In some papers, I see that the strength of the lattice anharmonicity can be estimated from the gruneisen parameters.
1. I can't understand how gruneisen parameters affect the lattice thermal conductivity.
2. Why a materials with large gruneisen parameter hold a low lattice thermal conductivity?
3. If a materials have a large negative gruneisen parameter, is the lattice thermal conductivity the same to that of the materials with large positive gruneisen parameter? are there some difference?
The answer to your questions can be found in Ziman's book Principles of the Theory of solids, Section 7.10. A quantitative relationship between the two quantities can only be derived at temperatures above the Debye temperature. There, Ziman shows that the thermal conductivity, which goes as 1/T, is inversely proportional to the square of the Grüneisen parameter, which directly answers your questions 2) and 3).
The answer to your questions can be found in Ziman's book Principles of the Theory of solids, Section 7.10. A quantitative relationship between the two quantities can only be derived at temperatures above the Debye temperature. There, Ziman shows that the thermal conductivity, which goes as 1/T, is inversely proportional to the square of the Grüneisen parameter, which directly answers your questions 2) and 3).
Grüneisen parameter shows the relationship between the thermal conductivity difference and volume
If the phonon-phonon scattering process is dominate factor in depending the lattice thermal conductivity of a material, then the lattice thermal conductivity is inversely proportional to the three phonon scattering rate which is proportional to the square of force constant anharmonicity. Consequently, a material with a large gruneisen parameter usually has small lattice thermal conductivity.
The grünenden parameter is related to the strength of phonon-phonon interacction
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