Ordered and disordered phases in CaCu5 -type derived structures: Dumbbell cluster modeling with first-principles calculations

We investigate the structural stabilities of ${\mathrm{CaCu}}₅$-type derived structures $({\mathrm{Sm}}_{m\ensuremath{-}n}{T}_5m+2n, T=\mathrm{Fe},\mathrm{Co})$ and predict metastable structures with the dumbbell cluster expansion model in which the dumbbell atoms are regarded as virtual single atoms. The metastable structures are concentrated from $n/m=1/3$ to $1/2$, suggesting the existence of compounds with high magnetization. The disordered ${\mathrm{TbCu}}₇$-type structures are stabilized by the configurational entropy of the dumbbell clusters. The estimated solubility limits of the $T\text{\ensuremath{-}}T$ dumbbell are close to the experimental results. The difference in the phase diagram for the Sm-Fe and Sm-Co systems is explained from their effective cluster interactions.