Thermoelectric (TE) materials are among very few sustainable yet feasible energy solutions of present time. This huge promise of energy harvesting is contingent on identifying/designing materials having higher efficiency than presently available ones. However, due to the vastness of the chemical space of materials, only its small fraction was scanned experimentally and/or computationally so far. Employing a compressed-sensing based symbolic regression in an active-learning framework, we have not only identified a trend in materials compositions for superior TE performance, but have also predicted and experimentally synthesized several extremely high performing novel TE materials. Among these, we found Ag$_{0.55}$Cu$_{0.45}$GaTe$_2$ to possess an experimental figure of merit as high as ~2.8 at 827 K, which is a breakthrough in the field. The presented methodology demonstrates the importance and tremendous potential of physically informed descriptors in material science, in particular for relatively small data sets typically available from experiments at well-controlled conditions.
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