Implications and Optimization of Domain Structures in IV-VI High-Entropy Thermoelectric Materials.

High-entropy semiconductors are now an important class of materials widely investigated for thermoelectric applications. Understanding the impact of chemical and structural heterogeneity on transport properties in these compositionally complex systems is essential for thermoelectric design. In this work, we uncover the polar domain structures in the high-entropy PbGeSnSe1.5Te1.5 system and assess their impact on thermoelectric properties. We found that polar domains induced by crystal symmetry breaking give rise to well-structured alternating strain fields. These fields effectively disrupt phonon propagation and suppress the thermal conductivity. We demonstrate that the polar domain structures can be modulated by tuning crystal symmetry through entropy engineering in PbGeSnAgxSbxSe1.5+xTe1.5+x. Incremental increases in the entropy enhance the crystal symmetry of the system, which suppresses domain formation and loses its efficacy in suppressing phonon propagation. As a result, the room-temperature lattice thermal conductivity increases from κL = 0.63 Wm-1 K-1 (x = 0) to 0.79 Wm-1 K-1 (x = 0.10). In the meantime, the increase in crystal symmetry, however, leads to enhanced valley degeneracy and improves the weighted mobility from µw = 29.6 cm2 V-1 s-1 (x = 0) to 35.8 cm2 V-1 s-1 (x = 0.10). As such, optimal thermoelectric performance can be achieved through entropy engineering by balancing weighted mobility and lattice thermal conductivity. This work, for the first time, studies the impact of polar domain structures on thermoelectric properties, and the developed understanding of the intricate interplay between crystal symmetry, polar domains, and transport properties, along with the impact of entropy control, provides valuable insights into designing GeTe-based high-entropy thermoelectrics.

Transport properties of indium-alloyed and indium telluride nanostructured bismuth telluride.

Nanostructured thermoelectric materials ideally reduce lattice thermal conductivity without harming the electrical properties. Thus, to truly improve the thermoelectric performance, the quality factor, which is proportional to the weighted mobility divided by the lattice thermal conductivity of the material, must be improved. Precipitates of In2Te3 form in the state-of-the-art Bi2Te3 with crystallographic alignment to the Bi2Te3 structure. Like epitaxy in films, this can be called endotaxy in solids. This natural epitaxy in a 3-dimensional solid is ideally situated to scatter phonons but produces minimal electronic scattering and, therefore, maintains high mobility. Here, we study the effects of In-alloying in Bi2Te3 at high In concentrations (about 4 at%), enough to produce the endotaxial microstructure. It is found that such concentrations of indium in Bi2Te3 significantly alter the electronic structure, reducing the effective mass and weighted mobility so significantly as to effectively destroy the thermoelectric properties even though the lattice thermal conductivity is successfully reduced.

Unraveling the Role of Entropy in Thermoelectrics: Entropy-Stabilized Quintuple Rock Salt PbGeSnCdxTe3+x.

Entropy-engineered materials are garnering considerable attention owing to their excellent mechanical and transport properties, such as their high thermoelectric performance. However, understanding the effect of entropy on thermoelectrics remains a challenge. In this study, we used the PbGeSnCdxTe3+x family as a model system to systematically investigate the impact of entropy engineering on its crystal structure, microstructure evolution, and transport behavior. We observed that PbGeSnTe3 crystallizes in a rhombohedral structure at room temperature with complex domain structures and transforms into a high-temperature cubic structure at ∼373 K. By alloying CdTe with PbGeSnTe3, the increased configurational entropy lowers the phase-transition temperature and stabilizes PbGeSnCdxTe3+x in the cubic structure at room temperature, and the domain structures vanish accordingly. The high-entropy effect results in increased atomic disorder and consequently a low lattice thermal conductivity of 0.76 W m-1 K-1 in the material owing to enhanced phonon scattering. Notably, the increased crystal symmetry is conducive to band convergence, which results in a high-power factor of 22.4 µW cm-1 K-1. As a collective consequence of these factors, a maximum ZT of 1.63 at 875 K and an average ZT of 1.02 in the temperature range of 300-875 K were obtained for PbGeSnCd0.08Te3.08. This study highlights that the high-entropy effect can induce a complex microstructure and band structure evolution in materials, which offers a new route for the search for high-performance thermoelectrics in entropy-engineered materials.

Printing thermoelectric inks toward next-generation energy and thermal devices.

The ability of thermoelectric (TE) materials to convert thermal energy to electricity and vice versa highlights them as a promising candidate for sustainable energy applications. Despite considerable increases in the figure of merit zT of thermoelectric materials in the past two decades, there is still a prominent need to develop scalable synthesis and flexible manufacturing processes to convert high-efficiency materials into high-performance devices. Scalable printing techniques provide a versatile solution to not only fabricate both inorganic and organic TE materials with fine control over the compositions and microstructures, but also manufacture thermoelectric devices with optimized geometric and structural designs that lead to improved efficiency and system-level performances. In this review, we aim to provide a comprehensive framework of printing thermoelectric materials and devices by including recent breakthroughs and relevant discussions on TE materials chemistry, ink formulation, flexible or conformable device design, and processing strategies, with an emphasis on additive manufacturing techniques. In addition, we review recent innovations in the flexible, conformal, and stretchable device architectures and highlight state-of-the-art applications of these TE devices in energy harvesting and thermal management. Perspectives of emerging research opportunities and future directions are also discussed. While this review centers on thermoelectrics, the fundamental ink chemistry and printing processes possess the potential for applications to a broad range of energy, thermal and electronic devices.

High Thermoelectric Performance in Chalcopyrite Cu1-xAgxGaTe2-ZnTe: Nontrivial Band Structure and Dynamic Doping Effect.

The understanding of thermoelectric properties of ternary I-III-VI2 type (I = Cu, Ag; III = Ga, In; and VI = Te) chalcopyrites is less well developed. Although their thermal transport properties are relatively well studied, the relationship between the electronic band structure and charge transport properties of chalcopyrites has been rarely discussed. In this study, we reveal the unusual electronic band structure and the dynamic doping effect that could underpin the promising thermoelectric properties of Cu1-xAgxGaTe2 compounds. Density functional theory (DFT) calculations and electronic transport measurements suggest that the Cu1-xAgxGaTe2 compounds possess an unusual non-parabolic band structure, which is important for obtaining a high Seebeck coefficient. Moreover, a mid-gap impurity level was also observed in Cu1-xAgxGaTe2, which leads to a strong temperature-dependent carrier concentration and is able to regulate the carrier density at the optimized value for a wide temperature region and thus is beneficial to obtaining the high power factor and high average ZT of Cu1-xAgxGaTe2 compounds. We also demonstrate a great improvement in the thermoelectric performance of Cu1-xAgxGaTe2 by introducing Cu vacancies and ZnTe alloying. The Cu vacancies are effective in increasing the hole density and the electrical conductivity, while ZnTe alloying reduces the thermal conductivity. As a result, a maximum ZT of 1.43 at 850 K and a record-high average ZT of 0.81 for the Cu0.68Ag0.3GaTe2-0.5%ZnTe compound are achieved.

Quantifying charge carrier localization in chemically doped semiconducting polymers.

Charge transport in semiconducting polymers ranges from localized (hopping-like) to delocalized (metal-like), yet no quantitative model exists to fully capture this transport spectrum and its dependency on charge carrier density. In this study, using an archetypal polymer-dopant system, we measure the temperature-dependent electrical conductivity, Seebeck coefficient and extent of oxidation. We then use these measurements to develop a semi-localized transport (SLoT) model, which captures both localized and delocalized transport contributions. By applying the SLoT model to published data, we demonstrate its broad utility. We are able to determine system-dependent parameters such as the maximum localization energy of the system, how this localization energy changes with doping, the amount of dopant required to achieve metal-like conductivity and the conductivity a system could have in the absence of localization effects. This proposed SLoT model improves our ability to predict and tailor electronic properties of doped semiconducting polymers.

Ultralow Thermal Conductivity in Diamondoid Structures and High Thermoelectric Performance in (Cu1-xAgx)(In1-yGay)Te2.

Owing to the diversity of composition and excellent transport properties, the ternary I-III-VI2 type diamond-like chalcopyrite compounds are attractive functional semiconductors, including as thermoelectric materials. In this family, CuInTe2 and CuGaTe2 are well investigated and achieve maximum ZT values of ∼1.4 at 950 K and an average ZT of 0.43. However, both compounds have poor electrical conductivity at low temperature, resulting in low ZT below 450 K. In this work, we have greatly improved the thermoelectric performance in the quinary diamondoid compound (Cu0.8Ag0.2)(In0.2Ga0.8)Te2 by understanding and controlling the effects of different constituent elements on the thermoelectric transport properties. Our combined theoretical and experimental effort indicates that Ga in the In site of the lattice decreases the carrier effective mass and improves the electrical conductivity and power factor of Cu0.8Ag0.2In1-xGaxTe2. Furthermore, Ag in the Cu site strongly suppresses the heat transport via the enhanced acoustic phonon-optical phonon coupling effects, leading to the ultralow thermal conductivity of ∼0.49 W m-1 K-1 at 850 K in Cu0.8Ag0.2In0.2Ga0.8Te2. Defect formation energy calculations suggest intrinsic Cu vacancies introduce defect levels that are important to the temperature-dependent hole density and electrical conductivity. Therefore, we introduced extra Cu vacancies to optimize the hole carrier density and improve the power factor of Cu0.8Ag0.2In0.2Ga0.8Te2. As a result, a maximum ZT of ∼1.5 at 850 K and an average ZT of 0.78 in the temperature range of 400-850 K are obtained, which is among the highest in the diamond-like compound family.

Na Doping in PbTe: Solubility, Band Convergence, Phase Boundary Mapping, and Thermoelectric Properties.

Many monumental breakthroughs in p-type PbTe thermoelectrics are driven by optimizing a Pb0.98Na0.02Te matrix. However, recent works found that x > 0.02 in Pb1-xNaxTe further improves the thermoelectric figure of merit, zT, despite being above the expected Na solubility limit. We explain the origins of improved performance from excess Na doping through computation and experiments on Pb1-xNaxTe with 0.01 ≤ x ≤ 0.04. High temperature X-ray diffraction and Hall carrier concentration measurements show enhanced Na solubility at high temperatures when x > 0.02 but no improvement in carrier concentration, indicating that Na is entering the lattice but is electrically compensated by high intrinsic defect concentrations. The higher Na concentration leads to band convergence between the light L and heavy Σ valence bands in PbTe, suppressing bipolar conduction and increasing the Seebeck coefficient. This results in a high temperature zT nearing 2 for Pb0.96Na0.04Te, ∼25% higher than traditionally reported values for pristine PbTe-Na. Further, we apply a phase diagram approach to explain the origins of increased solubility from excess Na doping and offer strategies for repeatable synthesis of high zT Na-doped materials. A starting matrix of simple, high performing Pb0.96Na0.04Te synthesized following our guidelines may be superior to Pb0.98Na0.02Te for continued zT optimization in p-type PbTe materials.

All-Inorganic Halide Perovskites as Potential Thermoelectric Materials: Dynamic Cation off-Centering Induces Ultralow Thermal Conductivity.

Halide perovskites are anticipated to impact next generation high performance solar cells because of their extraordinary charge transport and optoelectronic properties. However, their thermal transport behavior has received limited attention. In this work, we studied the thermal transport and thermoelectric properties of the CsSnBr3-xIx perovskites. We find a strong correlation between lattice dynamics and an ultralow thermal conductivity for series CsSnBr3-xIx reaching 0.32 Wm-1K-1 at 550 K. The CsSnBr3-xIx also possess a decent Seebeck coefficient and controllable electrical transport properties. The crystallography data and theoretical calculations suggest the Cs atom deviates from its ideal cuboctahedral geometry imposed by the perovskite cage and behaves as a heavy atom rattling oscillator. This off-center tendency of Cs, together with the distortion of SnX6 (X = Br or I) octahedra, produces a highly dynamic and disordered structure in CsSnBr3-xIx, which gives rise to a very low Debye temperature and phonon velocity. Moreover, the low temperature heat capacity data suggests strong coupling between the low frequency optical phonons and heat carrying acoustical phonons. This induces strong phonon resonance scattering that induces the ultralow lattice thermal conductivity of CsSnBr3-xIx.

Band Sharpening and Band Alignment Enable High Quality Factor to Enhance Thermoelectric Performance in n-Type PbS.

Low-cost and earth-abundant PbS-based thermoelectrics are expected to be an alternative for PbTe, and have attracted extensive attentions from thermoelectric community. Herein, a maximum ZT (ZTmax) ≈ 1.3 at 923 K in n-type PbS is obtained through synergistically optimizing quality factor with Sn alloying and PbTe phase incorporation. It is found that Sn alloying in PbS can sharpen the conduction band shape to balance the contradictory interrelationship between carrier mobility and effective mass, accordingly, a peak power factor of ∼19.8 µWcm-1K-2 is achieved. Besides band sharpening, Sn alloying can also narrow the band gap of PbS so as to make the conduction band position between Pb0.94Sn0.06S and PbTe well aligned, which can benefit high carrier mobility. Therefore, incorporating the PbTe phase into the Pb0.94Sn0.06S matrix can not only favorably maintain the carrier mobility at ∼150 cm2V-1s-1 but also suppress the lattice thermal conductivity to ∼0.61 Wm-1K-1 in Pb0.94Sn0.06S-8%PbTe, which contributes to a largely enhanced quality factor. Consequently, an average ZT (ZTave) ≈ 0.72 in 300-923 K is achieved in Pb0.94Sn0.06S-8%PbTe that outperforms other n-type PbS-based thermoelectric materials.

Contrasting SnTe-NaSbTe2 and SnTe-NaBiTe2 Thermoelectric Alloys: High Performance Facilitated by Increased Cation Vacancies and Lattice Softening.

Defect chemistry is critical to designing high performance thermoelectric materials. In SnTe, the naturally large density of cation vacancies results in excessive hole doping and frustrates the ability to control the thermoelectric properties. Yet, recent work also associates the vacancies with suppressed sound velocities and low lattice thermal conductivity, underscoring the need to understand the interplay between alloying, vacancies, and the transport properties of SnTe. Here, we report solid solutions of SnTe with NaSbTe2 and NaBiTe2 (NaSnmSbTem+2 and NaSnmBiTem+2, respectively) and focus on the impact of the ternary alloys on the cation vacancies and thermoelectric properties. We find introduction of NaSbTe2, but not NaBiTe2, into SnTe nearly doubles the natural concentration of Sn vacancies. Furthermore, DFT calculations suggest that both NaSbTe2 and NaBiTe2 facilitate valence band convergence and simultaneously narrow the band gap. These effects improve the power factors but also make the alloys more prone to detrimental bipolar diffusion. Indeed, the performance of NaSnmBiTem+2 is limited by strong bipolar transport and only exhibits modest maximum ZTs ≈ 0.85 at 900 K. In NaSnmSbTem+2 however, the doubled vacancy concentration raises the charge carrier density and suppresses bipolar diffusion, resulting in superior power factors than those of the Bi-containing analogues. Lastly, NaSbTe2 incorporation lowers the sound velocity of SnTe to give glasslike lattice thermal conductivities. Facilitated by the favorable impacts of band convergence, vacancy-augmented hole concentration, and lattice softening, NaSnmSbTem+2 reaches high ZT ≈ 1.2 at 800-900 K and a competitive average ZTavg of 0.7 over 300-873 K. The difference in ZT between two chemically similar compounds underscores the importance of intrinsic defects in engineering high-performance thermoelectrics.

Properties of galaxies reproduced by a hydrodynamic simulation.

Previous simulations of the growth of cosmic structures have broadly reproduced the 'cosmic web' of galaxies that we see in the Universe, but failed to create a mixed population of elliptical and spiral galaxies, because of numerical inaccuracies and incomplete physical models. Moreover, they were unable to track the small-scale evolution of gas and stars to the present epoch within a representative portion of the Universe. Here we report a simulation that starts 12 million years after the Big Bang, and traces 13 billion years of cosmic evolution with 12 billion resolution elements in a cube of 106.5 megaparsecs a side. It yields a reasonable population of ellipticals and spirals, reproduces the observed distribution of galaxies in clusters and characteristics of hydrogen on large scales, and at the same time matches the 'metal' and hydrogen content of galaxies on small scales.

Effect of Two-Dimensional Crystal Orbitals on Fermi Surfaces and Electron Transport in Three-Dimensional Perovskite Oxides.

Perovskite oxides are candidate materials in catalysis, fuel cells, thermoelectrics, and electronics, where electronic transport is vital to their use. While the fundamental transport properties of these materials have been heavily studied, there are still key features that are not well understood, including the temperature-squared behavior of their resistivities. Standard transport models fail to account for this atypical property because Fermi surfaces of many perovskite oxides are low-dimensional and distinct from traditional semiconductors. In this work, the low-dimensional Fermi surfaces of perovskite oxides are chemically interpreted in terms of two-dimensional crystal orbitals that form the conduction bands. Using SrTiO3 as a case study, the d/p-hybridization that creates these low-dimensional electronic structures is reviewed and connected to its fundamentally different electronic properties. A low-dimensional band model explains several experimental transport properties, including the temperature and carrier-density dependence of the effective mass, the carrier-density dependence of scattering, and the temperature dependence of resistivity. This work highlights how chemical bonding influences semiconductor transport.

Discovery of High-Performance Thermoelectric Chalcogenides through Reliable High-Throughput Material Screening.

High-throughput (HTP) material design is an emerging field and has been proved to be powerful in the prediction of novel functional materials. In this work, an HTP effort has been carried out for thermoelectric chalcogenides with diamond-like structures on the newly established Materials Informatics Platform (MIP). Specifically, the relaxation time is evaluated by a reliable yet efficient method, which greatly improves the accuracy of HTP electrical transport calculations. The results show that all the compounds may have power factors over 10 µW/cm·K2 if fully optimized. A new series of diamond-like chalcogenides with an atomic ratio of 1:2:4 possess relatively higher electrical transport properties among all the compounds investigated. One particular compound, CdIn2Te4, and its variations have been verified experimentally with a peak ZT over 1.0. Further analysis reveals the existence of general conductive networks and the similar Pisarenko relations under the same anion sublattice, and the transport distribution function is found to be a good indicator for the power factors for the compounds investigated. This work demonstrates a successful case study in HTP material screening.

Charge-transport model for conducting polymers.

The growing technological importance of conducting polymers makes the fundamental understanding of their charge transport extremely important for materials and process design. Various hopping and mobility edge transport mechanisms have been proposed, but their experimental verification is limited to poor conductors. Now that advanced organic and polymer semiconductors have shown high conductivity approaching that of metals, the transport mechanism should be discernible by modelling the transport like a semiconductor with a transport edge and a transport parameter s. Here we analyse the electrical conductivity and Seebeck coefficient together and determine that most polymers (except possibly PEDOT:tosylate) have s = 3 and thermally activated conductivity, whereas s = 1 and itinerant conductivity is typically found in crystalline semiconductors and metals. The different transport in polymers may result from the percolation of charge carriers from conducting ordered regions through poorly conducting disordered regions, consistent with what has been expected from structural studies.

Quaternary Pavonites A1+xSn2-xBi5+xS10 (A+ = Li+, Na+): Site Occupancy Disorder Defines Electronic Structure.

The field of mineralogy represents an area of untapped potential for the synthetic chemist, as there are numerous structure types that can be utilized to form analogues of mineral structures with useful optoelectronic properties. In this work, we describe the synthesis and characterization of two novel quaternary sulfides A1+xSn2-xBi5+xS10 (A = Li+, Na+). Though not natural minerals themselves, both compounds adopt the pavonite structure, which crystallizes in the C2/m space group and consists of two connected, alternating defect rock-salt slabs of varying thicknesses to create a three-dimensional lattice. Despite their commonalities in structure, their crystallography is noticeably different, as both structures have a heavy degree of site occupancy disorder that affects the actual positions of the atoms. The differences in site occupancy alter their electronic structures, with band gap values of 0.31(2) eV and 0.07(2) eV for the lithium and sodium analogues, respectively. LiSn2Bi5S10 exhibits ultralow thermal conductivity of 0.62 W m-1 K-1 at 723 K, and this result is corroborated by phonon dispersion calculations. This structure type is a promising host candidate for future thermoelectric materials investigation, as these materials have narrow band gaps and intrinsically low thermal conductivities.

Manipulating Band Structure through Reconstruction of Binary Metal Sulfide for High-Performance Thermoelectrics in Solution-Synthesized Nanostructured Bi13 S18 I2.

Reconstructing canonical binary compounds by inserting a third agent can significantly modify their electronic and phonon structures. Therefore, it has inspired the semiconductor communities in various fields. Introducing this paradigm will potentially revolutionize thermoelectrics as well. Using a solution synthesis, Bi2 S3 was rebuilt by adding disordered Bi and weakly bonded I. These new structural motifs and the altered crystal symmetry induce prominent changes in electrical and thermal transport, resulting in a great enhancement of the figure of merit. The as-obtained nanostructured Bi13 S18 I2 is the first non-toxic, cost-efficient, and solution-processable n-type material with z T=1.0.

Enhanced Strength Through Nanotwinning in the Thermoelectric Semiconductor InSb.

The conversion efficiency (zT) of thermoelectric (TE) materials has been enhanced over the last two decades, but their engineering applications are hindered by the poor mechanical properties, especially the low strength at working conditions. Here we used density functional theory (DFT) to show a strength enhancement in the TE semiconductor InSb arising from the twin boundaries (TBs). This strengthening effect leads to an 11% enhancement of the ideal shear strength in flawless crystalline InSb where this theoretical strength is considered as an upper bound on the attainable strength for a realistic material. DFT calculations reveal that the directional covalent bond rearrangements at the TB accommodating the structural mismatch lead to the anisotropic resistance against the deformation combined with the enhanced TB rigidity. This produces a strong stress response in the nanotwinned InSb. This work provides a fundamental insight for understanding the deformation mechanism of nanotwinned TE semiconductors, which is beneficial for developing reliable TE devices.

Superstrengthening Bi_{2}Te_{3} through Nanotwinning.

Bismuth telluride (Bi_{2}Te_{3}) based thermoelectric (TE) materials have been commercialized successfully as solid-state power generators, but their low mechanical strength suggests that these materials may not be reliable for long-term use in TE devices. Here we use density functional theory to show that the ideal shear strength of Bi_{2}Te_{3} can be significantly enhanced up to 215% by imposing nanoscale twins. We reveal that the origin of the low strength in single crystalline Bi_{2}Te_{3} is the weak van der Waals interaction between the Te1 coupling two Te1─Bi─Te2─Bi─Te1 five-layer quint substructures. However, we demonstrate here a surprising result that forming twin boundaries between the Te1 atoms of adjacent quints greatly strengthens the interaction between them, leading to a tripling of the ideal shear strength in nanotwinned Bi_{2}Te_{3} (0.6 GPa) compared to that in the single crystalline material (0.19 GPa). This grain boundary engineering strategy opens a new pathway for designing robust Bi_{2}Te_{3} TE semiconductors for high-performance TE devices.

Isotropic Zero Thermal Expansion and Local Vibrational Dynamics in (Sc,Fe)F3.

Scandium fluoride (ScF3) exhibits a pronounced negative thermal expansion (NTE), which can be suppressed and ultimately transformed into an isotropic zero thermal expansion (ZTE) by partially substituting Sc with Fe in (Sc0.8Fe0.2)F3 (Fe20). The latter displays a rather small coefficient of thermal expansion of -0.17 × 10-6/K from 300 to 700 K. Synchrotron X-ray and neutron pair distribution functions confirm that the Sc/Fe-F bond has positive thermal expansion (PTE). Local vibrational dynamics based on extended X-ray absorption fine structure indicates a decreased anisotropy of relative vibration in the Sc/Fe-F bond. Combined analysis proposes a delicate balance between the counteracting effects of the chemical bond PTE and NTE from transverse vibration. The present study extends the scope of isotropic ZTE compounds and, more significantly, provides a complete local vibrational dynamics to shed light on the ZTE mechanism in chemically tailored NTE compounds.