The interatomic interaction and the phonon dispersion relations of magnesium

In the present paper, the interatomic interaction between atoms in magnesium is calculated and the phonon dispersion relations for along the major symmetry directions, T, T', Sigma, and Delta, in this metal are computed by use of a method different from the traditional ones. Instead of being fitted using the elastic constants or determined from the phonon frequencies at some special points in the first Brillouin zone, the force constants are directly calculated using the calculated potential, which is obtained from the cohesive energy by use of the Mobius theorem of number theory. This calculated interaction does not have any of the adjustable parameters that are present in the previous model potentials. The calculated phonon dispersions are compared with experiments and good agreement found.