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

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.

Refining short-range order parameters from the three-dimensional diffuse scattering in single-crystal electron diffraction data

Our study compares short-range order parameters refined from the diffuse scattering in single-crystal X-ray and single-crystal electron diffraction data. Nb0.84CoSb was chosen as a reference material. The correlations between neighbouring vacancies and the displacements of Sb and Co atoms were refined from the diffuse scattering using a Monte Carlo refinement in DISCUS. The difference between the Sb and Co displacements refined from the diffuse scattering and the Sb and Co displacements refined from the Bragg reflections in single-crystal X-ray diffraction data is 0.012 (7) Å for the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Å for the refinement on the diffuse scattering in single-crystal electron diffraction data. As electron diffraction requires much smaller crystals than X-ray diffraction, this opens up the possibility of refining short-range order parameters in many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.

Selective Scatterings of Phonons and Electrons in Defective Half-Heusler Nb1- δ CoSb for the Figure of Merit zT > 1

The recently developed defective 19-electron half-Heusler (HH) compounds, represented by Nb1- δ CoSb, possess massive intrinsic vacancies at the cation site and thus intrinsically low lattice thermal conductivity that is desirable for thermoelectric (TE) applications. Yet the TE performance of defective HHs with a maximum figure of merit (zT) <1.0 is still inferior to that of the conventional 18-electron ones. Here, a peak zT exceeding unity is obtained at 1123 K for both Nb0.7 Ta0.13 CoSb and Nb0.6 Ta0.23 CoSb, a benchmark value for defective 19-electron HHs. The improved zT results from the achievement of selective scatterings of phonons and electrons in defective Nb0.83 CoSb, using lanthanide contraction as a design factor to select alloying elements that can strongly impede the phonon propagation but weakly disturb the periodic potential. Despite the massive vacancies induced strong point defect scattering of phonons in Nb0.83 CoSb, Ta alloying is still found effective in suppressing lattice thermal conductivity while maintaining the carrier mobility almost unchanged. In comparison, V alloying significantly deteriorates the carrier transport and thus the TE performance. These results enlarge the category of high-performance HH TE materials beyond the conventional 18-electron ones and highlight the effectiveness of selective scatterings of phonons and electrons in developing TE materials even with massive vacancies.

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.

Defect engineering in thermoelectric materials: what have we learned?

Thermoelectric energy conversion is an all solid-state technology that relies on exceptional semiconductor materials that are generally optimized through sophisticated strategies involving the engineering of defects in their structure. In this review, we summarize the recent advances of defect engineering to improve the thermoelectric (TE) performance and mechanical properties of inorganic materials. First, we introduce the various types of defects categorized by dimensionality, i.e. point defects (vacancies, interstitials, and antisites), dislocations, planar defects (twin boundaries, stacking faults and grain boundaries), and volume defects (precipitation and voids). Next, we discuss the advanced methods for characterizing defects in TE materials. Subsequently, we elaborate on the influences of defect engineering on the electrical and thermal transport properties as well as mechanical performance of TE materials. In the end, we discuss the outlook for the future development of defect engineering to further advance the TE 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.

Crystal structure and enantiomeric layer disorder of a copper(I) nitrate π-coordination compound

The novel π-coordination compound [CuI(m-dmphast)NO3], where m-dmphast = 5-(allylthio)-1-(3,5-dimethylphenyl)-1H-tetrazole, is characterized using single-crystal X-ray diffraction and crystallizes in a noncentrosymmetric space group. Additionally, for the first time in this group of materials, the streaks of X-ray diffuse scattering in the reciprocal space sections were observed and described. This gave the possibility for a deeper insight into the local structure of the title compound. The conjecture about the origin of diffuse scattering was derived from average structure solution. It was then confirmed using the local structure modelling. The extended [Cu(m-dmphast)NO3]∞ chains, connected by weak interactions, produce layers which can exist in two enantiomeric forms, one of which predominates.

Direct visualization of spatially correlated displacive short-range ordering in Nb0.8CoSb

Whether the atomic arrangement has a long-range order bifurcates solid-state matter into two major categories: crystalline and amorphous, between which lies a short-range order, a frontier research topic of fundamental and application implications. To date, it is still challenging to extract the details of short-range order from the corresponding diffuse diffraction pattern due to the phase problem. Here, we employed the high-angle annular dark field (HAADF) imaging technique to pinpoint the short-range order encoded in the one-of-a-kind diffuse the diffraction bands of defective half-Heusler Nb0.8CoSb. Utilizing a protocol based on two limiting cases, we found that the native Nb vacancies up to 20% are dominantly displacive short-range ordered yet spatially correlated. To the best of our knowledge, this is the first time that a dominantly displacive short-range order is reported at the atomic scale. These results are vital for an in-depth understanding and engineering of the thermodynamics and transport properties of the materials with abundant native defects, including but not limited to defective half-Heusler compounds.

Making sense of vacancy correlations with single-crystal diffuse scattering data

The results of Roth et al. [IUCrJ (2020). 7, 673-680] provide a clear picture of occupational correlations in half-Heusler compounds.