Crystal structures of highly-ordered long-period stacking-ordered phases with 18R, 14H and 10H-type stacking sequences in the Mg–Zn–Y system

A formation criterion for Order-Disorder (OD) phases of the Long-Period Stacking Order (LPSO)-type in Mg-Al-RE (Rare Earth) Ternary Systems

“…4(i,k)). For each of the OD phases formed with RE = Y, Dy, Ho and Er, the intensity of the additional spots in the centre of Al 6 RE 8 atomic clusters varies from cluster to cluster, indicating that the element (either Mg, Al or RE) occupying the central position and their occupancies vary from cluster to cluster, as we observed previously for the Mg-Zn-Y OD phases 25,26 . The intensity profile taken from a double dagger pattern including a central additional bright spot with the highest intensity for each of the OD phases (as outlined with dotted lines in Fig.…”

“…44 are summarized in Table 2. It is now obvious from previous theoretical and experimental investigations 25,26,31–36 as well as from the present theoretical calculation that the central site of the Al 6 RE 8 atomic cluster is occupied by either Mg, Al (or TM) or RE. Thus, it is quite reasonable to assume that the Mg-Al-RE OD phase formation should always be accompanied by the atom inclusion in the Al 6 RE 8 atomic cluster whatever the atom kind is.…”

“…Furthermore, recent first-principles calculations have predicted that the OD phases in the Mg-Al-RE and Mg-TM-RE ternary systems are stabilized by the inclusion of an additional Mg atom in the centre of each L1 2 -type atomic cluster 31–36 . In fact, we have experimentally confirmed that the additional atom inclusion in the OD phases in the Mg-Zn-Y and Mg-Al-Gd systems, although the additional atom is identified not to be restricted to Mg, but is either Mg, Zn or Y and either Mg, Al or Gd 25,26 . Thus, it should be important also to investigate whether the preference of the additional atom included in the L1 2 -type atomic cluster varies depending on the RE element or not for the detailed understanding of the formability of the LPSO-type phases in the Mg-Al-RE and Mg-TM-RE ternary systems.…”

“…The OD-phase formation energy ΔE form , stability factor ΔE stab and energy required to insert one additional atom i ( i  = Mg, Al or RE) in each Al 6 RE 8 atomic cluster ΔE ins (insertion energy) were evaluated with the following equations 25,26,34,35 : where E tot ( j ) is the total energy per atom of the phase j and E CH (Mg l Al m RE n ) is the energy of the convex hull at the composition of the OD phase with a formula unit of Mg l Al m RE n (( l , m , n ) = (58, 6, 8) when no additional atom is inserted). Each convex hull is composed of three convex hull phases mostly selected according to the selections made by Saal and Wolverton except for the Mg-Al-Pm ternary system 35 (listed in Table S1 of Supplementary).…”

“…S1(a) of Supplementary) 15 . In addition, the formation of L1 2 -type atomic clusters is common to both the OD and LPSO phases in the Mg-Al-Gd and Mg-Zn-RE ternary systems 15,16,25,26 and has been considered to play a key role in the formation of the OD and LPSO phases 17,27–30 . Furthermore, recent first-principles calculations have predicted that the OD phases in the Mg-Al-RE and Mg-TM-RE ternary systems are stabilized by the inclusion of an additional Mg atom in the centre of each L1 2 -type atomic cluster 31–36 .…”