The resistance and thermoelectric properties of the transition metals

TLDR

The author’s recent theory of electrical conduction for transition metals explains their high resistivities, alloy resistivity curves, and high‑temperature behavior, and highlights the thermoelectric interest in ferromagnetic metals. The study aims to demonstrate that the theory accounts for thermoelectric properties of transition metals and alloys, and to provide a detailed discussion of their electrical resistance compared with experiment. The authors model electron states in Brillouin zones, treating overlapping electrons and holes in partially filled zones to explain conductivity differences among metals. They find that a small number of overlapping electrons (n0) explains why divalent metals and bismuth conduct poorly compared to monovalent metals, without requiring different mean free paths.

Abstract

1—In two recent papers the author has given for the transition metals a theory of electrical conduction which accounts for many of their peculiarities. In Paper I a reason was given for their relatively high resistivities and for the shape of the curves obtained when the resistivity of an alloy such as Ag-Pd is plotted against atomic composition; in Paper II behaviour at high temperatures of Pd and Pt was discussed, and also of the resistance of ferromagnetic metals and of alloys such as constantan (Cu-Ni). In this paper it will be shown that the theory can give an account of some of the thermoelectric properties of these metals and alloys. The thermoelectric properties of ferromagnetic metals are of especial interest, because they have been cited as evidence that the same electrons are responsible for the ferromagnetism as for the conductivity. We shall also give a further discussion of the electrical resistance both of paramagnetic and of ferromagnetic metals and a more detailed comparison with experiments than was attempted in Paper II. In all metals the possible stationary stated of an electron may be divided into zones (the "Brillouin Zones"); for cubic metals the first zone contains 2N states per N atoms; Jones§ has shown that for the bismuth structure a zone exists containing 5N electrons. Two zones may either be separated by a range of forbidden energies, or they may overlap. If all the states of a given zone are occupied, that zone can make no contribution to the conductivity of the metal. In the divalent metals or in bismuth the available electrons could just fill a zone; but, since these metals are conductors, we must assume that there are a certain number N n 0 of "overlapping" electrons in the second zone and an equal number of vacant places or "positive holes" in the first zone. The assumption that n 0 is small compared with unity accounts for the fact that divalent metals and bismuth are poor conductors compared with monovalent metals; it is not necessary to assume that the mean free path is different for the two groups.