L. P. Bulat

Effect of boundary scattering on the thermal conductivity of a nanostructured semiconductor material based on the BixSb2 − xTe3 solid solution

This paper reports on a theoretical and experimental investigation of the behavior of the electrical and thermal conductivities of a nanostructured material based on BixSb2 − xTe3 solid solutions. The effect of boundary scattering has been taken into account by introducing the scattering mechanism with a constant mean free path equal to the nanoparticle size. A comparison with the results of the measurements has demonstrated that one can describe satisfactorily the experimental dependences of the electrical and thermal conductivities on the nanoparticle size by using only the parameters of the initial solid solution and its pure constituents. The estimates have revealed that the lattice thermal conductivity of nanostructured materials can be reduced by 20–30% as compared to the initial solid solution with nanoparticle sizes of the order of 20 nm, which should produce a favorable effect on the magnitude of the thermoelectric figure-of-merit.

The Influence of Anisotropy and Nanoparticle Size Distribution on the Lattice Thermal Conductivity and the Thermoelectric Figure of Merit of Nanostructured (Bi,Sb)2Te3

Two factors that are important for proper estimation of the thermoelectric figure of merit of bulk nanostructured materials based on bismuth telluride and its solid solutions have been investigated. First, the anisotropy of the thermoelectric properties of nanostructured (Bi,Sb)2Te3 fabricated by the spark plasma sintering (SPS) method was studied experimentally as a function of sintering temperature and pressure. Two measuring methods were used: (a) the Harman method and (b) separate measurements of electrical conductivity, Seebeck coefficient, and thermal conductivity (laser flash method). Anisotropy and transport property values obtained by these methods are compared. Secondly, the influence of the nanoparticle size distribution on the lattice thermal conductivity was taken into account theoretically for scattering of phonons both on nanoprecipitates with different compositions and orientations and on grain boundaries. The results of estimations based on different theoretical approaches (relaxation-time approximation, Monte Carlo simulations, and effective medium method) are compared using typical size distribution parameters from available experimental data.

Energy filtration of charge carriers in a nanostructured material based on bismuth telluride

The dependences of the electrical conductivity and thermopower on the size of grains in a nanocrystalline material based on Bi2Te3-Sb2Te3 solid solutions of the p type have been investigated theoretically and experimentally. The relaxation time in the case of hole scattering by nanograin boundaries in an isotropic polycrystal has been calculated taking into account the energy dependence of the probability of tunneling of charge carriers and the dependence of the scattering intensity on the nanograin size Ln. A decrease in the probability of boundary scattering with an increase in the energy of charge carriers leads to an increase in the thermopower. The dependences of the thermopower and electrical conductivity on the nanograin size, which have been obtained taking into account the boundary scattering and scattering by acoustic phonons, are in good agreement with experimental data. For the material under consideration, the thermopower coefficient increases by 10–20% compared to the initial solid solution at Ln = 20–30 nm. This can lead to an increase in the thermoelectric figure of merit by 20–40%, provided that the decrease in the electrical conductivity and the decrease in the lattice thermal conductivity compensate each other. Despite the absence of a complete compensation, it has been possible to increase the thermoelectric figure of merit for the samples under investigation to ZT = 1.10–1.12.

On fabrication of functionally graded thermoelectric materials by spark plasma sintering

A process of fabrication of thermoelectrics by the spark plasma sintering (SPS) method to obtain materials with advanced properties is simulated. The effect of the die dimensions and geometry on the temperature field distribution inside the sintered sample is analyzed. The feasibility of fabrication of functionally graded materials by the SPS process using dies of special configuration is demonstrated.

Effect of tunneling on the thermoelectric efficiency of bulk nanostructured materials

The possibility of increasing the thermoelectric figure of merit for bulk nanostructured materials has been investigated theoretically. The kinetic coefficients of the nanostructured material have been calculated and evaluated under the assumption that the dominant role in the transfer is played by the tunneling of electrons between nanoparticles. The limiting case of the absence of phonon thermal conductivity through barrier layers has been considered. It has been demonstrated using the estimates obtained for materials based on Bi2Te3 that the thermopower in the nanostructured material can be sufficiently high and that, despite the low electrical conductivity, the dimensionless thermoelectric figure of merit can be as large as 3–4 at room temperature.

Influence of grain size distribution on the lattice thermal conductivity of Bi2Te3-Sb2Te3-based nanostructured materials

The change of the lattice thermal conductivity of bulk nanostructured materials based on Bi2Te3-Sb2Te3 solid solutions with grain size distribution has been studied. These materials have a polycrystalline structure with grain sizes ranging from a few tens of a nanometer to a few micrometers. Large grains may contain inclusions or consist of several smaller parts which can be identified with coherent scattering regions seen in X-ray diffraction. The change of the lattice thermal conductivity mediated by additional scattering by inclusions and grain boundaries has been calculated. This calculation allows for the effect of nanoparticle size distribution. The calculated estimates are compared with the available experimental data.

Investigation of the possibilities for increasing the thermoelectric figure of merit of nanostructured materials based on Bi2Te3-Sb2Te3 solid solutions

The transport coefficients and thermoelectric figure of merit ZT for bulk nanostructured materials based on Bi2Te3-Sb2Te3 solid solutions have been investigated theoretically. Similar materials prepared by rapid quenching of the melt with the subsequent grinding and sintering contain amorphous and nanocrystalline regions with different sizes of particles. According to the performed estimations, the thermoelectric figure of merit of the amorphous phase can exceed the value of ZT for the initial solid solution by a factor of 2–3 primarily due to the significant decrease in the thermal conductivity. The effective transport coefficients of the medium as a whole have also been investigated as a function of the parameters of each phase, and the concentration range of the amorphous phase, which corresponds to the effective values ZT > 1, has been determined.

Temperature and current density distributions at spark plasma sintering of inhomogeneous samples

We analyze the effect of inhomogeneity in the properties of a material on the conditions of obtaining thermoelectrics by spark plasma sintering. Inclusions localized and distributed over the volume of materials with different values of electric and thermal conductivities are considered. It is found that the presence of macroscopic inhomogeneities changes the current density distribution in the cross section of the sample being sintered. It is shown that inhomogeneity in the properties of materials during sintering do not substantially affect the temperature field in the sample at the macroscopic level, but change the current density distribution profile. The ranges of variation of the current density in the regions with inhomogeneous electric and thermal conductivities are determined for various types of macroscopically inhomogeneous inclusions and their distribution. The applicability of various models for describing spark plasma sintering is considered.

Improved mechanical properties of thermoelectric (Bi0.2Sb0.8)2Te3 by nanostructuring

Temperature-dependent strength of Bi-Sb-Te under uniaxial compression is investigated. Bi-Sb-Te samples were produced by three methods: vertical zone-melting, hot extrusion, and spark plasma sintering (SPS). For zone-melted and extruded samples, the brittle-ductile transition occurs over a temperature range of 200-350 °C. In nanostructured samples produced via SPS, the transition is observed in a narrower temperature range of 170-200 °C. At room temperature, the strength of the nanostructured samples is higher than that of zone-melted and extruded samples, but above 300 °C, all samples decrease to roughly the same strength.

Temperature fields control in the process of spark plasma sintering of thermoelectrics

The process of creating thermoelectrics by spark plasma sintering of nanostructured powders in order to obtain materials with improved thermoelectric properties has been modeled. The factors that influence the distribution of thermal field in the sintering process have been analyzed. The influence of geometric parameters of tooling on the formation of temperature gradient field required for effective sintering of functionally gradient materials and segmented branches of thermo-elements has been considered. The results can be used to determine the conditions and modes of sintering of functionally gradient materials in installations of spark plasma sintering and hot pressing.