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Local order, disorder, and everything in between: using 91 Zr solid-state NMR spectroscopy to probe zirconium-based metal–organic frameworks
Characterization of metal centers in metal–organic frameworks (MOFs) is critical for rational design and further understanding of structure–property relationships. The short-range structure about Zr atoms is challenging to properly elucidate in many Zr MOFs, particularly when local disorder is present. Static 91 Zr solid-state NMR spectra of the seven zirconium MOFs UiO-66, UiO-66-NH 2 , UiO-67, MOF-801, MOF-808, DUT-68 and DUT-69 have been acquired at high magnetic fields of 35.2 T and 19.6 T, yielding valuable information on the local structure, site symmetry and order about Zr. 91 Zr NMR is very sensitive to differences in MOF short-range structure caused by guest molecules, linker substitution and post-synthetic treatment. Complementary density functional theory (DFT) calculations assist in the interpretation and assignment of 91 Zr solid-state NMR spectra, lend insight into structural origins of 91 Zr NMR parameters and enable determination of local Zr coordination environments. This approach can be extended to many other materials containing zirconium.
The relation of local order to material properties in relaxor ferroelectrics
Correlating electromechanical and dielectric properties with nanometre-scale order is the defining challenge for the development of piezoelectric oxides. Current lead (Pb)-based relaxor ferroelectrics can serve as model systems with which to unravel these correlations, but the nature of the local order and its relation to material properties remains controversial. Here we employ recent advances in diffuse scattering instrumentation to investigate crystals that span the phase diagram of PbMg1/3Nb2/3O3-xPbTiO(3) (PMN-xPT) and identify four forms of local order. From the compositional dependence, we resolve the coupling of each form to the dielectric and electromechanical properties observed. We show that relaxor behaviour does not correlate simply with ferroic diffuse scattering; instead, it results from a competition between local antiferroelectric correlations, seeded by chemical short-range order, and local ferroic order. The ferroic diffuse scattering is strongest where piezoelectricity is maximal and displays previously unrecognized modulations caused by anion displacements. Our observations provide new guidelines for evaluating displacive models and hence the piezoelectric properties of environmentally friendly next-generation materials.
Effects of local order parameter dependent transport coefficient in diblock copolymers under applied electric fields
In this work, we present an approach for constructing thermodynamically consistent time-dependent models relevant to thin films of diblock copolymers in applied electric fields. The approach is based on the principles of linear irreversible thermodynamics, and, in this work, it is applied to study the effects of electric fields on thin films of incompressible diblock copolymers. Enforcement of local incompressibility constraint at all times leads to a local order parameter dependent transport coefficient in the model for the diblock copolymers. The dependence of the transport coefficient on the local order parameter is used to relate it with the diffusion constant of Rouse chains and leads to sensitivity of the model to initial conditions. In addition, transient behavior is found to be affected when compared with an ad hoc model assuming a constant transport coefficient. Numerical results such as electric field induced alignment of lamellae domains due to the field are found to be in qualitative agreement with experiments. This approach opens up a systematic way of developing kinetic models for simulating effects of electrolytes added to thin films containing diblock copolymers in the presence of applied electric fields.
Local-order metric for condensed-phase environments
Here we introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that perfectly match the reference. The site-averaged LOM and its standard deviation define two scalar order parameters, S and δS, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that S, δS, and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling.
Unraveling Na and F coupling effects in stabilizing Li, Mn-rich layered oxide cathodes via local ordering modification
Regardless of the prevailing capacity and energy density of lithium, manganese-rich layered oxide (LMR-NMC) cathodes, continuous decay of voltage and overall energy density during cycling hinders this material from commercialization in Li-ion batteries. Although significant work focuses on single doping of Na and F, analysis in portraying the benefit of these ions in diminishing the structural distortion during activation cycle is in doubt. In this study, the effects of co-doping Na and F into the LMR-NMC structure in stabilizing the structure and mitigating oxygen loss during the first cycle are closely examined via in situ x-ray measurements. Na and F co-doping shows a 30% lower degree of Li + /Ni 2+ mixing in the Li layer (C2/m structure), 50% reduced Debye-Waller factor of Mn-O bonding, increase reversible TM migration, and faster Li diffusion relative to the pristine material. Due to the utilization of Ni redox chemistry below 4.4 V, less oxygen redox is required for charge compensation at high voltage. This study offers the first instance to quantitatively evaluate the effects of co-doping Na and F in LMR-NMC cathode in order to minimize voltage degradation by altering the local ordering of O3-type structure, which may rationalize strategies to overcome the issues of the material.
Similar local order in disordered fluorite and aperiodic pyrochlore structures
A major challenge to understanding the response of materials to extreme environments ( e.g. , nuclear fuels/waste forms and fusion materials) is to unravel the processes by which a material can incorporate atomic-scale disorder, and at the same time, remain crystalline. While it has long been known that all condensed matter, even liquids and glasses, possess short-range order, the relation between fully-ordered, disordered, and aperiodic structures over multiple length scales is not well understood. For example, when defects are introduced ( via pressure or irradiation) into materials adopting the pyrochlore structure, these complex oxides either disorder over specific crystallographic sites, remaining crystalline, or become aperiodic. Here we present neutron total scattering results characterizing the irradiation response of two pyrochlores, one that is known to disorder (Er 2 Sn 2 O 7 ) and the other to amorphize (Dy 2 Sn 2 O 7 ) under ion irradiation. The results demonstrate that in both cases, the local pyrochlore structure is transformed into similar short range configurations that are best fit by the orthorhombic weberite structure, even though the two compositions have distinctly different structures, aperiodic vs. disordered-crystalline, at longer length scales. Thus, a material's resistance to amorphization may not depend primarily on local defect formation energies, but rather on the structure's compatibility with meso-scale modulations of the local order in a way that maintains long-range periodicity.
Resolving local ordering and structure in Mn x Ge 1- x Te alloys through thermodynamic ensembles of pair distribution functions
Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.
Local ordering in Ge/Ge–Sn semiconductor alloy core/shell nanowires revealed by extended x-ray absorption fine structure (EXAFS)
Short-range atomic order in semiconductor alloys is a relatively unexplored topic that may promote design of new materials with unexpected properties. Here, local atomic ordering is investigated in Ge–Sn alloys, a group-IV system that is attractive for its enhanced optoelectronic properties achievable via a direct gap for Sn concentrations exceeding ≈10 at. %. The substantial misfit strain imposed on Ge–Sn thin films during growth on bulk Si or Ge substrates can induce defect formation; however, misfit strain can be accommodated by growing Ge–Sn alloy films on Ge nanowires, which effectively act as elastically compliant substrates. In this work, Ge core/Ge 1–x Sn x (x ≈ 0.1) shell nanowires were characterized with extended x-ray absorption fine structure (EXAFS) to elucidate their local atomic environment. Simultaneous fitting of high-quality EXAFS data collected at both the Ge K-edge and the Sn K-edge reveals a large (≈ 40%) deficiency of Sn in the first coordination shell around a Sn atom relative to a random alloy, thereby providing the first direct experimental evidence of significant short-range order in this semiconductor alloy system. Furthermore, comparison of path length data from the EXAFS measurements with density functional theory simulations provides alloy atomic structures consistent with this conclusion.
Description of the atomic disorder (local order) in crystals by the mixed-symmetry method
An approach to the description of local atomic disorder (short-range order) in single crystals by the mixed-symmetry method based on Bragg scattering data is proposed, and the corresponding software is developed. In defect-containing crystals, each atom in the unit cell can be described by its own symmetry space group. The expression for the calculated structural factor includes summation over different sets of symmetry operations for different atoms. To facilitate the search for new symmetry elements, an “atomic disorder expert” was developed, which estimates the significance of tested models. It is shown that the symmetry lowering for some atoms correlates with the existence of phase transitions (in langasite family crystals) and the anisotropy of physical properties (in rare-earth dodecaborides RB{sub 12}).
Elucidation of Local Ordering and Atomic-Scale Structure in Polymer-Derived SiOC
Silicon oxycarbide (SiOC) is a versatile ceramic material with tunable microstructure and compositions that can be modulated through precursor chemistry and processing conditions. Though there are several noteworthy uses of SiOC across a range of application spaces, the difficulties in elucidating the short- to medium-range order within these materials have limited the maturation of strategies to precisely control SiC x O 4–x compositions for user-tailored applications. In this contribution, we implement a range of synchrotron scattering and spectroscopy methods coupled with stochastic modeling techniques to elucidate changes in local chemistry and structure associated with the pyrolysis of a commercially available SiOC polymer precursor. Stochastic modeling approaches provide valuable insights into decoupling local Si–O and Si–C environments while confirming predominate heterogeneous phases in materials. Using pyrolysis temperatures between 250 to 800 °C results in a heterogeneous material predominately composed of SiOC and amorphous SiO 2 domains. At 1100 °C, redistribution of Si–C pairs in the SiOC network and Si–O from the SiO 2 domains create a more ordered SiOC phase with local cubic SiC-like ordering. In addition, residual carbon leads to a detectable carbon phases at 1100 °C that persist at higher temperatures. These efforts address the difficulties of obtaining atomic-scale insights into the local structure and nanoscale heterogeneities in SiOC, providing pathways toward establishing structure–property relationships for future materials development.
Tunable catalytic activity of cobalt-intercalated layered MnO2 for water oxidation through confinement and local ordering
We report that the lowering of reaction overpotentials is a persistent and universal goal in the development of catalysts for (photo)electrochemistry, which can usually be facilitated by selectively stabilizing one reaction inter-mediate over another. In this mechanistic study of the oxygen evolution reaction (OER) catalyzed by cobalt-intercalated layered MnO 2 , we show that confinement effects and local cobalt atomic ordering in the interlayer space can be synergistically used to tune the adsorption energies of O, OH, and OOH reaction intermediates and the scaling relationship between them. In general, the interlayer confinement destabilizes the adsorption of intermediates for the OER, but clustering Co atoms can selectively stabilize the adsorption of OOH in particular. After considering both effects, our model predicts an overpotential of 0.30 V for the Co-intercalated MnO 2 catalyzed OER, in excellent agreement with the experimental result of 0.36 V. These new insights explain the enhanced catalytic performance of MnO 2 by intercalating atoms and illuminate a route for engineering non-toxic precious-metal-free catalysts through designed layered materials.
Local Order in Liquid Gallium–Indium Alloys
Liquid metals such as eutectic Ga–In alloys have low melting points and low toxicity and are used in catalysis and micro-robotics. This study investigates the local atomic structure of liquid gallium-indium alloys by a combination of density measurements, diffraction data, and Monte-Carlo simulation via the empirical potential structure refinement approach. A high-Q shoulder observed in liquid Ga is related to structural rearrangements in the second coordination shell. Structure analysis found coordination environments close to a random distribution for eutectic Ga–In alloy, while electronic effects appear to dominate the mixing enthalpy.
Ebola and Marburg virus matrix layers are locally ordered assemblies of VP40 dimers
Filoviruses such as Ebola and Marburg virus bud from the host membrane as enveloped virions. This process is achieved by the matrix protein VP40. When expressed alone, VP40 induces budding of filamentous virus-like particles, suggesting that localization to the plasma membrane, oligomerization into a matrix layer, and generation of membrane curvature are intrinsic properties of VP40. There has been no direct information on the structure of VP40 matrix layers within viruses or virus-like particles. We present structures of Ebola and Marburg VP40 matrix layers in intact virus-like particles, and within intact Marburg viruses. VP40 dimers assemble extended chains via C-terminal domain interactions. These chains stack to form 2D matrix lattices below the membrane surface. These lattices form a patchwork assembly across the membrane and suggesting that assembly may begin at multiple points. Our observations define the structure and arrangement of the matrix protein layer that mediates formation of filovirus particles.
Revealing local order via high energy EELS
Short range order (SRO) is critical in determining the performance of many important engineering materials. However, accurate characterization of SRO with high spatial resolution – which is needed for the study of individual nanoparticles and at material defects and interfaces – is often experimentally inaccessible. Here, we locally quantify SRO via scanning transmission electron microscopy with extended energy loss fine structure analysis. Specifically, we use novel instrumentation to perform electron energy loss spectroscopy out to 12 keV, accessing energies which are conventionally only possible using a synchrotron. Our data is of sufficient energy resolution and signal-to-noise ratio to perform quantitative extended fine structure analysis, which allows determination of local coordination environments. To showcase this technique, we investigate a multicomponent metallic glass nanolaminate and locally quantify the SRO with <10 nm spatial resolution; this measurement would have been impossible with conventional synchrotron or electron microscopy methods. Finally, we discuss the nature of SRO within the metallic glass phase, as well as the wider applicability of our approach for determining processing–SRO–property relationships in complex materials.
Local ordering in disordered Nd x Zr 1-x O 2-0.5x pyrochlore as observed using neutron total scattering
Pyrochlore complex oxides (A 2 B 2 O 7 ) are an important class of fluorite-derivative ceramics with exceptional chemical and structural versatility which make them ideal model systems for studying disordering mechanisms over a range of spatial scales. Here, neutron total scattering methods were used to analyze the structural behavior in the non-stoichiometric series Nd x Zr 1-x O 2-0.5x (0.5 ≤ x ≤ 0.23) as a function of Nd content, x. Characterization of the structure functions using Rietveld refinement and the pair distribution functions with small-box refinement reveal complex disordering pathways; the average, long-range phase changes over a very narrow compositional range from pyrochlore ($Fd\bar{3}m$) to defect fluorite ($Fm\bar{3}m$) through full randomization of the cation and anion sublattices at x ~ 0.31, while the local, short-range structure continuously adopts a weberite-type atomic arrangement (C222 1 ). Comparison to a previously studied Ho 2 Ti 2-x Zr x O 7 solid solution series reveals how changes in chemical composition and stoichiometry modify defect formation and determine how disordering progresses across different length scales in pyrochlore oxides.
Local order of orthorhombic weberite-type Y 3 TaO 7 as determined by neutron total scattering and density functional theory calculations
Weberite-type oxides are a family of oxides with A 3 BO 7 stoichiometry that can adopt different space groups depending on chemical composition. There is a discrepancy in previous studies as to whether Y 3 TaO 7 is the orthorhombic C222 1 or the Ccmm space group. Here, we describe the short- and long-range structural properties of weberite-type Y 3 TaO 7 using neutron total scattering data, which has a high sensitivity to the oxygen sublattice. Simultaneous analysis of both short- and long-range structural data via conventional Rietveld and small box modelling demonstrates that Y 3 TaO 7 is best modeled as C222 1 . While the Ccmm describes equally well the long-range structure, pair distribution function analysis revealed that the local atomic configuration can be best modelled as C222 1 . This is corroborated by first-principles calculations that confirm the energetic preference of the C222 1 over Ccmm. Further, neutron total scattering data are reported for the first time for the Y 3 TaO 7 weberite-type ceramics.
The nature of dynamic local order in CH 3 NH 3 PbI 3 and CH 3 NH 3 PbBr 3
Hybrid organic-inorganic lead-halide perovskites (LHPs) are a class of semiconductors with remarkable properties relevant to optoelectronic applications. The structure-property-function relationship in LHPs, however, is poorly understood, leading to incomplete descriptions of optoelectronic properties and a persistent problem of device degradation due to ion migration. Here, we reveal the true structure to contain an assembly of dynamic, two-dimensional short-range structural correlations in the lead-halide octahedral sublattice, with additional correlations between organic molecules. Here, we propose that these correlations are the origin of large-amplitude halide displacements, which govern charge carrier mobility and the sharpness of the absorption edge. Correlations between organic molecules may introduce regions of transient ferroelectricity or antiferroelectricity, which increase charge carrier lifetime. Finally, the correlations introduce an ion diffusion barrier that is static on the timescale of diffusive jumps.