The electrical conductivity of transition metals

TLDR

Recent work has examined the electrical properties of transition metals Ni, Pd, Pt and their Cu, Ag, Au alloys using quantum‑mechanical electron theory, highlighting the link between unoccupied d states, magnetism, and conductivity. This paper develops a formal conductivity theory for transition metals, applies it to explain the anomalous temperature coefficients of Pd and Pt and the zero coefficient of constantan, and discusses ferromagnetic metal resistance. The authors model conductivity by considering two Brillouin zones and the enhanced scattering of conduction electrons into unoccupied d states due to lattice vibrations, which shortens the mean free path. They explain the high resistance of transition metals by showing that conduction electrons are mainly s‑state derived, with a comparable number of carriers to noble metals, yet experience much higher scattering into d states, leading to shorter mean free paths.

Abstract

1— In a recent paper certain property of the transition metals Ni, Pd, and Pt and of their alloys with Cu, Ag, and Au have been discussed from the point of view of the electron theory of metals based on quantum mechanics. In particular, a qualitative explanation was given of the relatively high electrical resistance of the transition metals. It was shown from an examination of the experimental evidence that the conduction electrons in these metals have wave functions derived mainly from s states just as in Cu, Ag, and Au, and that the effective number of conduction electrons is not much less than in the noble metals. On the other hand, the mean free path is much smaller, because under the influence other the lattice vibrations the conduction electrons may make transitions to the unoccupied d states, and the probability of these transitions is several times greater than the probability of ordinary scattering. Since the unoccupied d states are responsible for the ferromagnetism or high paramagnetism of the transition elements, there is a direct connexion between the magnetic properties and the electrical conductivity. The purpose of this paper is as follows: in 2, 3, and 4 we develop a formal theory of conductivity for metals, such as the tradition metals, where two Brillouin zone are of importance for the conductivity; in 5 we apply the theory to show why, at high temperatures, the temperature coefficient of the paramagnetic metals Pd and Pt falls below the normal value; and in 6 we discuss the resistance of ferromagnetic metals, and show in 7 qualitatively why constantan (Cu-Ni) has zero temperature coefficient at room temperature.