Local Structure and Dynamics in MPt(CN)6 Prussian Blue Analogues.

We use a combination of X-ray pair distribution function (PDF) measurements, lattice dynamical calculations, and ab initio density functional theory (DFT) calculations to study the local structure and dynamics in various MPt(CN)6 Prussian blue analogues. In order to link directly the local distortions captured by the PDF with the lattice dynamics of this family, we develop and apply a new "interaction-space" PDF refinement approach. This approach yields effective harmonic force constants, from which the (experiment-derived) low-energy phonon dispersion relations can be approximated. Calculation of the corresponding Grüneisen parameters allows us to identify the key modes responsible for negative thermal expansion (NTE) as arising from correlated tilts of coordination octahedra. We compare our results against the phonon dispersion relations determined using DFT calculations, which identify the same NTE mechanism.

Cluster dynamics of heterometallic trinuclear clusters during ligand substitution, redox chemistry, and group transfer processes.

Stepwise metalation of the hexadentate ligand tbsLH6 (tbsLH6 = 1,3,5-C6H9(NHC6H4-o-NHSiMe2tBu)3) affords bimetallic trinuclear clusters (tbsL)Fe2Zn(thf) and (tbsL)Fe2Zn(py). Reactivity studies were pursued to understand metal atom lability as the clusters undergo ligand substitution, redox chemistry, and group transfer processes. Chloride addition to (tbsL)Fe2Zn(thf) resulted in a mixture of species including both all-zinc and all-iron products. Addition of ArN3 (Ar = Ph, 3,5-(CF3)2C6H3) to (tbsL)Fe2Zn(py) yielded a mixture of two trinuclear products: (tbsL)Fe3(µ3-NAr) and (tbsL)Fe2Zn(µ3-NAr)(py). The two imido species were separated via crystallization, and outer sphere reduction of (tbsL)Fe2Zn(µ3-NAr)(py) resulted in the formation of a single product, [2,2,2-crypt(K)][(tbsL)Fe2Zn(µ3-NAr)]. These results provide insight into the relationship between heterometallic cluster structure and substitutional lability and could help inform both future catalyst design and our understanding of metal atom lability in bioinorganic systems.

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) Šfor the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Šfor 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.

K-Ion Slides in Prussian Blue Analogues.

We study the phenomenology of cooperative off-centering of K+ ions in potassiated Prussian blue analogues (PBAs). The principal distortion mechanism by which this off-centering occurs is termed a "K-ion slide", and its origin is shown to lie in the interaction between local electrostatic dipoles that couple through a combination of electrostatics and elastic strain. Using synchrotron powder X-ray diffraction measurements, we determine the crystal structures of a range of low-vacancy K2M[Fe(CN)6] PBAs (M = Ni, Co, Fe, Mn, Cd) and establish an empirical link between composition, temperature, and slide-distortion magnitude. Our results reflect the common underlying physics responsible for K-ion slides and their evolution with temperature and composition. Monte Carlo simulations driven by a simple model of dipolar interactions and strain coupling reproduce the general features of the experimental phase behavior. We discuss the implications of our study for optimizing the performance of PBA K-ion battery cathode materials and also its relevance to distortions in other, conceptually related, hybrid perovskites.

Thiocyanate-Stabilized Pseudo-cubic Perovskite CH(NH2)2PbI3 from Coincident Columnar Defect Lattices.

α-FAPbI3 (FA+ = CH(NH2)2+) with a cubic perovskite structure is promising for photophysical applications. However, α-FAPbI3 is metastable at room temperature, and it transforms to the δ-phase at a certain period of time at room temperature. Herein, we report a thiocyanate-stabilized pseudo-cubic perovskite FAPbI3 with ordered columnar defects (α'-phase). This compound has a √5ap × âˆš5ap × ap tetragonal unit cell (ap: cell parameter of primitive perovskite cell) with a band gap of 1.91 eV. It is stable at room temperature in a dry atmosphere. Furthermore, the presence of the α'-phase in a mixed sample with the δ-phase drastically reduces the δ-to-α transition temperature measured on heating, suggesting the reduction of the nucleation energy of the α-phase or thermodynamic stabilization of the α-phase through epitaxy. The defect-ordered pattern in the α'-phase forms a coincidence-site lattice at the twinned boundary of the single crystals, thus hinting at an epitaxy- or strain-based mechanism of α-phase formation and/or stabilization. In this study, we developed a new strategy to control defects in halide perovskites and provided new insight into the stabilization of α-FAPbI3 by pseudo-halide and grain boundary engineering.

Tuning electronic and phononic states with hidden order in disordered crystals.

Disorder in crystals is rarely random, and instead involves local correlations whose presence and nature are hidden from conventional crystallographic probes. This hidden order can sometimes be controlled, but its importance for physical properties of materials is not well understood. Using simple models for electronic and interatomic interactions, we show how crystals with identical average structures but different types of hidden order can have very different electronic and phononic band structures. Increasing the strength of local correlations within hidden-order states can open band gaps and tune mode (de)localisation-both mechanisms allowing for fundamental changes in physical properties without long-range symmetry breaking. Taken together, our results demonstrate how control over hidden order offers a new mechanism for tuning material properties, orthogonal to the conventional principles of (ordered) structure/property relationships.

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

The superionic conductor Cu2-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.

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

The name of the third author of the article by Koch et al. [Acta Cryst. (2021). A77, 611-636] is corrected.

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.

Effects of Voigt diffraction peak profiles on the pair distribution function.

Powder diffraction and pair distribution function (PDF) analysis are well established techniques for investigation of atomic configurations in crystalline materials, and the two are related by a Fourier transformation. In diffraction experiments, structural information, such as crystallite size and microstrain, is contained within the peak profile function of the diffraction peaks. However, the effects of the PXRD (powder X-ray diffraction) peak profile function on the PDF are not fully understood. Here, all the effects from a Voigt diffraction peak profile are solved analytically, and verified experimentally through a high-quality X-ray total scattering measurement on Ni powder. The Lorentzian contribution to the microstrain broadening is found to result in Voigt-shaped PDF peaks. Furthermore, it is demonstrated that an improper description of the Voigt shape during model refinement leads to overestimation of the atomic displacement parameter.

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.

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.

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

High-performing thermoelectric materials such as Zn4Sb3 and clathrates have atomic disorder as the root to their favorable properties. This makes it extremely difficult to understand and model their properties at a quantitative level, and thus effective structure-property relations are challenging to obtain. Cu2-xSe is an intensely studied, cheap and non-toxic high performance thermoelectric, which exhibits highly peculiar transport properties, especially near the ß-to-α phase transition around 400 K, which must be related to the detailed nature of the crystal structure. Attempts to solve the crystal structure of the low-temperature phase, ß-Cu2-xSe, have been unsuccessful since 1936. So far, all studies have assumed that ß-Cu2-xSe has a three-dimensional periodic structure, but here we show that the structure is ordered only in two dimensions while it is disordered in the third dimension. Using the three-dimensional difference pair distribution function (3D-ΔPDF) analysis method for diffuse single-crystal X-ray scattering, the structure of the ordered layer is solved and it is shown that there are two modes of stacking disorder present which give rise to an average structure with higher symmetry. The present approach allows for a direct solution of structures with disorder in some dimensions and order in others, and can be thought of as a generalization of the crystallographic Patterson method. The local and extended structure of a solid determines its properties and Cu2-xSe represents an example of a high-performing thermoelectric material where the local atomic structure differs significantly from the average periodic structure observed from Bragg crystallography.

Reconciling Crystallographic and Physical Property Measurements on Thermoelectric Lead Sulfide.

For many decades the lead chalcogenides PbTe, PbSe, and PbS (and their solid solutions) have been preferred high-performance thermoelectric materials due to their exceptional electronic and thermal properties as well as great stability during operation. However, there is a lack of understanding about the fundamental relation between the reported high-defect crystal structure containing cation disorder and vacancies and the observed transport properties, which follow expectations for an ideal rock salt crystal structure. Here we have studied a series of undoped lead sulfide samples (Pb1- xS) with presumed small chemical variations. Crystallographic refinements of high-resolution synchrotron powder X-ray diffraction data give unphysically low lead occupancies (0.75-0.98), in contradiction with the measured charge carrier concentration, resistivity, mobility, and Seebeck coefficient, which show no signs of lead vacancies. A new Rietveld refinement model including preferred orientation parameters and anisotropic strain gives almost full lead occupancy and improved agreement factors. However, transmission electron microscopy analysis reveals that there is no preferred orientation in this system. Instead it is the diffuse scattering due to directional correlated disorder in the structure that necessitates the additional parameters when modeling Bragg intensities. The present approach is a general method for absorbing effects of direction-dependent correlations in advanced materials.

Model-free reconstruction of magnetic correlations in frustrated magnets.

Frustrated magnetic systems exhibit extraordinary physical properties, but quantification of their magnetic correlations poses a serious challenge to experiment and theory. Current insight into frustrated magnetic correlations relies on modelling techniques such as reverse Monte-Carlo methods, which require knowledge about the exact ordered atomic structure. Here, we present a method for direct reconstruction of magnetic correlations in frustrated magnets by three-dimensional difference pair distribution function analysis of neutron total scattering data. The methodology is applied to the disordered frustrated magnet bixbyite, (Mn1-x Fe x )2O3, which reveals nearest-neighbor antiferromagnetic correlations for the metal sites up to a range of approximately 15 Å. Importantly, this technique allows for magnetic correlations to be determined directly from the experimental data without any assumption about the atomic structure.