Universal model for the surface energy of solids

Abstract

The surface energy $\sigma$ is considered as the work done in reversibly cleaving a bulk solid. Let $F\left(z\right)\mathrm{}$ be the force per unit area required to increase the spacing between the end planes from $a$ to $a+z$. For small $z$, $F\left(z\right)=Az$, where we show how $A$ can be determined from the bulk phonon spectrum, and for large $z$, $F\left(z\right)=\frac{C}{z^3}$, where $C$ can be determined from the bulk frequency-dependent dielectric constant. We assume that, apart from scale, the function $F\left(z\right)\mathrm{}$ has a universal shape $f^{*}\mathrm{}\left(z\right)\mathrm{}$. It then follows that $\sigma ={\alpha }^{*}{\mathrm{}\left(\mathrm{AC}\right)\mathrm{}}^{\frac{1}{2}}$ where ${\alpha }^{*}$ is a universal constant. Preliminary comparison with experiment gives good results with ${\alpha }^{*}=0.476\mathrm{}$.