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

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 Al₃M compounds in the L1₂ and DO₂₂ 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 Al₃V, Al₃Nb, and Al₃La, 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.