Violation of the Wiedemann–Franz law in some quasi-one-dimensional organic crystals
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KASIYAN, Anatolie, DASHEVSKY, Zinovi, SCHERRER, Hubert, BALMUŞ, Ion, DUSHCHAC, Viorel, NICIC, Veaceslav. Violation of the Wiedemann–Franz law in some quasi-one-dimensional organic crystals. In: Materials Science and Condensed Matter Physics, 13-17 septembrie 2010, Chișinău. Chișinău, Republica Moldova: Institutul de Fizică Aplicată, 2010, Editia 5, p. 49.
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Materials Science and Condensed Matter Physics
Editia 5, 2010
Conferința "Materials Science and Condensed Matter Physics"
Chișinău, Moldova, 13-17 septembrie 2010

Violation of the Wiedemann–Franz law in some quasi-one-dimensional organic crystals


Pag. 49-49

Kasiyan Anatolie1, Dashevsky Zinovi2, Scherrer Hubert3, Balmuş Ion1, Dushchac Viorel1, Nicic Veaceslav1
 
1 Technical University of Moldova,
2 Ben-Gurion University,
3 École des Mines de Paris–MINE
 
Disponibil în IBN: 14 aprilie 2021


Rezumat

The search of materials with a higher thermoelectric figure of merit ZT was and remains to be an important and urgent problem of solid state physics. Such materials are used in thermoelectric direct converters of energy. In spite of evident advantages of thermoelectric converters, their large application is limited by their low efficiency. The latter is determined by low ZT of used materials. In order to increase ZT, it needs to increase in the same material the electrical conductivity s, the thermopower (Seebeck coefficient) S, and to diminish the thermal conductivity k at operating temperature T. However, this strategy applied to known bulk materials has not yet produced materials with ZT > 1 at room temperature, because s, S and k are not independent each of other. In ordinary materials the increase of σ leads to the decrease of S and to the increase of carriers’ contribution ke to the total thermal conductivity k, in accordance with the Wiedemann – Franz law. Although an enormous effort has been made and a large number of materials has been investigated, the highest value of ZT at room temperature remains at the level of unity and the bulk alloys on the base of Bi2Te3 with rather low ZT ~ 0.7¸1 remain the most widely used commercial thermoelectric material. But from the theoretical point of view there is no an upper limit for ZT. Therefore, it is necessary to search new materials with more complicated internal interactions that would overcome this difficulty. The aim of this paper is to show that in quasi-one-dimensional organic crystals under certain conditions the Wiedemann–Franz law may be strongly violated. As a result, the Lorentz number may be significantly reduced in comparison with ordinary materials for a large interval of carriers’ concentrations. We consider a Q1D organic crystal of a tetragonal symmetry formed from linear chains of molecules [1]. The overlap of conduction electrons wave functions along chains is much greater than that of electrons from different chains. Accordingly, the transport mechanism along chains is of the band type and between chains is of hopping type. In the transport processes the latter is of less importance and can be neglected. Usually the ratio of longitudinal electrical conductivity along chains to the transversal one across the chains is of the order of 103. Thus, the electrons are moving in a 1D conduction band. The electronic states are described in the tight binding and nearest neighbor’s approximations. Two electron-phonon interaction mechanisms are considered simultaneously. The first interaction is similar to that of deformation potential, and the second is polaron similar, only the question is about the induced polarization. The carriers scattering on impurities is also taken into account. The relaxation time of carriers as a function of carrier energy takes the form of Lorentzian with rather pronounced maximum. The height of Lorentzian is determined by the carriers scattering on impurities. Such behavior of relaxation time is favorable for expected increase of ZT. We study the transport at temperatures T close to room temperature. At such T the scattering processes on acoustic phonons can be considered elastic. The linear kinetic equation takes the form of Boltzmann equation and is solved analytically. The electrical conductivity σ and electronic thermal conductivity ke are expressed through the transport integrals. The Lorentz number is defined as L =k e /sT . It has been modeled at room temperature for different values of Fermi energy EF, of parameter γ which is the ratio of amplitudes of above mentioned electron-phonon interactions and of parameter D that describes the scattering of carriers on impurities. It is found that the Wiedemann-Franz law is a strongly violated. The Lorentz number L is diminished into a large interval of Fermi energy and is increased in other intervals as compared with the usual values. The diminution of L is determined by the carriers with energies around the maximum of relaxation time. The contribution of these carriers to the charge transport leads to an increase of s, which achieves high maximum. Simultaneously ke grows too, but not so strongly as s, due to narrower interval of energy of carriers that give main contribution to the energy transport. The Lorenz number becomes dependent on crystal purity and may be reduced up to 10 times and even more in comparison with ordinary materials. It is favorable for thermoelectric applications of such materials.