Real-space Pair Distribution Function Research Articles

Quantifying local lattice distortions in refractory high-entropy alloys

Severe local lattice distortions (LLDs), originating from the size mismatch among atoms, have been proposed as one of the key mechanisms responsible for the excellent mechanical properties of bcc-structured high-entropy alloys (HEAs). They have also been connected to phase stability, as well as physical properties such as electrical conductivity. Experimental measurements of LLDs are, however, difficult and often ambiguous. Analysis of total scattering data in real space has been proposed to provide a uniquely suitable probe of LLDs, but its widespread application and validation are still limited. We conduct a thorough study of LLD measurements in refractory high-entropy alloys (RHEAs) using small-box pair distribution function (PDF) analysis. We start by reexamining existing literature data using a recently proposed coherent theoretical framework to demonstrate that LLDs in RHEAs can indeed be considered as severe and can be reliably measured even in the absence of known thermal components. We perform total scattering experiments of a typical RHEA (HfNbTaTiZr) using both x-rays and neutrons, and show that real-space PDF analysis of data from different types of radiation gives consistent values of LLDs. The results are also in good agreement with the values derived from reciprocal-space data. Finally, through simulation and analysis of theoretical two-phase PDFs, we demonstrate that the effect of the chemical segregation in the investigated RHEA on the measured LLDs is limited when dealing with comparatively large LLDs. The results show that PDF analysis using small-box modeling provides a fast and reliable tool for measuring LLDs in RHEAs, which makes it ideal for analysis of large data sets from time-resolved measurements. Published by the American Physical Society 2024

Synthesis, Structure, and Photophysical Properties of Platinum Compounds with Thiophene-Derived Cyclohexyl Diimine Ligands.

Platinum(II) and platinum(IV) compounds were prepared by the stereoselective and regioselective reactions of thiophene-derived cyclohexyl diimine C^N^N-ligands with [Pt2Me4(μ-SMe2)2]. Newly synthesized ligands were characterized by NMR spectroscopy and elemental analysis, and Pt(II)/Pt(IV) compounds were characterized by NMR spectroscopy, elemental analysis, high-resolution mass spectrometry, and single-crystal X-ray diffraction. UV-vis absorbance and photoluminescence measurements were performed on newly synthesized complexes, as well as structurally related Pt(II)/Pt(IV) compounds with benzene-derived cyclohexyl diimine ligands, in dichloromethane solution, as solids, and as 5% by weight PMMA-doped films. DFT and TD-DFT calculations were performed, and the results were compared with the observed spectroscopic properties of the newly synthesized complexes. X-ray total scattering measurements and real space pair distribution function analysis were performed on the synthesized complexes to examine the local- and intermediate-range atomic structures of the emissive solid states.

Symmetry-mode analysis for local structure investigations using pair distribution function data

Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe2, where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. The analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort, which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools, which converts the ISODISTORT output into a DiffPy-compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software.

Describing small-angle scattering profiles by a limited set of intensities.

Small-angle scattering (SAS) probes the size and shape of particles at low resolution through the analysis of the scattering of X-rays or neutrons passing through a solution of particles. One approach to extracting structural information from SAS data is the indirect Fourier transform (IFT). The IFT approach parameterizes the real-space pair distribution function [P(r)] of a particle using a set of basis functions, which simultaneously determines the scattering profile [I(q)] using corresponding reciprocal-space basis functions. This article presents an extension of an IFT algorithm proposed by Moore [J.Appl. Cryst. (1980), 13, 168-175] which used a trigonometric series to describe the basis functions, where the real-space and reciprocal-space basis functions are Fourier mates. An equation is presented relating the Moore coefficients to the intensities of the SAS profile at specific positions, as well as a series of new equations that describe the size and shape parameters of a particle from this distinct set of intensity values. An analytical real-space regularizer is derived to smooth the P(r) curve and ameliorate systematic deviations caused by series termination. Regularization is commonly used in IFT methods though not described in Moore's original approach, which is particularly susceptible to such effects. The algorithm is provided as a script, denss.f it_data.py, as part of the DENSS software package for SAS, which includes both command line and interactive graphical interfaces. Results of the program using experimental data show that it is as accurate as, and often more accurate than, existing tools.

Microscopic insights of magnetism in Sm2NiMnO6 double perovskite

The functional characteristics of double perovskites with unique ferromagnetic-insulator ground state have been controversial due to the unavoidable presence of anti-site disorders (ASDs). Here, we aim to investigate the origin of magnetic ordering on local and global scales in Sm$_{2}$NiMnO$_{6}$ (SNMO) double perovskite system. Different calcination routes are exploited to generate different cation arrangements in SNMO and the corresponding magnetic configurations are examined using the high energy (E $ \sim $0.3 eV) `hot neutrons', which has helped to overcome Sm absorption as well as to record total (Bragg's+diffuse) scattering profiles with high momentum transfer (Q$ _{max} \sim $24 angstrom$ ^{-1} $). We have observed that the Ni-Mn sublattice adopts long range collinear ferromagnetic $ F_{x}F_{z} $ structure with commensurate $k$=(0, 0, 0) propagation vector, below ordering temperature T $ \lesssim $ 160 K, irrespective of variable ASD concentrations. In addition, the signatures indicating the antiparallel polarization of Sm paramagnetic moments with respect to Ni-Mn network, are noticed in the vicinity of anomalous magnetic transitions at T $ \lesssim $ 35 K. The real space pair distribution function calculations have provided a direct visualization of ASDs by means of broadening in Ni/Mn-Mn/Ni linkage. Employing the Reverse Monte Carlo approach on diffuse magnetic scattering profiles, we have observed the negative spin-spin correlation function which suggests the Ni-Ni antiferromagnetic exchange interactions ranging up to first nearest neighbor distance. These results confirm that the existence of ASDs in cation ordered host matrix leads to competing ferromagnetic-antiferromagnetic phases in a broad temperature range, which quantitatively governs the temperature dependent bulk magnetic observables of SNMO system.

Nematic state of the FeSe superconductor

We study the crystal structure of the tetragonal iron selenide FeSe and its nematic phase transition to the low-temperature orthorhombic structure using synchrotron x-ray and neutron scattering analyzed in both real and reciprocal space. We show that in the local structure the orthorhombic distortion associated with the electronically driven nematic order is more pronounced at short length scales. It also survives up to temperatures above 90 K where reciprocal-space analysis suggests tetragonal symmetry. Additionally, the real-space pair distribution function analysis of the synchrotron x-ray diffraction data reveals a tiny broadening of the peaks corresponding to the nearest Fe-Fe, nearest Fe-Se, and the next-nearest Fe-Se bond distances as well as the tetrahedral torsion angles at a short length scale of 20 angstr\"om. This broadening appears below 20 K and is attributed to a pseudogap. However, we did not observe any further reduction in local symmetry below orthorhombic down to 3 K. Our results suggest that the superconducting gap anisotropy in FeSe is not associated with any symmetry-lowering short-range structural correlations.

A previously unknown cyclic alkanolamine and molecular ranking using the pair distribution function

A new six-membered cyclic alkanolamine with chemical formula C6H15N3O3 was synthesized by the reaction of glycolaldehyde with gaseous ammonia. The molecular structure, characterized by a hexagonal ring of alternating carbon and nitrogen atoms with three hydroxymethyl groups attached to the carbon atoms, could not be unambiguously determined by elemental analysis and 1H/13C/15N NMR. The molecular structure and conformation were further determined using a combination of vibrational spectroscopy (IR and Raman) and real-space pair distribution function (PDF) analysis. The crystal structure was determined ab initio from laboratory X-ray powder diffraction (XRPD) with orthorhombic space group Ama2 (No. 40) and unit-cell parameters a = 12.1054 (2) Å, b = 13.5537 (2) Å and c = 5.20741 (8) Å. Consistent structure models could be obtained by symmetry-independent PDF and PDF-Rietveld co-refinements. Independent local structure refinements indicate that the most likely deviations from the average structure consist of small tilting and translational distortions of hydrogen-bonded molecular stacks. Thermal analysis (TG/DTA) and temperature-dependent XRPD measurements were also performed to determine the thermal behavior.

Photophysical Properties of Cyclometalated Platinum(II) Diphosphine Compounds in the Solid State and in PMMA Films.

Platinum(II) compounds were synthesized with both chelate cyclometalated ligands and chelate diphosphine ligands. The cyclometalated ligands include phenylpyridine and a benzothiophene-containing ligand. The three new benzothiophene compounds were characterized by nuclear magnetic resonance (NMR) spectroscopy, high-resolution mass spectrometry (HR-MS), and photophysical measurements. In the case of one compound, L1-DPPM, the structure was determined by single crystal X-ray diffraction. The structural coherence of the noncrystalline emissive solid state was measured by X-ray total scattering real space pair distribution function analysis. Quantum yield values of all of the platinum compounds measured in the solid state and in PMMA films were much greater than in solution.

Fast Water-Assisted Lithium Ion Conduction in Restacked Lithium Tin Sulfide Nanosheets

While two-dimensional (2D) materials may preserve some intrinsic properties of the corresponding layered bulk material, new characteristics arise from their pronounced anisotropy or confinement effects. Recently, exceptionally high ionic conductivities were discovered in 2D materials such as graphene oxide and vermiculite. Here, we report on the water-assisted fast conduction of lithium ions in restacked lithium tin sulfide nanosheets. Li0.8Sn0.8S2 exfoliates spontaneously in water and can be restacked into homogeneous films in which the lithium content is decreased, and a partial substitution of sulfur with hydroxyl groups takes place. Using a recursive supercell refinement approach in reciprocal space along with real-space pair distribution function analysis, we describe restacked lithium tin sulfide as a partially turbostratically disordered material composed of lithium-containing and lithium-depleted layers. In humid air, the material takes up multiple layers of water that coordinate lithium ions in the space between the layers, increasing the stacking distance and screening the interaction between lithium ions and the anionic layers. This results in a 1000-fold increase in ionic conductivity up to 47 mS cm–1 at high humidities. Orientation-dependent impedance spectroscopy suggests a facile in-plane conduction and a hindered out-of-plane conduction. Pulsed field gradient nuclear magnetic resonance spectroscopy reveals a fast, simultaneous diffusion of a majority and a minority species for both 7Li and 1H, suggesting water-assisted lithium diffusion to be at play. This study enlarges the family of nanosheet-based ionic conductors and helps to rationalize the transport mechanism of lithium ions enabled by hydration in a nanoconfined 2D space.

Probing the Local Site Disorder and Distortion in Pyrochlore High-Entropy Oxides.

High-entropy oxides (HEOs) have attracted great interest in diverse fields because of their inherent opportunities to tailor and combine materials functionalities. The control of local order/disorder in the class is by extension a grand challenge toward realizing their vast potential. Here we report the first examples of pyrochlore HEOs with five M-site cations, for Nd2M2O7, in which the local structure has been investigated by neutron diffraction and pair distribution function (PDF) analysis. The average structure of the pyrochlores is found to be orthorhombic Imma, in agreement with radius-ratio rules governing the structural archetype. The computed PDFs from density functional theory relaxed special quasirandom structure models are compared with real space PDFs in this work to evaluate M-site order/disorder. Reverse Monte Carlo combined with ab initio molecular dynamics and Metropolis Monte Carlo simulations demonstrates that Nd2(Ta0.2Sc0.2Sn0.2Hf0.2Zr0.2)2O7 is synthesized with its M-site local to nanoscale order highly randomized/disordered, while Nd2(Ti0.2Nb0.2Sn0.2Hf0.2Zr0.2)2O7+x exhibits a strong distortion of the TiO6 octahedron and small degree of Ti chemical short-range order (SRO) on the subnanometer scale. Calculations suggest that this may be intrinsic, energetically favored SRO rather than due to sample processing. These results offer an important demonstration that the engineered variation of participating ions in HEOs, even among those with very similar radii, provides richly diverse opportunities to control local order/disorder motifs-and therefore materials properties for future designs. This work also hints at the exquisite level of detail that may be needed in computational and experimental data analysis to guide structure-property tuning in the emerging HEO materials class.

Atomic structure and grain shape evolution of nanodiamond during annealing in oxidizing atmosphere from neutron diffraction and MD simulations

Real space pair-distribution function (PDF) analysis in conjunction with molecular dynamics (MD) simulations was applied to characterize crystal structure, shape and surface structure of diamond nanoparticles annealed in air up to 880 °C. MD simulated models of individual nanodiamond particles of various shapes and sizes were used to calculate theoretical radial distribution functions G(r) for powders with different grain size distributions. The calculated curves, showing distinct differences for the explored parameter space, were compared to the experimental G(r) functions obtained from neutron scattering for annealed detonated nanodiamond samples in a search for a model best describing the actual powders. It was found that as-synthesized nanodiamond grains are terminated by equally abundant (100), (110) and (111) crystallographic faces and their structure does not change upon annealing in air up to 280 °C. The shape and size of grains annealed above 480 °C changes due to surface etching. The etching rate differs between crystals faces and depends on temperature, resulting in the observed differences in grain shape. Below 680 °C the share of the (110) facets gradually increases and at 680 °C the grains become rhombic dodecahedra terminated solely by (110) surfaces. Further increase of the annealing temperature promotes formation of (111) surfaces and at 880 °C the preferred grain shape becomes an octahedron terminated by a variant of (111) surfaces possessing three dangling sp3 bonds per atom. At lower temperatures all grains become smaller and the size distribution moves towards the lower values. As the annealing temperature increases, the smallest grains disappear entirely and the average grain size grows back.

Time-of-flight neutron total scattering with applied electric fields: Ex situ and in situ studies of ferroelectric materials.

Characterizing the structural response of functional materials (e.g., piezoelectrics and ferroelectrics) to electric fields is key for the creation of structure-property relationships. Here, we present a new sample environment and data reduction routines which allow the measurement of time-of-flight neutron total scattering during the in situ or ex situ application of high voltage (<10 kV) to a sample. Instead of utilizing the entire detector space of the diffractometer, only selected regions of detector pixels with scattering at the desired angle to the sample electric field are interrogated, which allows the generation of orientation-dependent reciprocal space patterns and real-space pair distribution functions (PDFs). We demonstrate the method using the relaxor ferroelectric Na1/2Bi1/2TiO3 and observe lattice expansion parallel and contraction perpendicular to the electric field for both in situ and ex situ experiments, revealing the irreversible nature of the local scale structural changes to this composition. Additionally, changes in the distributions of nearest neighbor metal-oxygen bond lengths are observed, which have been difficult to observe in previously measured analogous orientation-dependent X-ray PDFs. Considerations related to sample positioning and background subtraction are discussed, and future research directions are suggested.

Precise implications for real-space pair distribution function modeling of effects intrinsic to modern time-of-flight neutron diffractometers.

Total scattering and pair distribution function (PDF) methods allow for detailed study of local atomic order and disorder, including materials for which Rietveld refinements are not traditionally possible (amorphous materials, liquids, glasses and nanoparticles). With the advent of modern neutron time-of-flight (TOF) instrumentation, total scattering studies are capable of producing PDFs with ranges upwards of 100-200 Å, covering the correlation length scales of interest for many materials under study. Despite this, the refinement and subsequent analysis of data are often limited by confounding factors that are not rigorously accounted for in conventional analysis programs. While many of these artifacts are known and recognized by experts in the field, their effects and any associated mitigation strategies largely exist as passed-down `tribal' knowledge in the community, and have not been concisely demonstrated and compared in a unified presentation. This article aims to explicitly demonstrate, through reviews of previous literature, simulated analysis and real-world case studies, the effects of resolution, binning, bounds, peak shape, peak asymmetry, inconsistent conversion of TOF to d spacing and merging of multiple banks in neutron TOF data as they directly relate to real-space PDF analysis. Suggestions for best practice in analysis of data from modern neutron TOF total scattering instruments when using conventional analysis programs are made, as well as recommendations for improved analysis methods and future instrument design.

Structural modifications in sub-Tg annealed CuZr-based metallic glass

Short term sub-glass transition annealing controls the structural reordering and nanocrystallization of CuZr−based bulk metallic glasses (BMGs). Using this method, 5 times higher resistance against strain softening as confirmed by three-point bending tests is attained. Homogenously dispersed nanoparticles in sizes of 20–50nm accounts for the remarkable shifts and peak formations on reciprocal space together with the diffraction spots observed on 2D diffraction pattern. Real-space pair distribution function analysis reveals noticeable changes in peak shapes and positions correlated with the changes in short- to medium-range ordering. The differences in the partial nearest neighbor numbers upon annealing mark the dominant Zr−Zr pair to diminish whereas the Cu−Cu pair becomes prominent, hinting that Cu diffusion is mainly responsible for structural reordering and formation of new phases. The pursued study using hard X-ray synchrotron radiation reveals important aspects of structural changes preceding nanocrystallization, which in turn enhances the mechanical performance in BMGs.

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.

Local Structure of Disordered Bi0.5K0.5TiO3 Investigated by Pair Distribution Function Analysis and First-Principles Calculations

We investigate A-site cation ordering in the ferroelectric perovskite Bi0.5K0.5TiO3 (BKT) by density functional theory (DFT) calculations and synchrotron X-ray total scattering. Using BKT as a prototypical lead-free ferroelectric perovskite with mixed A-site cations, we use a combination of theory and experiments to assess the energetics and resulting physical properties of cation ordering. Ten different Bi/K configurations in a 2 × 2 × 2 supercell were assessed by real space pair distribution functions (PDFs) and DFT calculations. None of these configurations were identified as particularly favorable from experiment or theory. Ferroelectric polarization calculated by the Berry phase method for all ten configurations yields values of 50–105 μC/cm2. This is significantly larger than previously reported experimental results in the range of 22–49 μC/cm2, indicating that BKT does not possess long-range A-site cation order. Reverse Monte Carlo (RMC) modeling of the total scattering data with a 12 × 12 × 12 sup...

Correlated rattling-ion origins of dielectric properties in reentrant dipole glasses BaTiO3-BiScO3

The local structure of the pseudo-cubic solid solution 0.6BaTiO3-0.4BiScO3, which exhibits reentrant dipole-glass behavior, has been determined using the Reverse Monte Carlo method to simultaneously fit (1) neutron and X-ray total scattering data (including the corresponding real-space pair-distribution functions), (2) Bi and Sc extended X-ray absorption fine structure, and (3) patterns of diffuse scattering in electron diffraction. These structural refinements revealed the multi-site probability density distributions for both Bi (14-sites) and Ti (8 sites), whereas Ba and Sc featured normal unimodal distributions. Bi atoms are displaced along both the 〈111〉 and 〈100〉 directions, while Ti atoms are shifted along 〈111〉. Correlated dynamic hopping of Bi and Ti over their corresponding split sites combined with chemical disorder is proposed as the origin of the strong frequency dispersion observed in dielectric measurements. The existence of split sites also explains the reentrant dipole-glass behavior reported for this system.

Mitigation of errors in pair distribution function analysis of nanoparticles

Information on the size and structure of nanoparticles can be obtainedviaanalysis of the atomic pair distribution function (PDF), which is calculated as the Fourier transform of X-ray/neutron total scattering. The structural parameters are commonly extracted by fitting a model PDF calculated from atomic coordinates to the experimental data. This paper discusses procedures for minimizing systematic errors in PDF calculations for nanoparticles and also considers the effects of noise due to counting statistics in total scattering data used to obtain the PDF. The results presented here demonstrate that smoothing of statistical noise in reciprocal-space data can improve the precision of parameter estimates obtained from PDF analysis, facilitating identification of the correct model (from multiple plausible choices) from real-space PDF fits.

On the atomic structure of Zr–Ni and Zr–Ni–Al metallic glasses

Using real space pair distribution functions derived from high precision x-ray diffraction data, the local atomic structure of Zr–Ni and Zr–Ni–Al metallic glasses was investigated. Unlike Zr–Cu metallic glasses, the structure of Zr–Ni metallic glasses cannot be approached with an ideal solution model, due to strong attractive interactions between Zr and Ni atoms, which promote chemical short range order. Addition of Al can be beneficial for the glass forming ability of Zr–Ni metallic glasses. The atomic size of Al, being intermediate to those of Zr and Ni and the strongly attractive interactions between Zr–Al and Zr–Ni atoms can lead to highly negative volumes of mixing ΔVmix, and to denser atomic structures, reduced atomic mobility in the liquid and easier suppression of crystallization in the undercooled liquid state

Atomic displacements in the charge ice pyrochloreBi2Ti2O6O′studied by neutron total scattering

The oxide pyrochlore ${\text{Bi}}_{2}{\text{Ti}}_{2}{\text{O}}_{6}{\text{O}}^{\ensuremath{'}}$ is known to be associated with large displacements of Bi and ${\text{O}}^{\ensuremath{'}}$ atoms from their ideal crystallographic positions. Neutron total scattering, analyzed in both reciprocal and real space, is employed here to understand the nature of these displacements. Rietveld analysis and maximum entropy methods are used to produce an average picture of the structural nonideality. Local structure is modeled via large-box reverse Monte Carlo simulations constrained simultaneously by the Bragg profile and real-space pair distribution function. Direct visualization and statistical analyses of these models show the precise nature of the static Bi and ${\text{O}}^{\ensuremath{'}}$ displacements. Correlations between neighboring Bi displacements are analyzed using coordinates from the large-box simulations. The framework of continuous symmetry measures has been applied to distributions of ${\text{O}}^{\ensuremath{'}}{\text{Bi}}_{4}$ tetrahedra to examine deviations from ideality. Bi displacements from ideal positions appear correlated over local length scales. The results are consistent with the idea that these nonmagnetic lone-pair containing pyrochlore compounds can be regarded as highly structurally frustrated systems.