Electron-phonon interactions in transition metals

The problem of the electron-phonon interaction in transition metals is approached from the point of view that nonorthogonal tight-binding representations of the d-band electronic structure are very appropriate in such materials. Expressions for the electron-phonon matrix elements using this representation are derived. The quantitative validity of the method is demonstrated by calculating 〈I²〉, the Fermi-surface average of the electron-phonon coupling constant for $4d$ bcc transition metals and alloys. The variation of 〈I²〉 in these materials is understood physically as arising from the variation of the average Fermi velocity and of the bond order.