I synthesised CuFeS2, chalcopyrite system. How to calculate phonon mean free path for this system?
That will probably depend on the mechanisms of phonon scattering that you wish to consider and the conditions in which you are interested or which constrain your (real) material.
Phonons are the (quantized) eigenmodes of lattice vibrations in the harmonic approximation. Phonon phonon interactions on the purely vibrational level are then (e.g.) linked to the presence (and density) of crystal defects or the anharmonicity of the interatomic interaction potential. The latter is also reflected in the thermal expansion coefficient of the material. So the coefficient of thermal expansion might provide a practical means to estimate the phonon lifetime (and hence "mean free path").
Have no experience with doing this, though.
If your material is metallic, then electron phonon interaction provides yet another channel to reduce the phonon lifetime. The same will in principle be true for interaction with magnetic degrees of freedom if present.
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