Abstract
In the present paper the M\obius inversion theorem in number theory is applied to diamond-type materials and a transform formula of the pair potential from the cohesive energy is proposed and proved. Then the phonon dispersions of these materials are calculated by the use of the calculated pair potentials. The results show that a three-body interaction is needed to agree with the experimental data. The present work indicates that the M\obius theorem can be used for diamond-type materials.
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