(Invited) Computation-Driven Materials Search for Thermoelectric Applications

Solid-state thermoelectric (TE) devices have the ability to directly convert heat into electricity for power generation.  Despite its many energy-harvesting applications, the potential impact of TE technology is largely hindered by the relatively low performance of commercial materials. In physics, the effectiveness of TE materials is evaluated by their TE figure of merit (ZT), defined as ZT = S²σT/k, where S, σ, k, and T represent Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively.  Here k can be further split into the lattice contribution k_L and electronic contribution k_E.  Within the same material, challenge exists in obtaining a low k but a high power factor S²σ.  As the result, ZTs of commercial materials are still around unity after decades of research though ZT>2 is preferred for TE to compete with other technologies.

Along this line, nanostructured bulk materials, which are synthesized by hot pressing nanopowder into a bulk material, have been widely studied as an effective approach to improve ZTs of existing or novel materials [1]. By introducing nanostructured interfaces within a bulk material, the interdependent electron and phonon transport can be decoupled to dramatically reduce k_L but still maintain S²σ, resulting in enhanced ZT.  Unrestricted to conventional materials, this approach may also lead to high ZTs in unconventional TE materials with both a high S²σ and a high k_L, such as bulk Si [2,3].  This will reach beyond conventional materials that heavily depend on toxic, rare, and expensive elements, e.g. Te.  Based on the nanostructuring approach, broad material search is in urgent need for novel TE materials using nontoxic, cheap, and abundant elements. 

For computation-driven TE material search, challenge generally exists in accurately predicting the energy-dependent electron and phonon mean free paths (MFPs) for TE property predictions.  For phonon transport, there exist first-principles-based studies for standard materials such as Si and Ge. However, such calculations are intrinsically very time-consuming and are limited to relatively simple material structures. On the other hand, first-principles electrical property predictions are also restricted to well-studied materials and are thus unsuitable for high-throughput material search, in which thousands of complicated materials will be screened based on the computed ZTs.  As the result, highthroughput TE material search is mostly based on S²σ/τ or ZTs further estimated with guessed k_L/τ values [4-6], in which τ is the averaged relaxation time of all charge carriers.  For materials screening, experimental inputs of σ and k_Lare often required and the guidance from computations becomes very limited.   

For nanograined bulk materials synthesized by hot press, however, the need of computing electron and phonon MFPs can be eliminated when these MFPs are largely restricted by the grain size.  In such materials, the optimum grain size should be larger than electron MFPs but shorter than phonon MFPs to reduce k_L without deteriorating σ.  The maximum ZT is anticipated when the grain size is reduced to the majority electron MFPs, called the small-grain-size (SGS) limit for nanograined bulk materials [7].  This simple treatment has been used to compare the power factor of new TE materials [8] but no ZTs are computed without phonon calculations. In this work, we propose a ZT formulation of general materials under the SGS limit, which is solely based on phonon dispersions and electronic band structures predicted by first-principles calculations. The materials search is demonstrated with representative oxides that can be potentially used for high-temperature energy harvesting.

References:

[1]          A. J. Minnich, M. S. Dresselhaus, Z. F. Ren, and G. Chen, Energy & Environmental Science 2, 466 (2009).

[2]          S. K. Bux, R. G. Blair, P. K. Gogna, H. Lee, G. Chen, M. S. Dresselhaus, R. B. Kaner, and J.-P. Fleurial, Advanced Functional Materials 19, 2445 (2009).

[3]          Q. Hao, G. Zhu, G. Joshi, X. Wang, A. Minnich, Z. Ren, and G. Chen, Applied Physics Letters 97, 063109 (2010).

[4]          I. Opahle, G. K. H. Madsen, and R. Drautz, Physical Chemistry Chemical Physics 14, 16197 (2012).

[5]          O. Ingo, P. Alessandro, J. M. Eunan, D. Ralf, and H. M. Georg K New Journal of Physics 15, 105010 (2013).

[6]          G. K. Madsen, Journal of the American Chemical Society 128, 12140 (2006).

[7]          C. Bera, M. Soulier, C. Navone, G. Roux, J. Simon, S. Volz, and N. Mingo, Journal of Applied Physics 108, 124306 (2010).

[8]          S. Wang, Z. Wang, W. Setyawan, N. Mingo, and S. Curtarolo, Physical Review X 1, 021012 (2011).