Band Structure of Transition Metals and Their Alloys

A departure from the conventional approach to the energy-band problem is achieved in three ways. First, it is noted that there is a critical atomic separation $R_c\lesssim (2.9\mathrm{}\pm 0.1)$ A such that for $R<\mathrm{}{R}_c$ electrons from atomic $3d$ orbitals that are directed along a ligand must be treated as collective electrons, for $R>\mathrm{}{R}_c$ the corresponding electrons are localized, Heitler-London electrons. Since the $3d$ wave functions are anisotropic, this implies that there may be localized and collective $3d$ electrons simultaneously present. Second, it is pointed out that localized electrons obey Hund's rule and may therefore contribute an atomic moment. This means the corresponding energy levels, or narrow bands, are split into discrete subbands. Any moment from collective $3d$ electrons is induced by the simultaneously present localized electrons via intra-atomic exchange. Third, it is asserted that if nearest-neighbor antiferromagnetic order can be propagated throughout a lattice and the nearest-neighbor-directed $3d$ orbitals are half-or-less filled, the collective electrons ($R<\mathrm{}{R}_c$) can be stabilized by bonding-band formation. If the orbitals are more than half filled, the "extra" electrons cannot be stabilized by antiferromagnetic correlations between nearest neighbors. If antiferromagnetic, nearest-neighbor order is not possible, the electrons form a conventional metallic band. These observations provide sharp criteria for Pauli paramagnetism, antiferromagnetism, ferrimagnetism, and ferromagnetism in transition metals and their alloys. They are used to explicitly introduce electron correlations into the construction of qualitative energy diagrams from which semiempirical density-of-states curves are constructed. The resulting model is shown to provide a consistent interpretation of phase stability, magnetic properties, electronic specific heats, Hall effect data, and form-factor measurements for the bcc and close-packed transition metals of the first long period and their alloys. The model is only partially successful for elements of the second and third long periods.