Approximate Compressibility of Elements and Compounds

The zero-pressure incompressibilities and volumes per atom for metals and solid nonmetals are found to fit the relation $\left(K_0{Z}^{\frac{-10\mathrm{}}{3}}\right){\left(Z{v}_0\right)}^{\frac{7}{3}}=\left(\frac{{\pi }^{\frac{10}{3}}{6}^{\frac{2}{3}}}{15}\right)a_0^{}{}_{}{}^3{e}^2$ to good accuracy. The relation is derived by an empirical attempt to interpolate between the finite-strain equation of state and the Thomas-Fermi equation of state. The strain energy is quadratic in the finite strain for the heavier alkali metals but higher order terms are important for the silicates, at least to twofold compression.