On the Binding Forces in the Alkali and Alkaline Earth Metals According to the Free Electron Theory

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Abstract
Although there have been a considerable number of attempts to work out in some detail the nature of the cohesive forces in the alkali metals, it has seemed worth while to see how far one could go with the simplest possible hypothesis, according to which the metal consists simply of singly charged positive ions in a sea of free electrons. Frenkel first showed that the fact that the electrons obey the Fermi statistics, results in an effective repulsive force which will be balanced by attractive electrical forces; but, as he pointed out, the finite size of the ions prevents this being more than a qualitative picture, and he suggested taking this into account by including repulsive forces between electrons and ions. In the present work an intrinsic ionic volume has been introduced into which the electrons are supposed to be unable to penetrate; this is simply subtracted from the atomic volume in the Fermi expression for the kinetic energy of the electrons. For the attractive potential an expression like those commonly employed to get the electrical potential of crystals is used; it involves a ``Madelung constant'' of a size about equal to those occurring in cases of uni-univalent crystals, and the same for all the alkali metals. For the alkaline earth metals appropriate modifications can be made. One can then calculate the energy of the metals from the experimental value of the atomic volume, getting excellent agreement with experiment in the case of the alkali metals, but not such good agreement in the case of the alkaline earth metals. The method appears not to be very successful in calculating the compressibilities, even in the case of the alkali metals (for which, alone, it was tried); but aside from the fact that the compressibilities at absolute zero may only be inferred from measurements around room temperature, it appears that a relatively small correction to the energy expression can give the correct compressibility without greatly upsetting the calculation of the energy. The latter then is to be considered as of significance, and gives some confidence in the essential correctness of the simple picture of the metal described above.