zn/Y atoms into
the SESF are firstly estimated according to the Hillert's parallel tangent law,
followed by the possible disorder-order phase transformation within the SESF
using the multiple-sublattice model. We find that the Zn/Y co-segregations at
the SESF provide a remarkable condition that the fcc layers become more stable
than the hcp-Mg matrix. Besides, within the SESF, the following spinodal-like
decomposition into the Mg-rich solid-solution and the Zn/Y-rich L12-type order
phase causes a significant reduction of the total Gibbs energy of the system.
These thermodynamic behaviors explain fairly well a phenomenological origin of
the Zn-Y clustering with the L12-type short-range order, which is known to
occur for the LPSO phases and also confirmed for the present SESF by electron
microscopy experiments. Therefore, strong Zn-Y interactions even in dilute
conditions play a key role to stabilize firmly the SESF in the Mg-Zn-Y alloys.
