Computational and theoretical studies on lattice thermal conductivity and thermal properties of silicon clathrates

Abstract

The lattice thermal conductivity is usually an intrinsic property in the study of thermoelectricity. In particular, relatively low lattice thermal conductivity is usually a desired feature when higher thermoelectric efficiency is pursued. The mechanisms which lower the lattice thermal conductivity are not known in sufficient detail and deeper understanding about the phenomena is needed and if such understanding is achieved it can be used to design more efficient thermoelectric materials. In this thesis, the lattice thermal conductivity and other thermal properties of several silicon clathrates, which are known to be promising candidates for the thermoelectric applications, are studied by theoretical and computational techniques. The studied clathrates were the silicon clathrate frameworks I, II, IV, V, VII, VIII (Si23), H and the semiconducting (Zintl) clathrates [Si19P4]Cl4 and Na4[Al4Si19]. The relevance of seemingly unrelated phenomena such as the negative thermal expansion on the lattice thermal conductivity was studied.

The harmonic phonon dispersion relations of the studied structures were investigated. In particular, the number of the so-called phonon band gaps was found to be two in the case of the silicon clathrate framework V differing in this respect from the other structures studied. In general, it was found that all the other clathrates, except VII and Na4[Al4Si19], have rather similar phonon dispersion relations. Also, an anomalous negative thermal expansion temperature range was found for the silicon clathrate framework VII, which appears to be mostly due to stronger third-order interatomic force constants.

At 300 K, the lattice thermal conductivity of the clathrate Na4[Al4Si19] was found to be about ten times smaller than obtained for the clathrate [Si19P4]Cl4 which possess the same space group symmetry than the former. It appears that the main reason for the preceding is in the second-order interatomic force constants of the clathrate Na4[Al4Si19], which change the phonon spectrum such that the phonon group velocities are lower and the anharmonicity of the lattice increases, which in turn leads to the reduction in the relaxation times of acoustic phonons. The results indicate, that the effect of harmonic quantities can be rather large on the anharmonicity of two similar crystals and may lead to one-order lower lattice thermal conductivities, even when there are no such large differences in the third-order interatomic force constants.

Expressions to calculate different elastic and thermal properties of crystal were derived by using the technique of many-body Green’s functions and many-body perturbation theory. The expressions derived extend the existing results and allow a systematic study of elastic and thermal properties of crystals. For instance, the results obtained can be used to calculate the kth-order elastic constants such that the so-called phonon contribution is taken into account, a contribution which is usually neglected in the computational studies applied to real materials at the present