Solving the disordered structure of β-Cu2-xSe using the three-dimensional difference pair distribution function

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.

Chemical-Vapor-Deposition-Synthesized Two-Dimensional Non-Stoichiometric Copper Selenide (β-Cu2-xSe) for Ultra-Fast Tetracycline Hydrochloride Degradation under Solar Light

The high concentration of antibiotics in aquatic environments is a serious environmental issue. In response, researchers have explored photocatalytic degradation as a potential solution. Through chemical vapor deposition (CVD), we synthesized copper selenide (β-Cu2-xSe) and found it an effective catalyst for degrading tetracycline hydrochloride (TC-HCl). The catalyst demonstrated an impressive degradation efficiency of approximately 98% and a reaction rate constant of 3.14 × 10-2 min-1. Its layered structure, which exposes reactive sites, contributes to excellent stability, interfacial charge transfer efficiency, and visible light absorption capacity. Our investigations confirmed that the principal active species produced by the catalyst comprises O2- radicals, which we verified through trapping experiments and electron paramagnetic resonance (EPR). We also verified the TC-HCl degradation mechanism using high-performance liquid chromatography-mass spectrometry (LC-MS). Our results provide valuable insights into developing the β-Cu2-xSe catalyst using CVD and its potential applications in environmental remediation.

Quantitative three-dimensional local order analysis of nanomaterials through electron diffraction

Structure-property relationships in ordered materials have long been a core principle in materials design. However, the introduction of disorder into materials provides structural flexibility and thus access to material properties that are not attainable in conventional, ordered materials. To understand disorder-property relationships, the disorder - i.e., the local ordering principles - must be quantified. Local order can be probed experimentally by diffuse scattering. The analysis is notoriously difficult, especially if only powder samples are available. Here, we combine the advantages of three-dimensional electron diffraction - a method that allows single crystal diffraction measurements on sub-micron sized crystals - and three-dimensional difference pair distribution function analysis (3D-ΔPDF) to address this problem. In this work, we compare the 3D-ΔPDF from electron diffraction data with those obtained from neutron and x-ray experiments of yttria-stabilized zirconia (Zr0.82Y0.18O1.91) and demonstrate the reliability of the proposed approach.

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.

Epitaxial intergrowths and local oxide relaxations in natural bixbyite Fe2-x Mn x O3

The scattering pattern of a crystal obeys the symmetry of the crystal structure through the corresponding Laue group. This is usually also true for the diffuse scattering, containing information about disorder, but here a case is reported where the diffuse scattering is of lower symmetry than the parent crystal structure. The mineral bixbyite has been studied by X-ray and neutron scattering techniques since 1928 with some of the most recent studies characterizing the low-temperature transition to a magnetically disordered spin-glass state. However, bixbyite also exhibits structural disorder, and here single-crystal X-ray and neutron scattering is used to characterize the different modes of disorder present. One-dimensional rods of diffuse scattering are observed in the cubic mineral bixbyite, which break the expected symmetry of the scattering pattern. It is shown that this scattering arises from epitaxial intergrowths of the related mineral, braunite. The presence of this disorder mode is found to be directly observable as well-defined residuals in the average structure refined against the Bragg diffraction. An additional three-dimensional diffuse scattering component is observed in neutron scattering data, which is shown to originate from the substitutional disorder on the Fe/Mn sites. This occupational disorder gives rise to local relaxations of the oxide sublattice, and the pattern of oxide displacements can be rationalized based on crystal-field theory. The combined use of neutron and X-ray single-crystal scattering techniques highlights their great complementarity. In particular, the large sample requirements for neutron scattering experiments prove to be an obstacle in solving the intergrowth disorder due to several growth orientations, whereas for X-ray scattering the one-dimensional nature of the intergrowth disorder renders solving this a more tractable task. On the other hand, the oxide relaxations cannot be resolved using X-rays due to the low Mn/Fe contrast. By combining the two approaches both types of disorder have been characterized.

Electrically Tunable Antiferroelectric to Paraelectric Switching in a Semiconductor

The monoclinic α-Cu₂Se phase is the first multipolar antiferroelectric semiconductor identified recently by electron microscopy. As a semiconductor, although there are no delocalized electrons to form a static macroscopic polarization, a spontaneous and localized antiferroelectric polarization was found along multiple directions. In conventional ferroelectrics, the polarity can be switched by an applied electric field, and a ferroelectric to paraelectric transition can be modulated by temperature. Here, we show that a reversible and robust antiferroelectric to paraelectric switching in a Cu₂Se semiconductor can be tuned electrically by low-voltage and high-frequency electric pulses, and the structural transformations are imaged directly by transmission electron microscopy (TEM). The atomic mechanism of the transformation was assigned to an electrically triggered cation rearrangement with a low-energy barrier. Due to differences of the antiferroelectric and paraelectric phases regarding their electrical, mechanical, and optical properties, such an electrically tunable transformation has a great potential in various applications in microelectronics.

Characterizing thermoelectric stability

The limited stability of thermoelectric materials under operating conditions is a major inhibiting factor in the development of thermoelectric technology. With increasing awareness of the stability issue, many stability studies have been carried out during the past decade, and a wide range of characterization methods have been employed for evaluating stability. Here, we present a perspective on the most common characterization methods used in the thermoelectric literature for testing materials stability. Based on the parameter control and comparability to real-world conditions, we propose a division of stability tests into three overall levels to encourage more elaborate stability studies to be made with a high degree of real-world resemblance. For each level, we propose a reporting protocol to streamline the experimental information in stability studies, which will make comparison of results across studies much more reliable. We believe that these steps will help bridge the gap between fundamental materials science and actual application, which is necessary for better maturing thermoelectric technology towards broad commercialization.

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.

On single-crystal total scattering data reduction and correction protocols for analysis in direct space

Data reduction and correction steps and processed data reproducibility in the emerging single-crystal total-scattering-based technique of three-dimensional differential atomic pair distribution function (3D-ΔPDF) analysis are explored. All steps from sample measurement to data processing are outlined using a crystal of CuIr₂S₄ as an example, studied in a setup equipped with a high-energy X-ray beam and a flat-panel area detector. Computational overhead as pertains to data sampling and the associated data-processing steps is also discussed. Various aspects of the final 3D-ΔPDF reproducibility are explicitly tested by varying the data-processing order and included steps, and by carrying out a crystal-to-crystal data comparison. Situations in which the 3D-ΔPDF is robust are identified, and caution against a few particular cases which can lead to inconsistent 3D-ΔPDFs is noted. Although not all the approaches applied herein will be valid across all systems, and a more in-depth analysis of some of the effects of the data-processing steps may still needed, the methods collected herein represent the start of a more systematic discussion about data processing and corrections in this field.

Operando structural investigations of thermoelectric materials

Operando characterization provides direct insight into material response under application conditions and it is essential to understand the stability limits of thermoelectric materials and their decomposition mechanisms. An operando setup capable of maintaining a thermal gradient while running DC current through a bar-shaped sample has been developed. Under operating conditions, X-ray scattering data can be measured along the sample to obtain spatially resolved structural knowledge in concert with measurement of electrical resistance and the Seebeck coefficient. Here thermoelectric β-Zn4Sb3, which is a mixed ionic–electronic conductor, is studied, and a significant temperature dependence of the Zn migration is directly observed. Measurements with the thermal gradient applied either along or opposite to the DC current establish that the ion migration is an electrochemical effect rather than a thermodiffusion. Consideration of only the applied critical voltage or current density is insufficient for deducing the stability limits and structural integrity of materials with temperature-dependent ion mobility. The present operando setup is not limited to studies of thermoelectric materials, and it also lends itself to studies of, for example, ion diffusion in solid-state electrolytes or structural transformations in solid-state reactions.

Tuneable local order in thermoelectric crystals

Although crystalline solids are characterized by their periodic structures, some are only periodic on average and deviate on a local scale. Such disordered crystals with distinct local structures have unique properties arising from both collective and localized behaviour. Different local orderings can exist with identical average structures, making their differences hidden to Bragg diffraction methods. Using high-quality single-crystal X-ray diffuse scattering the local order in thermoelectric half-Heusler Nb1-x CoSb is investigated, for which different local orderings are observed. It is shown that the vacancy distribution follows a vacancy repulsion model and the crystal composition is found always to be close to x = 1/6 irrespective of nominal sample composition. However, the specific synthesis method controls the local order and thereby the thermoelectric properties thus providing a new frontier for tuning material properties.

A simple model for vacancy order and disorder in defective half-Heusler systems

Defective half-Heusler systems X 1-x YZ with large amounts of intrinsic vacancies, such as Nb1-x CoSb, Ti1-x NiSb and V1-x CoSb, are a group of promising thermoelectric materials. Even with high vacancy concentrations they maintain the average half-Heusler crystal structure. These systems show high electrical conductivity but low thermal conductivity arising from an ordered YZ substructure, which conducts electrons, while the large amounts of vacancies in the X substructure effectively scatters phonons. Using electron scattering, it was recently observed that, in addition to Bragg diffraction from the average cubic half-Heusler structure, some of these samples show broad diffuse scattering indicating short-range vacancy order, while other samples show sharp additional peaks indicating long-range vacancy ordering. Here it is shown that both the short- and long-range ordering can be explained using the same simple model, which assumes that vacancies in the X substructure avoid each other. The samples showing long-range vacancy order are in agreement with the predicted ground state of the model, while short-range order samples are quenched high-temperature states of the system. A previous study showed that changes in sample stoichiometry affect whether the short- or long-range vacancy structure is obtained, but the present model suggests that thermal treatment of samples should allow controlling the degree of vacancy order, and thereby the thermal conductivity, without changes in composition. This is important as the composition also dictates the amount of electrical carriers. Independent control of electrical carrier concentration and degree of vacancy order should allow further improvements in the thermoelectric properties of these systems.

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.

K-space algorithmic reconstruction (KAREN): a robust statistical methodology to separate Bragg and diffuse scattering

Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. Herein, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a `K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr4 using pair distribution function analysis.