Nanostructured Materials for Thermoelectrics

Thermoelectric materials that allow a direct conversion of temperature differences to electrical voltage and vice versa could have an important role in a global sustainable energy solution. A thermoelectric device produces a voltage when there is a temperature differences between both sides. Conversely when a external voltage is applied, a temperature difference is generated. At the atomic scale, an applied temperature gradient generates carriers (electroncs or holes) in the material, which diffuse from the hot side to the cold side, similar to a classical gas that expands when heated.

The thermoelectric effect can be used to generate electricity, to measure temperature, and to cool or heat objects. Because the direction of heating and cooling is determined by the sign of the applied voltage, thermoelectric devices make convenient temperature controllers.

The main challenge in the search for efficient materials is to optimize the electrical transport while minimizing the thermal conductivity. From a macroscopic thermodynamic point of view, the efficiency of the thermoelectric energy conversion depends on both the Carnot efficiency hc of the system and the thermoelectric figure of merit ZT = (S2s/l)T of materials constituting the thermoelectric power generating devices, where S and s are the Seebeck coefficient and the electrical conductivity and l is the total thermal conductivity (l = lL+ lE, where lL and lE are the lattice and electronic contributions, respectively). The electronic component or power factor, S2s, is typically optimized as a function of carrier concentration through doping to give the largest ZT. High-mobility carriers are desirable in order to reach a high electrical conductivity for a given carrier concentration.

What makes a good thermoelectric?

One of the problems in finding a good thermoelectric is to translate thermodynamic or physical quantities such as Carnot efficiency and fundamental material parameters such as the Seebeck coefficient and the carrier concentration into chemical composition, constituting elements, crystal structure, melting point etc.

Transport parameters. The transport parameters that appear in the figure of merit ZT, except the lattice thermal conductivity, can be expressed as functions of a band parameter (the effective mass m*), a scattering parameter (the relaxation time tE) and the Fermi energy EF. For a given m* and scattering parameter the highest ZT can be obtained for weakly degenerate semiconductors. Materials with large mass m* and high mobility (m) carriers and at the same time low lattice thermal conductivity are promising candidates for thermoelectric applications.

Crystal structure. Thus, there are two strategies to obtain highly anisotropic carrier pockets: (1) searching for anisotropic materials and (2) high symmetry crystal structure (i.e. a high density of states).

Electronegativities of the constituent atoms. A piece of information that is available for every compound of known composition are the Pauling electronegativites of the constituting elements. The average electronegativity differences over all bonds in a material are a reasonable indicator for the electrical quality of a thermoelectric material. For a large number of compounds the average electronegativity difference ΔX is correlated with the weighted mobility m(m*)3/2. This is equivalent to βlLand therefore a good measure for the electric quality of a thermoelectric. Given a very low thermal conductivity one may estimate that for ZT = 1 the weighted mobility has to be U > 150 cm2/Vs which requires a ΔX < 1, while for ZT = 2 the limits are U > 300 cm2/Vs and ΔX < 0.8. For ZT = 4 a ΔX < 0.8 would be required.

Lattice thermal conductivity. The lattice thermal conductivity – as opposed to the thermo-power, the resistivity and the electronic conductivity – is the only factor entering the figure of merit which does not relate to the electronic properties. The majority of the electronic term (lE) is related to the electrical conductivity through the Wiedemann–Franz law. A low lattice thermal conductivity is essential for a good thermoelectric material. Thermoelectrics therefore require a rather unusual material: a “phonon-glass and electron-crystal”.

Strategies to reduce thermal conductivity

The key to designing high ZT materials is to manipulate phonons and electrons at the nanoscale. Introducing defects that scatter phonons but not electrons can decrease the thermal conductivity without appreciably affecting the power factor. Let us have a look at several strategies to reduce lattice thermal conductivity that have been successfully used: (i) The first is to scatter phonons within the unit cell by creating rattling structures or point defects such as interstitials, vacancies or by alloying. Typical examples are encountered for clathrates or filled skutterudites. (ii) The second strategy is to use complex crystal structures to separate the electron-crystal from the phonon-glass. The idea in here is to achieve a phonon glass without disrupting the crystallinity of the electron-transport region. Good examples are complex “hybrid” oxides. (iii) A third strategy is to scatter phonons at interfaces, leading to the use of multiphase composites mixed on the nanometer scale. These nanostructured materials can be formed as thin-film superlattices or as intimately mixed composite structures.

Nanostructured materials. The first demonstration of proof-of-principle that a low-dimensional material system could enhance thermoelectric performance was for a 2D superlattice consisting of PbTe quantum wells and Pb1–xEuxTe barriers. Nanostructured thermoelectrics, two phase materials with a mi­crostructure on the nanometer scale, can scatter phonons on multiple length scales. This gives rise to extraordinary low thermal conductivity and high ther­moelectric efficiency.

We apply three different strategies to decrease the thermal transport in these intermetallic phases: synthesis of nanoparticles, fabrication of nanorods, and generation of nano-sized segregations of binary intermetallic phases in bulk ternary intermetallics.

We have developed a wet-chemistry route for the synthesis of nanoparticles (10– 40nm) of the binary intermetallic “Zn4Sb3”. This strategy can be extended to ternary and quaternary intermetallic phases.

1D intermetallic nanoparticles are fabricated by electrodeposition.

Based on the phase diagram we are developing routes to nanocomposites (MSby)x@MM’Sb from off-stoichiometric mixtures, e.g. M1+xM’Sb1+y·x, by applying different quenching and annealing strategies.

C. S. Birkel, E. Mugnaioli, M. Panthöfer, U. Kolb, W. Tremel, J. Am. Chem. Soc. 2010, 132, 9881–9889.