Experimental Pair Distribution Function Research Articles

Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs

The methods currently used to calculate atomic pair distribution functions (PDFs) from organic structural models do not distinguish between the intramolecular and intermolecular distances. Owing to the stiff bonding between atoms within a molecule, the PDF peaks arising from intramolecular atom–atom distances are much sharper than those of the intermolecular atom–atom distances. This work introduces a simple approach to calculate PDFs of molecular systems without building a supercell model by using two different isotropic displacement parameters to describe atomic motion: one parameter is used for the intramolecular, the other one for intermolecular atom–atom distances. Naphthalene, quinacridone and paracetamol were used as examples. Calculations were done with theDiffPy-CMIcomplex modelling infrastructure. The new modelling approach produced remarkably better fits to the experimental PDFs, confirming the higher accuracy of this method for organic materials.

Reverse Monte Carlo Modeling of the Rigidity Percolation Threshold in Ge<SUB>x</SUB>Se<SUB>1-x</SUB> Glassy Networks

Based on Maxwell’s constraint counting theory, rigidity percolation in GexSe1-x glasses occurs when the mean coordination number reaches the value of 2.4. This corresponds to Ge0.20Se0.80 glass. At this composition, the number of constraints experienced by an atom equals the number of degrees of freedom in three dimensions. Hence, at this composition, the network changes from a floppy phase to a rigid phase, and rigidity starts to percolate. In this work, we use reverse Monte Carlo (RMC) modeling to model the structure of Ge0.20Se0.80 glass by simulating its experimental total atomic pair distribution function (PDF) obtained via high energy synchrotron radiation. A three-dimensional configuration of 2836 atoms was obtained, from which we extracted the partial atomic pair distribution functions associated with Ge-Ge, Ge-Se and Se-Se real space correlations that are hard to extract experimentally from total scattering methods. Bond angle distributions, coordination numbers, mean coordination numbers and the number of floppy modes were also extracted and discussed. More structural insights about network topology at this composition were illustrated. The results indicate that in Ge0.20Se0.80 glass, Ge atoms break up and cross-link the Se chain structure, and form structural units that are four-fold coordinated (the GeSe4 tetrahedra). These tetrahedra form the basic building block and are connected via shared Se atoms or short Se chains. The extent of the intermediate ranged oscillations in real space (as extracted from the width of the first sharp diffraction peak) was found to be around 19.6 ?. The bonding schemes in this glass are consistent with the so-called “8-N” rule and can be interpreted in terms of a chemically ordered network model.

Synthesis-atomic structure-properties relationships in metallic nanoparticles by total scattering experiments and 3D computer simulations: case of Pt-Ru nanoalloy catalysts.

An approach to determining the 3D atomic structure of metallic nanoparticles (NPs) in fine detail and using the unique knowledge obtained for rationalizing their synthesis and properties targeted for optimization is described and exemplified on Pt-Ru alloy NPs of importance to the development of devices for clean energy conversion such as fuel cells. In particular, PtxRu100-x alloy NPs, where x = 31, 49 and 75, are synthesized by wet chemistry and activated catalytically by a post-synthesis treatment involving heating under controlled N2-H2 atmosphere. So-activated NPs are evaluated as catalysts for gas-phase CO oxidation and ethanol electro-oxidation reactions taking place in fuel cells. Both as-synthesized and activated NPs are characterized structurally by total scattering experiments involving high-energy synchrotron X-ray diffraction coupled to atomic pair distribution functions (PDFs) analysis. 3D structure models both for as-synthesized and activated NPs are built by molecular dynamics simulations based on the archetypal for current theoretical modelling Sutton-Chen method. Models are refined against the experimental PDF data by reverse Monte Carlo simulations and analysed in terms of prime structural characteristics such as metal-to-metal bond lengths, bond angles and first coordination numbers for Pt and Ru atoms. Analysis indicates that, though of a similar type, the atomic structure of as-synthesized and respective activated NPs differ in several details of importance to NP catalytic properties. Structural characteristics of activated NPs and data for their catalytic activity are compared side by side and strong evidence found that electronic effects, indicated by significant changes in Pt-Pt and Ru-Ru metal bond lengths at NP surface, and practically unrecognized so far atomic ensemble effects, indicated by distinct stacking of atomic layers near NP surface and prevalence of particular configurations of Pt and Ru atoms in these layers, contribute to the observed enhancement of the catalytic activity of PtxRu100-x alloy NPs at x ∼ 50. Implications of so-established relationships between the atomic structure and catalytic activity of Pt-Ru alloy NPs on efforts aimed at improving further the latter by tuning-up the former are discussed and the usefulness of detailed NP structure studies to advancing science and technology of metallic NPs - exemplified.

Structural analysis of lignin-derived carbon composite anodes

The development of novel lignin-based carbon composite anodes consisting of nanocrystalline and amorphous domains motivates the understanding of the relationship of the structural properties characterizing these materials, such as crystallite size, intracrystallitedspacing, crystalline volume fraction and composite density, with their pair distribution functions (PDFs), obtained from both molecular dynamics simulation and neutron scattering. A model for these composite materials is developed as a function of experimentally measurable parameters and realized in 15 composite systems, three of which directly match all parameters of their experimental counterparts. The accurate reproduction of the experimental PDFs using the model systems validates the model. The decomposition of the simulated PDFs provides an understanding of each feature in the PDF and allows for the development of a mapping between the defining characteristics of the PDF and the material properties of interest.

Magic Sized Clusters in ZnO Nanoparticle Formation – an in-situ PDF study

Semiconductor nanoparticles (NP) such as zinc oxide (ZnO) are commonly produced in sol-gel processes. The final NP powders are well characterized with respect to their crystallinity, which fundamentally governs their physical and chemical properties. Nevertheless, the nucleation process and the evolution of crystallinity of the nucleating NPs is not yet understood [1]. With the advent of the Rapid Acquisition Pair Distribution Function (PDF) method, time-resolved PDF studies have become possible, and the distinction between molecular clusters and nanoparticles in 1 M aqueous solutions of metal oxide NPs [2] has been demonstrated. However, nucleation in dilute sol-gel processes in more complex organic solutions remains untackled [1]. Our experiments are, to our knowledge, the first in-situ PDF studies in organic solvents. We used a 30 mM ethanolic solution of zinc acetate dihydrate. Several hours after the addition of the organic base tetramethylammonium hydroxide, monodisperse ZnO powders can be obtained. However, directly upon the base addition primary tetrahedral precursors Zn4OAc6 form. Approx. 1 hour later, they evolve into stable magic sized clusters (MSC) of 1.3 nm diameter and wurtzitic structure. Though known to exist for II-VI semiconductor NP such as CdSe [3], MSCs have not been demonstrated for ZnO before. With ongoing reaction time, the final spherical NPs of 2.5 nm diameter evolve at the expense of the MSCs and exist for several hours without undergoing further growth. SAXS studies confirm the PDF data. Fig. 1 shows the experimental PDFs and their fits. The fits are multiphase models of the precursor, the MSC and NP. The solvent shows intermolecular ordering effects whose contribution to the PDF was modelled by a low-frequency wave function. The MSC and NP sketches show a view along the crystallographic c-axis. Based upon these state-of-the art in-situ PDF studies, we suggest a nucleation model based on the existence of magic-sized clusters.

The local atomic structures of liquid CO at 3.6 GPa and polymerized CO at 0 to 30 GPa from high-pressure pair distribution function analysis.

The local atomic structures of liquid and polymerized CO and its decomposition products were analyzed at pressures up to 30 GPa in diamond anvil cells by X-ray diffraction, pair distribution function (PDF) analysis, single-crystal diffraction, and Raman spectroscopy. The structural models were obtained by density functional calculations. Analysis of the PDF of a liquid CO-rich phase revealed that the local structure has a pronounced short-range order. The PDFs of polymerized amorphous CO at several pressures revealed the compression of the molecular structure; covalent bond lengths did not change significantly with pressure. Experimental PDFs could be reproduced with simulations from DFT-optimized structural models. Likely structural features of polymerized CO are thus 4- to 6-membered rings (lactones, cyclic ethers, and rings decorated with carbonyl groups) and long bent chains with carbonyl groups and bridging atoms. Laser heating polymerized CO at pressures of 7 to 9 GPa and 20 GPa resulted in the formation of CO(2).

Breakthroughs in hard X-ray diffraction: towards a multiscale science approach in heterogeneous catalysis.

Breakthroughs in hard X-ray diffraction: towards a multiscale science approach in heterogeneous catalysis.

Domain structure for an amorphous iridium-oxide water-oxidation catalyst characterized by X-ray pair distribution function analysis

The domain structure of an amorphous, "blue layer" iridium-oxide water-oxidation catalyst film (BL) electrodeposited from the soluble precursor complex, [Cp*Ir(H2O)3]SO4, was characterized by X-ray pair distribution function (PDF) analysis. The results show that the experimental PDF can be fit remarkably well using a single Ir5O22 cluster extracted from the rutile lattice. The model includes distortions that indicate the presence of Ir(μ-O)3Ir or distorted Ir(μ-O)2Ir substructures, and hence deviations from a rutile structure. The five Ir atom cluster is suggested to represent the population-averaged distribution of metal-oxo clusters in the film. BL is found to be distinguished from other amorphous film water-oxidation catalysts because of the remarkably small domain size and homogeneity. As such, the blue layer catalyst provides a model for investigating ligand-determined metal-oxide cluster assembly and catalyst mechanism.

The local structure of Pd(x)Ce(1-x)O(2-x-δ) solid solutions.

PdxCe1-xO2-x-δ solid solutions, which are highly efficient catalysts for the low-temperature oxidation of carbon monoxide, were examined using a set of structural (XRD-PDF, HRTEM, XRD) and spectral (XPS, Raman spectroscopy) methods in combination with quantum-chemical calculations. A comparison of the experimental results and pair distribution function (PDF) modeling data enabled reliable verification of the model of non-isomorphic substitution of Ce(4+) ions by Pd(2+) ions in PdxCe1-xO2-x-δ solid solutions. Palladium ions were shown to be in a near square planar environment with C4v symmetry, which is typical for Pd(2+) ions. Such a near square planar environment was revealed by Raman spectroscopy due to the appearance of the band at ω = 187 cm(-1), which corresponds to the A1 vibrational mode of Pd(2+) ions in [PdO4] subunits. The binding energy of Pd3d5/2 (Eb(Pd3d5/2)) for the Pd(2+) ion in the CeO2 lattice is 1 eV higher than that of Eb(Pd3d5/2) for PdO oxide due to a decrease in the Pd-O distances and the formation of more ionic bonds because of the displacement of Pd(2+) ions with respect to the position of Ce(4+) ions in the fluorite structure. Five structural models of solid solutions are considered in this work. As demonstrated by the DFT calculations, the most realistic model is based on the displacement of palladium ions leading to a near square planar PdO4 environment, which includes water molecules stabilizing the region of anion vacancies in their dissociated state as two hydroxyl groups. The introduction of water molecules in the composition of the PdxCe1-xO2-x-δ solution leads to a decrease in the formation energy and to additional stabilization of palladium in the CeO2 matrix. The formation of PdxCe1-xO2-x-δ solid solutions is accompanied by the dispersing effect caused by distortions of the fluorite structure induced by Pd(2+) ions. The coprecipitation method, which allows Pd(2+) ions to be introduced at the stage of fluorite structure formation, was demonstrated to be the optimal method for the synthesis of a homogeneous PdxCe1-xO2-x-δ solid solution.

Local Structure of Proton-Conducting Lanthanum Tungstate La28–xW4+xO54+δ: a Combined Density Functional Theory and Pair Distribution Function Study

Lanthanum tungstate (La28–xW4+xO54+δ) is a good proton conductor and exhibits a complex fluorite-type structure. To gain further understanding of the short-range order in the structure we correlate the optimized configurations obtained by density functional theory (DFT) with the experimental atomic pair distribution function analysis (PDF) of time-of-flight neutron and synchrotron X-ray data, collected at room temperature. The local atomic arrangements cannot be described by means of any average symmetric structure. Tungsten forms WO6 octahedra in alternating directions, La1 is mainly 8-fold coordinated in relatively symmetric cubes, and La2 is coordinated with 6 or 7 oxygens in heavily distorted cubes. Both DFT and PDF confirm that the excess tungsten (x) is incorporated in La2 (1/4, 1/4, 1/4) sites in the La27W5O55.5 composition. This additional tungsten can be considered as a donor self-dopant in the material and has implications to the conducting properties and the defect structure.

PDFgetX3: a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions

PDFgetX3is a new software application for converting X-ray powder diffraction data to an atomic pair distribution function (PDF).PDFgetX3has been designed for ease of use, speed and automated operation. The software can readily process hundreds of X-ray patterns within a few seconds and is thus useful for high-throughput PDF studies that measure numerous data sets as a function of time, temperature or other environmental parameters. In comparison to the preceding programs,PDFgetX3requires fewer inputs and less user experience and it can be readily adopted by novice users. The live-plotting interactive feature allows the user to assess the effects of calculation parameters and select their optimum values.PDFgetX3uses anad hocdata correction method, where the slowly changing structure-independent signal is filtered out to obtain coherent X-ray intensities that contain structure information. The output fromPDFgetX3has been verified by processing experimental PDFs from inorganic, organic and nanosized samples and comparing them with their counterparts from a previous established software. In spite of the different algorithm, the obtained PDFs were nearly identical and yielded highly similar results when used in structure refinement.PDFgetX3is written in the Python language and features a well documented reusable code base. The software can be used either as a standalone application or as a library of PDF processing functions that can be called from other Python scripts. The software is free for open academic research but requires paid license for commercial use.

Confirmation of disordered structure of ultrasmall CdSe nanoparticles from X-ray atomic pair distribution function analysis

The atomic pair distribution function (PDF) analysis of X-ray powder diffraction data has been used to study the structure of small and ultra-small CdSe nanoparticles. A method is described that uses a wurtzite and zinc-blende mixed phase model to account for stacking faults in CdSe particles. The mixed-phase model successfully describes the structure of nanoparticles larger than 2 nm yielding a stacking fault density of about 30%. However, for ultrasmall nanoparticles smaller than 2 nm, the models cannot fit the experimental PDF showing that the structure is significantly modified from that of larger particles and the bulk. The observation of a significant change in the average structure at ultra-small size is likely to explain the unusual properties of the ultrasmall particles such as their white light emitting ability.

Ab initio modeling of metallic Pd80Si20 glass

A realistic amorphous Pd80Si20 model is generated by means of ab initio molecular dynamics simulations, and its local structure is analyzed using various techniques. The model successfully reproduces the experimental pair distribution function and has an average coordination number of 12.10. The mean coordination number of Pd and Si atoms are 12.95 and 8.70, respectively. Si-centered atoms form principally two types of polyhedras; the tri-capped trigonal prism, ∼63%, and the standard square dodecahedron, 25%, whereas Pd-centered atoms present more complex packing with a coordination number ranging from 11 to 15. Common neighbor analysis suggests that icosahedral-, hexagonal-, and fcc defect-like bonding environments are the leading building units in Pd80Si20.

Structural features of pyrocarbon atomistic models constructed from transmission electron microscopy images

We report on atomistic models of laminar pyrocarbons constructed using a combination of 2D high resolution transmission electron microscopy (HRTEM) lattice fringe image analysis, 3D image synthesis and atomistic simulated annealing. In a first step, the effectiveness of the method and the convergence of the models with respect to the quench rate are checked on small systems. Then, the nanostructural features of large fully carbonaceous atomistic models obtained from the HRTEM images of a rough laminar pyrocarbon, as-prepared and after partial graphitization, are discussed. Both models show a very pronounced sp2 character (⩾97%), essentially made of hexagonal rings (⩾88%) and pentagonal and heptagonal rings in similar amounts (≈6%). The latter mostly form pentagon-heptagon pairs or networks of line defects between misoriented hexagonal domains. Numerous pairs of screw dislocations, connecting different graphene domains, are also observed while edge dislocations with unsaturated carbon atoms are almost absent. The models are validated with respect to experimental pair distribution functions, showing excellent agreement.

Pair distribution function analysis of molecular compounds: significance and modeling approach discussed using the example ofp-terphenyl

Modeling the pair distribution function (PDF) of molecular compounds is a challenging task because intra- and intermolecular interactions lead to very different features in the PDF. This article discusses the different peak shapes in PDFs of molecular compounds in detail. Moreover, the common methods to calculate PDFs from structural models are summarized and evaluated with respect to molecular systems and an approach to calculate PDFs from molecular crystals more accurately is introduced.p-Terphenyl was chosen as a test compound. It adopts a crystal structure with disordered features and short-range order. The short-range order was previously investigated by analyzing single-crystal diffuse scattering and it was also extracted from experimental PDFs during this study.

Probing Complex Disorder in Ce1-xGdxO2-x/2Using the Pair Distribution Function Analysis

In this work the first Pair Distribution Function (PDF) study on Ce1-xGdxO2-x/2 (CGO) electrolytes for solid oxide fuel cells is presented, aiming to unveil the complex positional disorder induced by gadolinium doping and oxygen vacancies formation in these materials. The whole range of Gd concentration xGd (0 ≤ xGd ≤ 1) of the CGO solid solutions was investigated through high resolution synchrotron radiation powder diffraction. The reciprocal space Rietveld analysis revealed in all the solid solutions the presence of positional disorder, which has been explicitly mapped into the real space. The average structural models, as obtained by the Rietveld method, fit well the experimental PDF data only for a spatial range r > ∼10 A. The same models applied at lower r values fails to reproduce the experimental curves. A clear improvement of the fit quality in the 1.5 < r < ∼6 A range was obtained for all the CGO samples applying a biphasic model encompassing both a fluorite CeO2-like and a C-type Gd2O3-like phas...

Ab initio molecular dynamics model for density, elastic properties and short range order of Co–Fe–Ta–B metallic glass thin films

Density, elastic modulus and the pair distribution function of Co–Fe–Ta–B metallic glasses were obtained by ab initio molecular dynamics simulations and measured for sputtered thin films using x-ray reflectivity, nanoindentation and x-ray diffraction using high energy photons. The computationally obtained density of 8.19 g cm−3 for Co43Fe20Ta5.5B31.5 and 8.42 g cm−3 for Co45.5Fe24Ta6B24.5, as well as the Young’s moduli of 273 and 251 GPa, respectively, are consistent with our experiments and literature data. These data, together with the good agreement between the theoretical and the experimental pair distribution functions, indicate that the model established here is useful to describe the density, elasticity and short range order of Co–Fe–Ta–B metallic glass thin films. Irrespective of the investigated variation in chemical composition, (Co, Fe)–B cluster formation and Co–Fe interactions are identified by density-of-states analysis. Strong bonds within the structural units and between the metallic species may give rise to the comparatively large stiffness.

Insight into the Hydrogenation Properties of Mechanically Alloyed Mg50Co50 from the Local Structure

The local structure of mechanically alloyed Mg50Co50 and its deuteride, Mg50Co50D75, was investigated using the atomic pair distribution function (PDF) analysis of neutron and synchrotron X-ray total scattering data. The purpose of our study was to obtain the structural information of these amorphous alloys and understand their hydrogen storage properties. We found that the body centered cubic (bcc) structural model with the uniform distribution of Mg and Co atoms proposed by earlier studies was not able to explain neutron and X-ray PDFs at the same time. Our data suggest that the local environment of Mg is different from that of Co. A two-phase model composed of MgCo2 and Mg2CoD5 (Mg2Co for the alloy sample) qualitatively reproduced the main features of experimental PDFs and explained the amount of hydrogen absorbed by MgxCo100-x.

Structural Interpretation in Composite Systems Using Powder X-ray Diffraction: Applications of Error Propagation to the Pair Distribution Function

To develop a method for drawing statistical inferences from differences between multiple experimental pair distribution function (PDF) transforms of powder X-ray diffraction (PXRD) data. The appropriate treatment of initial PXRD error estimates using traditional error propagation algorithms was tested using Monte Carlo simulations on amorphous ketoconazole. An amorphous felodipine:polyvinyl pyrrolidone:vinyl acetate (PVPva) physical mixture was prepared to define an error threshold. Co-solidified products of felodipine:PVPva and terfenadine:PVPva were prepared using a melt-quench method and subsequently analyzed using PXRD and PDF. Differential scanning calorimetry (DSC) was used as an additional characterization method. The appropriate manipulation of initial PXRD error estimates through the PDF transform were confirmed using the Monte Carlo simulations for amorphous ketoconazole. The felodipine:PVPva physical mixture PDF analysis determined ±3σ to be an appropriate error threshold. Using the PDF and error propagation principles, the felodipine:PVPva co-solidified product was determined to be completely miscible, and the terfenadine:PVPva co-solidified product, although having appearances of an amorphous molecular solid dispersion by DSC, was determined to be phase-separated. Statistically based inferences were successfully drawn from PDF transforms of PXRD patterns obtained from composite systems. The principles applied herein may be universally adapted to many different systems and provide a fundamentally sound basis for drawing structural conclusions from PDF studies.

Crystal structure solution from experimentally determined atomic pair distribution functions

An extension of the Liga algorithm for structure solution from atomic pair distribution functions (PDFs), to handle periodic crystal structures with multiple elements in the unit cell, is described. The procedure is performed in three separate steps. First, pair distances are extracted from the experimental PDF. In the second step the Liga algorithm is used to find unit-cell sites consistent with these pair distances. Finally, the atom species are assigned over the cell sites by minimizing the overlap of their empirical atomic radii. The procedure has been demonstrated on synchrotron X-ray PDF data from 16 test samples. The structure solution was successful for 14 samples, including cases with enlarged supercells. The algorithm success rate and the reasons for the failed cases are discussed, together with enhancements that should improve its convergence and usability.