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-XS 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 to form 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 FCC lattice and the size mismatch together serve as excellent criteria determining XL LPSO formation.