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A method for generating the atomic pair distribution function (PDF) from powder diffraction data by the removal of instrument contributions, such as Kα2 from laboratory instruments or peak asymmetry from neutron time-of-flight data, has been implemented in the computer programs TOPAS and TOPAS-Academic. The resulting PDF is sharper, making it easier to identify structural parameters. The method fits peaks to the reciprocal-space diffraction pattern data whilst maximizing the intensity of a background function. The fit to the raw data is made `perfect' by including a peak at each data point of the diffraction pattern. Peak shapes are not changed during refinement and the process is a slight modification of the deconvolution procedure of Coelho [J. Appl. Cryst. (2018), 51, 112–123]. Fitting to the raw data and subsequently using the calculated pattern as an estimation of the underlying signal reduces the effects of division by small numbers during atomic scattering factor and polarization corrections. If the peak shape is sufficiently accurate then the fitting process should also be able to determine the background if the background intensity is maximized; the resulting calculated pattern minus background should then comprise coherent scattering from the sample. Importantly, the background is not allowed complete freedom; instead, it comprises a scan of an empty capillary sample holder with a maximum of two additional parameters to vary its shape. Since this coherent scattering is a calculated pattern, it can be easily recalculated without instrumental aberrations such as capillary sample aberration or Kα2 from laboratory emission profiles. Additionally, data reduction anomalies such as incorrect integration of data from two-dimensional detectors, resulting in peak position errors, can be easily corrected. Multiplicative corrections such as polarization and atomic scattering factors are also performed. Once corrected, the pattern can be scaled to produce the total scattering structure factor F(Q) and from there the sine transform is applied to obtain the pair distribution function G(r).

We present a new processing & analysis package of the atomic pair distribution function (PDF) for the electron diffraction (ED) pattern based on the total scattering theory which has been broadly used in the X-ray or neutron diffraction to reveal the local atomic structures, but PDF analysis based on the electron diffraction is still rarely used for the lack of an efficient PDF tool. The program was written as a package of DigitalMicrograph, a very popular software to record and analyze the data of transmission electron microscopes (TEM) in the most of TEM laboratories. The azimuthal rotation-average projection algorithm was implemented to enhance the signal-noise ratio of the intensity profile. In order to obtain the reduced structure function, the cubic spline fitting method was utilized to subtract the background scattering. The real-time displayed PDF makes data normalization easier and more accurate, and results of coordination numbers and averaged bond angles can be extracted from calibrated PDFs in real time. Program summary Program Title: ePDF tools Program Files doi: http://dx.doi.org/10.17632/ff94wp42wd.1 Licensing provisions: GPLv3 Programming language: DigitalMicrograph scripting language Nature of problem: The total scattering technique has been widely used in X-ray or neutron diffraction, but for the electron diffraction it still lacks an efficient analysis tool for the atomic pair distribution function. Solution method: Intensity profile is obtained by azimuthal rotation-average projection of 2D SAED pattern, the background scattering is subtracted by the cubic spline method, data normalization is real-time performed based on the total scattering theory, the atomic pair distribution functions obtained by Fourier transform will be used to quantitative analysis.

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

Made available in DSpace on 2018-12-11T16:49:14Z (GMT). No. of bitstreams: 0 Previous issue date: 2017-09-01 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.A setup for total scattering experiments at the multi-purpose XDS beamline of the Brazilian Synchrotron Light Laboratory (LNLS) is described. Also, a preliminary characterization of the Pb1-xLaxZr0.40Ti0.60O3 (x = 0.11, 0.12 and 0.15) ferroelectric system using pair distribution function analysis is presented. Instituto de Física 'Gleb Wataghin' Universidade de Campinas (UNICAMP) Laboratório Nacional de Luz Síncrotron, Caixa Postal 6192 Instituto Geociências and Ciências Exatas Universidade Estadual Paulista (UNESP) Instituto de Física de São Carlos Universidade de São Paulo, CP 369 CONICET - Centro Atómico Bariloche CNEA Instituto Geociências and Ciências Exatas Universidade Estadual Paulista (UNESP)

A novel approach for finding and evaluating structural models of small metallic nanoparticles is presented., A novel approach for finding and evaluating structural models of small metallic nanoparticles is presented. Rather than fitting a single model with many degrees of freedom, libraries of clusters from multiple structural motifs are built algorithmically and individually refined against experimental pair distribution functions. Each cluster fit is highly constrained. The approach, called cluster-mining, returns all candidate structure models that are consistent with the data as measured by a goodness of fit. It is highly automated, easy to use, and yields models that are more physically realistic and result in better agreement to the data than models based on cubic close-packed crystallographic cores, often reported in the literature for metallic nanoparticles.

International audience; The atomic pair distribution function (PDF) as obtained from X-ray or neutron total scattering experiments has proved to be powerful in obtaining valuable structural information for many complex functional materials, be they amorphous or crystalline. In the case of measurements made with X-rays and for samples containing more than one kind of atom, the usefulness of the PDF is, however, somewhat hampered because of the lack of an exact and simple expression relating it to the structure of the materials. Only an approximate relationship exits, which is still in use today. This is particularly detrimental given the wide availability of X-ray sources and the increasing quality of PDFs obtained with laboratory sources. In this paper, the exact and explicit expression of the PDF as obtained from X-ray scattering is derived with respect to partial functions. This expression allows exact and efficient calculation of the PDF from any structure model without using approximate formulae.

X-ray atomic pair distribution functions (PDFs) were collected from a range of canonical metallic nanomaterials, both elemental and alloyed, prepared using different synthesis methods and exhibiting drastically different morphological properties. Widely applied shape-tuned attenuated crystal (AC) fcc models proved inadequate, yielding structured, coherent, and correlated fit residuals. However, equally simple discrete cluster models could account for the largest amplitude features in these difference signals. A hypothesis testing based approach to nanoparticle structure modeling systematically ruled out effects from crystallite size, composition, shape, and surface faceting as primary factors contributing to the AC misfit. On the other hand, decahedrally twinned cluster cores were found to be the origin of the AC structure misfits for a majority of the nanomaterials reported here. It is further motivated that the PDF can readily differentiate between the arrangement of domains in these multiply twinned mo...

The methods for studying nanometre-scale structure in materials from powder diffraction data are often referred to as `total scattering' or atomic pair distribution function (PDF) analysis. This chapter aims to present the background theory in a rigorous but intuitive way. Different approaches to modelling the data are also described.

Atomic pair distribution function (PDF) analysis has been widely used to investigate nanocrystalline and structurally disordered materials. Experimental PDFs retrieved from electron diffraction (ePDF) in transmission electron microscopy (TEM) represent an attractive alternative to traditional PDF obtained from synchrotron X-ray sources, when employed on minute samples. Nonetheless, the inelastic scattering produced by the large dynamical effects of electron diffraction may obscure the interpretation of ePDF. In the present work, precession electron diffraction (PED-TEM) has been employed to obtain the ePDF of two different sub-monolayer samples ––lipoic acid protected (~ 4.5 nm) and hexanethiolated(~ 4.2 nm, ~ 400-kDa core mass) gold nanoparticles­­––randomly oriented and measured at both liquid-nitrogen and room temperatures, with high dynamic-range detection of a CMOS camera. The electron diffraction data were processed to obtain ePDFs which were subsequently compared with PDF of different ideal structure-models. The results demonstrate that the PED-ePDF data is sensitive to different crystalline structures such as monocrystalline (truncated octahedra) versus multiply-twinned (decahedra, icosahedra) structuresof the face-centered cubic gold lattice. The results indicate that PED reduces the residual from 46% to 29%; in addition, the combination of PED and low temperature further reduced the residual to 23%, which is comparable to X-ray PDF analysis. Furthermore, the inclusion of PED resulted in a better estimation of the coordination number from ePDF. To the best of our knowledge, the precessed electron-beam technique (PED) has not been previously applied to nanoparticles for analysis by the ePDF method.

A new approach is presented to obtain candidate structures from atomic pair distribution function (PDF) data in a highly automated way. It fetches, from web-based structural databases, all the structures meeting the experimenter's search criteria and performs structure refinements on them without human intervention. It supports both x-ray and neutron PDFs. Tests on various material systems show the effectiveness and robustness of the algorithm in finding the correct atomic crystal structure. It works on crystalline and nanocrystalline materials including complex oxide nanoparticles and nanowires, low-symmetry and locally distorted structures, and complicated doped and magnetic materials. This approach could greatly reduce the traditional structure searching work and enable the possibility of high-throughput real-time auto analysis PDF experiments in the future., Comment: 41 pages, 8 figures

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.

The conventional X-ray diffraction (XRD) methods probe for the presence of long-range order towards a solution of the average crystal structure. Experimentally, structural information about long-range, periodic atomic ordering is reflected in the Bragg scattering while local atomic structural deviations from the average structure mainly affect the diffuse scattering intensities. In order to obtain structural information about both average and local atomic structures, a technique that takes in account both Bragg and diffuse scattering needs to be employed, such as the total scattering atomic pair distribution function (PDF) technique. This article introduces a PDF-based methodology that can be applied to extract precise structural information about nanoparticles such as the size of the crystalline core region, the degree of crystallinity, the atomic structure of the core region, local bonding, and the degree of the internal disorder, as a function of the nanoparticle diameter. This article sheds li...

Although the atomistic structure and the deformation characteristics of calcium silicate hydrates (C-S-H) are of primary interest in cement chemistry, they have not been fully investigated. In this study, pair distribution function (PDF) analysis was conducted on a 53-year-old fully hydrated tricalcium silicate (C3S) paste using in situ synchrotron high-energy X-ray scattering to probe the atomic structural deformation of C-S-H under external loading. The results were compared with those from our previous PDF study of a 131-day-old C3S paste in order to elucidate the effect of aging on the mechanical characteristics of C-S-H. Three different strains measured by the strain gauge, by the lattice shifts (d-spacing) in the reciprocal space, and by the shift of the interatomic distance (r) in the real space were compared. In the range of r

MXenes are a recently discovered family of two-dimensional (2D) early transition metal carbides and carbonitrides, which have already shown many attractive properties and great promise in energy storage and many other applications. However, a complex surface chemistry and small coherence length have been obstacles in some applications of MXenes, also limiting the accuracy of predictions of their properties. In this study, we describe and benchmark a novel way of modeling layered materials with real interfaces (diverse surface functional groups and stacking order between the adjacent monolayers) against experimental data. The structures of three kinds of Ti3C2Tx MXenes (T stands for surface terminating species, including O, OH, and F) produced under different synthesis conditions were resolved for the first time using atomic pair distribution function obtained by high-quality neutron total scattering. The true nature of the material can be easily captured with the sensitivity of neutron scattering to the s...

A fast method for calculating the atomic pair distribution function is described in the context of performing refinements of structural models. Central to the speed of synthesis is the approximation of Gaussian functions of varying full widths at half-maximum using a narrower Gaussian with a fixed full width at half-maximum. The initial Gaussians are first laid down as delta functions which are then convoluted with the narrower Gaussian to form the final pattern. The net result is an algorithm, which has been included in the Rietveld refinement computer program TOPAS, that synthesizes and refines structural parameters a factor of 300–1000 times faster than alternative algorithms/programs, with speed advantages increasing as the number of atomic pairs increases.

In this work, the concept of complex modeling (CM) is tested by carrying out a co-refinement of the atomic pair distribution function and small-angle X-ray scattering data from CdS nanoparticles. It is shown that, compared with either single technique alone, the CM approach yields a more accurate and robust structural insight into the atomic structure and morphology of nanoparticles. This work opens the door for the application of CM to a wider class of nanomaterials and for the incorporation of additional experimental and theoretical techniques into these studies.

Reduction in reversible hydrogen storage capacity with increasing hydrogenation and dehydrogenation cycle number is observed in numerous hydrogen storage materials, but the mechanism behind this unfavorable change has not been elucidated yet. In this study, we have investigated the development of structural defects or disorders in V1–xTixH2, x = 0, 0.2, and 0.5, during the first 15 hydrogen absorption and desorption cycles using the atomic pair distribution function (PDF) analysis of synchrotron X-ray total scattering data to find out the possible structural origin of the poor cyclic stability of V1–xTix alloys. While pure vanadium shows no significant change in the PDF, alloy samples subject to several hydrogenation and dehydrogenation cycles display fast decaying of the PDF profile due to a progressive increase in the PDF peak width with increasing r. This r-dependent PDF peak broadening effect becomes stronger with cycle number. Molecular dynamics (MD) simulations demonstrated that dislocation defects ...

Milling-time-dependent local structural evolution of mechanically alloyed Mg50Co50 was investigated by the atomic pair distribution function analysis using both neutron and synchrotron X-ray powder...

The materials from Fe-Co-B-Si-Nb system have several interesting and useful properties such as high mechanical strength, abrasive and corrosion resistance and good electrical properties useful in many applications, for example: materials for sensors and precise current transformers. The aim of the presented work was to obtain Fe-based alloy in an amorphous state and examination atoms arrangement in its structure which has an influence on material properties. Multicomponent alloy with nominal composition of Fe37.44Co34.56B19.2Si4.8Nb4 was obtained by pressure die casting method in form of plate with thickness of d=1mm. The structure of rapidly solidified plate was examined by X-ray diffraction. This investigation revealed that the studied sample was amorphous. Based on experimental X-ray data the pair distribution function was calculated and discussion on possible atoms arrangement was carried out.

X-ray pair distribution function (PDF) analysis has been applied to five carbon-supported platinum nanoparticles with sizes ranging from 1.78(2) to 11.2(2) nm. Debye (θD) and Einstein (θE) temperatures were extracted from temperature-dependent PDF peak widths. A monotonic decrease in (θD) with nanoparticle diameter was found and could be well explained by the effect of increased surface area except in the case of the 1.78(2) nm diameter nanoparticle where the measured Debye temperature is significantly depressed from that predicted. This suggests an anomalous bond softening in the smallest sample.

Pair distribution function (PDF) analysis is a long-established technique for studying the local structure of amorphous and disordered crystalline materials. In today's increasingly complex materials landscape, the coexistence of amorphous and crystalline phases within single samples is not uncommon. Though a couple of reports have been published studying samples with amorphous and crystalline phases utilizing PDF analysis, to date little has been done to determine the sensitivity that the method currently has in resolving such contributions. This article reports a series of experiments that have been conducted on samples with known ratios of crystalline quartz and amorphous glassy silica to examine this question in detail. Systematic methods are proposed to obtain the best possible resolution in samples with unknown phase ratios and some problems that one might encounter during analysis are discussed.

Recent studies of crystalline materials by the atomic pair distribution function (PDF) analysis are introduced.Wide Q-range of diffraction patterns obtained by total scattering diffractometers at intense pulsed neutron facilities such as Materials and Life Science Facility in J-PARC are suitable for the PDF analysis, where high Q-resolution measurement can also be carried out simultaneously. One of the novel research topics is the size and the form of nano-structured materials. Another is local lattice distortion in a functional material, i. e., a giant negative thermal expansion material Mn3Cu1-xGexN.

Studying the atomic structure of nanostructured materials presents a special chal- lenge because our extensive crystallographic toolbox begins to lose its power on the nano- scale. The presumption of periodicity is a poor approximation when structural correlation lengths are limited to a few tens of nanometres or less and alternative approaches are needed. Here we give an overview of recent results where the use of the atomic pair distribution function analysis of x-ray and neutron powder diffraction has yielded useful insights in dif- ferent classes of nanostructure problem.

Knowledge of the atomic-scale structure is an important prerequisite to understanding and predicting properties of materials. With bulk crystals it is routinely obtained by X-ray diffraction. With nanocrystals, however, traditional X-ray crystallography fails because of their substantially limited length of structural coherence. Here we illustrate, step by step, how a nontraditional approach involving high-energy X-ray diffraction and atomic pair distribution function analysis is applied to determine the atomic-scale structure of a typical nanocrystalline material-Fe{sub x}Pd{sub 100-x} (x = 0, 26, 28, 48) nanoparticles exhibiting useful magnetic properties.

The atomic-scale structure of nanocrystalline BaxSr1-xTiO3 (x = 1, 0.5, 0) powders has been studied using high-energy X-ray diffraction, Rietveld refinement, and the atomic pair distribution function technique. The studies show that the materials are well-ordered at nanometer length distances. The three-dimensional atomic ordering in Ba0.5Sr0.5TiO3 and SrTiO3 nanopowders may well be described by a cubic structure of the perovskite type, similar to that occurring in the corresponding bulk crystals. The three-dimensional atomic ordering in BaTiO3 is more complex. It is cubic-like on average, but locally shows slight distortions of a tetragonal-type. The new structural information helps one to understand better the dielectric properties of these nanomaterials.

Without a doubt, our ability to determine the atomic structure of complex materials has revolutionized our understanding of these materials over the last decades. Neutron scattering with its unique abilities has contributed greatly to this success. The range of applications of neutron scattering in geosciences are apparent when reading through this volume of Reviews in Mineralogy & Geochemistry. Usual structure determination, the realm of crystallography, is based on the analysis of Bragg intensities. In this article we want to look beyond or underneath the Bragg peaks and discuss the atomic pair distribution function (PDF) method as an approach to more fully understand the atomic structure of complex materials, from the local to the medium range all the way to the long range structure of the material. As mentioned above, structure determination is commonly based on the analysis of Bragg peaks either using single crystal diffraction (Ross and Hoffman 2006, this volume) or powder diffraction (Harrison 2006, this volume). However, one needs to keep in mind, that the structure resulting from Bragg scattering is only the long range average structure of the material. Many materials owe their interesting properties to defects within the material and obviously a complete structural picture and understanding of the properties will require knowledge of the “true” atomic structure. Geological samples are no exception and in fact are among the most complex systems known. Deviations from the average structure, e.g., in form of defects, manifest themselves as diffuse scattering. This is illustrated in an example shown in Figure 1⇓. Two 2D structures have been simulated; both have the same lattice parameters, contain one atomic site in the unit cell as well as contain a total of 30% vacant sites. The difference is the vacancy ordering. Figure 1a⇓ shows the structure with a …

The structure of the recently discovered systematically reproducible Mo6SyIz nanowires has been determined from the atomic pair distribution function (PDF) analysis of powder X-ray diffraction data. This total scattering approach was required because the nanowires are not perfectly crystalline and, therefore, the structure cannot be obtained crystallographically. Several nanotube and nanowire models were fit to the PDF data. The resulting best-fit model structure consists of nanowires of Mo6 octahedra that are bridged by sulfur and terminated on the outside by iodine. This demonstrates the power of total scattering methods in accurately resolving structural issues in nanostructured materials where traditional crystallographic methods fail.

The instantaneous structure of the cyanide-bridged negative thermal expansion (NTE) material Zn(CN)(2) has been probed using atomic pair distribution function (PDF) analysis of high energy X-ray scattering data (100-400 K). The temperature dependence of the atomic separations extracted from the PDFs indicates an increase of the average transverse displacement of the cyanide bridge from the line connecting the Zn(II) centers with increasing temperature. This allows the contraction of non-nearest-neighbor Zn...Zn' and Zn...C/N distances despite the observed expansion of the individual direct Zn-C/N and C-N bonds. Thus, this analysis provides definitive structural confirmation that an increase in the average displacement of bridging atoms is the origin of the NTE behavior. The lattice parameters reveal a slight reduction in the NTE behavior at high temperature from a minimum coefficient of thermal expansion (alpha = dl/ldT) of -19.8 x 10(-6) K(-1) below 180 K, which is attributed to interaction between the doubly interpenetrated frameworks that comprise the structure.

The three-dimensional structure of nanocrystalline magnesium ferrite, MgFe2O4, prepared by ball milling, has been determined using synchrotron radiation powder diffraction and employing both Rietveld and atomic pair distribution function (PDF) analysis. The nanocrystalline ferrite exhibits a very limited structural coherence length and a high degree of structural disorder. Nevertheless, the nanoferrite possesses a very well defined local atomic ordering that may be described in terms of a spinel-type structure with Mg2+and Fe3+ions almost randomly distributed over its tetrahedral and octahedral sites. The new structural information helps explain the material's unusual magnetic properties.

The approach of the atomic pair distribution function (PDF) technique to determine the atomic-scale structure of nanocrystalline materials is introduced and illustrated with results of studies on V2O5 nanotubes and clusters of Cs atoms intercalated inside the pores of the zeolite ITQ-4. We find that V2O5 nanotubes are built of double layers of V-O5 and V-O4 units. Inside the channels in ITQ-4 Cs atoms are found to assemble in short-range ordered zigzag chains.

The knowledge of the detailed atomic structure of modern materials is the key to understanding the their macroscopic properties. The atomic pair distribution function (PDF) reveals short-range and medium-range structural information. In this paper we present an overview of refinement and modelling techniques. In short, we will be trying to answer the question: What can I learn from my PDF?

An atomic pair distribution function (PDF) neutron powder diffraction round-robin experiment was performed on six diffractometers at three spallation sources. Instrument-specific effects on the real-space PDF were investigated, such as finite measurement range, the instrument resolution and the asymmetric shape of diffraction peaks. Two illustrative samples, a perfectly long-range-ordered element, Pb, and a locally strained alloy ZnSe0.5Te0.5, were measured at low temperatures. Various aspects of the PDF were explored, either qualitatively by direct comparison or quantitativelyviastructural modelling. Future implementation of modelling codes incorporating some of these instrumental effects are also discussed.

The structures of nanocrystalline pristine, potassium hydroxide and sodium acetate intercalated new two-dimensional materials ${\mathrm{Ti}}_{3}{\mathrm{C}}_{2}$ MXenes were studied using the x-ray atomic pair distribution function technique. Pristine MXene has a hexagonal structure with $a=b=3.0505(5)\text{ }\text{ }\AA{}$, $c=19.86(2)\text{ }\text{ }\AA{}$ (S.G. $P{6}_{3}/mmc$ No. 194). Both hydroxyl and fluoride terminating species are present. The intercalation of ${\mathrm{K}}^{+}$ or ${\mathrm{Na}}^{+}$ ions expands the ${\mathrm{Ti}}_{3}{\mathrm{C}}_{2}$ layers perpendicular to the planes but shrinks the in-plane $a$ and $b$ lattice parameters.

We report on the atomic pair distribution function determination in the ternary compound CeRuSn using high-energy synchrotron x-ray diffraction. Above room temperature CeRuSn orders in a monoclinic structure that is related to the CeCoAl type of structure by a doubling of the $c$-axis parameter. Upon cooling a very broad hysteretic structural transition has been observed in CeRuSn leading to an ill-defined structure with a main component three times larger than the $c$ parameter. The pair distribution functions collected between 90 and 315 K suggest that the local symmetry type does not change significantly during the phase transformation. However, anomalously large atomic displacement factors suggest that a wide distribution of interatomic distances exists in the sample. Limited agreement between the data at 90 K and the best fit suggests that the structure with a three times larger $c$ lattice parameter with respect to the CeCoAl type can only be regarded as an approximation to the real crystal structure of CeRuSn at low temperatures.

The history of the PDF method is briefly reviewed. Recent results, principally from the Billinge group, are also reviewed.

The three-dimensional structure of metastable exfoliated-restacked WS2 (r-WS2) has been determined by the atomic pair distribution function (PDF) technique. We show that the structure of r-WS2is not a random turbostratic assembly of layers, as previously thought, but it can be better regarded as a monoclinic structure with considerable intrinsic disorder. At room temperature, the atomic-scale structure of r-WS2 is well described in the space group P1121 of the monoclinic system with four formula units in the cell, and lattice parameters a = 3.270(5) A, b = 5.717(5) A, c = 12.309(5) A, and γ = 88.43°. Analysis of the X-ray scattering data, collected with Synchrotron radiation (λ = 0.202 A) over a wide scattering angle, shows that the metastable material is built of layers of distorted (WS6) octahedral units, in contrast to hexagonal 2H-WS2 which is built of layers of perfect (WS6) trigonal prisms. A characteristic structural feature of the restacked material is that W atoms within a single layer form zigza...

The introduction of neutron spallation-source instruments, such as the General Materials Diffractometer (GEM) at ISIS, allows measurement of pair distribution function (PDF) data at significantly higher rates than previously possible. As a result of the increased rate, a single experiment can produce over a hundred individual runs. Manual processing of all these data using traditional methods becomes inconvenient and inefficient. This article presents quality criteria that help produce automated direct Fourier transformed PDFs of quality similar to hand-processed data, and compares optimization methods.

The programPDFFITis designed for the full profile structural refinement of the atomic pair distribution function (PDF). In contrast to conventional structure refinement based on Bragg intensities, the PDF probes thelocalstructure of the studied material. The program presented here allows the refinement of atomic positions, anisotropic thermal parameters and site occupancies as well as lattice parameters and experimental factors. By selecting individual atom types one can calculate partial and differential PDFs in addition to the total PDF. Furthermore one can refine multiple data sets and/or multiple structural phases. The program is controlled by a command language which includes a Fortran style interpreter supporting loops and conditional statements. This command language is also used to define the relation between refinement parameters and structural or experimental information, allowing virtually any constraint to be implemented in the model.PDFFITis written in Fortran-77, and the source code and documentation are availableviathe World Wide Web.

In this chapter the atomic pair distribution function (PDF) is defined. The equations are derived from basic scattering equations. The full range of PDF related equations are laid out and a brief history of the method is presented. A number of extensions to the basic PDF method are presented such as PDFs in higher dimensions and compositionally resolved PDFs. Finally, the theory behind some practical aspects of the method are presented, such as handling and estimating errors and the application of the Nyquist-Shannon sampling theorem to the method.

We have used atomic pair distribution function (PDF) analysis based on neutron powder diffraction data to investigate the local structure of the colossal magnetore- sistant manganite La0.75Ca0.25MnO3 as a function of tem- perature. In the doping range 0.17 < x < 0. 5t hese materi- als show a metal-to-insulator transition, transforming from a ferromagnetic metal (FM) at low temperature to a param- agnetic insulator (PI). We can probe the charge distribution of the sample using the PDF by searching for evidence of Jahn-Teller (JT) distorted octahedra, implying the presence of Mn 3+ ions. A two-phase model based on the local struc- tures of the FM and PI phases was used to refine the experi- mental PDFs quantitatively. We observe the co-existence of both phases over a wide temperature range: approximately 10% of the localized JT phase (PI) is present even at the lowest temperature (T = 20 K), whereas at room temperature nearly half of the sample remains in the delocalized (FM) phase.

The evolution of the short-range structural signature of the Ir4+ dimer state in CuIr2S4 thiospinel has been studied across the metal-insulator phase transitions as the metallic state is induced by temperature, Cr doping, and x-ray fluence. An atomic pair distribution function (PDF) approach reveals that there are no local dimers that survive into the metallic phase when this is invoked by temperature and doping. The PDF shows Ir4+ dimers when they exist, regardless of whether or not they are long-range ordered. At 100 K, exposure to a 98 keV x-ray beam melts the long-range dimer order within a few seconds, though the local dimers remain intact. This shows that the metallic state accessed on warming and doping is qualitatively different from the state obtained under x-ray irradiation.

The average and local structures of the ${(\text{PbTe})}_{1\ensuremath{-}x}{(\text{PbS})}_{x}$ system of thermoelectric materials has been studied using the Rietveld and atomic pair distribution function methods. Samples with $0.25\ensuremath{\le}x$ are macroscopically phase separated. Phase separation was suppressed in a quenched $x=0.5$ sample which, nonetheless, exhibited a partial spinodal decomposition. The promising thermoelectric material with $x=0.16$ showed intermediate behavior. Combining TEM and bulk scattering data suggests that the sample is a mixture of PbTe-rich material and a partially spinodally decomposed phase similar to the quenched 50% sample. This confirms that, in the bulk, this sample is inhomogeneous on a nanometer length scale, which may account for its enhanced thermoelectric figure of merit.

Atomic pair distribution functions are useful because they have an easy intuitive interpretation and can be obtained both experimentally and from computer-generated structure models. For bulk materials, atomic pair distribution functions are solely determined by the intrinsic atomic geometry, i.e., how atoms are positioned with respect to one another. For a nanomaterial, however, the atomic pair distribution function also depends on the shape and size of the nanomaterial. A modified form of the radial distribution function is discussed that decouples shape and size effects from intrinsic effects so that nanomaterials of any shape and size, sharing a common atomic geometry, map onto a universal curve, by using a form factor. Mapping onto this universal curve allows differences in the intrinsic atomic geometry of nanomaterials of various shapes and sizes to be directly compared. This approach is demonstrated on nanoscale amorphous and crystalline silica models. It is shown how form factors can be computed for arbitrary shapes and this is illustrated for tetrahedral nanoparticles of vitreous silica. © 2009 The American Physical Society.

Here we show explicitly the relationship between the functions used in the atomic pair distribution function (PDF) method and those commonly used in small angle scattering (SAS) analyses. The origin of the sloping baseline, $-4\pi r\rho_0$, in PDFs of bulk materials is identified as originating from the SAS intensity that is neglected in PDF measurements. The non-linear baseline in nanoparticles has the same origin, and contains information about the shape and size of the nanoparticles., Comment: 19 pages, 0 figures

The size-dependent structure of CdSe nanoparticles, with diameters ranging from 2 to 4 nm, has been studied using the atomic pair distribution function (PDF) method. The core structure of the measured CdSe nanoparticles can be described in terms of the wurtzite atomic structure with extensive stacking faults. The density of faults in the nanoparticles ~50% . The diameter of the core region was extracted directly from the PDF data and is in good agreement with the diameter obtained from standard characterization methods suggesting that there is little surface amorphous region. A compressive strain was measured in the Cd-Se bond length that increases with decreasing particle size being 0.5% with respect to bulk CdSe for the 2 nm diameter particles. This study demonstrates the size-dependent quantitative structural information that can be obtained even from very small nanoparticles using the PDF approach., Comment: 10 pages, 7 figures and 3 tables. Phys. Rev. B, submitted (2007)