Ultralow Thermal Conductivity in Chain-like TlSe Due to Inherent Tl+ Rattling

Hidden structures: a driving factor to achieve low thermal conductivity and high thermoelectric performance

The long-range periodic atomic arrangement or the lack thereof in solids typically dictates the magnitude and temperature dependence of their lattice thermal conductivity (κlat). Compared to crystalline materials, glasses exhibit a much-suppressed κlat across all temperatures as the phonon mean free path reaches parity with the interatomic distances therein. While the occurrence of such glass-like thermal transport in crystalline solids captivates the scientific community with its fundamental inquiry, it also holds the potential for profoundly impacting the field of thermoelectric energy conversion. Therefore, efficient manipulation of thermal transport and comprehension of the microscopic mechanisms dictating phonon scattering in crystalline solids are paramount. As quantized lattice vibrations (i.e., phonons) drive κlat, atomistic insights into the chemical bonding characteristics are crucial to have informed knowledge about their origins. Recently, it has been observed that within the highly symmetric 'averaged' crystal structures, often there are hidden locally asymmetric atomic motifs (within a few Å), which exert far-reaching influence on phonon transport. Phenomena such as local atomic off-centering, atomic rattling or tunneling, liquid-like atomic motion, site splitting, local ordering, etc., which arise within a few Å scales, are generally found to drastically disrupt the passage of heat carrying phonons. Despite their profound implication(s) for phonon dynamics, they are often overlooked by traditional crystallographic techniques. In this review, we provide a brief overview of the fundamental aspects of heat transport and explore the status quo of innately low thermally conductive crystalline solids, wherein the phonon dynamics is majorly governed by local structural phenomena. We also discuss advanced techniques capable of characterizing the crystal structure at the sub-atomic level. Subsequently, we delve into the emergent new ideas with examples linked to local crystal structure and lattice dynamics. While discussing the implications of the local structure for thermal conductivity, we provide the state-of-the-art examples of high-performance thermoelectric materials. Finally, we offer our viewpoint on the experimental and theoretical challenges, potential new paths, and the integration of novel strategies with material synthesis to achieve low κlat and realize high thermoelectric performance in crystalline solids via local structure designing.

Ultralow lattice thermal conductivity in type-I Dirac MBene TiB2

MBenes, the emergent novel two-dimensional family of transition metal borides have recently attracted remarkable attention. Transport studies of such two-dimensional structures are very rare and are of sparking interest. In this paper Using Boltzmann transport theory with ab-initio inputs from density functional theory, we examined the transport in TiB2MBene system, which is highly dependent on number of layers. We have shown that the addition of an extra layer (as in bilayer BL) destroys the formation of type-I Dirac state by introducing the positional change and tilt to the Dirac cones, thereby imparting the type-II Weyl metallic character in contrast to Dirac-semimetallic character in monolayer ML. Such non-trivial electronic ordering significantly impacts the transport behavior. We further show that the anisotropic room temperature lattice thermal conductivityκLfor ML (BL) is observed to be 0.41 (0.52) and 2.00 (2.04) W m-1 K-1forxandydirections, respectively, while the high temperatureκL(ML 0.13 W m-1 K-1and BL 0.21 W m-1 K-1at 900 K inxdirection) achieves ultralow values. Our analysis reveals that such values are attributed to enhanced anharmonic phonon scattering, enhanced weighted phase space and co-existence of electronic and phononic Dirac states. We have further calculated the electronic transport coefficients for TiB2MBene, where the layer dependent competing behavior is observed at lower temperatures. Our results further unravels the layer dependent thermoelectric performance, where ML is shown to have promising room-temperature thermoelectric figure of merit (ZT) as 1.71 compared to 0.38 for BL.

Three-Fold Coordination of Copper in Sulfides: A Blockade for Hole Carrier Delocalization but a Driving Force for Ultralow Thermal Conductivity

Copper-rich sulfides are very promising for energy conversion applications due to their environmental compatibility, cost effectiveness, and earth abundance. Based on a comparative analysis of the structural and transport properties of Cu3BiS3 with those of tetrahedrite (Cu12Sb4S13) and other Cu-rich sulfides, we highlight the role of the cationic coordination types and networks on the electrical and thermal properties. By precession-assisted 3D electron diffraction analysis, we find very high anisotropic thermal vibration of copper attributed to its 3-fold coordination, with an anisotropic atomic displacement parameter up to 0.09 Å2. Density functional theory calculations reveal that these Cu atoms are weakly bonded and give rise to low-energy Einstein-like vibrational modes that strongly scatter heat-carrying acoustic phonons, leading to ultralow thermal conductivity. Importantly, we demonstrate that the 3-fold coordination of copper in Cu3BiS3 and in other copper-rich sulfides constituted of interconnected CuS3 networks causes a hole blockade. This phenomenon hinders the possibility of optimizing the carrier concentration and electronic properties through mixed valency Cu+/Cu2+, differently from tetrahedrite and most other copper-rich chalcogenides, where the main interconnected Cu-S network is built of CuS4 tetrahedra. The comparison with various copper-rich sulfides demonstrates that seeking for frameworks characterized by the coexistence of tetrahedral and 3-fold coordinated copper is very attractive for the discovery of efficient thermoelectric copper-rich sulfides. Considering that lattice vibrations and carrier concentration are key factors for engineering transport phenomena (electronic, phonon, ionic, etc.) in copper-rich chalcogenides for various types of applications, our findings improve the guidelines for the design of materials enabling sustainable energy solutions with wide-ranging applications.

Pushing thermal conductivity to its lower limit in crystals with simple structures

Materials with low thermal conductivity usually have complex crystal structures. Herein we experimentally find that a simple crystal structure material AgTlI2 (I4/mcm) owns an extremely low thermal conductivity of 0.25 W/mK at room temperature. To understand this anomaly, we perform in-depth theoretical studies based on ab initio molecular dynamics simulations and anharmonic lattice dynamics. We find that the unique atomic arrangement and weak chemical bonding provide a permissive environment for strong oscillations of Ag atoms, leading to a considerable rattling behaviour and giant lattice anharmonicity. This feature is also verified by the experimental probability density function refinement of single-crystal diffraction. The particularly strong anharmonicity breaks down the conventional phonon gas model, giving rise to non-negligible wavelike phonon behaviours in AgTlI2 at 300 K. Intriguingly, unlike many strongly anharmonic materials where a small propagative thermal conductivity is often accompanied by a large diffusive thermal conductivity, we find an unusual coexistence of ultralow propagative and diffusive thermal conductivities in AgTlI2 based on the thermal transport unified theory. This study underscores the potential of simple crystal structures in achieving low thermal conductivity and encourages further experimental research to enrich the family of materials with ultralow thermal conductivity.

Chemical Bonding Tuned Lattice Anharmonicity Leads to a High Thermoelectric Performance in Cubic AgSnSbTe3

Comprehension of chemical bonding and its intertwined relation with charge carriers and heat propagation through a crystal lattice is imperative to design compounds for thermoelectric energy conversion. Here, we report the synthesis of large single crystal of new p-type cubic AgSnSbTe3 which shows an innately ultra-low lattice thermal conductivity (κlat ) of 0.47-0.27 Wm-1  K-1 and a high electrical conductivity (1238 - 800 S cm-1 ) in the temperature range 294-723 K. We investigated the origin of the low κlat by analysing the nature of the chemical bonding and its crystal structure. The interaction between Sn(5 s)/Ag(4d) and Te(5p) orbitals was found to generate antibonding states just below the Fermi level in the electronic band structure, resulting in a softening of the lattice in AgSnSbTe3 . Furthermore, the compound exhibits metavalent bonding which provides highly polarizable bonds with a strong lattice anharmonicity while maintaining the superior electrical conductivity. The electronic band structure exhibits nearly degenerate valence-band maxima that help to achieve a high Seebeck coefficient throughout the measured temperature range and, as a result, the maximum thermoelectric figure of merit reaches to ≈1.2 at 661 K in pristine single crystal of AgSnSbTe3 .

Excellent thermoelectric properties of the Tl2S3 monolayer for medium-temperature applications

Exploring materials with high thermoelectric (TE) performance can alleviate energy pressure and protect the environment, and thus, TE materials have attracted extensive attention in the new energy field. In this paper, we systematically study the TE properties of Tl₂S₃ using first-principles combined with Boltzmann transport theory (BTE). The calculation results show an excellent power factor (1.12 × 10^-2 W m^-1 K^-2) and ultra-low lattice thermal conductivity (k_l = 0.88 W m^-1 K^-1) at room temperature. Through analysis, we attribute the ultra-low k_l of Tl₂S₃ to the lower phonon group velocity (v_g) and larger phonon anharmonicity. Meanwhile, discussion of chemical bonding showed that the filling of the anti-bonding state leads to the weakening of the Tl-S chemical bond, resulting in low v_g. Furthermore, this research also investigates the scattering processes (the out-of-plane acoustic mode (ZA) + optical mode (O) → O (ZA + O → O), the in-plane transverse acoustic mode (TA) + O → O (TA + O → O), and the in-plane longitudinal acoustic mode (LA) + O → O (LA + O → O)), from which we find that 2D Tl₂S₃ possesses strong acoustic-optical scattering. Based on the analysis of electron transport properties under electron-phonon coupling, 2D Tl₂S₃, as a novel TE material, exhibits a ZT value as high as 2.8 at 400 K. Our calculations suggest that Tl₂S₃ is a potential TE material at medium temperature.

Dynamic Lone Pair Expression as Chemical Bonding Origin of Giant Phonon Anharmonicity in Thermoelectric InTe

Loosely bonded ("rattling") atoms with s² lone pair electrons are usually associated with strong anharmonicity and unexpectedly low thermal conductivity, yet their detailed correlation remains largely unknown. Here we resolve this correlation in thermoelectric InTe by combining chemical bonding analysis, inelastic X-ray and neutron scattering, and first principles phonon calculations. We successfully probe soft low-lying transverse phonons dominated by large In¹⁺ z-axis motions, and their giant anharmonicity. We show that the highly anharmonic phonons arise from the dynamic lone pair expression with unstable occupied antibonding states induced by the covalency between delocalized In¹⁺ 5s² lone pair electrons and Te 5p states. This work pinpoints the microscopic origin of strong anharmonicity driven by rattling atoms with stereochemical lone pair activity, important for designing efficient materials for thermoelectric energy conversion.

Strong Antibonding I (p)-Cu (d) States Lead to Intrinsically Low Thermal Conductivity in CuBiI4

Chemical bonding present in crystalline solids has a significant impact on how heat moves through a lattice, and with the right chemical tuning, one can achieve extremely low thermal conductivity. The desire for intrinsically low lattice thermal conductivity (κ_lat) has gained widespread attention in thermoelectrics, in refractories, and nowadays in photovoltaics and optoelectronics. Here we have synthesized a high-quality crystalline ingot of cubic metal halide CuBiI₄ and explored its chemical bonding and thermal transport properties. It exhibits an intrinsically ultralow κ_lat of ∼0.34-0.28 W m^-1 K^-1 in the temperature range 4-423 K with an Umklapp crystalline peak of 1.82 W m^-1 K^-1 at 20 K, which is surprisingly lower than other copper-based halide or chalcogenide materials. The crystal orbital Hamilton population analysis shows that antibonding states generated just below the Fermi level (E_f), which arise from robust copper 3d and iodine 5p interactions, cause copper-iodide bond weakening, which leads to reduction of the elastic moduli and softens the lattice, finally to produce extremely low κ_lat in CuBiI₄. The chemical bonding hierarchy with mixed covalent and ionic interactions present in the complex crystal structure generates significant lattice anharmonicity and a low participation ratio in low-lying optical phonon modes originating mostly from localized copper-iodide bond vibrations. We have obtained experimental evidence of these low-lying modes by low-temperature specific heat capacity measurement as well as Raman spectroscopy. The presence of strong p-d antibonding interactions between copper and iodine leads to anharmonic soft crystal lattice which gives rise to low-energy localized optical phonon bands, suppressing the heat-carrying acoustic phonons to steer intrinsically ultralow κ_lat in CuBiI₄.

Insights into Low Thermal Conductivity in Inorganic Materials for Thermoelectrics

Efficient manipulation of thermal conductivity and fundamental understanding of the microscopic mechanisms of phonon scattering in crystalline solids are crucial to achieve high thermoelectric performance. Thermoelectric energy conversion directly and reversibly converts between heat and electricity and is a promising renewable technology to generate electricity by recovering waste heat and improve solid-state refrigeration. However, a unique challenge in thermal transport needs to be addressed to achieve high thermoelectric performance: the requirement of crystalline materials with ultralow lattice thermal conductivity (κ_L). A plethora of strategies have been developed to lower κ_L in crystalline solids by means of nanostructural modifications, introduction of intrinsic or extrinsic phonon scattering centers with tailored shape and dimension, and manipulation of defects and disorder. Recently, intrinsic local lattice distortion and lattice anharmonicity originating from various mechanisms such as rattling, bonding heterogeneity, and ferroelectric instability have found popularity. In this Perspective, we outline the role of manipulation of chemical bonding and structural chemistry on thermal transport in various high-performance thermoelectric materials. We first briefly outline the fundamental aspects of κ_L and discuss the current status of the popular phonon scattering mechanisms in brief. Then we discuss emerging new ideas with examples of crystal structure and lattice dynamics in exemplary materials. Finally, we present an outlook for focus areas of experimental and theoretical challenges, possible new directions, and integrations of novel techniques to achieve low κ_L in order to realize high-performance thermoelectric materials.

High-Throughput Screening of Rattling-Induced Ultralow Lattice Thermal Conductivity in Semiconductors

Thermoelectric (TE) materials with rattling model show ultralow lattice thermal conductivity for high-efficient energy conversion between heat and electricity. In this work, by analysis of the key spirit of the rattling model, we propose an efficient empirical descriptor to realize the high-throughput screening of ultralow thermal conductivity in a series of semiconductors. This descriptor extracts the structural information of rattling atoms whose bond lengths with all the nearest neighboring atoms are larger than the sum of corresponding covalent radiuses. We obtain 1171 candidates from the Materials Project (MP) Database that contains more than 100 000 materials. Combining the empirical equation of high-throughput computation with a machine learning algorithm, we compute the approximate lattice thermal conductivities (κ_L) and find the κ_L values of 532 materials are less than 2.0 W m^-1 K^-1 at 300 K, which can be regarded as the criteria of ultralow κ_L in general. In particular, we demonstrate that halide double perovskites structures show ultralow κ_L, which provides valuable references for promising low κ_L materials in future experiments. In order to further verify our computational results, we calculate accurate κ_L for Rb₂SnBr₆ and CsCu₃O₂ as candidates with the low lattice thermal conductivity by solving the phonon Boltzmann transport equation. In particular, we demonstrate that Rb₂SnBr₆ has the lowest κ_L value of 0.1 W m^-1 K^-1 at 300 K of all known thermal conductivity materials with the rattling model so far.

A Tunable Structural Family with Ultralow Thermal Conductivity: Copper-Deficient Cu1-x□xPb1-xBi1+xS3

Understanding the mechanism that connects heat transport with crystal structures and order/disorder phenomena is crucial to develop materials with ultralow thermal conductivity (κ), for thermoelectric and thermal barrier applications, and requires the study of highly pure materials. We synthesized the n-type sulfide CuPbBi₅S₉ with an ultralow κ value of 0.6-0.4 W m^-1 K^-1 in the temperature range 300-700 K. In contrast to prior studies, we show that this synthetic sulfide does not exhibit the ordered gladite mineral structure but instead forms a copper-deficient disordered aikinite structure with partial Pb replacement by Bi, according to the chemical formula Cu_1/3□_2/3Pb_1/3Bi_5/3S₃. By combining experiments and lattice dynamics calculations, we elucidated that the ultralow κ value of this compound is due to very low energy optical modes associated with Pb and Bi ions and, to a smaller extent, Cu. This vibrational complexity at low energy hints at substantial anharmonic effects that contribute to enhance phonon scattering. Importantly, we show that this aikinite-type sulfide, despite being a poor semiconductor, is a potential matrix for designing novel, efficient n-type thermoelectric compounds with ultralow κ values. A drastic improvement in the carrier concentration and thermoelectric figure of merit have been obtained upon Cl for S and Bi for Pb substitution. The Cu_1-x□_xPb_1-xBi_1+xS₃ series provides a new, interesting structural prototype for engineering n-type thermoelectric sulfides by controlling disorder and optimizing doping.

Direct observation of one-dimensional disordered diffusion channel in a chain-like thermoelectric with ultralow thermal conductivity

Structural disorder, highly effective in reducing thermal conductivity, is important in technological applications such as thermal barrier coatings and thermoelectrics. In particular, interstitial, disordered, diffusive atoms are common in complex crystal structures with ultralow thermal conductivity, but are rarely found in simple crystalline solids. Combining single-crystal synchrotron X-ray diffraction, the maximum entropy method, diffuse scattering, and theoretical calculations, here we report the direct observation of one-dimensional disordered In1+ chains in a simple chain-like thermoelectric InTe, which contains a significant In1+ vacancy along with interstitial indium sites. Intriguingly, the disordered In1+ chains undergo a static-dynamic transition with increasing temperature to form a one-dimensional diffusion channel, which is attributed to a low In1+-ion migration energy barrier along the c direction, a general feature in many other TlSe-type compounds. Our work provides a basis towards understanding ultralow thermal conductivity with weak temperature dependence in TlSe-type chain-like materials.

Local-Disorder-Induced Low Thermal Conductivity in Degenerate Semiconductor Cu22Sn10S32

S-based semiconductors are attracting attention as environmentally friendly materials for energy-conversion applications because of their structural complexity and chemical flexibility. Here, we show that the delicate interplay between the chemical composition and cationic order/disorder allows one to stabilize a new sphalerite derivative phase of cubic symmetry in the Cu-Sn-S diagram: Cu₂₂Sn₁₀S₃₂. Interestingly, its crystal structure is characterized by a semiordered cationic distribution, with the Cu-Sn disorder being localized on one crystallographic site in a long-range-ordered matrix. The origin of the partial disorder and its influence on the electronic and thermal transport properties are addressed in detail using a combination of synchrotron X-ray diffraction, Mössbauer spectroscopy, transmission electron microscopy, theoretical modeling, and transport property measurements. These measurements evidence that this compound behaves as a pseudogap, degenerate p-type material with very low lattice thermal conductivity (0.5 W m^-1 K^-1 at 700 K). We show that localized disorder is very effective in lowering κ_L without compromising the integrity of the conductive framework. Substituting pentavalent Sb for tetravalent Sn is exploited to lower the hole concentration and doubles the thermoelectric figure of merit ZT to 0.55 at 700 K with respect to the pristine compound. The discovery of this semiordered cubic sphalerite derivative Cu₂₂Sn₁₀S₃₂ furthers the understanding of the structure-property relationships in the Cu-Sn-S system and more generally in ternary and quaternary Cu-based systems.

High thermoelectric performance enabled by convergence of nested conduction bands in Pb7Bi4Se13 with low thermal conductivity

Thermoelectrics enable waste heat recovery, holding promises in relieving energy and environmental crisis. Lillianite materials have been long-term ignored due to low thermoelectric efficiency. Herein we report the discovery of superior thermoelectric performance in Pb7Bi4Se13 based lillianites, with a peak figure of merit, zT of 1.35 at 800 K and a high average zT of 0.92 (450-800 K). A unique quality factor is established to predict and evaluate thermoelectric performances. It considers both band nonparabolicity and band gaps, commonly negligible in conventional quality factors. Such appealing performance is attributed to the convergence of effectively nested conduction bands, providing a high number of valley degeneracy, and a low thermal conductivity, stemming from large lattice anharmonicity, low-frequency localized Einstein modes and the coexistence of high-density moiré fringes and nanoscale defects. This work rekindles the vision that Pb7Bi4Se13 based lillianites are promising candidates for highly efficient thermoelectric energy conversion.

Structural, Vibrational, and Electronic Properties of 1D-TlInTe2 under High Pressure: A Combined Experimental and Theoretical Study

Analogous to 2D layered transition-metal dichalcogenides, the TlSe family of quasi-one dimensional chain materials with the Zintl-type structure exhibits novel phenomena under high pressure. In the present work, we have systematically investigated the high-pressure behavior of TlInTe₂ using Raman spectroscopy, synchrotron X-ray diffraction (XRD), and transport measurements, in combination with first principles crystal structure prediction (CSP) based on evolutionary approach. We found that TlInTe₂ undergoes a pressure-induced semiconductor-to-semimetal transition at 4 GPa, followed by a superconducting transition at 5.7 GPa (with T_c = 3.8 K). An unusual giant phonon mode (A_g) softening appears at ∼10-12 GPa as a result of the interaction of optical phonons with the conduction electrons. The high-pressure XRD and Raman spectroscopy studies reveal that there is no structural phase transitions observed up to the maximum pressure achieved (33.5 GPa), which is in agreement with our CSP calculations. In addition, our calculations predict two high-pressure phases above 35 GPa following the phase transition sequence as I4/mcm (B37) → Pbcm → Pm3̅m (B2). Electronic structure calculations suggest Lifshitz (L1 & L2-type) transitions near the superconducting transition pressure. Our findings on TlInTe₂ open up a new avenue to study unexplored high-pressure novel phenomena in TlSe family induced by Lifshitz transition (electronic driven), giant phonon softening, and electron-phonon coupling.

Intrinsically ultralow thermal conductive inorganic solids for high thermoelectric performance

Thermoelectric materials which can convert heat energy to electricity rely on crystalline inorganic solid state compounds exhibiting low phonon transport (i.e. low thermal conductivity) without much inhibiting the electrical transport. Suppression of phonons traditionally has been carried out via extrinsic pathways, involving formation of point defects, foreign nanostructures, and meso-scale grains, but the incorporation of extrinsic substituents also influences the electrical properties. Crystalline materials with intrinsically low lattice thermal conductivity (κlat) provide an attractive paradigm as it helps in simplifying the complex interrelated thermoelectric parameters and allows us to focus largely on improving the electronic properties. In this feature article, we have discussed the chemical bonding and structural aspects in determining phonon transport through a crystalline material. We have outlined how the inherent material properties like lone pair, bonding anharmonicity, presence of intrinsic rattlers, ferroelectric instability, weak and rigid substructures, etc. influence in effectively suppressing the heat transport. The strategies summarized in this feature article should serve as a general guide to rationally design and predict materials with low κlat for potential thermoelectric applications.

Syntheses of five new layered quaternary chalcogenides SrScCuSe3, SrScCuTe3, BaScCuSe3, BaScCuTe3, and BaScAgTe3: crystal structures, thermoelectric properties, and electronic structures

Five new layered transition metal-based chalcogenides (SrScCuSe3, SrScCuTe3, BaScCuSe3, BaScCuTe3, and BaScAgTe3) were discovered by the exploratory solid-state method.

First-Principles Study of Anharmonic Lattice Dynamics in Low Thermal Conductivity AgCrSe_{2}: Evidence for a Large Resonant Four-Phonon Scattering

We report a study of the anharmonic lattice dynamics in low lattice thermal conductivity (κ_{l}) material AgCrSe_{2} by many-body perturbation theory. We demonstrate surprisingly giant four-phonon scattering exclusive for the heat-carrying transverse acoustic phonons due to large quartic anharmonicity and nondispersive phonon band structure, which lead to four-phonon Fermi resonance and breaks the classical τ^{-1}∼ω^{m}T^{n} relation for phonon-phonon interactions. This strong resonant scattering extends over the Brillouin zone and substantially suppresses the thermal transport, even down to a low temperature of 100 K. The present results provide fundamental insights into the four-phonon resonant dynamics in the low-κ_{l} system with flat phonon dispersions, i.e., cuprous halides and skutterudites.

A new type of novel salt-inclusion chalcogenide with ultralow thermal conductivity

The design and development of novel chalcogenides with ultralow thermal conductivity is extremely important but very challenging for promoting the efficiencies of thermoelectric (TE) materials. Herein, a new type of salt-inclusion chalcogenide (SIC), [Rb6Cl][RE23Mn7Se44] (RE = Ho-Yb), was discovered via a modified flux method. They possessed [RESe6] and [MSe6] (M = RE/Mn) octahedra as basic building units, which interlinked to form a three-dimensional quasi-NaCl-type [RE23Mn7Se44]5- host framework, where the [Rb6Cl]5+ guest ions resided. Interestingly, these isomorphic compounds showed ultralow thermal conductivities (0.28-0.37 W m-1 K-1) at 673 K, which are reported for the first time in SICs. This work not only enriches SIC chemistry but also broadens the application of SICs in the TE field.