Composition Engineering of Thermoelectric Performance of High-Entropy Ge-Te Based Alloys by First Principles

The thermoelectric effect offers a promising pathway for energy harvesting through direct converting waste heat into electricity, however, it is mainly limited by the performance of thermoelectric material evaluated by figure of merit <i>ZT=S²σ/κ</i>, where <i>S</i>, <i>σ</i>, and <i>κ</i> are Seebeck coefficient, electrical conductivity, and total thermal conductivity, respectively. To pursue good thermoelectric performance, various successful strategies have been proposed to enhance electrical transport properties through the creation of ordered band structure and reduce lattice thermal conductivity by introducing disordered atomic arrangement, following the phonon-glass electron-crystal concept. However, further improvement in thermoelectric performance requires the decoupling of electrical and thermal transport properties and their simultaneous optimization.<br/><br/>High-entropy material, where a stabilized structure coexists with disordered atomic arrangement, hold tremendous potential for enhancing thermoelectric performance. This potential arises from the ability to maintain long-range order in atomic arrangement to support efficient electrical transport, while simultaneously introducing short-range disorder through lattice distortion, which effectively scatter phonons and lead to low thermal conductivity. The GeTe that stabilizes as a rhombohedral lattice at room temperature by distorting high-temperature cubic structure, has been demonstrated to exhibit high thermoelectric performance. Most recently, a significant improvement in ZT, reaching 2.7 at 750 K, has been achieved in high-entropy GeTe-based alloys. This accomplishment was realized in several sample with specific composition by increasing the entropy, which enhanced crystal symmetry to promote delocalization of electron distribution and concurrently localize phonons to effectively hinder the propagation of transverse phonons. However, the high-entropy concept also offers a means to create crystals with an extended chemical composition range, providing ample room for optimizing electronic properties by modulating phase composition and band structure across a wide spectrum of chemical composition.<br/><br/>In this study, we take a significant stride towards engineering the composition for thermoelectric performance of high-entropy GeTe-based alloys. To predict the formation energy, we employed cluster expansion to construct a machine learning model, which was trained and validated using datasets generated from first-principles calculations. Through the Monte Carlo simulation, the configurations with low formation energy were suggested by sampling the structure for various composition, incorporating silver, lead, and antimony atoms as solutes. We designed seven distinct composition-changing paths that involved the alloying of one element, two elements, and all elements, allowing the thorough investigation on the impact of alloying each individual element component as well as their collective influence on ZT. For each composition, the average ZT was calculated from five possible configurations by semi-classical Boltzmann transport theory within relaxation time approximation. The analysis of electrical transport properties through electronic band structure and charge distribution, along with the examination of thermal conductivity via phonon dispersion relations and phonon properties, unveiled the underlying mechanism responsible for the compositional dependence of ZT. This study not only demonstrates the potential for optimizing thermoelectric performance of GeTe-based alloys, but also encourages further exploration of high-entropy alloys in the future.