Constant-volume pair potential for Al–transition-metal compounds

Abstract

We treat the problem of two transition-metal atoms embedded in Al by means of a simple s-d model Hamiltonian with localized d orbitals. A Green’s-function analysis gives the electronic density of states and total energy as functions of the separation between the two transition-metal atoms. The pair potential thus obtained is strong and has Ruderman-Kittel-Kasuga-Yosida-type oscillations as its asymptotic behavior. It is applicable to cases in which transition metals are not nearest neighbors. With this pair potential, we calculate the structural energy differences of ${\mathrm{Al}}_3$M compounds in the L$1_2$ and ${\mathit{DO}}_{22}$ structures, where M includes all of the group III, IV, V transition metals and the whole 4d row. Comparison with ab initio results reveals good agreement for the transition metals in group V and beyond, but not for the earlier transition metals, in which the p-d covalent bonding and three-body interactions are likely more important. We also calculate the (100) antiphase boundary (APB) energies for ${\mathrm{Al}}_3$V, ${\mathrm{Al}}_3$Nb, and ${\mathrm{Al}}_3$La, and find a strong correlation between the APB energy and the structural energy difference. The low-order moment-expansion method is used to obtain short-ranged potentials in an effort to obtain better convergence for the structural energies. This approach fails, giving magnitudes for the structural energy differences that are much too small.