Universal model for the surface energy of solids

The surface energy σ is considered as the work done in reversibly cleaving a bulk solid. Let $F(z)$ be the force per unit area required to increase the spacing between the end planes from a to $a+z$. For small z, $F(z)=Az$, where we show how A can be determined from the bulk phonon spectrum, and for large z, F(z)=Cz³, where C can be determined from the bulk frequency-dependent dielectric constant. We assume that, apart from scale, the function $F(z)$ has a universal shape f*(z). It then follows that σ=α*(AC)1/2 where α* is a universal constant. Preliminary comparison with experiment gives good results with α*=0.476.