Calculation of electronic density of states for an amorphous Zr-Cu alloy

The recursion method has been used to calculate the $d$-band density of states for a cluster simulating amorphous ${\mathrm{Zr}}_{41}$ ${\mathrm{Cu}}_{59}$. Normally these calculations are performed using energies and overlap parameters obtained by detailed fitting of a linear combination of atomic orbitals scheme to existing crystalline calculations. Here an alternative approach is illustrated, where the relative position of the $d$ resonances for the alloy is determined by self-consistently adjusting the diagonal elements of the Hamiltonian to ensure that a given amount of charge transfer takes place. For transition-metal—transition-metal alloys, the assumption of zero charge transfer is usually a good approximation. The overlap integrals tabulated by Harrison are used for the off-diagonal elements. The energy spread among atoms of the same kind due to different local environments is obtained and shown to be small. The results of the calculations are in good agreement with x-ray photoelectron spectroscopy data and we find the density of states at the Fermi level to be consistent with measured values.