Hopping Time Scales and the Phonon-Liquid Electron-Crystal Picture in Thermoelectric Copper Selenide

Ion transport induced room-temperature insulator-metal transition in single-crystalline Cu2Se

Cu2Se is a superionic conductor above 414 K, with ionic conductivities reaching that of molten salts. The superionic behavior results from hopping Cu ions between different crystallographic sites within the Se scaffold. However, the properties of Cu2Se below 414 K are far less known due to experimental limitations imposed by the bulk or polycrystalline samples that have been available so far. Here, we report the synthesis of ultra-thin, large-area single crystalline Cu2Se samples using a chemical vapor deposition method. The as-synthesized Cu2Se crystals exhibit optically and electrically detectable and controllable robust phases at room temperature and above. We demonstrate that Cu ion vacancies can be manipulated to induce an insulator-metal transition, which exhibits 6 orders of magnitude change in the electrical resistance of two terminal devices, accompanied by an optical change in the phase configuration. Our experiments show that the high mobility of the liquid-like Cu ion vacancies in Cu2Se causes macroscopic ordering in the Cu vacancies. Consequently, phase distribution over the crystals is not dictated by the diffusive motion of the ions but by the local energy minima formed due to the phase transition. As a result, long-range vacancy ordering of the crystal below 414 K becomes optically observable at a micrometer scale. This work demonstrates that Cu2Se could be a prototypical system where long-range ordering properties can be studied via electrical and optical methods.

Configurational Disorder, Strong Anharmonicity, and Coupled Host Dynamics Lead to Superionic Transport in Li3YCl6 (LYC)

In superionic crystals, liquid-like ionic diffusivities often come hand-in-hand with ultra-low thermal conductivity and soft vibrational dynamics. However, generalized relationships between ion transport and vibrational dynamics remain elusive due to the diversity of superionic materials and complex underlying mechanisms. Here, the links between vibrational dynamics and ion transport in close-packed lithium halide ion conductor Li3YCl6 (LYC) are examined using a suite of atomistic first-principles methods. It is shown that configurational disorder, lattice anharmonicity, and coupled host-mobile ion vibrational dynamics together induce a transition to the superionic state. Statistical correlations between ionic hops and activation of the distribution of vibrational modes are found. However, typical phenomena associated with superionic conductors such as selective breakdown of zone-boundary soft phonons, or long wavelength transverse acoustic modes as in the 'phonon-liquid-electron crystal' concept, are not present. Instead, anharmonic zone-boundary modes aiding Li diffusion are found to broaden and soften selectively but persist across the superionic transition. These anharmonic modes couple Li ion motion with the vibrations of the flexible close-packed anion framework, which remains stable and facilitates ionic hopping. The results provide insights into how configurational disorder and soft-yet-resilient vibrational modes enable ionic hopping, particularly in 3D close-packed crystals.

Beyond Rattling: Tetrahedrites as Incipient Ionic Conductors

Materials with ultralow thermal conductivity are crucial to many technological applications, including thermoelectric energy harvesting, thermal barrier coatings, and optoelectronics. Liquid-like mobile ions are effective at disrupting phonon propagation, hence suppressing thermal conduction. However, high ionic mobility leads to the degradation of liquid-like thermoelectric materials under operating conditions due to ion migration and metal deposition at the cathode, hindering their practical application. Here, a new type of behavior, incipient ionic conduction, which leads to ultralow thermal conductivity, while overcoming the issues of degradation inherent in liquid-like materials, is identified. Using neutron spectroscopy and molecular dynamics (MD) simulations, it is demonstrated that in tetrahedrite, an established thermoelectric material with a remarkably low thermal conductivity, copper ions, although mobile above 200 K, are predominantly confined to cages within the crystal structure. Hence the undesirable migration of cations to the cathode can be avoided. These findings unveil a new approach for the design of materials with ultralow thermal conductivity, by exploring systems in which incipient ionic conduction may be present.

Extreme phonon anharmonicity underpins superionic diffusion and ultralow thermal conductivity in argyrodite Ag8SnSe6

Ultralow thermal conductivity and fast ionic diffusion endow superionic materials with excellent performance both as thermoelectric converters and as solid-state electrolytes. Yet the correlation and interdependence between these two features remain unclear owing to a limited understanding of their complex atomic dynamics. Here we investigate ionic diffusion and lattice dynamics in argyrodite Ag8SnSe6 using synchrotron X-ray and neutron scattering techniques along with machine-learned molecular dynamics. We identify a critical interplay of the vibrational dynamics of mobile Ag and a host framework that controls the overdamping of low-energy Ag-dominated phonons into a quasi-elastic response, enabling superionicity. Concomitantly, the persistence of long-wavelength transverse acoustic phonons across the superionic transition challenges a proposed 'liquid-like thermal conduction' picture. Rather, a striking thermal broadening of low-energy phonons, starting even below 50 K, reveals extreme phonon anharmonicity and weak bonding as underlying features of the potential energy surface responsible for the ultralow thermal conductivity (<0.5 W m-1 K-1) and fast diffusion. Our results provide fundamental insights into the complex atomic dynamics in superionic materials for energy conversion and storage.

Local Sn Dipolar-Character Displacements behind the Low Thermal Conductivity in SnSe Thermoelectric

The local atomic structure of SnSe was characterized across its orthorhombic-to-orthorhombic structural phase transition using x-ray pair distribution function analysis. Substantial Sn displacements with a dipolar character persist in the high-symmetry high-temperature phase, albeit with a symmetry different from that of the ordered displacements below the transition. The analysis implies that the transition is neither order-disorder nor displacive but rather a complex crossover. Robust ferrocoupled SnSe intralayer distortions suggest a ferroelectriclike instability as the driving force. These local symmetry-lowering Sn displacements are likely integral to the ultralow lattice thermal conductivity mechanism in SnSe.

Anisotropic Phonon Scattering and Thermal Transport Property Induced by the Liquid-like Behavior of AgCrSe2

Superionic conductors exhibiting a periodic crystalline lattice and liquid-like ionic conductivity have emerged as promising materials in energy-conversion devices. Herein, we have investigated the interplay among anharmonic lattice dynamics, thermal conduction, and ultrafast atomic diffusion across the superionic transition of AgCrSe₂. We show that the thermal conductivity (κ) contributions from convection and conduction-convection interactions increase simultaneously due to the gradual fluidization of Ag atoms, leading to a temperature-independent κ in the superionic state. We demonstrate a non-Peierls type thermal transport behavior induced by the strong lattice anharmonicity of Ag atoms, which promotes a nontrivial wave-like phonon tunneling in the normal state of AgCrSe₂. Our current fluctuation analysis demonstrates an anisotropic phonon-liquid scattering behavior that the in-plane nondispersive transverse acoustic (TA) phonons near the zone boundary collapse, while the zone center and boundary TA phonons in the direction perpendicular to the liquid-like flow of Ag atoms survive.

Dynamic correlations and possible diffusion pathway in the superionic conductor Cu2-xSe

The superionic conductor Cu_2-xSe has regained interest as a thermoelectric material owing to its low thermal conductivity, suggested to arise from a liquid-like Cu substructure, and the material has been coined a phonon-liquid electron-crystal. Using high-quality three-dimensional X-ray scattering data measured up to large scattering vectors, accurate analysis of both the average crystal structure as well as the local correlations is carried out to shed light on the Cu movements. The Cu ions show large vibrations with extreme anharmonicity and mainly move within a tetrahedron-shaped volume in the structure. From the analysis of weak features in the observed electron density, the possible diffusion pathway of Cu is identified, and it is clear from its low density that jumps between sites are infrequent compared with the time the Cu ions spend vibrating around each site. These findings support the conclusions drawn from recent quasi-elastic neutron scattering data, casting doubt on the phonon-liquid picture. Although there is diffusion of Cu ions in the structure, making it a superionic conductor, the jumps are infrequent and probably not the origin of the low thermal conductivity. From three-dimensional difference pair distribution function analysis of the diffuse scattering data, strongly correlated movements are identified, showing atomic motions which conserve interatomic distances at the cost of large changes in angles.

LO-mode phonon of KCl and NaCl at 300 K by inelastic x-ray scattering measurements and first principles calculations

Longitudinal-optical (LO) mode phonon branches of KCl and NaCl were measured using inelastic x-ray scattering (IXS) at 300 K and calculated by the first-principles phonon calculation with the stochastic self-consistent harmonic approximation. Spectral shapes of the IXS measurements and calculated spectral functions agreed well. We analyzed the calculated spectral functions that provide higher resolutions of the spectra than the IXS measurements. Due to strong anharmonicity, the spectral functions of these phonon branches have several peaks and the LO modes along Γ-L paths are disconnected.

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.

Compression Induced Deformation Twinning Evolution in Liquid-Like Cu2Se

For practical applications of copper selenide (Cu₂Se) thermoelectric (TE) materials with liquid-like behavior, it is essential to determine the structure-property relations as a function of temperature. Here, we investigate β-Cu₂Se structure evolution during uniaxial compression over the temperature range of 400-1000 K using molecular dynamics simulations. We find that at temperatures above 800 K, Cu₂Se exhibits poor stability with breaking order that is described as a liquid-like or hybrid structure comprising a rigid Se sublattice and mobile Cu ions. A uniaxial load causes accumulated structural heterogeneity that is alleviated by diffusion-induced accommodation of local deformations. With increasing strain, the deformation mode changes into a combination of compression and shear, accompanied by restructuring in terms of twinning. Interestingly, in addition to a plastic behavior rarely found in inorganic semiconductors, we find that higher temperature promotes deformation twinning in liquid-like Cu₂Se, showing the role of thermal instability, including Cu diffusion, in structural adaptation and mechanical modulation. These findings reveal the micromechanism of hybrid structural evolution as well as performance tuning through twinning, which provides a theoretical guide toward advanced Cu₂Se TE materials design.

A two-dimensional type I superionic conductor

Superionic conductors possess liquid-like ionic diffusivity in the solid state, finding wide applicability from electrolytes in energy storage to materials for thermoelectric energy conversion. Type I superionic conductors (for example, AgI, Ag₂Se and so on) are defined by a first-order transition to the superionic state and have so far been found exclusively in three-dimensional crystal structures. Here, we reveal a two-dimensional type I superionic conductor, α-KAg₃Se₂, by scattering techniques and complementary simulations. Quasi-elastic neutron scattering and ab initio molecular dynamics simulations confirm that the superionic Ag⁺ ions are confined to subnanometre sheets, with the simulated local structure validated by experimental X-ray powder pair-distribution-function analysis. Finally, we demonstrate that the phase transition temperature can be controlled by chemical substitution of the alkali metal ions that compose the immobile charge-balancing layers. Our work thus extends the known classes of superionic conductors and will facilitate the design of new materials with tailored ionic conductivities and phase transitions.

Strategies for Manipulating Phonon Transport in Solids

In this review, we summarize the recent efforts on manipulating phonon transport in solids by using specific techniques that modify their phonon thermal conductivity (i.e., specific heat, phonon group velocity, and mean free path) and phonon thermal conductance (i.e., transmission probability and density of states). The strategies discussed for tuning thermal conductivity are as follows: large unit cell approach and liquid-like conduction for maneuvering specific heat; rattler, mini-bandgap, and phonon confinement for manipulating phonon group velocity; nanoparticles, nanosized grains, coated grains, alloy (isotope) scattering, selection rules in phonon dispersion, Grüneisen parameter, lone-pair electronics, dynamic disorder, and local static distortion for restricting mean free path. We have also included the discussion on tuning phonon thermal conductance, as thermal conduction can be viewed as a transmission process. Additionally, phonon filtering, ballistic transport, and waveguiding are discussed to alter density of states and transmission probability. We hope this review can bring meaningful insights to the researchers in the field of phonon transport in solids.

Blocking Ion Migration Stabilizes the High Thermoelectric Performance in Cu2 Se Composites

The applications of mixed ionic-electronic conductors are limited due to phase instability under a high direct current and large temperature difference. Here, it is shown that Cu₂ Se is stabilized through regulating the behaviors of Cu⁺ ions and electrons in a Schottky heterojunction between the Cu₂ Se host matrix and in-situ-formed BiCuSeO nanoparticles. The accumulation of Cu⁺ ions via an ionic capacitive effect at the Schottky junction under the direct current modifies the space-charge distribution in the electric double layer, which blocks the long-range migration of Cu⁺ and produces a drastic reduction of Cu⁺ ion migration by nearly two orders of magnitude. Moreover, this heterojunction impedes electrons transferring from BiCuSeO to Cu₂ Se, obstructing the reduction reaction of Cu⁺ into Cu metal at the interface and hence stabilizes the β-Cu₂ Se phase. Furthermore, incorporation of BiCuSeO in Cu₂ Se optimizes the carrier concentration and intensifies phonon scattering, contributing to the peak figure of merit ZT value of ≈2.7 at 973 K and high average ZT value of ≈1.5 between 400 and 973 K for the Cu₂ Se/BiCuSeO composites. This discovery provides a new avenue for stabilizing mixed ionic-electronic conduction thermoelectrics, and gives fresh insights into controlling ion migration in these ionic-transport-dominated materials.

Cu-Embedded SnSe2 with a High Figure of Merit at Ecofriendly Temperature

There are many studies concentrated on high-temperature performance of SnSe₂, but few studies were conducted on low-temperature properties of embedded SnSe₂. In this work, a series of SnCu _x Se₂ (x = 0, 0.01, 0.02, and 0.05) layered structures have been successfully synthesized by a melt quenching, mechanical milling process, and spark plasma sintering (SPS) method. Meanwhile, the thermal and electrical transport properties of all synthesized samples are measured. These results suggest that the embedding of Cu into SnSe₂ results in a high carrier concentration (10¹⁹/cm³). In addition, the enhancement of defect and interfacial phonon scattering caused by Cu embedding as well as the weak van der Waals force between layers makes a low thermal conductivity (0.81 W/mK) for the SnCu_0.01Se₂ at 300 K. Moreover, the maximum ZT is acquired up to 0.75 for the SnCu_0.01Se₂ sample at 300 K, which is about 2 orders of magnitude higher than the pristine sample (0.009). These features indicate that Cu-embedded SnSe₂ can be a promising thermoelectric material at gentle temperature.

Anharmonic lattice dynamics and superionic transition in AgCrSe2

Intrinsically low lattice thermal conductivity ([Formula: see text]) in superionic conductors is of great interest for energy conversion applications in thermoelectrics. Yet, the complex atomic dynamics leading to superionicity and ultralow thermal conductivity remain poorly understood. Here, we report a comprehensive study of the lattice dynamics and superionic diffusion in [Formula: see text] from energy- and momentum-resolved neutron and X-ray scattering techniques, combined with first-principles calculations. Our results settle unresolved questions about the lattice dynamics and thermal conduction mechanism in [Formula: see text] We find that the heat-carrying long-wavelength transverse acoustic (TA) phonons coexist with the ultrafast diffusion of Ag ions in the superionic phase, while the short-wavelength nondispersive TA phonons break down. Strong scattering of phonon quasiparticles by anharmonicity and Ag disorder are the origin of intrinsically low [Formula: see text] The breakdown of short-wavelength TA phonons is directly related to the Ag diffusion, with the vibrational spectral weight associated to Ag oscillations evolving into stochastic decaying fluctuations. Furthermore, the origin of fast ionic diffusion is shown to arise from extended flat basins in the energy landscape and collective hopping behavior facilitated by strong repulsion between Ag ions. These results provide fundamental insights into the complex atomic dynamics of superionic conductors.

Promising and Eco-Friendly Cu2 X-Based Thermoelectric Materials: Progress and Applications

Due to the nature of their liquid-like behavior and high dimensionless figure of merit, Cu₂ X (X = Te, Se, and S)-based thermoelectric materials have attracted extensive attention. The superionicity and Cu disorder at the high temperature can dramatically affect the electronic structure of Cu₂ X and in turn result in temperature-dependent carrier-transport properties. Here, the effective strategies in enhancing the thermoelectric performance of Cu₂ X-based thermoelectric materials are summarized, in which the proper optimization of carrier concentration and minimization of the lattice thermal conductivity are the main focus. Then, the stabilities, mechanical properties, and module assembly of Cu₂ X-based thermoelectric materials are investigated. Finally, the future directions for further improving the energy conversion efficiency of Cu₂ X-based thermoelectric materials are highlighted.

First-principles prediction of large thermoelectric efficiency in superionic Li2SnX3 (X = S, Se)

Thermoelectric materials create an electric potential when subjected to a temperature gradient and vice versa; hence they can be used to harvest waste heat into electricity and in thermal management applications. However, finding highly efficient thermoelectrics with high figures of merit, zT ≥ 1, is very challenging because the combination of a high power factor and low thermal conductivity is rare in materials. Here, we use first-principles methods to analyze the thermoelectric properties of Li2SnX3 (X = S, and Se), a recently synthesized class of lithium fast-ion conductors presenting high thermal stability. In p-type Li2SnX3, we estimate highly flat electronic valence bands that produce high Seebeck coefficients exceeding 400 μV K-1 at 700 K. In n-type Li2SnX3, the electronic conduction bands are slightly dispersive; however, the accompanying electron-acoustic phonon scattering is weak, which induces high electrical conductivity. The combination of a high Seebeck coefficient and electrical conductivity gives rise to high power factors, reaching a maximum of ∼4.5 mW m-1 K-2 at 300 K in both n-type Li2SnS3 and Li2SnSe3. Likewise, the thermal conductivity in Li2SnX3 is low as compared to conventional thermoelectric materials, 1.35-4.65 W m-1 K-1 at room temperature. As a result, we estimate a maximum zT of 1.1 in n-type Li2SnS3 at 700 K and of 2.1 (1.1) in n-type Li2SnSe3 at the same temperature (300 K). Our findings of large zT in Li2SnX3 suggest that lithium fast-ion conductors, typically employed as electrolytes in solid-state batteries, hold exceptional promise as thermoelectric materials.

Anharmonic phonon frequency and ultralow lattice thermal conductivity in β-Cu2Se liquid-like thermoelectrics

The prototype phonon-liquid electron-crystal β-Cu₂Se has been ranked among the best thermoelectric material with its ultralow lattice thermal conductivity (κ_L).

Fracture structure and thermoelectric enhancement of Cu2Se with substitution of nanostructured Ag2Se

Nano-Ag₂Se inclusions strongly impact the microstructure and resultant heat and charge carrier transport in Cu₂Se.

Phase Stability of Dynamically Disordered Solids from First Principles

Theoretical studies of phase stability in solid materials with dynamic disorder are challenging due to the failure of the standard picture of atoms vibrating around fixed equilibrium positions. Dynamically disordered solid materials show immense potential in applications. In particular, superionic conductors, where the disorder results in exceptionally high ionic conductivity, are very promising as solid state electrolytes in batteries and fuel cells. The biggest obstacle in living up to this potential is the limited stability of the dynamically disordered phases. Here, we outline a method to obtain the free energy of a dynamically disordered solid. It is based on a stress-strain thermodynamic integration on a deformation path between a mechanically stable ordered variant of the disordered phase, and the dynamically disordered phase itself. We show that the large entropy contribution associated with the dynamic disorder is captured in the behavior of the stress along the deformation path. We apply the method to Bi_{2}O_{3}, whose superionic δ phase is the fastest known solid oxide ion conductor. We accurately reproduce the experimental transition enthalpy and the critical temperature of the phase transition from the low temperature ground state α phase to the superionic δ phase. The method can be used for a first-principles description of the phase stability of superionic conductors and other materials with dynamic disorder, when the disordered phase can be connected to a stable phase through a continuous deformation path.

Thermal transport crossover from crystalline to partial-crystalline partial-liquid state

Phase-change materials (crystalline at low temperatures and partial-crystalline partial-liquid state at high temperatures) are widely used as thermoelectric converters and battery electrodes. Here, we report the underlying mechanisms driving the thermal transport of the liquid component, and the thermal conductivity contributions from phonons, vibrations with extremely short mean free path, liquid and lattice-liquid interactions in phase-changed Li₂S. In the crystalline state (T ≤ 1000 K), the temperature dependent thermal conductivity manifests two different behaviors, i.e., a typical trend of 1/T below 800 K and an even faster decrease between 800 and 1000 K. For the partial-crystalline partial-liquid Li₂S when T ≥ 1100 K, the contributions of liquid and lattice-liquid interactions increase significantly due to the fluidization of Li ions, and the vibrations with extremely short mean free path, presumably assimilated to diffusons, can contribute up to 46% of the total thermal conductivity at T = 1300 K.

Phase-change materials are applied as thermoelectric converters and battery electrodes, but underlying mechanisms are not fully understood. Here, the authors comprehensively describe thermal transport mechanisms of lithium sulfide based on molecular dynamics and first-principles simulations.

Liquid-like thermal conduction in intercalated layered crystalline solids

As a generic property, all substances transfer heat through microscopic collisions of constituent particles ¹ . A solid conducts heat through both transverse and longitudinal acoustic phonons, but a liquid employs only longitudinal vibrations^2,3. As a result, a solid is usually thermally more conductive than a liquid. In canonical viewpoints, such a difference also serves as the dynamic signature distinguishing a solid from a liquid. Here, we report liquid-like thermal conduction observed in the crystalline AgCrSe₂. The transverse acoustic phonons are completely suppressed by the ultrafast dynamic disorder while the longitudinal acoustic phonons are strongly scattered but survive, and are thus responsible for the intrinsically ultralow thermal conductivity. This scenario is applicable to a wide variety of layered compounds with heavy intercalants in the van der Waals gaps, manifesting a broad implication on suppressing thermal conduction. These microscopic insights might reshape the fundamental understanding on thermal transport properties of matter and open up a general opportunity to optimize performances of thermoelectrics.

Recent advances in inorganic material thermoelectrics

Time line of representative inorganic bulk thermoelectric materials from 1960s to the present.