Pair Distribution Function Refinement Research Articles

Synthesis, structural and spectroscopic characterization of defect-rich forsterite as a representative phase of Martian regolith.

Regolith draws intensive research attention because of its importance as the basis for fabricating materials for future human space exploration. Martian regolith is predicted to consist of defect-rich crystal structures due to long-term space weathering. The present report focuses on the structural differences between defect-rich and defect-poor forsterite (Mg2SiO4) - one of the major phases in Martian regolith. In this work, forsterites were synthesized using reverse strike co-precipitation and high-energy ball milling (BM). Subsequent post-processing was also carried out using BM to enhance the defects. The crystal structures of the samples were characterized by X-ray powder diffraction and total scattering using Cu and synchrotron radiation followed by Rietveld refinement and pair distribution function (PDF) analysis, respectively. The structural models were deduced by density functional theory assisted PDF refinements, describing both long-range and short-range order caused by defects. The Raman spectral features of the synthetic forsterites complement the ab initio simulation for an in-depth understanding of the associated structural defects.

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

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

Toward an Understanding of the Anisotropy in Hcp Zinc Metal: Total Scattering Structural Study Using Synchrotron-Based, Temperature-Dependent, X-Ray Pair Distribution Function Analysis

Abstract: Among hexagonal close packing (hcp) metals, zinc has a non-ideal hcp structure due to a significantly increased axial ratio c/a. We studied the behavior of the ratio of lattice constants c/a and the ratio of thermal displacement parameters (U_33 / U_11) in the temperature range of 100-300 K, using the X-ray total scattering atomic pair distribution function (PDF) analysis over different refinement r-ranges. The temperature-dependent PDF analysis confirmed that the crystal structure of zinc has significant static distortion along the c-direction. The measured value of atomic displacement parameters of zinc showed a notable anisotropy as expressed by the ratio U_33 / U_11 of ≈ 2.2 at 100 K. The lattice parameter ratio c/a was slightly reduced at low temperatures but remained unusually large. The extrapolated value of the ratio c/a reached 1.832 at 0 K. The PDF refinements using the crystallographic model revealed that there are some local structure features in zinc that are not captured by the crystallographic model. On the other hand, our local structure refinement indicated a presence of local bond distortion along the z-direction that averaged out over wider r-range refinements with a large U_33 value. Keywords: Hcp anisotropy, Zinc metal, Total scattering, X-ray scattering, Pair distribution function. PACs numbers: 61.46.Df, 61.10.-i, 78.66.Hf, 61.46.-w.

ClusterFinder: a fast tool to find cluster structures from pair distribution function data.

A novel automated high-throughput screening approach, ClusterFinder, is reported for finding candidate structures for atomic pair distribution function (PDF) structural refinements. Finding starting models for PDF refinements is notoriously difficult when the PDF originates from nanoclusters or small nanoparticles. The reported ClusterFinder algorithm can screen 104 to 105 candidate structures from structural databases such as the Inorganic Crystal Structure Database (ICSD) in minutes, using the crystal structures as templates in which it looks for atomic clusters that result in a PDF similar to the target measured PDF. The algorithm returns a rank-ordered list of clusters for further assessment by the user. The algorithm has performed well for simulated and measured PDFs of metal-oxido clusters such as Keggin clusters. This is therefore a powerful approach to finding structural cluster candidates in a modelling campaign for PDFs of nanoparticles and nanoclusters.

Time-dependent phase quantification and local structure analysis of hydroxide-activated slag via X-ray total scattering and molecular modeling

Here, an approach to quantify the amorphous-to-disordered/crystalline transformation occurring in NaOH-activated ground granulated blast-furnace slag (GGBS) is outlined that combines atomistic modeling with in situ pair distribution function (PDF) analysis. Firstly, by using force-field molecular dynamics (MD) simulations, a detailed structural representation is generated for the amorphous GGBS that is in agreement with experimental X-ray scattering data. Use of this structural representation along with literature-derived structures for the reaction products allows for real space X-ray PDF refinement of the alkaline activation of GGBS, resulting in the quantification of all phases and the degree of reaction (DOR) as a function of reaction time. All phases and the DOR are seen to approximately follow a logarithmic-type time-dependent behavior up to 5 months, while at the early age (up to 11 h), the DOR is accurately captured by a modified pseudo-single step first-order reaction model. Lastly, the evolution of DOR is found to agree with several other complementary in situ data containing quantitative reaction information, including isothermal conduction calorimetry, Fourier transform infrared spectroscopy, and quasi-elastic neutron scattering.

Local Structures of Oxygen-Deficient Perovskite Sr2ScGaO5 Polymorphs Explored by Total Neutron Scattering and EXAFS Spectroscopy.

Depending on the synthesis route, the oxygen ion electrolyte Sr2ScGaO5 shows two polymorphs, a brownmillerite and a cubic perovskite framework. In order to better explore oxygen diffusion pathways and mechanisms, we report here on a multitechnical approach to characterize local structural changes for Sr2ScGaO5 polymorphs as a function of temperature, using a neutron pair distribution function (PDF) analysis together with an extended X-ray absorption fine structure (EXAFS) analysis. While for the brownmillerite type structure PDF and Rietveld refinements yield identical structural descriptions, considerable differences are found for the cubic oxygen-deficient polymorph. On a local scale a brownmillerite type vacancy structure could be evidenced for the cubic phase, suggesting a complex short-range ordering and respective microstructure. Both PDF and EXAFS data confirm an octahedral and tetrahedral coordination for Sc and Ga, respectively, at a local scale for both polymorphs. Related changes in the bond distances and oxygen vacancy ordering are discussed.

Total-scattering pair-distribution function analysis of zinc from high-energy synchrotron data

The crystal structure of zinc metal deviates from the ideal hexagonal close packing structure by a significantly increased axial ratio (c/a). The local atomic structure of zinc metal is investigated using the total scattering atomic pair distribution function (PDF) analysis based on X-ray powder diffraction data collected at ambient conditions. The X-ray total scattering PDF analysis confirms that the crystal structure of zinc can be described in terms of wurtzite structure, but with an anomalously atomic displacement parameters [Formula: see text], indicating a significant displacement disorder along the [Formula: see text]-axis. For the long [Formula: see text]-range PDF refinements, the thermal motion of zinc shows a notable anisotropy as expressed by the ratio [Formula: see text]/[Formula: see text] of 2.5 at ambient conditions. This average distortion level along the [Formula: see text]-axis, was not reflected locally for the features below 5.0 Å as it fits the high [Formula: see text] region. Based on PDF refinements over different [Formula: see text]-ranges, we measure an interesting increase of the [Formula: see text] value with decreasing the [Formula: see text]-range of the refinement. This suggests that the local structure features in zinc metal differ from the average structure ones.

Investigating temperature-induced structural changes of lead halide perovskites by in situ X-ray powder diffraction

In situ X-ray diffraction experiments offer a unique opportunity to investigate structural dynamics at atomic resolution, by collecting several patterns in an appropriate time sequence (data matrix) while varying the applied stimulus (e.g. temperature changes). Individual measurements can be processed independently by refinement procedures that are based on prior knowledge of the average structure of each crystal phase present in the sample. If the refinement converges, parameters of the average structural model can be assessed and studied as a function of the stimulus variations. An alternative approach consists in applying a multivariate analysis to the data matrix as a whole. Methods such as principal component analysis (PCA) and phase-sensitive detection perform fast, blind and model-independent calculations that can be used for on-site analysis to identify trends in data actually related to the applied stimulus. Both classical and multivariate approaches are here applied to the in situ X-ray diffraction pair distribution function (PDF) setup on two samples of the hybrid perovskite methylammonium (MA) lead iodide obtained by different synthetic routes, subjected to temperature variations. The PDF refinement allows assessing the occurrence of temperature-induced rotations of the PbI6 octahedra and variations in the relative amount of MAPbI3 and intermediate PbI2–MAI–DMSO (dimethyl sulfoxide) crystal phases. A change in the orientation of the methylammonium molecule with temperature is also characterized. Results of the multivariate analysis tools, which include a newly introduced space-dependent variant of PCA, are described, interpreted and validated against simulated data, and their specificity and relation to refinement results are highlighted. The interaction between nearby octahedra is identified as the driving force for the tetragonal-to-cubic phase transition, and three fundamental trends in data having different temperature behaviours are unveiled: (i) irreversible weight-fraction variations of the MAPbI3 and PbI2–MAI–DMSO phases; (ii) reversible structural changes related to the MAPbI3 crystalline phase and its lattice distortion in the ab plane, having the same frequency as the temperature variations; (iii) reversible lattice distortion along the c axis, occurring at twice the frequency of the temperature changes.

Oxygen point defect accumulation in single-phase UO2+x

$\mathrm{U}{\mathrm{O}}_{2.07}$ was characterized using neutron total scattering in order to elucidate defect morphology in the low oxygen-to-metal regime $(x<0.125$ for $\mathrm{U}{\mathrm{O}}_{2+x})$. Data were collected at temperatures (600 and 1000 \ifmmode^\circ\else\textdegree\fi{}C) coinciding with the single-phase $\mathrm{U}{\mathrm{O}}_{2+x}$ region of the established phase diagram, and results were compared with data of stoichiometric $\mathrm{U}{\mathrm{O}}_{2}$ collected at near-identical temperatures. Experimental data were modeled and interpreted using a holistic approach employing a combination of analyses that characterized multiple spatial length scales. Preferential modeling of long-range atomic arrangements with Rietveld refinement suggests the existence of primarily monointerstitials in $\mathrm{U}{\mathrm{O}}_{2.07}$, whereas preferential modeling of short-range atomic structures with small-box pair distribution function (PDF) refinement indicates the presence of defect clusters in $\mathrm{U}{\mathrm{O}}_{2.07}$. Simultaneous modeling of multiple length scales using complementary reverse Monte Carlo (RMC) and molecular dynamics (MD) methods confirms that excess oxygen atoms in $\mathrm{U}{\mathrm{O}}_{2.07}$ exist as small defects, such as monointerstitials and di-interstitials. RMC and MD results agree with diffraction analysis but differ significantly from small-box PDF refinements, which may be related to a lack of intermediate- and long-range structural information gained from the small-box PDF refinement procedure. Employing a combination of analysis methods with varying length-scale sensitivities enabled more accurate assessment of the $\mathrm{U}{\mathrm{O}}_{2+x}$ defect structure. Our findings provide experimental support for previously predicted di-interstitial defect morphologies in $\mathrm{U}{\mathrm{O}}_{2+x}$ that highly influence the accurate prediction of bulk physiochemical properties of $\mathrm{U}{\mathrm{O}}_{2+x}$, such as oxygen diffusivity.

Pushing data quality for laboratory pair distribution function experiments.

Over the last decade, some studies with laboratory pair distribution function (PDF) data emerged. Yet, limited Qmax or instrumental resolution impeded in-depth structural refinements. With more advanced detector technologies, the question arose how to design novel PDF equipment for laboratories that will allow decent PDF refinements over r = 1-70 Å. It is crucial to reflect the essential requirements, namely, monochromatic X-rays, suppression of air scattering, instrumental resolution, and overall measurement times. The result is a novel PDF setup based on a STOE STADI P powder diffractometer in transmission-/Debye-Scherrer geometry with monochromatic Ag Kα1 radiation, featuring a MYTHEN2 4K detector covering a Q range of 0.3-20.5 Å-1. PDF data are collected in a moving PDF mode within 6 h. Structural signatures of liquids can be satisfactorily resolved in the PDF as shown for the ionic liquid hmimPF6. The high instrumental resolution is mirrored in low qdamp values determined from LaB6 measurements. PDF data from a powder sample of ca. 7 nm TiO2 nanoparticles were successfully refined over up to 70 Å with goodness-of-fit values Rw < 0.22 (respectively Rw = 0.18 over 30 Å), thanks to the low background and high instrumental resolution, hereby enlarging the accessible r range by several tens of Angstroms compared to previous laboratory PDF studies.

Characterization of Oxygen Defect Clusters in UO2+ x Using Neutron Scattering and PDF Analysis.

In hyper-stoichiometric uranium oxide, both neutron diffraction work and, more recently, theoretical analyses report the existence of clusters such as the 2:2:2 cluster, comprising two anion vacancies and two types of anion interstitials. However, little is known about whether there exists a region of low deviation-from-stoichiometry in which defects remain isolated, or indeed whether at high deviation-from-stoichiometry defect clusters prevail that contain more excess oxygen atoms than the di-interstitial cluster. In this study, we report pair distribution function (PDF) analyses of UO2 and UO2+ x ( x ≈ 0.007 and x ≈ 0.16) samples obtained from high-temperature in situ neutron scattering experiments. PDF refinement for the lower deviation from stoichiometry sample suggests the system is too dilute to differentiate between isolated defects and di-interstitial clusters. For the UO2.16 sample, several defect structures are tested, and it is found that the data are best represented assuming the presence of center-occupied cuboctahedra.

Development of an in situ synchrotron X-ray total scattering setup under pressurized hydrogen gas

This article describes the development of an in situ gas-loading sample holder for synchrotron X-ray total scattering experiments, particularly for hydrogen storage materials, designed to collect diffraction and pair distribution function (PDF) data under pressurized hydrogen gas. A polyimide capillary with a diameter and thickness of 1.4 and 0.06 mm, respectively, connected with commercially available Swagelok fittings was used as an in situ sample holder. Leakage tests confirmed that this sample holder allows 3 MPa of hydrogen gas pressure and 393 K to be achieved without leakage. Using the developed in situ sample holder, significant background and Bragg peaks from the sample holder were not observed in the X-ray diffraction patterns and their signal-to-noise ratios were sufficiently good. The PDF patterns showed sharp peaks in the r range up to 100 Å. The results of Rietveld and PDF refinements of Ni are consistent with those obtained using a polyimide capillary (1.0 mm diameter and 0.04 mm thickness) that has been used for ex situ experiments. In addition, in situ synchrotron X-ray total scattering experiments under pressurized hydrogen gas up to 1 MPa were successfully demonstrated for LaNi4.6Cu.

TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++

TOPAS and its academic variant TOPAS-Academic are nonlinear least-squares optimization programs written in the C++ programming language. This paper describes their functionality and architecture. The latter is of benefit to developers seeking to reduce development time. TOPAS allows linear and nonlinear constraints through the use of computer algebra, with parameter dependencies, required for parameter derivatives, automatically determined. In addition, the objective function can include restraints and penalties, which again are defined using computer algebra. Of importance is a conjugate gradient solution routine with bounding constraints which guide refinements to convergence. Much of the functionality of TOPAS is achieved through the use of generic functionality; for example, flexible peak-shape generation allows neutron time-of-flight (TOF) peak shapes to be described using generic functions. The kernel of TOPAS can be run from the command line for batch mode operation or from a closely integrated graphical user interface. The functionality of TOPAS includes peak fitting, Pawley and Le Bail refinement, Rietveld refinement, single-crystal refinement, pair distribution function refinement, magnetic structures, constant wavelength neutron refinement, TOF refinement, stacking-fault analysis, Laue refinement, indexing, charge flipping, and structure solution through simulated annealing.

Local structural behavior of PbZr0.5Ti0.5O3 during electric field application via in situ pair distribution function study

The local structural behavior of PbZr0.5Ti0.5O3 (PZT 50/50) ceramics during application of an electric field was investigated using pair distribution function (PDF) analysis. In situ synchrotron total scattering was conducted, and the PDFs were calculated from the Fourier transform of the total scattering data. The PDF refinement of the zero-field data suggests a local-structure model with [001] Ti-displacement and negligible Zr-displacement. The directional PDFs at different field amplitudes indicate the bond-length distribution of the nearest Pb-B (B = Zr/Ti) pair changes significantly with the field. The radial distribution functions (RDFs) of a model for polarization rotation were calculated. The calculated and the experimental RDFs are consistent. This result suggests the changes in Pb-B bond-length distribution could be dominantly caused by polarization rotation. Peak fitting of the experimental RDFs was also conducted. The peak position trends with increasing field are mostly in agreement with the calculation result of the polarization rotation model. The area ratio of the peaks in the experimental RDFs also changed with field amplitude, indicating that Zr atoms have a detectable displacement driven by the electric field. Our study provides an experimental observation of the behaviors of PZT 50/50 under field at a local scale which supports the polarization rotation mechanism.

Pair distribution function analysis of nanostructural deformation of calcium silicate hydrate under compressive stress

AbstractDespite enormous interest in calcium silicate hydrate (C–S–H), its detailed atomic structure and intrinsic deformation under an external load are lacking. This study demonstrates the nanostructural deformation process of C–S–H in tricalcium silicate (C3S) paste as a function of applied stress by interpreting atomic pair distribution function (PDF) based on in situ X‐ray scattering. Three different strains in C3S paste under compression were compared using a strain gauge, Bragg peak shift, and the real space PDF. PDF refinement revealed that the C–S–H phase mostly contributed to PDF from 0 to 20 Å whereas crystalline phases dominated that beyond 20 Å. The short‐range atomic strains exhibited two regions for C–S–H: I) plastic deformation (0‐10 MPa) and II) linear elastic deformation (&gt;10 MPa), whereas the long‐range deformation beyond 20 Å was similar to that of Ca(OH)2. Below 10 MPa, the short‐range strain was caused by the densification of C–S–H induced by the removal of interlayer or gel‐pore water. The strain is likely to be recovered when the removed water returns to C–S–H.

Atomic pair distribution function at the Brazilian Synchrotron Light Laboratory: application to the Pb1-xLaxZr0.40Ti0.60O3 ferroelectric system.

This work reports the setting up of the X-ray diffraction and spectroscopy beamline at the Brazilian Synchrotron Light Laboratory for performing total scattering experiments to be analyzed by atomic pair distribution function (PDF) studies. The results of a PDF refinement for Al2O3 standard are presented and compared with data acquired at a beamline of the Advanced Photon Source, where it is common to perform this type of experiment. A preliminary characterization of the Pb1-xLaxZr0.40Ti0.60O3 ferroelectric system, with x = 0.11, 0.12 and 0.15, is also shown.

X-ray and neutron total scattering analysis of Hy·(Bi0.2Ca0.55Sr0.25)(Ag0.25Na0.75)Nb3O10·xH2O perovskite nanosheet booklets with stacking disorder

Ion-exchanged Aurivillius materials form perovskite nanosheet booklets wherein well-defined bi-periodic sheets, with ~11.5 Å thickness, exhibit extensive stacking disorder. The perovskite layer contents were defined initially using combined synchrotron X-ray and neutron Rietveld refinement of the parent Aurivillius structure. The structure of the subsequently ion-exchanged material, which is disordered in its stacking sequence, is analyzed using both pair distribution function (PDF) analysis and recursive method simulations of the scattered intensity. Combined X-ray and neutron PDF refinement of supercell stacking models demonstrates sensitivity of the PDF to both perpendicular and transverse stacking vector components. Further, hierarchical ensembles of stacking models weighted by a standard normal distribution are demonstrated to improve PDF fit over 1–25 Å. Recursive method simulations of the X-ray scattering profile demonstrate agreement between the real space stacking analysis and more conventional reciprocal space methods. The local structure of the perovskite sheet is demonstrated to relax only slightly from the Aurivillius structure after ion exchange.

In situ reduction study of cobalt model Fischer-Tropsch synthesis catalyst

Fischer-Tropsch (FT) synthesis is an important process to manufacture hydrocarbons and oxygenated hydrocarbons from mixtures of carbon monoxide and hydrogen (syngas). The catalysis process occurs on for example cobalt metal surfaces at elevated temperatures and pressures. A fundamental understanding of the reduction pathway of supported cobalt oxides, and the intermediate species present during the activation, can assist in developing improved industrial supported cobalt catalysts. Measurements were done during in-situ hydrogen activation of a model Co/alumina catalyst using in-situ synchrotron X-ray powder diffraction and pair-distribution function (PDF) analysis. Strong metal-support interactions between the Co and the support1 can make the catalyst more stable towards sintering. The supported cobalt oxide catalyst precursors have to undergo reductive pre-treatments before their use as FT catalysts. During activation the cobalt oxides evolve, resulting in the formation of metallic cobalt depending on temperature, pressure of activation gases, concentration, time of exposure etc. The effect of hydrogen activation treatments on model catalysts were reported previously [1,2], however analysis of the alumina support phases was excluded from the interpretation by subtraction and normalisation. The PDF refinement accounted for all cobalt present in the catalyst sample and after reduction mainly Co(fcc) with a little Co(hcp) was found to be present. This is a novel approach to in situ PDF analysis of catalysts containing a mixture of phases [3].

Structural analysis of highly porous γ-Al2O3

Two highly porous γ-aluminas, a commercial catalyst obtained from the calcination of boehmite and a highly mesoporous product obtained from amorphous aluminum (oxy)hydroxide via a sol–gel-based process were investigated by 27Al nuclear magnetic resonance (NMR), transmission electron microscopy (TEM), and atomic pair distribution function (PDF) analysis of synchrotron powder diffraction data. NMR data showed for both materials a distribution of tetrahedrally and octahedrally coordinated Al at a 0.30:0.70 ratio, which is typical for γ-aluminas. TEM studies revealed that rod-shaped particles with about 5nm in thickness are the building blocks of the porous structure in both materials. These particles often extend to a length of 50nm in the commercial catalyst and are considerably shorter in the sol–gel-based material, which has a higher surface area. Refinement of PDFs revealed the presence of a ~1nm scale local structure and the validity of a tetragonal average structure for both materials. This tetragonal average structure contains a substantial fraction of non-spinel octahedral Al atoms. It is argued that the presence of local structure is a general feature of γ-alumina, independent of precursor and synthesis conditions. The concentration of “non-spinel” Al atoms seems to correlate with surface properties, and increases with increasing pore size/surface area. This should have implications to the catalytic properties of porous γ-alumina.

A large-area CMOS detector for high-energy synchrotron powder diffraction and total scattering experiments

A complementary metal-oxide semiconductor (CMOS) detector with an active area of 290.8 × 229.8 mm has been evaluated for X-ray scattering experiments at energies between 20 and 50 keV. Detector calibration and integration procedures are discussed in addition to the determination of the linearity, angular resolution and energy response of the detector in the context of its envisaged use. Data on reference compounds and samples with different crystallinity were collected and analysed with classical Rietveld and pair distribution function refinements. Comparisons with literature and high-resolution data from the same beamline demonstrate that the presented detector is suitable for crystallographic and total scattering experiments.