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## Giant Thermoelectric Effect (GTE) in Graded Porous Micro-nanostructured Thermoelectric Materials

The efficiency of thermoelectric materials can be described in terms of the dimensionless figure-of-merit ZT = oS2T/K, where σ is the electrical conductivity, S the Seebeck coefficient, T the temperature and κ the total thermal conductivity. The key ideas for improving the efficiency of thermoelectric devices are connected with the enhancement of the power factor P=oS2 and reduction in the thermal conductivity K=KL+Ke, where Ke is the contribution of the free charge carriers and KL is the lattice thermal conductivity (LTC).

Among various types of thermoelectric materials, porous media play an important role and represent a highly dynamic research area that aims at the creation of the next generation of efficient solid-state thermoelectric energy conversion devices. In this work we report of opportunities for the reduction in LTC of graded porous nanostructures with inhomogeneous porosity. We employ the effective medium theory to calculate the LTC of a porous media with spherical or cylindrical hole pores of variable radius and show that the filling fraction and the pore diameters play a major role in the thermal conductivity reduction. This reduction is caused by enhanced scattering of thermal phonons with the pore boundaries. Thus, high frequency phonons are scattered by small pores while low frequency phonons having longer wavelengths are scattering by bigger pores.

It means that porous materials with inhomogeneous porosity are expected to have stronger reduction in thermal conductivity than that with pores of equal sizes The variation of the KL o and S as a function of porosity, pore sizes and the number of pore groups with different sizes have been studied. A reduction of K can reach values of more than 100, without too much reduction of the electrical conductivity. An small enhancement of the Seebeck coefficient is also calculated based on the reduction of the charge carriers. A condition is found at which the reduction in KL of a composite with ordered inhomogeneous porosity is much more effective than that in the case of homogeneous porosity. We have used data from literature in order to validate our results and we found excellent agreement.

Work performed in collaboration with R.H. Tarkhanyan and A. Ioannidou and supported by the Project NEXTEC of the EU.