Experimental Pair Distribution Function Research Articles

Structural Analysis of Ligand-Protected Smaller Metallic Nanocrystals by Atomic Pair Distribution Function under Precession Electron Diffraction

Atomic pair distribution function (PDF) analysis has been widely used to investigate nanocrystalline and structurally disordered materials. Experimental PDFs retrieved from electron diffraction (eP...

Using a machine learning approach to determine the space group of a structure from the atomic pair distribution function.

A method is presented for predicting the space group of a structure given a calculated or measured atomic pair distribution function (PDF) from that structure. The method utilizes machine learning models trained on more than 100 000 PDFs calculated from structures in the 45 most heavily represented space groups. In particular, a convolutional neural network (CNN) model is presented which yields a promising result in that it correctly identifies the space group among the top-6 estimates 91.9% of the time. The CNN model also successfully identifies space groups for 12 out of 15 experimental PDFs. Interesting aspects of the failed estimates are discussed, which indicate that the CNN is failing in similar ways as conventional indexing algorithms applied to conventional powder diffraction data. This preliminary success of the CNN model shows the possibility of model-independent assessment of PDF data on a wide class of materials.

Disorder in La1−x Ba1+x GaO4−x/2 ionic conductor: resolving the pair distribution function through insight from first-principles modeling

Ionic conduction in dry LaBaGaO4 occurs through the vacant oxygen sites formed by the substitution of Ba for La. The resulting La1−x Ba1+x GaO4−x/2 solid solution shows significant disorder characteristics. The local structure of compositions x = 0, 0.20 and 0.30 was studied using the pair distribution function (PDF). Unfortunately, increasing peak overlap and the number of independent structural parameters make PDF modeling challenging when dealing with low-symmetry phases. To overcome this problem, density functional theory (DFT) was employed to create different structural models, each one with a different relative position for the substitutional Ba ion with respect to the oxygen vacancy. The atomic distributions generated by DFT were used as a starting point to refine experimental PDF data. All models result in the formation of Ga2O7 dimers, with their major axis oriented along the c axis. At the local scale, the most stable DFT model also provides the best fit of the PDF. This accounts for the dopant as first and second neighbors of the vacancy and of the O bridge in the dimer, suggesting that substitutional barium ions act as pinning centers for oxygen vacancies. Above 6 Å the average orthorhombic structure fits the PDF better than the DFT models, thus indicating that Ga2O7 dimers are not correlated with each other to form extended ordered structures. The combination of DFT simulations and X-ray diffraction/PDF refinements was used successfully to model the local atomic structure in La1−x Ba1+x GaO4−x/2, thus suggesting that this approach could be positively applied in general to disordered systems.

Atomic structure of nanodiamond and its evolution upon annealing up to 1200 °C: Real space neutron diffraction analysis supported by MD simulations

Lattice strain, crystallite shape and the crystallite size distribution in nanocrystalline diamond were determined from powder diffraction data. The data were analyzed by the direct space PDF method in combination with Molecular Dynamics simulations. Experimental Pair Distribution Functions were obtained from the large Q neutron diffraction data. Lattice strains were determined by comparison of the atomic pair distances at different length scales. The experimental pair-distance data were matched against the Molecular Dynamics models of diamond nanograins. Lattice relaxation at the surface and in the bulk of the simulated nanodiamond grains varied with their shape and size. Comparison of the model data to the experimentally determined strain characteristics yielded accurate information on the structure of the actual nanodiamond powders. In the as-synthesized nanodiamond the grains are polyhedrons predominantly terminated by (100) and (111) surfaces. Upon annealing the (111) surfaces with one dangling bond per atom graphitize and transform into surfaces with three dangling bond per atom. In the samples annealed at 1200 °C all grains are octahedrons terminated only by three dangling bond (111) surfaces. The mechanism of the atom rearrangement during the transformation of the (111) diamond surface into a graphite double-sheet was proposed.

Roles of Hydration and Magnetism on the Structure of Ferrihydrite from First Principles

We report density functional theory calculations aimed at predicting thermodynamically stable structures for ferrihydrite across a range of possible compositions determined by the amount of structural water. Based on an assumed formula unit of Fe5O8H + nH2O, we performed ab initio calculations with evolutionary searching to find the lowest enthalpy structures as a function of the water content up to n = 2. This is the most exhaustive search for the ferrihydrite structure conducted so far; more than 5000 unique configurations were generated and evaluated over five states of hydration. Among them, the Michel akdaliate model was generated, along with several energetically comparable new structures at higher states of hydration. However, a direct comparison between calculated and experimental pair distribution function and X-ray diffraction patterns for the 50 lowest energy structures shows that none beyond the Michel model could be associated with ferrihydrite. Nevertheless, this energetically comparable str...

Polytypism in Hexagonal Tungsten Trioxide: Insights from Ab Initio Molecular Dynamics Simulations

Temperature-dependent microstructural evolution of hexagonal WO3 (h-WO3) polytypes is explored via ab initio molecular dynamics calculations within the density-functional theory framework. We present simulated finite temperature radial distribution function and X-ray diffraction patterns to reinterpret recent experimental pair distribution function analysis. This work clearly demonstrates that after a more careful analysis of the finite temperature structural properties of h-WO3, an intermediate H1-like structure is predicted at higher temperatures, while the more stable H4 polytype (and not the experimentally suggested H2 polytype) is obtained nearer ambient temperatures. This is further corroborated by our electronic structure analysis which shows that the electronic band gap energy of the ambient temperature H4-like structure agrees much better with the experimentally reported band gap energies.

Analysis of stacking disorder in ice I using pair distribution functions

Stacking-disordered materials display crystalline order in two dimensions but are disordered along the direction in which layered structural motifs are stacked. Countless examples of stacking disorder exist, ranging from close-packed metals, ice I and diamond to open-framework materials and small-molecule pharmaceuticals. In general, the presence of stacking disorder can have profound consequences for the physical and chemical properties of a material. Traditional analyses of powder diffraction data are often complicated by the presence of memory effects in the stacking sequences. Here it is shown that experimental pair distribution functions of stacking-disordered ice I can be used to determine local information on the fractions of cubic and hexagonal stacking. Ice is a particularly challenging material in this respect, since both the stacking disorder and the orientational disorder of the water molecules need to be described. Memory effects are found to contribute very little to the pair distribution functions, and consequently, the analysis of pair distribution functions is the method of choice for characterizing stacking-disordered samples with complicated and high-order memory effects. In the context of this work, the limitations of current structure-reconstruction approaches are also discussed.

On the origins of strain inhomogeneity in amorphous materials

Strain is a crucial measure of materials deformation for evaluating and predicting the mechanical response, strength, and fracture. The spatial resolution attainable by the modern real and reciprocal space techniques continues to improve, alongside the ability to carry out atomistic simulations. This is offering new insights into the very concept of strain. In crystalline materials, the presence of well-defined, stable atomic planes allows defining strain as the relative change in the interplanar spacing. However, the presence of disorder, e.g. locally around defects such as dislocation cores, and particularly the pervasive atomic disorder in amorphous materials challenge existing paradigms: disorder prevents a reference configuration being defined, and allows strain to be accommodated in a different manner to crystalline materials. As an illustration, using experimental pair distribution function analysis in combination with Molecular Dynamic (MD) simulations, we highlight the importance of bond angle change vs bond stretching for strain accommodation in amorphous systems.

Multiphase modelling of Pb(Zr1-xTix)O3 structure

ABSTRACTWe provide a description of the structural motifs of PbZr1-xTixO3 (PZT) at x = 0.4 using multiphase approach. We developed a novel methodology that uses a set of local phases predicted by ab initio structure searching to reproduce the experimental pair distribution function profile. Our results demonstrate that the permutation of B-site cations stabilises a variety of local PZT phases that reflects the flatness of energy landscape in vicinity of morphotropic phase boundary. We found that PZT at x = 0.4 can be described by a complex multiphase structure with variety of low-symmetry phases at the local scale.

Local structure and oxide-ion conduction mechanism in apatite-type lanthanum silicates

The local structure of apatite-type lanthanum silicates of general formula La9.33+x(SiO4)6O2+3x/2 has been investigated by combining the atomic pair distribution function (PDF) method, conventional X-ray and neutron powder diffraction (NPD) data and density functional theory (DFT) calculations. DFT was used to build structure models with stable positions of excess oxide ions within the conduction channel. Two stable interstitial positions were obtained in accordance with literature, the first one located at the very periphery of the conduction channel, neighbouring the SiO4 tetrahedral units, and the second one closer to the channel axis. The corresponding PDFs and average structures were then calculated and tested against experimental PDFs obtained by X-ray total scattering and NPD Rietveld refinements results gathered from literature. It was shown that of the two stable interstitial positions obtained with DFT only the second one located within the channel is consistent with experimental data. This result consolidates one of the two main conduction mechanisms along the c-axis reported in the literature, namely the one involving cooperative movement of O4 and Oi ions.

TEM-based Pair Distribution Function study of interatomic distances in C-supported Pt

The interatomic distances have been characterised for a Pt on Carbon based fuel cell catalyst studied by analysing the atomic pair distribution functions (PDF) obtained from electron diffraction (ED) data taken in a transmission electron microscope (TEM). The experimental PDFs have been compared with atomistic models to examine C-C and Pt-Pt interatomic distances. Further, the models have been refined by reverse Monte-Carlo simulations (RMC) based on the experimental PDF, enabling the investigation of Pt-C interatomic distances. This has demonstrated the existence of an interatomic contact between the Pt and C.

Local structure of liquid gallium under pressure

In situ high energy X-ray pair distribution function (PDF) measurements, microtomography and reverse Monte Carlo simulations were used to characterize the local structure of liquid gallium up to 1.9 GPa. This pressure range includes the well-known solid-solid phase transition from Ga-I to Ga-II at low temperature. In term of previous research, the local structure of liquid gallium within this domain was suggested a mixture of two local structures, Ga I and Ga II, based on fitting experimental PDF to known crystal structure, with a controversy. However, our result shows a distinctly different result that the local structure of liquid gallium resembles the atomic arrangement of both gallium phase II and III (the high pressure crystalline phase). A melting mechanism is proposed for Ga, in which the atomic structure of phase Ι breaks up at the onset of melting, providing sufficient free volume for atoms to rearrange, to form the melt.

Local structure study of the orbital order/disorder transition inLaMnO3

We use a combination of neutron and X-ray total scattering measurements together with pair distribution function (PDF) analysis to characterise the variation in local structure across the orbital order--disorder transition in LaMnO$_3$. Our experimental data are inconsistent with a conventional order--disorder description of the transition, and reflect instead the existence of a discontinuous change in local structure between ordered and disordered states. Within the orbital-ordered regime, the neutron and X-ray PDFs are best described by a local structure model with the same local orbital arrangements as those observed in the average (long-range) crystal structure. We show that a variety of meaningfully-different local orbital arrangement models can give fits of comparable quality to the experimental PDFs collected within the disordered regime; nevertheless, our data show a subtle but consistent preference for the anisotropic Potts model proposed in \emph{Phys Rev.\ B} {\bf 79}, 174106 (2009). The key implications of this model are electronic and magnetic isotropy together with the loss of local inversion symmetry at the Mn site. We conclude with a critical assessment of the interpretation of PDF measurements when characterising local symmetry breaking in functional materials.

Local and average structure of Mn- and La-substituted BiFeO3

The local and average structure of solid solutions of the multiferroic perovskite BiFeO3 is investigated by synchrotron X-ray diffraction (XRD) and electron density functional theory (DFT) calculations. The average experimental structure is determined by Rietveld refinement and the local structure by total scattering data analyzed in real space with the pair distribution function (PDF) method. With equal concentrations of La on the Bi site or Mn on the Fe site, La causes larger structural distortions than Mn. Structural models based on DFT relaxed geometry give an improved fit to experimental PDFs compared to models constrained by the space group symmetry. Berry phase calculations predict a higher ferroelectric polarization than the experimental literature values, reflecting that structural disorder is not captured in either average structure space group models or DFT calculations with artificial long range order imposed by periodic boundary conditions. Only by including point defects in a supercell, here Bi vacancies, can DFT calculations reproduce the literature results on the structure and ferroelectric polarization of Mn-substituted BiFeO3. The combination of local and average structure sensitive experimental methods with DFT calculations is useful for illuminating the structure-property-composition relationships in complex functional oxides with local structural distortions.

Paracrystalline Disorder from Phosphate Ion Orientation and Substitution in Synthetic Bone Mineral.

Hydroxyapatite is an inorganic mineral closely resembling the mineral phase in bone. However, as a biological mineral, it is highly disordered, and its composition and atomistic structure remain poorly understood. Here, synchrotron X-ray total scattering and pair distribution function analysis methods provide insight into the nature of atomistic disorder in a synthetic bone mineral analogue, chemically substituted hydroxyapatite. By varying the effective hydrolysis rate and/or carbonate concentration during growth of the mineral, compounds with varied degrees of paracrystallinity are prepared. From advanced simulations constrained by the experimental pair distribution function and density functional theory, the paracrystalline disorder prevalent in these materials appears to result from accommodation of carbonate in the lattice through random displacement of the phosphate groups. Though many substitution modalities are likely to occur in concert, the most predominant substitution places carbonate into the mirror plane of an ideal phosphate site. Understanding the mineralogical imperfections of a biologically analogous hydroxyapatite is important not only to potential bone grafting applications but also to biological mineralization processes themselves.

Modeling Pair Distribution Functions of Rare-Earth Phosphate Glasses Using Principal Component Analysis.

The use of principal component analysis (PCA) to statistically infer features of local structure from experimental pair distribution function (PDF) data is assessed on a case study of rare-earth phosphate glasses (REPGs). Such glasses, codoped with two rare-earth ions (R and R') of different sizes and optical properties, are of interest to the laser industry. The determination of structure-property relationships in these materials is an important aspect of their technological development. Yet, realizing the local structure of codoped REPGs presents significant challenges relative to their singly doped counterparts; specifically, R and R' are difficult to distinguish in terms of establishing relative material compositions, identifying atomic pairwise correlation profiles in a PDF that are associated with each ion, and resolving peak overlap of such profiles in PDFs. This study demonstrates that PCA can be employed to help overcome these structural complications, by statistically inferring trends in PDFs that exist for a restricted set of experimental data on REPGs, and using these as training data to predict material compositions and PDF profiles in unknown codoped REPGs. The application of these PCA methods to resolve individual atomic pairwise correlations in t(r) signatures is also presented. The training methods developed for these structural predictions are prevalidated by testing their ability to reproduce known physical phenomena, such as the lanthanide contraction, on PDF signatures of the structurally simpler singly doped REPGs. The intrinsic limitations of applying PCA to analyze PDFs relative to the quality control of source data, data processing, and sample definition, are also considered. While this case study is limited to lanthanide-doped REPGs, this type of statistical inference may easily be extended to other inorganic solid-state materials and be exploited in large-scale data-mining efforts that probe many t(r) functions.

Structural transition in sputter-deposited amorphous germanium films by aging at ambient temperature

The structure of amorphous Ge (a-Ge) films prepared by sputter-deposition and the effects of aging at ambient temperature and pressure were studied by pair-distribution-function (PDF) analysis from electron scattering and molecular dynamics simulations. The PDFs of the as-deposited and aged samples for 3–13 months showed that the major peaks for Ge-Ge bonds decrease in intensity and broaden with aging for up to 7 months. In the PDFs of a-Ge of molecular dynamics simulation obtained by quenching liquid at different rates, the major peak intensities of a slowly cooled model are higher than those of a rapidly cooled model. Analyses on short- and medium-range configurations show that the slowly cooled model includes a certain amount of medium-range ordered (MRO) clusters, while the rapidly cooled model includes liquid-like configurations rather than MRO clusters. The similarity between experimental and computational PDFs implies that as-deposited films are similar in structure to the slowly cooled model, whereas the fully aged films are similar to the rapidly cooled model. It is assumed that as they undergo room-temperature aging, the MRO clusters disintegrate and transform into liquid-like regions in the same matrix. This transition in local configurations is discussed in terms of instability and the non-equilibrium of nanoclusters produced by a vapor-deposition process.

Influence of interstitial Mn on local structure and magnetism inMn1+δSb

We report x-ray total scattering and pair distribution function (PDF) studies of the structural relaxation around interstitial manganese (Mn$_i$) in ferromagnetic Mn$_{1+\delta}$Sb ($0.03 \le \delta \le 0.23$) alloys, guided by density functional theory (DFT). Refinements to the experimental PDF using a crystallographically constrained structural model indicate an expansion in the equatorial plane of the Mn$_i$Sb$_5$ trigonal bipyramidal site, which introduces significant positional disorder in addition to the nominally-random occupation of interstitial voids. Observation of a weak diffuse signal near the symmetry-forbidden (001) reflection position is indicative of correlated disorder from the clustering of Mn$_i$. Density functional relaxation of supercells approximating the $\delta = 0.08$, $0.15,$ and $0.23$ compositions provides improved models that accurately describe the short-range structural distortions captured in the PDFs. Such structural relaxation increases the DFT calculated moment on Mn$_i$, which aligns antiparallel to the primary Mn moments, but leads to insubstantial changes in the average Mn and Sb moments and moments of Mn and Sb proximal to interstitials, thus providing a more accurate description of the observed bulk magnetic properties.

Targeted Single-Site MOF Node Modification: Trivalent Metal Loading via Atomic Layer Deposition

Postsynthetic functionalization of metal organic frameworks (MOFs) enables the controlled, high-density incorporation of new atoms on a crystallographically precise framework. Leveraging the broad palette of known atomic layer deposition (ALD) chemistries, ALD in MOFs (AIM) is one such targeted approach to construct diverse, highly functional, few-atom clusters. We here demonstrate the saturating reaction of trimethylindium (InMe3) with the node hydroxyls and ligated water of NU-1000, which takes place without significant loss of MOF crystallinity or internal surface area. We computationally identify the elementary steps by which trimethylated trivalent metal compounds (ALD precursors) react with this Zr-based MOF node to generate a uniform and well characterized new surface layer on the node itself, and we predict a final structure that is fully consistent with experimental X-ray pair distribution function (PDF) analysis. We further demonstrate tunable metal loading through controlled number density of t...

Comparison of total scattering data from various sources: the case of a nanometric spinel

Total scattering data of nanocrystalline gahnite (ZnAl2O4, 2–3 nm) have been collected with three of the most commonly used instruments: (i) ID31 high-resolution diffractometer at the European Synchrotron Radiation Facility (ESRF) (Qmax = 22 Å−1); (ii) ID11 high-energy beamline at the ESRF (Qmax = 26.6 Å−1); and (iii) Empyrean laboratory diffractometer by PANalytical with molybdenum anode X-ray tube (Qmax = 17.1 Å−1). Pair distribution functions (PDFs) for each instrument data-set have been obtained, changing some of the parameters, by PDFgetX3 software, with the aim of testing the software in the treatment of different total scattering data. The material under analysis has been chosen for its nanometric (and possibly disordered) nature, to give rise to a challenge for all the diffractometers involved. None of the latter should have a clear advantage. The PDF and F(Q) functions have been visually compared, and then the three PDF sets have been used for refinements by means of PDFgui suite. All the refinements have been made exactly in the same way for the sake of a fair comparison. Small differences could be observed in the experimental PDFs and the derived results, but none of them seemed to be significant.