The specific heat and resistivity of dilute non-magnetic alloys of the noble metals

In this paper we formulate a general theory for dilute alloys using a Green function approach. The solute atoms are assumed to be randomly distributed. Expressions for the density of states and the total transition probability for scattering are obtained to terms linear in the concentration. The general theory is then specialized to examine two particular models of the alloy: namely, the model used by Jones in 1964 and the localized model of Koster and Slater in 1954. In this latter model we are able to show why the mechanism suggested by Jones for the increase in specific heat of copper alloys is not likely to lead to large effects. Finally, we compare our results with experiment and find that for the specific heat good agreement is obtained with recent measurements carried out by Isaacs and Massalski by 1965. The resistivity results are less satisfactory and we suggest that is a fault of the model which gives rise only to S-wave scattering.