On the binding energy of atoms in crystals and the speed of sound

The speed of sound depends on the structure and on the material properties of the crystal, such as the density and the Young’s modulus. On the other hand, from atomistic arguments it is possible to link the Young’s modulus to other material properties. These observations drive to a relation between the binding energy of the atoms in a crystal (which is one of the parameters appearing in the Mie-Lennard-Jones potential), the speed of sound in the longitudinal direction and the mass of one atom in the lattice. Applications of this relation to rare gases, some metals and some rare earths are presented and the results compared to others taken from literature.