PHONON DISPERSIONS AND ELASTIC-CONSTANTS OF NI3AL AND MOBIUS-INVERSION

The Mobius inversion formulation corresponding to inequally weighted summations for solving some three-dimensional lattice problems introduced by Chen et al. [Phys. Lett. A 184 (1994) 347] has been used for the first time to obtain the pair potentials for fee and L1(2) structures. The derivation is exact for radial potentials not only between identical atoms, but also between distinct atoms. We have tested this formulation for Ni3Al using the empirical total energy function in the Rose model. The phonon dispersions and the elastic constants have been evaluated based on our calculated pair potentials and the results are in good agreement with the experimental data. This method shows a convenient route from electronic structure calculation or empirical formula of binding energy curve to mechanical properties of materials. It also indicates the potential application of the number theory method to condensed matter physics.