On the Binding Energy of Atoms in Crystals of Noble Gases and Metals and the Speed of Sound

The speed of sound depends on the structure and material properties of the crystal, such as density and Young’s modulus. On the other hand, from atomistic arguments it is possible to associate Young’s modulus with other material properties. These observations lead to a relationship between binding energy of atoms in a crystal (which is one of the parameters appearing in Mie-Lennard-Jones potential), speed of sound in the longitudinal direction and mass of one atom in the lattice. This subject was addressed by several authors, providing different implementations of this relation. A literature review on this topic is made and the mathematical derivation of the relation is carried out. Applications of this relationship to rare gases, some metals and some rare earths are presented and the results compared to others taken from literature.