The Hall coefficient and other transport properties of dilute alloys of copper and silver

The low field Hall coefficient of a number of polycrystalline foils of dilute (2%) alloys of copper and silver has been measured in the temperature range 1.5–50°K, and at room temperature. The alloys chosen wereCu-Au andAg-Au (uncharged impurity),Cu Ge andAg-Sn (charged impurity), andCu-Ni andAg-Pd (transition metal impurity). At 20°K and below, the Hall coefficients of the different copper alloys differ widely from each other,Cu-Ge giving the highest (negative) values (up to twice the room temperature value for pure copper), andCu-Au the lowest (down to 0.7 of this value). There are also significant concentration dependences. The silver alloys show corresponding but smaller changes. A relationship, due to Tsuji, gives the Hall coefficient as a function of the Fermi velocityν and the mean curvature 1/ϱ of the Fermi surface, for the case of an isotropic relaxation time. The integrals over the Fermi surface have been numerically estimated using the known Fermi surface and electron velocities. For both Cu and Ag the results agree with the experimental room temperature values, which we take as evidence thatτ(k) for phonon scattering is here close to isotropic. On the other hand, to account for the Hall coefficients of the alloys, it is necessary to assume that the relaxation timeτ varies over the Fermi surface. It is seen that in Cu and Ag the neck regions contribute relatively little toR since both 1/ϱ andν are small there. The main change inR in different alloys arises from the variation in the relative weighting given to the belly regions by different kinds of impurity scattering. A closer analysis shows that the bulges in the Fermi surface of copper in the 〈100〉 directions contribute relatively heavily because of their high positive curvature. The anisotropy ofτ deduced from the Hall coefficient is compared with that deduced from other measurements.