Compressibilities of the Alkali Metals

As a further test of the method of Wigner and Seitz (for the calculation of the energies of the monovalent metals), the pressure variation of the compressibilities of the alkali metals is determined and compared with recent experimental results of Bridgman which extend to pressures of the order of 45,000 kg/cm². Fröhlich's approximate analytic expression for the dependence of the energies of the alkali metals on volume suggests the following semi‐empirical form: $${\mathrm{W=a/v+b/v}}^{\frac{2}{3}}{\mathrm{-c/v}}^{\frac{1}{2}}.$$ If the parameters are determined from (1) the lattice constant, (2) the energy, and (3) the compressibility (all at zero pressure), the expression gives values for the relative change in volume with pressure in close agreement with Bridgman's results. The constants so determined agree fairly well with Fröhlich's theoretical values. Compressibilities of Li and Na, as obtained from the more exact and fundamental calculations of the energies given in the preceding paper, are compared with the experimental values. Theoretical values for Na are in good agreement with experiment, but the corresponding values for Li are about fifteen percent too high. It is suggested that the polymorphic transition in Cs, which occurs at a pressure of about 22,000 kg/cm², is a transition from the normal body‐centered to a face‐centered form, resulting from the nonelectrostatic interaction energy of the ions, which favors close packing.