''Quantum structural diagram'' as a thermoelectric performance indicator

Abstract

The performance of a thermoelectric material is given by its so-called figure-of-merit z ˆ AE2o=o, where AE is the Seebeck coefficient, and o and o are the electrical and thermal conductivities, respectively. Since the pioneering work of Ioffe et al. [1] efforts of researchers have concentrated on identifying and developing materials with higher figures-ofmerit in order to increase the competitiveness of thermoelectric devices in generation and refrigeration applications. Crucial to the search for improved thermoelectric materials is the provision of realistic guidelines to assist in identifying materials combinations, structures and mechanisms, which can increase the thermoelectric figure-of-merit. Over the past 40 years an improved understanding of electrical and thermal transport processes has resulted in the establishment of some guidelines based upon a deterministic approach. These include: the use of point defects as a phonon scattering mechanism to increase the ratio of electrical to thermal conductivities [1]; control of the energy band gap to determine suitable operating temperature ranges of thermoelectric materials [2]; use of the material parameter in assessment of thermoelectric properties [3]; and, more recently, the study of quantum well structures [4] and multiple potential barriers [5] in identifying desirable materials structures. An alternative approach outlined in this letter, which may prove fruitful, is based upon a statistical analysis of the physical properties of known materials to identify materials’ trends which can be used to identify new thermoelectric materials. It has been reported that the thermal conductivity appears to depend upon the materials’ atomic weight and melting point [6, 7]; while the electrical conductivity exhibits some correlation with the electronegativity difference of constituent elements [8]. Recently, progress has also been reported in identifying crystal structures using a similar phenomenological approach based on a so-called ‘‘quantum structural diagram’’ (QSD) [9–12]. The applications of QSDs have also provided encouraging results in predicting ferroelectric, high-Tc superconductors and stable quasicrystals [13–15]. In this work, a similar QSD approach has been employed to identify trends in materials and provide guidelines in the search for new thermoelectric materials. The difference in electronegativities, X, of two atoms in a chemical bond determines how the electrons in the bond are shared and thus one can use the electronegativity difference to predict the type of chemical bonds. It is expected that the crystal structure and physical properties are affected by the electronegativity difference. Previous investigations by Slack [8] showed that some properties such as energy band gap and ‘‘weighted mobility’’, correlate with the electronegativity difference. As a result, X < 0.5 has been proposed as an initial screening value in the search for good thermoelectric materials. Since the electrical power factor, AE2o, is affected significantly by the ‘‘weighted mobility’’ [16], it is also expected to be related to the electronegativity difference. Fig. 1 shows the electrical power factor of bismuth based binary compounds and alloys as a function of the electronegativity difference. The materials were prepared using mechanical alloying followed by cold pressing and sintering. (Although materials prepared by the mechanical alloying exhibit thermoelectric properties which are, in general, inferior to corresponding ‘‘single crystals’’, they are satisfactory for use in comparative studies.) The Seebeck coefficient and electrical conductivity were measured at room temperature using hot probe and four probe apparatus, respectively. Binary compounds and alloys based upon tellurium, antimony or germanium have also been investigated [17]. The electrical power factors of those binary compounds and alloys exhibit a similar trend to that shown in Fig. 1. The results