Pair Distribution Function Measurements Research Articles

Exploring the Role of Cluster Formation in UiO Family Hf Metal-Organic Frameworks with in Situ X-ray Pair Distribution Function Analysis.

The structures of Zr and Hf metal-organic frameworks (MOFs) are very sensitive to small changes in synthetic conditions. One key difference affecting the structure of UiO MOF phases is the shape and nuclearity of Zr or Hf metal clusters acting as nodes in the framework; although these clusters are crucial, their evolution during MOF synthesis is not fully understood. In this paper, we explore the nature of Hf metal clusters that form in different reaction solutions, including in a mixture of DMF, formic acid, and water. We show that the choice of solvent and reaction temperature in UiO MOF syntheses determines the cluster identity and hence the MOF structure. Using in situ X-ray pair distribution function measurements, we demonstrate that the evolution of different Hf cluster species can be tracked during UiO MOF synthesis, from solution stages to the full crystalline framework, and use our understanding to propose a formation mechanism for the hcp UiO-66(Hf) MOF, in which first the metal clusters aggregate from the M6 cluster (as in fcu UiO-66) to the hcp-characteristic M12 double cluster and, following this, the crystalline hcp framework forms. These insights pave the way toward rationally designing syntheses of as-yet unknown MOF structures, via tuning the synthesis conditions to select different cluster species.

Lithiation phase behaviors of metal oxide anodes and extra capacities

Binary metal oxides have received sustained interest as anode materials due to their desirable capacities, exceeding theoretical values particularly in the first discharge. Although they have received increasing attention in recent years, topical debates persist regarding not only their lithiation mechanisms but also the origin of additional capacity. Aiming to resolve these disagreements, we perform a systematic study of a series of iron and manganese oxides to investigate their phase behavior during first discharge. Using a combination of in operando pair distribution function measurements and our recently developed Metropolis non-negative matrix factorization approach to address the analytical challenges concerning materials’ nanoscopic nature and phase heterogeneity, here we report unexpected observation of non-equilibrium FeO x solid-solution phases and pulverization of MnO. These processes are correlated with the extra capacities observed at different depths of discharge, pointing to a metal-dependent nature of this additional capacity and demonstrating the advantage of our approach with promising prospects for diverse applications. The extra capacity may have a dominant source depending on specific metal species bcc -FeO x intermediate lithiate via oxygen extraction from the Fe sublattice Local structure characterization using pair distribution function Robust phase deconvolution using Metropolis non-negative matrix factorization Binary metal oxide anodes in lithium-ion batteries show extra capacities at their initial discharge. In this article, Hua et al. perform a systematic study of iron and manganese oxides’ lithiation phase behaviors and report unexpected observations of bcc -FeO x solid solution and MnO pulverization, processes correlated with the extra capacities seen at different depths of discharge.

Cluster mediated conversion of amorphous Al(OH)3 to γ-AlOOH

We report a synthetic pathway by which amorphous Al(OH)3 is converted to γ-AlOOH through hydrothermal reaction in the presence of water at temperature T ​= ​473 ​K. X-ray pair distribution function measurements reveal that the initially amorphous Al(OH)3 possesses a locally γ-Al(OH)3-like structure, while nanocrystalline γ-AlOOH precipitates within 1 ​h of continuous hydrothermal exposure. Solid state nuclear magnetic resonance measurements show that resonant features associated with four- and five-member Al clusters persist through 20 ​min of hydrothermal treatment, and ultraviolet (UV) spectra mark the onset of UV-induced photoluminescent features characteristic to γ-AlOOH with 10 ​min of exposure, indicating a coexistence region of γ-Al(OH)3-like and γ-AlOOH-like amorphous species. Powder x-ray diffraction measurements of desiccated powders reveal that the conversion process takes place in distinct, power law-defined stages with initial γ-AlOOH nucleation occurring within the first 20 ​min, followed by a ~ 1 ​h period of rapid grain coarsening and the subsequent onset of Lifshitz-Slyozov-Wagner-like coalescence.

Dynamical origins of weakly coupled relaxor behavior in Sn-doped (Ba,Ca)TiO3−BiScO3

The peculiar characteristics of relaxors, viz., a frequency-dependent dielectric permittivity peak and good functional properties (dielectric, electromechanical, electrocaloric, etc.), are attributed to nanoscale regions with correlated dipoles, or polar nanoregions (PNRs). However, the exact nature of PNRs and their contribution to relaxor behavior remains debatable. In recent years, solid solutions of $\mathrm{BaTi}{\mathrm{O}}_{3}\text{\ensuremath{-}}\mathrm{Bi}\mathrm{Me}{\mathrm{O}}_{3}$ (where Me is a metal), have emerged as an interesting system with characteristics in between that of relaxors and dipole glasses. Here, we have examined the atomistic origins of weakly coupled relaxor behavior, specifically with regard to formation of PNRs, in Sn-doped $(1\ensuremath{-}x)(\mathrm{Ba},\mathrm{Ca})\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}x\mathrm{BiSc}{\mathrm{O}}_{3}$ using macroscopic polarization and neutron dynamic pair distribution function measurements. We show that the short-range atomic correlations observed within the PNRs dynamically fluctuate with frequencies of the order of THz. Furthermore the composition-dependent dielectric and polarization behaviors are critically influenced by the relative stability of the atomic correlations near \ensuremath{\sim}1 THz, while the instantaneous atomic correlations are largely independent of $x$. The current results are discussed based on a model of intrinsic local modes distributed in a dielectrically soft matrix.

Resolving Single-layer Nanosheets as Short-lived Intermediates in the Solution Synthesis of FeS

Short-lived reaction intermediates play a critical role in mediating material synthesis. Such short-lived species often elude characterization because of the mismatch between the time scale of measurements capable of describing them and their lifetimes. Thus, we have limited ability to probe, understand, and control the mechanism for material synthesis. Here we demonstrate a new approach to in situ X-ray pair distribution function (PDF) measurements of dynamic nanomaterials structure that yields an unprecedented combination of reaction time resolution and sensitivity. Reaction time is resolved spatially as a function of position along a flow path. By applying this approach to the well-studied aqueous reaction leading to FeS, mackinawite, we identify a novel metastable intermediate, FeSlayer, that forms in the first second of the reaction and which can be described as individual FeS nanosheets. Recognizing these nanosheets as synthons in the reaction opens up the possibility to deliberately redirect this assembly of the nanosheet toward different phases, including novel heterostructures.

Structural Insights into the Vapochromic Behavior of Pt- and Pd-Based Compounds

Anionic complexes having vapochromic behavior are investigated: [K(H2O)][M(ppy)(CN)2], [K(H2O)][M(bzq)(CN)2], and [Li(H2O)n][Pt(bzq)(CN)2], where ppy = 2-phenylpyridinate, bzq = 7,8-benzoquinolate, and M = Pt(II) or Pd(II). These hydrated potassium/lithium salts exhibit a change in color upon being heated to 380 K, and they transform back into the original color upon absorption of water molecules from the environment. The challenging characterization of their structure in the vapochromic transition has been carried out by combining several experimental techniques, despite the availability of partially ordered and/or impure crystalline material. Room-temperature single-crystal and powder X-ray diffraction investigation revealed that [K(H2O)][Pt(ppy)(CN)2] crystallizes in the Pbca space group and is isostructural to [K(H2O)][Pd(ppy)(CN)2]. Variable-temperature powder X-ray diffraction allowed the color transition to be related to changes in the diffraction pattern and the decrease in sample crystallinity. Water loss, monitored by thermogravimetric analysis, occurs in two stages, well separated for potassium Pt compounds and strongly overlapped for potassium Pd compounds. The local structure of potassium compounds was monitored by in situ pair distribution function (PDF) measurements, which highlighted changes in the intermolecular distances due to a rearrangement of the crystal packing upon vapochromic transition. A reaction coordinate describing the structural changes was extracted for each compound by multivariate analysis applied to PDF data. It contributed to the study of the kinetics of the structural changes related to the vapochromic transition, revealing its dependence on the transition metal ion. Instead, the ligand influences the critical temperature, higher for ppy than for bzq, and the inclination of the molecular planes with respect to the unit cell planes, higher for bzq than for ppy. The first stage of water loss triggers a unit cell contraction, determined by the increase in the b axis length and the decrease in the a (for ppy) or c (for bzq) axis lengths. Consequent interplane distance variations and in-plane roto-translations weaken the π-stacking of the room-temperature structure and modify the distances and angles of Pt(II)/Pd(II) chains. The curve describing the intermolecular Pt(II)/Pd(II) distances as a function of temperature, validated by X-ray absorption spectroscopy, was found to reproduce the coordinate reaction determined by the model-free analysis.

Cryo-ePDF: Overcoming Electron Beam Damage to Study the Local Atomic Structure of Amorphous ALD Aluminum Oxide Thin Films within a TEM.

Atomic layer deposition (ALD) provides uniform and conformal thin films that are of interest for a range of applications. To better understand the properties of amorphous ALD films, we need an improved understanding of their local atomic structure. Previous work demonstrated measurement of how the local atomic structure of ALD-grown aluminum oxide (AlOx) evolves in operando during growth by employing synchrotron high-energy X-ray diffraction (HE-XRD). In this work, we report on efforts to employ electron diffraction pair distribution function (ePDF) measurements using more broadly available transmission electron microscope (TEM) instrumentation to study the atomic structure of amorphous ALD-AlOx. We observe electron beam damage in the ALD-coated samples during ePDF at ambient temperature and successfully mitigate this beam damage using ePDF at cryogenic temperatures (cryo-ePDF). We employ cryo-ePDF and reverse Monte Carlo (RMC) modeling to obtain structural models of ALD-AlOx coatings formed at a range of deposition temperatures from 150 to 332 °C. From these model structures, we derive structural metrics including stoichiometry, pair distances, and coordination environments in the ALD-AlOx films as a function of deposition temperature. The structural variations we observe with growth temperature are consistent with temperature-dependent changes in the surface hydroxyl density on the growth surface. The sample preparation and cryo-ePDF procedures we report here can be used for the routine measurement of ALD-grown amorphous thin films to improve our understanding of the atomic structure of these materials, establish structure–property relationships, and help accelerate the timescale for the application of ALD to address technological needs.

Structural Evolution of SiO_{2} Glass with Si Coordination Number Greater than 6.

Pair distribution function measurement of SiO_{2} glass up to 120GPa reveals changes in the first-, second-, and third-neighbor distances associated with an increase in Si coordination number C_{Si} to >6 above 95GPa. Packing fractions of Si and O determined from the first- and second-neighbor distances show marked changes accompanied with the structural evolution from C_{Si}=6 to >6. Structural constraints in terms of ionic radius ratio of Si and O, and ratio of nonbonded radius to bonded Si─O distance support the structural evolution of SiO_{2} glass with C_{Si}>6 at high pressures.

Intra- and Interchain Interactions in (Cu1/2Au1/2)CN, (Ag1/2Au1/2)CN, and (Cu1/3Ag1/3Au1/3)CN and Their Effect on One-, Two-, and Three-Dimensional Order.

Mixed-metal cyanides (Cu1/2Au1/2)CN, (Ag1/2Au1/2)CN, and (Cu1/3Ag1/3Au1/3)CN adopt an AuCN-type structure in which metal-cyanide chains pack on a hexagonal lattice with metal atoms arranged in sheets. The interactions between and within the metal-cyanide chains are investigated using density functional theory (DFT) calculations, 13C solid-state NMR (SSNMR), and X-ray pair distribution function (PDF) measurements. Long-range metal and cyanide order is found within the chains: (−Cu–NC–Au–CN−)∞, (−Ag–NC–Au–CN−)∞, and (−Cu–NC–Ag–NC–Au–CN−)∞. Although Bragg diffraction studies establish that there is no long-range order between chains, X-ray PDF results show that there is local order between chains. In (Cu1/2Au1/2)CN and (Ag1/2Au1/2)CN, there is a preference for unlike metal atoms occurring as nearest neighbors within the metal sheets. A general mathematical proof shows that the maximum average number of heterometallic nearest-neighbor interactions on a hexagonal lattice with two types of metal atoms is four. Calculated energies of periodic structural models show that those with four unlike nearest neighbors are most favorable. Of these, models in space group Immm give the best fits to the X-ray PDF data out to 8 Å, providing good descriptions of the short- and medium-range structures. This result shows that interactions beyond those of nearest neighbors must be considered when determining the structures of these materials. Such interactions are also important in (Cu1/3Ag1/3Au1/3)CN, leading to the adoption of a structure in Pmm2 containing mixed Cu–Au and Ag-only sheets arranged to maximize the numbers of Cu···Au nearest- and next-nearest-neighbor interactions.

Understanding the Instability of the Halide Perovskite CsPbI3 through Temperature‐Dependent Structural Analysis

Despite the tremendous interest in halide perovskite solar cells, the structural reasons that cause the all-inorganic perovskite CsPbI3 to be unstable at room temperature remain mysterious, especially since many tolerance-factor-based approaches predict CsPbI3 should be stable as a perovskite. Here single-crystal X-ray diffraction and X-ray pair distribution function (PDF) measurements characterize bulk perovskite CsPbI3 from 100 to 295 K to elucidate its thermodynamic instability. While Cs occupies a single site from 100 to 150 K, it splits between two sites from 175 to 295 K with the second site having a lower effective coordination number, which, along with other structural parameters, suggests that Cs rattles in its coordination polyhedron. PDF measurements reveal that on the length scale of the unit cell, the PbI octahedra concurrently become greatly distorted, with one of the IPbI angles approaching 82° compared to the ideal 90°. The rattling of Cs, low number of CsI contacts, and high degree of octahedral distortion cause the instability of perovskite-phase CsPbI3. These results reveal the limitations of tolerance factors in predicting perovskite stability and provide detailed structural information that suggests methods to engineer stable CsPbI3 -based solar cells.

Severe local lattice distortion in Zr- and/or Hf-containing refractory multi-principal element alloys

Whereas exceptional mechanical and radiation performances have been found in the emergent body-centered cubic (BCC) refractory multi-principal element alloys (RMPEAs), the importance of their complex atomic environment, reflecting diversity in atomic size and chemistry, has been largely unexplored at the atomic level. Here, we adopt a local structure approach based on the atomic pair distribution function measurements in combination with density functional theory (DFT) calculations to investigate a series of BCC RMPEAs. Our results demonstrate that all the analyzed RMPEAs exhibit local lattice distortions (LLD) to some extent, but a severe LLD, a breakdown of the 15% atomic size difference in Hume-Rothery rules, occurs only in the Zr- and/or Hf-containing RMPEAs. In addition, through the DFT calculations we show that charge transfer among the elements profoundly reduces the size mismatch effect in average to stabilize this energy-unfavorable severe LLD. The observed competitive coexistence between LLD and charge transfer demonstrates the importance of the electronic effects on the local environments in RMPEAs.

Role of Ni and Co in tailoring magnetic and mechanical properties of Fe84Si2B13P1 metallic glass

The disastrous annealing embrittlement of Fe-based metallic glasses with excellent soft magnetic properties is a long-standing issue. In order to alleviate the annealing embrittlement without worsening the soft magnetic properties, ferromagnetic elements Co and Ni are introduced to the Fe84Si2B13P1 metallic glasses. The microstructure, mechanical and magnetic properties are investigated by synchrotron diffraction, two-point bending test and magnetometry. It is found that, in contrast to Co, proper Ni substitution for Fe significantly optimizes the Hc of Fe84Si2B13P1 metallic glasses and keeps the Bs at a high level. According to bending tests, the ductile-brittle transition temperature of the metallic glasses increases slightly with Ni substitution and decreases prominently with Co substitution. Ultimately, the ductile Fe82Ni2Si2B13P1 metallic glasses with Bs of 1.65 T and Hc of 3.4 A/m have been successfully obtained. Macroscopically, the cheerful propensity to form well-distributed shear bands during bending of Ni-substituted annealed alloys contributes to their good ductility. Furthermore, the alteration of ductile-brittle transition temperature can be conducted by the structural change at the medium-range scale as revealed by the pair distribution function measurements. After annealing the compression at atomic scale ranging from 6 Å to 16 Å of Co-substituted metallic glasses may hinder the creation of well-distributed shear bands and give rise to the deterioration of bending ductility. This work provides a perspective to understand the ductile-brittle transition of metallic glasses from the atomic scale.

A simple correction for the parallax effect in X-ray pair distribution function measurements

Total scattering and pair distribution function (PDF) analysis has created new insights that traditional powder diffraction methods have been unable to achieve in understanding the local structures of materials exhibiting disorder or complex nanostructures. Care must be taken in such analyses as subtle and discrete features in the PDF can easily be artefacts generated in the measurement process, which can result in unphysical models and interpretation. The focus of this study is an artefact called the parallax effect, which can occur in area detectors with thick detection layers during the collection of X-ray PDF data. This effect results in high-Q peak offsets, which subsequently cause an r-dependent shift in the PDF peak positions in real space. Such effects should be accounted for if a truly accurate model is to be achieved, and a simple correction that can be conducted via a Rietveld refinement against the reference data is proposed.

Expanded lithiation of titanium disulfide: Reaction kinetics of multi-step conversion reaction

Phase evolution during a thorough Li ion's insertion of electrode materials governs their battery performance during charge and discharge. Here we investigated the lithiation pathway of titanium disulfide using in situ TEM combined with synchrotron-based pair distribution function measurement and first-principles calculations. A 2D intercalation reaction proceeds along with a transition from van der Waals interaction between Ti–S slabs to the covalent bonding of S–Li–S, with no symmetry broken. Further lithiation triggers unconventionally multiple step conversion reactions as proved: LiTiS2→TiS→Ti2S→Ti. The conversion reaction pathway is also verified in fully discharged sample in coin-cell. The expanded conversion chemistry is supposed to increase the capacity of TiS2 electrode and downgrade the cyclability, whereas the existence of intermediate phases shows the promise of improving the reversibility with a successful control of the state of charge.

Room temperature local nematicity in FeSe superconductor

We report pair distribution function measurements of the iron-based superconductor FeSe above and below the structural transition temperature. Structural analysis reveals a local orthorhombic distortion with a correlation length of about 4 nm at temperatures where an average tetragonal symmetry is observed. The analysis further demonstrates that the local distortion is larger than the distortion at temperatures where the average observed symmetry is orthorhombic. Our results suggest that the low-temperature macroscopic nematic state in FeSe forms from an imperfect ordering of orbital-degeneracy-lifted nematic fluctuations which persist up to at least 300 K.

Structure Distortion Induced Monoclinic Nickel Hexacyanoferrate as High‐Performance Cathode for Na‐Ion Batteries

AbstractPrussian blue analogs with an open framework are ideal cathodes for Na‐ion batteries. A superior high‐rate and highly stable monoclinic nickel hexacyanoferrate (NiHCF‐3) is synthesized via a facile one‐step crystallization‐controlled co‐precipitation method. It gives a high specific capacity of 85.7 mAh g−1, nearly to its theoretical value. It also exhibits an excellent rate capability with a high capacity retention ratio of 78% at 50 C and a stable cycling performance over 1200 cycles. Through the ex situ X‐ray diffraction and pair distribution function measurements, it is found that the monoclinic structure with distorted framework is greatly related to the high Na content. The electronic structure studies by density functional theory (DFT) calculation demonstrate that NiHCF‐3 deformation promotes the framework conductivity and improves the electrochemical activity of Fe, which results in an ultrahigh‐rate performance of monoclinic phase. Furthermore, the high‐quality monoclinic (NiHCF‐3) exhibits excellent compatibility with both hard carbon and NaTi2(PO4)3 anodes in full cells, which shows great prospects for the application in the large‐scale energy storage systems.

Widespread orthorhombic fluctuations in the (Sr,Na)Fe2As2 family of superconductors

We report comprehensive pair distribution function measurements of the hole-doped iron-based superconductor system Sr$_{1-x}$Na$_{x}$Fe$_2$As$_2$. Structural refinements performed as a function of temperature and length scale reveal orthorhombic distortions of the instantaneous local structure across a large region of the phase diagram possessing average tetragonal symmetry, indicative of fluctuating nematicity. These nematic fluctuations are present up to high doping levels ($x \gtrsim 0.48$, near optimal superconductivity) and high temperatures (above room temperature for $x = 0$, decreasing to 150 K for $x = 0.48$), with a typical length scale of 1-3 nm. This work highlights the ubiquity of nematic fluctuations in a representative iron-based superconductor and provides important details about the evolution of these fluctuations across the phase diagram.

Effect of calcium and lithium on alkali-silica reaction kinetics and phase development

This study aims to investigate the influence of lithium and calcium content on the alkali-silica reaction kinetics and phase formation processes at atomic scales. The atomic structure of the reacted ASR gels was analyzed with the Pair Distribution Function (PDF) measurement. The analysis results can explain the expansion potential difference of gels with different chemical composition. The in situ PDF characterizations of the samples containing lithium compounds identified the formation of the LiSi phase, and thus both the alkali-silica reaction and the reaction between dissolved silica and Ca(OH)2 were suppressed. The alkali-silica reaction kinetics was further indicated with the changes of SiO peak intensity. The amorphous structure of the generated LiSi phase was confirmed with in situ XRD tests. The results strongly support the formed amorphous LiSi phase can act as a surface barrier for silica dissolution, and thus prohibit both the alkali-silica reaction and pozzolanic reaction in hardened concrete.

Liquid phase blending of metal-organic frameworks

The liquid and glass states of metal–organic frameworks (MOFs) have recently become of interest due to the potential for liquid-phase separations and ion transport, alongside the fundamental nature of the latter as a new, fourth category of melt-quenched glass. Here we show that the MOF liquid state can be blended with another MOF component, resulting in a domain structured MOF glass with a single, tailorable glass transition. Intra-domain connectivity and short range order is confirmed by nuclear magnetic resonance spectroscopy and pair distribution function measurements. The interfacial binding between MOF domains in the glass state is evidenced by electron tomography, and the relationship between domain size and Tg investigated. Nanoindentation experiments are also performed to place this new class of MOF materials into context with organic blends and inorganic alloys.

Zeolites with isolated-framework and oligomeric-extraframework hafnium species characterized with pair distribution function analysis.

Zeolites containing framework heteroatoms (e.g., Ti, Sn, and Hf) with open coordination sites behave as solid-state Lewis acids and exhibit remarkable catalytic properties unachievable with bulk oxides. However, direct evidence confirming the incorporation of such heteroatom species into the zeolite framework is difficult to obtain because of the limited number of analytical methods capable of discerning framework incorporation from extraframework species. In this work, the structural environments of hafnium (Hf) framework and extraframework species added post-synthetically into *BEA zeolites were analyzed using coupled pair distribution function (PDF) and diffuse reflectance (DR) UV-vis measurements. PDF analysis enabled the visualization and identification of framework and extraframework HfOx species, both of which were undetectable by traditional X-ray and neutron diffraction methods. Reactivity data from the aldol condensation of benzaldehyde and acetone confirmed that framework Hf species are responsible for catalytic activity.