Cohesion in Monovalent Metals

Abstract

The theory of metallic structure, of Sommerfeld, Heisenberg, and Bloch, is carried far enough to explain cohesive forces, and calculations are made for atoms with one valence electron, particularly metallic sodium. The numerical results, though rough, are in qualitative agreement with experiment. It is found that the forces in general are of the same nature as those met in ordinary homopolar binding, discussed by Heitler and London; except that the purely electrostatic force from penetration of one atom by another is relatively more important, the valence effect from the exchange of electrons relatively less important, than in diatomic molecules.As a preliminary to the calculation, the relations of the methods of Heisenberg and of Bloch are discussed, and it is shown that they are essentially equivalent in their results when properly handled. Remarks are made both about conductivity and ferromagnetism. In connection with conduction, it is shown that a definite meaning can be given to free electrons, that they are necessary to conduction, and that a method can be set up for computing their number, which is rather small compared with the number of atoms. Ferromagnetism is discussed in connection with a recent paper of Bloch. It is shown that a metal like an alkali cannot be ferromagnetic, for atoms at such a distance that the interatomic forces keep the metal in equilibrium, are too close to be magnetic. For ferromagnetism, rather, it seems necessary to have one group of electrons responsible for cohesion, and another group, of smaller orbit and therefore relatively farther apart, producing the magnetism; a situation actually found only in the iron group and the similar groups.