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Can phonons of solid solutions be calculated?

Indeed the supercell approach in the present formulation can only approximatelly treat solid solutions. Typicaly, one takes a few combinations of the atomic distribution in supercell (usually 1 - 5 supercells). It is wise to find these combinations for which the supercells possess the lowest ground state energy. The configurational entropy should be taken into acount by other approach. However, calculation of phonons can give a good estimate how much the atomic vibrations contribute to thermodynamic functions and possible phases. Such a treatment can be used to construct the phase diagram.