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 t
he 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
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