Soft anharmonic phonons and ultralow thermal conductivity in Mg3(Sb, Bi)2 thermoelectrics

High throughput screening of semiconductors with low lattice thermal transport induced by long-range interactions

Semiconductors with long-range interactions (LRI) due to resonant bonding exhibit delocalized electronic states and low lattice thermal conductivity, contributing to the efficiency of heat-to-electricity conversion. Here, we build a descriptor for high-throughput screening of LRI materials from the second-order interaction force constants. We identify 75 semiconducting candidates from the binary compounds in the MatHub-3d database that contain LRI. By analyzing the bonding properties of LRI atoms, we classify LRI in materials into two categories: type I and type II. In the structural unit of type I LRI, the atoms have strong bond connections, while a weak bond exists between the two groups in the structural unit of type II LRI. We have identified atypical type I LRI formed by Sb-Sb and Mg-Mg pairs in the emerging thermoelectric material Mg3Sb2, resulting in the softening of TA1 phonons and large anharmonicity. For type II LRI, the LRI of Ge-Ge and Se-Se pairs in R3m-GeSe can cross different layers. Moreover, we observe a combination of type II LRI and rattling effect in BaSe2 to restrict thermal transport. This work is of great significance for understanding the relationship between LRI and thermal transport properties, and for designing new LRI-induced low lattice thermal conductivity materials.

Thermal Property of Fullerene Fibers: One-Dimensional Material with Exceptional Thermal Performance

The recent groundbreaking achievement in the synthesis of large-sized single crystal C60 monolayer, which is covalently bonded in a plane using C60 as building blocks. The asymmetric lattice structure endows it with anisotropic phonon modes and conductivity. If these C60 are arranged in form of 1D fiber, the improved manipulation of phonon conduction along the fiber axis could be anticipated. Here, thermal properties of C60-fiber, including thermal transfer along the C60-fiber axis and across the interlayer interface are investigated using molecular dynamic simulations. Taking advantage of the distinctively hollow spherical structure of C60 building blocks, the spherical structure deformation and encapsulation induced thermal reduction can be up to 56% and 80%, respectively. By applying external electronic fields in H2O@C60 model, its thermal conductivity decreases up to 60%, which realizes the contactless thermal regulation. ln particular, the thermal rectification phenomenon is discovered by inserting atoms/molecules in C60 with a rational designed mass-gradient, and its maximum thermal rectification factor is predicted to ≈45%. These investigations aim to achieve effective regulation of the thermal conductivity of C60-fibers. This work showcases the potential of C60-fiber in the realms of thermal management and thermal sensing, paving the way to C60-based functional materials.

Inhibiting Mg Diffusion and Evaporation by Forming Mg-Rich Reservoir at Grain Boundaries Improves the Thermal Stability of N-Type Mg3 Sb2 Thermoelectrics

N-type Mg3 Sb2 -based thermoelectric materials show great promise in power generation due to their mechanical robustness, low cost of Mg, and high figure of merit (ZT) over a wide range of temperatures. However, their poor thermal stability hinders their practical applications. Here, MgB2 is introduced to improve the thermal stability of n-type Mg3 Sb2 . Enabled by MgB2 decomposition, extra Mg can be released into the matrix for Mg compensation thermodynamically, and secondary phases of Mg─B compounds can kinetically prevent Mg diffusion along grain boundaries. These synergetic effects inhibit the formation of Mg vacancies at elevated temperatures, thereby enhancing the thermal stability of n-type Mg3 Sb2 . Consequently, the Mg3.05 (Sb0.75 Bi0.25 )1.99 Te0.01 (MgB2 )0.03 sample exhibits negligible variation in thermoelectric performance during the 120-hour continuous measurement at 673 K. Moreover, the ZT of n-type Mg3 Sb2 can be maintained by adding MgB2 , reaching a high average ZT of ≈1.1 within 300-723 K. An eight-pair Mg3 Sb2 -GeTe-based thermoelectric device is also fabricated, achieving an energy conversion efficiency of ≈5.7% at a temperature difference of 438 K with good thermal stability. This work paves a new way to enhance the long-term thermal stability of n-type Mg3 Sb2 -based alloys and other thermoelectrics for practical applications.

Thermoelectric Properties of Mg3(Bi,Sb)2 under Finite Temperatures and Pressures: A First-Principles Study

Mg3Bi2-vSbv (0 ≤ v ≤ 2) is a class of promising thermoelectric materials that have a high thermoelectric performance around room temperatures, whereas their thermoelectric properties under pressures and temperatures are still illusive. In this study, we examined the influence of pressure, temperature, and carrier concentration on the thermoelectric properties of Mg3Bi2-vSbv using first-principle calculations accompanied with Boltzmann transport equations method. There is a decrease in the lattice thermal conductivity of Mg3Sb2 (i.e., v = 2) with increasing pressure. For a general Mg3Bi2-vSbv system, power factors are more effectively improved by n-type doping where electrons are the primary carriers over holes in n-type doping, and can be further enhanced by applied pressure. The figure of merit (zT) exhibits a positive correlation with temperature. A high zT value of 1.53 can be achieved by synergistically tuning the temperature, pressure, and carrier concentration in Mg3Sb2. This study offers valuable insights into the tailoring and optimization of the thermoelectric properties of Mg3Bi2-vSbv.

Lattice Thermal Conductivity of Mg3(Bi,Sb)2 Nanocomposites: A First-Principles Study

Mg3(BixSb1-x)2 (0 ≤ x ≤ 1) nanocomposites are a highly appealing class of thermoelectric materials that hold great potential for solid-state cooling applications. Tuning of the lattice thermal conductivity is crucial for improving the thermoelectric properties of these materials. Hereby, we investigated the lattice thermal conductivity of Mg3(BixSb1-x)2 nanocomposites with varying Bi content (x = 0.0, 0.25, 0.5, 0.75, and 1.0) using first-principles calculations. This study reveals that the lattice thermal conductivity follows a classical inverse temperature-dependent relationship. There is a significant decrease in the lattice thermal conductivity when the Bi content increases from 0 to 0.25 or decreases from 1.0 to 0.75 at 300 K. In contrast, when the Bi content increases from 0.25 to 0.75, the lattice thermal conductivity experiences a gradual decrease and reaches a plateau. For the nanohybrids (x = 0.25, 0.5, and 0.75), the distribution patterns of the phonon group velocity and phonon lifetime are similar, with consistent distribution intervals. Consequently, the change in lattice thermal conductivity is not pronounced. However, the phonon group speed and phonon lifetime are generally lower compared to those of the pristine components with x = 0 and x = 1.0. Our results suggest that the lattice thermal conductivity is sensitive to impurities but not to concentrations. This research provides valuable theoretical insights for adjusting the lattice thermal conductivity of Mg3(BixSb1-x)2 nanocomposites.

Mg Compensating Design in the Melting-Sintering Method For High-Performance Mg3 (Bi, Sb)2 Thermoelectric Devices

N-type Mg3 (Bi, Sb)2 -based thermoelectric (TE) alloys show great promise for solid-state power generation and refrigeration, owing to their excellent figure-of-merit (ZT) and using cheap Mg. However, their rigorous preparation conditions and poor thermal stability limit their large-scale applications. Here, this work develops an Mg compensating strategy to realize n-type Mg3 (Bi, Sb)2 by a facile melting-sintering approach. "2D roadmaps" of TE parameters versus sintering temperature and time are plotted to understand the Mg-vacancy-formation and Mg-diffusion mechanisms. Under this guidance, high weight mobility of 347 cm2  V-1  s-1 and power factor of 34 µW cm-1  K-2 can be obtained for Mg3.05 Bi1.99 Te0.01 , and a peak ZT≈1.55 at 723 K and average ZT≈1.25 within 323-723 K can be obtained for Mg3.05 (Sb0.75 Bi0.25 )1.99 Te0.01 . Moreover, this Mg compensating strategy can also improve the interfacial connecting and thermal stability of corresponding Mg3 (Bi, Sb)2 /Fe TE legs. As a consequence, this work fabricates an 8-pair Mg3 Sb2 -GeTe-based power-generation device reaching an energy conversion efficiency of ≈5.0% at a temperature difference of 439 K, and a one-pair Mg3 Sb2 -Bi2 Te3 -based cooling device reaching -10.7 °C at the cold side. This work paves a facile way to obtain Mg3 Sb2 -based TE devices at low cost and also provides a guide to optimize the off-stoichiometric defects in other TE materials.

Assessing Effects of van der Waals Corrections on Elasticity of Mg3Bi2-xSbx in DFT Calculations

As a promising room-temperature thermoelectric material, the elastic properties of Mg3Bi2-xSbx (0 ≤ x ≤ 2), in which the role of van der Waals interactions is still elusive, were herein investigated. We assessed the effects of two typical van der Waals corrections on the elasticity of Mg3Bi2-xSbx nanocomposites using first-principles calculations within the frame of density functional theory. The two van der Waals correction methods, PBE-D3 and vdW-DFq, were examined and compared to PBE functionals without van der Waals correction. Interestingly, our findings reveal that the lattice constant of the system shrinks by approximately 1% when the PBE-D3 interaction is included. This leads to significant changes in certain mechanical properties. We conducted a comprehensive assessment of the elastic performance of Mg3Bi2-xSbx, including Young's modulus, Poisson's ratio, bulk modulus, etc., for different concentration of Sb in a 40-atom simulation box. The presence or absence of van der Waals corrections does not change the trend of elasticity with respect to the concentration of Sb; instead, it affects the absolute values. Our investigation not only clarifies the influence of van der Waals correction methods on the elasticity of Mg3Bi2-xSbx, but could also help inform the material design of room-temperature thermoelectric devices, as well as the development of vdW corrections in DFT calculations.

Improved figure of merit (z) at low temperatures for superior thermoelectric cooling in Mg3(Bi,Sb)2

The low-temperature thermoelectric performance of Bi-rich n-type Mg3(Bi,Sb)2 was limited by the electron transport scattering at grain boundaries, while removing grain boundaries and bulk crystal growth of Mg-based Zintl phases are challenging due to the volatilities of elemental reactants and their severe corrosions to crucibles at elevated temperatures. Herein, for the first time, we reported a facile growth of coarse-grained Mg3Bi2-xSbx crystals with an average grain size of ~800 μm, leading to a high carrier mobility of 210 cm2 · V-1 · s-1 and a high z of 2.9 × 10-3 K-1 at 300 K. A [Formula: see text]T of 68 K at Th of 300 K, and a power generation efficiency of 5.8% below 450 K have been demonstrated for Mg3Bi1.5Sb0.5- and Mg3Bi1.25Sb0.75-based thermoelectric modules, respectively, which represent the cutting-edge advances in the near-room temperature thermoelectrics. In addition, the developed grain growth approach can be potentially extended to broad Zintl phases and other Mg-based alloys and compounds.

Atomic Local Ordering and Alloying Effects on the Mg3(Sb1-xBix)2 Thermoelectric Material

Mg3(Sb1-xBix)2 alloy has been extensively studied in the last 5 years due to its exceptional thermoelectric (TE) performance. The absence of accurate force field for inorganic alloy compounds presents great challenges for computational studies. Here, we explore the atomic microstructure, thermal, and elastic properties of the Mg3(Sb1-xBix)2 alloy at different solution concentrations through atomic simulations with a highly accurate machine learning interatomic potential (ML-IAP). We find atomic local ordering in the optimized structure with the Bi-Bi pair inclined to join adjacent layers and Sb-Sb pair preferring to stay within the same layer. The thermal conductivity changes with the solution concentrations can be correctly predicted through ML-IAP-based molecular dynamics simulations. Spectral thermal conductance analysis shows that the continuous movement of low-frequency peak to high frequency is responsible for the reduction of the thermal conductivity upon alloying. Elastic calculations reveal that similar to the thermal conductivity, solid solution alloying can reduce the overall elastic properties at both Mg3Sb2 and Mg3Bi2 ends, while anisotropic behavior is clearly observed with linear interpolation relationship upon alloying along the interlayer direction and nonlinearity along the intralayer direction. Although the atomic local ordering shows little effects on the properties of the Mg3(Sb1-xBix)2 alloy with only two alloying elements, it possesses potential important impacts on multiprincipal element inorganic TE alloys. This work provides a recipe for computational studies on the TE alloy systems and thus can accelerate the discovery and optimization of TE materials with high TE performance.

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.

Elastic Moduli: a Tool for Understanding Chemical Bonding and Thermal Transport in Thermoelectric Materials

The elastic behavior of a material can be a powerful tool to decipher thermal transport. In thermoelectrics, measuring the elastic moduli-directly tied to sound velocity-is critical to understand trends in lattice thermal conductivity, as well as study bond anharmonicity and phase transitions, given the sensitivity of elastic moduli to the chemical bonding. In this review, we introduce the basics of elasticity and explain the origin of high-temperature lattice softening from a bonding perspective. We then review elasticity data throughout classes of thermoelectrics, and explore trends in sound velocity, anharmonicity, and thermal conductivity. We reveal how experimental sound velocities can improve the accuracy of common thermal conductivity models and present a critical discussion of Grüneisen parameter estimates from elastic moduli. Readers will be equipped with tools to leverage elasticity measurements or calculations to accurately interpret thermal transport trends.

Elasticity of Mg3Bi2-xSbx

Mg₃Bi_2-xSb_x is a promising thermoelectric material working around room temperatures. Compared to electronic and thermoelectric properties, its mechanical properties are of great importance in practical applications but much less understood. Herein, we have systematically studied the elasticity of Mg₃Bi_2-xSb_x by means of first-principles calculations with a large supercell of 40 atoms. We demonstrated that the 10-atom-unitcell is undersized with improper electronic structures. With the elastic constants, we have explored the comprehensive elastic features and the three-dimensional distribution of fundamental characteristics of Young's modulus and Poisson's ratio and their variation with respect to the Sb content x. We interpolate the variation in terms of the valence electron concentration. We have further examined the hardness, ductility, anisotropicity, and Debye temperatures. The elasticity exhibits strong anisotropy where the maxima are approximately three times larger than the minima for modules. A nearly linear dependence is also observed on the Sb content except x in the vicinity of 0.5. Our atomistic insights on elasticity might be helpful in the material design of thermoelectrics with desirable mechanical properties. Our work could serve as a map for tuning the mechanical properties of Mg₃Bi_2-xSb_x and guide the possible synthesizing of novel thermoelectric material.

Solid-State Janus Nanoprecipitation Enables Amorphous-Like Heat Conduction in Crystalline Mg3 Sb2 -Based Thermoelectric Materials

Solid-state precipitation can be used to tailor material properties, ranging from ferromagnets and catalysts to mechanical strengthening and energy storage. Thermoelectric properties can be modified by precipitation to enhance phonon scattering while retaining charge-carrier transmission. Here, unconventional Janus-type nanoprecipitates are uncovered in Mg₃ Sb_1.5 Bi_0.5 formed by side-by-side Bi- and Ge-rich appendages, in contrast to separate nanoprecipitate formation. These Janus nanoprecipitates result from local comelting of Bi and Ge during sintering, enabling an amorphous-like lattice thermal conductivity. A precipitate size effect on phonon scattering is observed due to the balance between alloy-disorder and nanoprecipitate scattering. The thermoelectric figure-of-merit ZT reaches 0.6 near room temperature and 1.6 at 773 K. The Janus nanoprecipitation can be introduced into other materials and may act as a general property-tailoring mechanism.

Novel insights into lattice thermal transport in nanocrystalline Mg3Sb2 from first principles: the crucial role of higher-order phonon scattering

Zintl phase Mg₃Sb₂, which has ultra-low thermal conductivity, is a promising anisotropic thermoelectric material. It is worth noting that the prediction and experiment value of lattice thermal conductivity (κ) maintain a remarkable difference, troubling the development and application. Thus, we firstly included the four-phonon scattering processes effect and performed the Peierls-Boltzmann transport equation (PBTE) combined with the first-principles lattice dynamics to study the lattice thermal transport in Mg₃Sb₂. The results showed that our theoretically predicted κ is consistent with the experimentally measured, breaking through the limitations of the traditional calculation methods. The prominent four-phonon scatterings decreased phonon lifetime, leading to the κ of Mg₃Sb₂ at 300 K from 2.45 (2.58) W m^-1 K^-1 to 1.94 (2.19) W m^-1 K^-1 along the in (cross)-plane directions, respectively, and calculation accuracy increased by 20%. This study successfully explains the lattice thermal transport behind mechanism in Mg₃Sb₂ and implies guidance to advance the prediction accuracy of thermoelectric materials.

Enhancement of the thermoelectric properties of Zintl phase SrMg2Bi2 by Na-doping

Due to their low lattice thermal conductivity and manipulable electronic properties, AB₂X₂ Zintl phases have been widely studied for thermoelectric applications. This has motivated numerous efforts to focus on the exploration of novel AB₂X₂ Zintl thermoelectrics. In this study, SrMg₂Bi₂ was systematically investigated to reveal its potential for thermoelectric application. Pristine SrMg₂Bi₂ exhibits an intrinsic p-type semiconducting behavior. The Hall carrier concentration (n_H) was efficiently increased to ∼9 × 10¹⁹ cm^-3 by Na-substitution at the Sr site. The increased n_H leads to enhanced electrical conductivity, but reduced Seebeck coefficient. Moreover, Na doping effectively decreased the thermal conductivity because of the intensified scattering from defects and lattice distortion. Thus, the zT of the Na-doped SrMg₂Bi₂ can reach 0.44 and be extremely higher than that of the pristine one. The well-known single parabolic band (SPB) model estimated that the increase in N_v and m* through doping boosts the electrical conductivity. This work sheds light on the discovery of new prospective thermoelectric materials and demonstrates that Bi-based p-type AB₂X₂ Zintl phases can achieve high thermoelectric performance.