Topics in the Electronic Theory of Solids.

A tight-binding model Hamiltonian, used to study the electronic properties of a disordered alloy, is presented. Both the local energy levels and the interatomic transfer integrals were allowed to vary randomly. The problem is simplified considerably if it is assumed that the values of the transfer integrals are additive. The conventional methods of perturbation theory were applicable, and a mean-field approach, analogous to the coherent-potential approximation (CPA), was formulated. The resulting equations were compared to exact results concerning the dilute and split-band limits. It was concluded that, regarding the problem of additive off-diagonal disorder, an unambiguous generalization of the CPA was properly formulated. Also studied was positron annihilation anqular distributions in aluminum. Within the context of an independent particle model for positron annihilation, two photon angular correlation distributions were calculated in aluminum. Good agreement between theory and experiment was obtained with respect to many of the features in the angular distributions.