A Discussion of the Transition Metals on the Basis of Quantum Mechanics

The magnetic susceptibilities and electrical conductivities of cobalt, nickel and palladium and of their alloys with copper, silver and gold are discussed on the basis of the quantum theory of metals. It is shown that the number of electrons in the outermost s state must be about 0.6 per atom in the transition metals and one in the noble metals; certain magnetic properties of the alloys are explained on the basis of this fact. A quantum-mechanical explanation of the relatively high resistance of the transition metals is given and is shown to be supported by measurements of the resistance of alloys. § I . I N T R O D U C T I O N W I G N E R A N D SEITZ(') have recently shown that the quantum theory is capable of accounting quantitatively for the cohesive forces in a typical metal (sodium); the purpose of this paper is to give a qualitative discussion, based on the same theory, of some properties of the transition metals and in particular of the elements nickel and palladium, which come immediately before copper and silver in the periodic table. After an introductory discussion of the electronic structure of these metals and a comparison between the binding forces of nickel and copper, we shall consider (i) the saturation moments of the ferromagnetic metals and alloys, and the reason why they are not equal to integral numbers of Bohr magnetons per atom ($92 and 3); (ii) the paramagnetism of palladium and of its alloys with copper, silver and gold ($9 4 and 5 ) ; and (iii) the electrical conductivity of the transition elements, and the reason for their low conductivity as compared with that of the noble metals. The resistance of alloys of the transition metals with copper, silver and gold is also discussed ($ 6) . T o obtain an approximate solution of the Schrodinger equation for the electrons in a metal we may start from one or other of two models; we may picture the electrons as bound to individual atoms (method of Heitler and London and of Heisenberg) or we may think of them as belonging to the crystal as a whole (method of Bloch). It is to be emphasized that these two models do not correspond to different physical states of the crystal; both lead to wave functions of the whole system which are approximations to the true wave function. Insulators, as well as conductors can be treated, to a certain degree of approximation, by the use of either model, In this paper we shall use that of Bloch not only for the outermost s electrons, which are responsible for the cohesion and for the conductivity, but also