Thermodynamic stability of Mg-based ternary long-period stacking ordered structures

Mg alloys containing long-period stacking ordered (LPSO) structures exhibit remarkably high tensile yield strength and ductility. They have been found in a variety of ternary Mg systems of the general form Mg-XL-XS, where XL and XS are elements larger and smaller than Mg, respectively. In this work, we examine the thermodynamic stability of these LPSO precipitates with density functional theory, using a newly proposed structure model based on the inclusion of a Mg interstitial atom. We predict the stabilities for 14H and 18R LPSO structures for many Mg-XL-XL ternary systems: 85 systems consisting of XL = rare earths (RE) Sc, Y, La-Lu and XS = Zn, Al, Cu, Co, Ni. We predict thermodynamically stable LPSO phases in all systems where LPSO structures are observed. In addition, we predict several stable LPSO structures in new, as-yet-unobserved Mg-RE-XS systems. Many non-RE XL elements are also explored on the basis of size mismatch between Mg and XL, including Tl, Sb, Pb, Na, Te, Bi, Pa, Ca, Th, K, Sr-an additional 55 ternary systems. XL = Ca, Sr and Th are predicted to be most promising in terms of forming stable LPSO phases, particularly with XS = Zn. Lastly, several previously observed trends amongst known XL elements are examined. We find that favorable mixing energy between Mg and XL on the face-centered cubic lattice and the size mismatch together serve as excellent criteria determining XL LPSO formation.