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A theory have been evolved for obtaining the second, third and fourth order elastic constants at any temperature starting from nearest neighbour distance and hardness parameter assuming Coulomb and Born Mayer potentials for face centered cubic crystals. Elastic energy density for a deformed crystal expanded as a power series of strains using Taylor’s series. Several expressions for the seconds, third and fourth order elastic constants are obtained at 0K and elevated temperature and the results are tabulated. The anharmonicities of chalcogen materials also obtained using these constants.
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