A chemical appproach to the first-principles modeling of novel thermoelectric materials

Competitive thermoelectric (TE) materials have a high figure of merit ZT, defined as ZT=(?2?/?)oT. The Seebeck coefficient ?, the electrical conductivity ?, and the total thermal conductivity ?, given by the sum of the lattice and the electronic contributions ?L and ?e, are all critically dependent on the geometry and the electronic band structure, whose detailed understanding is therefore crucial. The theoretical tools coming from physics (bands) and chemistry (bonds) might appear contradictory in describing solid state systems, especially when the relevant properties are tuned by doping, native defects, and nanostructuring. Indeed, it is possible to account for these effects either by considering the perturbations they induce on the electronic band structure, or by viewing the defect as real space local modification of the crystal atomic structure and of the bonding network. Most experimental techniques to study bulk materials recover information on the geometric and electronic structure as a space-time average over the entire sample, or at least a nanoscale portion of it, and the total experimental duration. In TE materials positional disorder and defects play a fundamental role, and therefore the main interpretative effort is to deconvolve the experimental information, and to establish the relations between local structural arrangement within the crystal cells and transport bulk properties. To this respect, the theoretical modeling proves very useful, especially when combined with the appropriate experiments, as shown for a number of cases in this chapter. First we discuss the role of guest-host interactions in type I inorganic clathrates. Second, we present the theoretical modeling of doping in Co4Sb12 skutterudites. Finally, we outline the recovery of the atomistic structure of a quite disordered material, the ? phase of zinc antimonides, by combining an experimental X-Rays Diffraction (XRD) study and theoretical computations. A number of investigative tools, encompassing both those typical of solid state physics and of chemical understanding were adopted. The electronic band structure of these materials was obtained with fully periodic Density Functional Theory computations and within the linear combination of atomic orbitals formalism, as implemented in the CRYSTAL98 code1. Gradient corrected density functionals and Gaussian basis sets especially designed for each system were used. In general, both the electronic structure of the ideal crystal and of its defective modifications were computed, so as to determine by first principles the relations between doping element, local defective structure, and electronic transport properties. These latter were evaluated according to the Boltzmann's semi-classical formalism,2 as a continuum function of the charge carriers' concentration, and using either the electron bands of the unperturbed or of the fully doped defective system within the frozen band approximation. These calculations were performed with the ELTRAP3 code, interfaced with CRYSTAL98. The frozen band approximation accounts for the actual doping level by filling or emptying out the electronic bands of the reference system and it is the more justified the lower the doping level is. A complementary description was also adopted, closer to the chemists' point of view and given by the direct space analysis of the materials Electron Density Distributions (EDD) within the formalism of the Quantum Theory of Atoms In Molecules (QTAIM).4 This theory is firmly rooted in quantum mechanics, defines atomic subsystems whose properties are determined by physics and, contrary to more conventional methods of analysis, makes no use of any Hilbert space partitioning to extract information from the wavefunction. More importantly, the QTAIM recovers the concepts of atom and bond, which are cornerstones of chemical thinking, on an unambiguous basis. The QTAIM analysis was carried out using the TOPOND98 code,5 interfaced with CRYSTAL98.