A DFT Study of Al_nTi_n (n = 2–12) Alloy Clusters

Abstract

Herein, Al n Ti n (n = 2–12) clusters are studied by density‐functional theory method. The evolution of the geometric structure shows that Ti atoms tend to gather inside the clusters. The analysis of the relative stability and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gap show that Al n Ti n (n = 2–12) clusters tend to be stable and the bonding probability increases when n > 8. Nature bond orbitals (NBO) results show that the strong d‐orbital effect between Ti atoms results in the formation of TiTi bonds more easily than AlTi bonds, which leads to the enrichment of Ti atoms inside the Al n Ti n (n = 2–12) clusters. When n ≥ 8, Al atoms that surround the core formed by Ti atoms tend to form stable triangular configuration, which is stable adsorption site for Al atoms. Herein, the grain‐refining effect of TiAl3 grain refiners in Al alloys at the atomic level can be explained.

Investigation of Structures, Stability, and Electronic and Magnetic Properties of InnSnnClusters Using Density‐Functional Theory

“…Based on the structural evolution law of In n Sn n ( n = 2–12) clusters, the thermodynamic stability of In n Sn n ( n = 2–12) clusters was further analyzed against cluster size n . The average binding energies ( E b ), fragmentation energies (Δ E ), and second‐order energy differences (Δ 2 E ) of In n Sn n ( n = 2–12) clusters can be defined as [ 59–61 ] where E (Sn), E (In), E (In n −1 Sn n −1 ), E (In n Sn n ), and E (In n +1 Sn n +1 ) are the energies of the single Sn atoms, single In atoms, In n ‐1 Sn n −1 clusters, In n Sn n clusters, and In n +1 Sn n +1 clusters, respectively.…”

“…Based on the structural evolution law of In n Sn n (n = 2-12) clusters, the thermodynamic stability of In n Sn n (n = 2-12) clusters was further analyzed against cluster size n. The average binding energies (E b ), fragmentation energies (ΔE), and second-order energy differences (Δ 2 E) of In n Sn n (n = 2-12) clusters can be defined as [59][60][61] The E b of the In n Sn n clusters increased with an increase in the cluster size n, indicating that the interaction of atoms is enhanced and the stability of the cluster increases (Figure 2). By comparing the E b of In n Sn n clusters with those of In 2n and Sn 2n clusters with the same atomic number, [27,30,34,35,40,44,48] the E b of Sn 2n clusters were significantly higher than those of In n Sn n clusters but much higher than that of In 2n clusters, which may be the reason for the Sn atom aggregation in the In n Sn n (n = 2-12) clusters.…”

Density Functional Theory Study of Structural Evolution, Relative Stability, and Electronic Properties of SnnAln (n = 2–12) Clusters

“…This phenomenon is more common in the structural evolution of Al n Ti n clusters. [39] During crystal growth, this stable triangular structure was more inclined to adsorb Ti atoms. A similar phenomenon was observed for the triangular structure of Al 3 .…”