Explanation of structural differences and similarities between the AT${}_2$Al${}_{10}$ phases (where A=actinide, lanthanide or rare earth element and T=transition metal)

In the current work we have studied the crystallographic relationship between the AT${}_2$Al${}_{10}$ phases (where A = actinide, lanthanide and rare earth element and T = transition metal). It is known that with this stoichiometry two structure types exist: tetragonal CaCr${}_2$Al${}_{10}$ and orthorhombic YbFe${}_2$Al${}_{10}$. It was found that both CaCr${}_2$Al${}_{10}$ and YbFe${}_2$Al${}_{10}$ types are structural derivatives of the ThMn${}_{12}$ type structure (which has more general formula of AT${}_x$Al${}_{12-x}$, with x > 2). CaCr${}_2$Al${}_{10}$ structure has a group-subgroup relationship with the ThMn${}_{12}$ structure, while the relationship of the YbFe${}_2$Al${}_{10}$ to the ThMn${}_{12}$ was proved applying the strong reflection approach, suggested initially for approximants of quasi-crystals. Proposed here relationship between the studied structures explains the small difference in total energies, calculated using Density Functional Theory. Understanding the connection between these phases allows regarding AT${}_2$Al${}_{10}$ composition as somewhat extension of the AT${}_x$Al${}_{12-x}$ compositional range. Due to the unique magnetic properties of the AT${}_x$Al${}_{12-x}$ phases, tunable as a function of crystallographic structure, study of structural stability and crystallographic relationships of related phases are of outmost importance.