Electrical Resistivity of Noble Metals

Abstract

The temperature variation of the electrical resistivity of copper, silver, and gold has been studied within the free electron approximation on the basis of the lattice dynamical models of Chéveau, and Bhatia and Horton. The first-order variational solution of the Boltzmann transport equation as developed by Ziman has been incorporated in the study for the calculation of the transport coefficients of noble metals. The force constants appearing in the secular equation for the lattice vibrations have been estimated with the help of the experimental values of the elastic constants of the noble metals. The phonon spectrum has been calculated by the modified Houston spherical six-term procedure as elaborated by Betts et al. The Normal and the Umklapp contributions to the electrical resistivity have been considered separately in the present study. A comparison of the theoretical results with the experimental data shows that the calculations are able to explain satisfactorily the temperature dependence of the electrical resistivity of the noble metals. However, as compared to the Bhatia–Horton model, the theoretical resistivity values of the noble metals as furnished by the Chéveau model give a better overall fit with the experimental data.