Localized Impurity States in Metals: Dilute Alloys of Ni in Be

The results of an experimental study of the residual resistivity, specific heat, and magnetic susceptibility of dilute solid solutions of nickel in beryllium are presented. The addition of small amounts of Ni to the Be host metal gives rise to large changes in all three quantities. The residual resistivity due to the impurities is found to be 10 μΩ cm per at.% Ni, and each Ni atom contributes 1.15 states per eV to the total density of states at the Fermi level as measured by the linear term in the low-temperature specific heat. Susceptibility measurements indicate that there is no localized moment on the Ni, but the addition of Ni gives rise to a large change in the temperature-independent susceptibility. Comparison of the susceptibility and specific-heat results indicates that the added susceptibility is enhanced relative to the added state density arising from the Ni impurities. The Anderson theory of localized transition-atom impurity states is developed for the case of five-fold orbitally degenerate $d$ states, and the equivalence of the Anderson approach and the scattering approach is demonstrated from the theory of resonance scattering. It is shown in this manner that the Anderson theory can be made consistent with the Friedel sum rule. Using the Anderson model the residual resistivity, specific heat, and $d$-state contribution to the susceptibility are calculated for dilute alloys where the host-metal density of states is a function of energy. The experimental results are found to be consistent with theoretical expectations and are used to determine magnitudes for the parameters of the theory. It is found that there are between 8 and 9 $d$ electrons on each nickel atom, in agreement with the Friedel sum rule. The virtual level width is determined to be 0.4 eV, and the Coulomb-exchange quantity $\mathrm{}(U+4J)\mathrm{}$ is evaluated as 7 eV. Analysis of similar data on Cu: Ni alloys yields values for these quantities which are fully consistent with the results obtained from the Be: Ni data.