Cell-cluster development for the pair distribution function - Application to rigid disks at hight density.
Molecular pair distribution function in perfect crystalline solids, using method based on cell cluster theory
MOLECULAR STRUCTURE↗
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Hard-sphere solid - Pair distribution functions at high density.
High density form of molecular pair distribution function for rigid spheres system, using cell- cluster technique
Larsen, R. D.↗
Operando pair distribution function analysis of nanocrystalline functional materials: the case of TiO 2 -bronze nanocrystals in Li-ion battery electrodes
Structural modelling of operando pair distribution function (PDF) data of complex functional materials can be highly challenging. To aid the understanding of complex operando PDF data, this article demonstrates a toolbox for PDF analysis. The tools include denoising using principal component analysis together with the structureMining , similarityMapping and nmfMapping apps available through the online service `PDF in the cloud' ( PDFitc , https://pdfitc.org/). The toolbox is used for both ex situ and operando PDF data for 3 nm TiO 2 -bronze nanocrystals, which function as the active electrode material in a Li-ion battery. The tools enable structural modelling of the ex situ and operando PDF data, revealing two pristine TiO 2 phases (bronze and anatase) and two lithiated Li x TiO 2 phases (lithiated versions of bronze and anatase), and the phase evolution during galvanostatic cycling is characterized.
Chemistry↗
Magnetic pair distribution function and half polarized neutron powder diffraction at the HB-2A powder diffractometer
Local magnetic order and anisotropy are often central for understanding fundamental behavior and emergent functional properties in quantum materials and beyond. Advances in neutron powder diffraction experiments and analysis tools now allow for quantitative determination. Here, we demonstrate this here with complementary total neutron scattering and polarized neutron measurements on the HB-2A neutron powder diffractometer at the High Flux Isotope Reactor (HFIR). In recent years, magnetic pair distribution function (mPDF) analysis has emerged as a powerful technique for probing local magnetic spin ordering of magnetic materials. This method can be broadly applied to any magnetic material but is particularly effective for studying systems with short-range magnetic order, such as materials with reduced dimensionality, geometrically frustrated magnets, thermoelectrics, multiferroics, and correlated paramagnets. Magnetic anisotropy often underpins the short-range order adopted. Half-polarized neutron powder diffraction (pNPD) can be used to determine the local susceptibility tensor on the magnetic sites to quantify the magnetic anisotropy. Combining the techniques of mPDF and pNPD can therefore provide valuable insights into local magnetic behavior. A series of measurements optimized for these techniques are presented as exemplar cases focused on frustrated materials where short-range order dominates, these include measurements to ultra-low temperature (<100 mK) not typically accessible for such experiments.
Half polarized neutron scattering↗
Solving disorder in (3D) real space: a comparative study of the three-dimensional difference pair distribution function and atomic resolution holography reconstructions
The quantitative analysis of local ordering principles in disordered crystalline systems has gained much attention over the past few years, as it is often considered crucial for optimizing material functionality. This development has been driven by significant advancements in computational and experimental methods, which have led to the establishment and widespread use of various analytical techniques. In this study, we perform model calculations to compare the effectiveness of atomic resolution holography and three-dimensional difference pair distribution function analysis (3D-ΔPDF). Using Cu 3 Au as a model system, we demonstrate an approach to derive local order parameters quantitatively and show that both techniques are well suited to quantifying chemical short-range order correlations and local bond-distance variations. By evaluating the strengths and limitations of both techniques, we advocate for their combined use to solve complex short-range order problems accurately.
3D-ΔPDF↗
Structural coherence model for predicting molten salt thermal conductivity informed by the pair distribution function
To enable thermal behavior prediction and design optimization of molten salt reactors, thermal conductivity of molten salts must be characterized in terms of salt composition and temperature. Current theoretical models fail to provide consistent approximations for all halide mixtures, particularly actinide-bearing melts. This study aims to link the short-range order structure of molten salts to the mean free path of energy carriers through a simple structural coherence model informed by the partial pair distribution function. The proposed method is used to predict the thermal conductivity of 33 alkali and alkaline earth halide salts. Predictions approximate experimental measurements with a mean absolute error of 15.7% for dissociating, complexing, and actinide salts, including unary LiCl, NaCl, and MgCl 2 as well as mixtures LiF–NaF–KF (FLiNaK), LiF–BeF 2 (FLiBe), and NaCl–UCl 3 . The work provides evidence for the validity of energy carrier descriptions of molecular-level heat transfer in molten salts, with implications for improved theories of liquid energy transport in general.
Actinide mixtures↗
Local structure of zinc–indium–tin oxide films via grazing-incidence x-ray pair-distribution functions and theoretical methods
A detailed experimental and theoretical study on the local (r ≤ 4.5 Å) atomic structure of amorphous and crystalline zinc–indium–tin oxide (ZITO) thin films using grazing-incidence x-ray Pair-Distribution Functions (PDFs), ab initio Molecular Dynamics (MD), and Empirical Potential Structure Refinement (EPSR) Monte Carlo simulations is presented. High-energy synchrotron x rays, a two-dimensional detector, and different incident angles were used to probe the depth uniformity of five (ZnO) 0.15 (In 2 O 3 ) 0.70 (SnO 2 ) 0.15 films that were deposited via pulsed-laser deposition at growth temperatures (T G ) ranging from 25 to 300 °C. Films deposited at T G ≤ 150 °C were amorphous. The partially crystalline (T G = 200 °C) and fully crystalline (T G = 300 °C) films were highly textured. Both crystalline and amorphous structures were investigated using ab initio MD and EPSR Monte Carlo simulations. The density of the amorphous films determined from the experimental data agreed with MD calculations. Coordination numbers, bond lengths, and distortion for metal–oxygen and for both the edge- and corner-shared In–metal shells up to 4.5 Å obtained from PDF analysis closely agreed with MD and EPSR simulations. There is a pronounced decrease in the edge- and corner-shared In–Zn distances arising from the shorter Zn–O bond length, Zn–O tetrahedral coordination, and In–O–Zn angle in amorphous ZITO compared to its crystalline counterpart. A maximum in electrical mobility was observed for the amorphous film just before crystallization occurred. While the peak is broad, consistent with nearly unchanged overall cation–oxygen coordination in the amorphous films, ESPR results indicate that the tetrahedral coordination follows the conductivity trend.
Grazing Incidence X-ray↗
Absorption Correction for Reliable Pair Distribution Functions from Low Energy X-ray Sources
This paper explores the development and testing of a simple absorption correction model for processing powder X-ray diffraction data from Debye−Scherrer geometry laboratory X-ray experiments. This may be used as a preprocessing step before using PDFGETX3 to obtain reliable pair distribution functions (PDFs). Various experimental and theoretical methods for estimating μR were explored, and the most appropriate μR values for correction were identified for different capillary diameters and X-ray beam sizes. We identify operational ranges of μR where a reasonable signal-to-noise ratio is possible after correction. A user-friendly software package, DIFFPY.LABPDFPROC, is presented that can help estimate μR and perform absorption corrections with a rapid calculation for efficient processing.
Absorption↗
Resolving local ordering and structure in Mn x Ge 1- x Te alloys through thermodynamic ensembles of pair distribution functions
Characterizing local bonding environments in complex materials is essential for understanding and optimizing their properties. Equally as important is the ability to predict local motifs as a function of synthesis conditions, enhancing chemists’ ability to design properties into materials. In this study, we present an approach to leverage statistical mechanics to generate temperature- and energy-informed ensemble averaged pair distribution functions (PDFs). This method, which we have named Thermodynamic Ensemble Averages of PDFs for Ordering and Transformations (TEAPOT), utilizes density functional theory (DFT) to relax supercells while incorporating energetic penalties for local order, enabling accurate and computationally efficient analysis of local structure. We apply this method to the neutron PDF measurements of the pseudobinary MnTe–GeTe (MGT) alloy, demonstrating its capability to resolve complex local distortions and chemical ordering. Our results reveal detailed insights into phase transformations and local distortions driven by Mn substitution. For compositions that globally present as rock salt, our analysis reveals that Ge coordination geometry is heavily impacted by synthesis temperature. We propose that high temperature synthesis conditions promote a lowered Ge polyhedra distortion, promoting high charge carrier mobility due to the alignment of local and global structure. Incorporating statistical mechanics and computation into experimental analysis thus guides synthesis of tailored local structure.
36 MATERIALS SCIENCE↗
Local orthorhombic phase in zirconium oxide nanocrystals: insights from X-ray pair distribution function analysis
Zirconium dioxide (ZrO 2 ) and hafnium dioxide (HfO 2 ) have emerged as promising alternatives to conventional ferroelectric materials. Understanding the crystal phases of these oxides under different conditions is crucial for optimizing their properties. There are several theories for the (anti)ferroelectric properties; however, comprehensive analysis, particularly at the local structure level, is lacking. In this study, we investigate the local structure of ZrO 2 nanocrystals using X-ray pair distribution function (PDF) analysis, revealing an unexpected local orthorhombic distortion irrespective of crystallite size. This finding suggests the potential existence of an intermediate orthorhombic phase during the microscopic switching pathway observed in previous studies. Additionally, we explore the influence of crystallite size and surface effects on the PDF. These results contribute to a deeper understanding of the structural dynamics in ZrO 2 and offer insights for the design of next-generation ferroelectric materials.
Pokratath, Rohan (ORCID:0000000268383939)↗
Structure refinement and anisotropic atomic displacement parameters of 1M Illite: Rietveld and pair distribution function analysis using synchrotron X-ray radiation
Illite, a widespread clay mineral, plays a pivotal role in geological processes, notably as an indicator in diagenetic and hydrothermal alteration environments, and possesses significant industrial relevance in applications including ceramics, construction and catalysis. However, challenges including its nanoscale crystallinity, structural disorder and frequent interstratification with other clay minerals have hindered detailed structural characterization using conventional X-ray diffraction (XRD) techniques. This study employs integrated synchrotron XRD and pair distribution function (PDF) analysis to elucidate the crystal structure of the 1M illite polytype, yielding the first determination of its anisotropic atomic displacement parameters (U aniso ). TheseU aniso parameters provide critical insights into atomic dynamics and static disorder within the structure, enabling a more refined understanding of structure–property relationships. This integrated approach, combining synchrotron XRD, Rietveld refinement and PDF analysis, yields a comprehensive structural characterization, capturing both average crystallographic and local atomic arrangements. Considering illite's widespread geological occurrence and industrial importance, this high-precision structural dataset, especially the determinedU aniso values, provides a crucial benchmark for future modeling and simulation efforts targeting accurate prediction of its physicochemical behavior.
Chemistry↗
Amorphous Analogs of Martian Global Soil: Pair Distribution Function Analyses and Implications for Scattering Models of Chemin X-ray Diffraction Data
Soils on Mars have been analyzed by the Mars Exploration Rovers (MER) and most recently by the Mars Science Laboratory (MSL) rover. Chemical analyses from a majority of soil samples suggest that there is a relatively uniform global soil composition across much of the planet. A soil site, Rocknest, was sampled by the MSL science payload including the CheMin X-ray diffractometer and the Alpha Particle X-ray Spectrometer (APXS). Che- Min X-ray diffraction (XRD) data revealed crystalline phases and a broad, elevated background, indicating the presence of amorphous or poorly ordered materials (Fig 1). Based on the chemical composition of the bulk soil measured by APXS and the composition of crystalline phases derived from unit-cell parameters determined with CheMin data, the percentages of crystalline and amorphous phases were calculated at 51% and 49%, respectively. Attempts to model the amorphous contribution to CheMin XRD patterns were made using amorphous standards and full-pattern fitting methods and show that the broad, elevated background region can be fitted by basaltic glass, allophane, and palagonite. However, the modeling shows only that these phases have scattering patterns similar to that for the soil, not that they represent unique solutions. Here, we use pair distribution function (PDF) analysis to determine the short-range order of amorphous analogs in martian soils and better constrain the amorphous material detected by CheMin.
Achilles, C. N.↗
Examination of the Atomic Pair Distribution Function (PDF) of SiC Nanocrystals by In-situ High Pressure Diffraction
Key properties of nanocrystals are determined by their real atomic structure, therefore a reasonable understanding and meaningful interpretation of their properties requires a realistic model of the structure. In this paper we present an evidence of a complex response of the lattice distances to external pressure indicating a presence of a complex structure of Sic nanopowders. The experiments were performed on nanocrystalline Sic subjected to hydrostatic or isostatic pressure using synchrotron and neutron powder diffraction. Elastic properties of the samples were examined based on X-ray diffraction data using a Diamond Anvil Cell (DAC) in HASYLAB at DESY. The dependence'of the lattice parameters and of the Bragg reflections width with pressure exhibits a ha1 nature of the properties (compressibilities) of the powders and indicates a complex structure of the grains. We interpreted tws behaviour as originating from different elastic properties of the grain interior and surface. Analysis of the dependence of individual interatomic distances on pressure was based on in-situ neutron diffraction measurements done with HbD diffractometer at LANSCE in Los Alamos National Laboratory with the Paris-Edinburgh cell under pressures up to 8 GPa (Qmax = 26/A). Interatomic distances were obtained by PDF analysis using the PDFgetN program. We have found that the interatomic distances undergo a complex, non-monotonic changes. Even under substantial pressures a considerable relaxation of the lattice may take place: some interatomic distances increase with an increase in pressure. We relate this phenomenon to: (1), changes of the microstructure of the densified material, in particular breaking of its fractal chain structure and, (2), its complex structure resembling that of a material composed of two phases, each with its distinct elastic properties.
Grzanka, E.↗
Inertial Effects in Suspension Dynamics
The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.
J. F. Brady↗
Coordinate-based simulation of pair distance distribution functions for small and large molecular assemblies: implementation and applications
X-ray scattering has become a major tool in the structural characterization of nanoscale materials. Thanks to the widely available experimental and computational atomic models, coordinate-based X-ray scattering simulation has played a crucial role in data interpretation in the past two decades. However, simulation of real-space pair distance distribution functions (PDDFs) from small- and wide-angle X-ray scattering, SAXS/WAXS, has been relatively less exploited. This study presents a comparison of PDDF simulation methods, which are applied to molecular structures that range in size from β-cyclodextrin [1 kDa molecular weight (MW), 66 non-hydrogen atoms] to the satellite tobacco mosaic virus capsid (1.1 MDa MW, 81 960 non-hydrogen atoms). The results demonstrate the power of interpretation of experimental SAXS/WAXS from the real-space view, particularly by providing a more intuitive method for understanding of partial structure contributions. Furthermore, the computational efficiency of PDDF simulation algorithms makes them attractive as approaches for the analysis of large nanoscale materials and biological assemblies. The simulation methods demonstrated in this article have been implemented in stand-alone software, SolX 3.0 , which is available to download from https://12idb.xray.aps.anl.gov/solx.html.
Zuo, Xiaobing (ORCID:0000000201344804)↗
Experimental and Theoretical Confirmation of Covalent Bonding in α‐Pu
Plutonium's radioactivity provides functionality for nuclear batteries, nuclear reactors, etc., but its complex electronic properties harbor strongly correlated behavior giving rise to a host of interesting phenomena including the presence of a ca. 25% volume collapse between δ-Pu and α-Pu. The complex bonding environments of the ground state allotrope, α-Pu, serve as a unique testing ground for new computational and experimental approaches within the Pu science community. For the first time, a combination of novel ansatzes is used in all-electron density functional theory (DFT) and pair distribution functions (PDF) obtained from high-Q X-ray diffraction to study the bonding behavior in α-Pu. This first experimental and theoretical co-informed description of local bonding behavior for α-Pu reveals covalent bonds, which is a topic that remains of interest in this allotrope. The covalent bonding present at the atomistic level accounts for several of α-Pu's macropscopic properties (e.g., Poisson's ratio) that in turn explains its physical functionalities relative to other allotropic phases like δ-Pu.
36 MATERIALS SCIENCE↗
Ab-initio molecular dynamics study of eutectic chloride salt: MgCl2–NaCl–KCl
Ionic liquid materials are viable candidates as a heat transfer fluid (HTF) in a wide range of applications, notably within concentrated solar power (CSP) technology and molten salt reactors (MSRs). For next-generation CSP and MSR technologies that strive for higher power generation efficiency, a HTF with wide liquid phase range and energy storage capabilities is crucial. Studies have shown that eutectic chloride salts exhibit thermal stability at high temperatures, high heat storage capacity, and are less expensive than nitrate and carbonate salts. However, the experimental data needed to fully evaluate the potential of eutectic chloride salts as a HTF contender are scarce and entail large uncertainties. Considering the high cost and potential hazards associated with the experimental methods used to determine the properties of ionic liquids, molecular modeling can be used as a viable alternative resource. In this study, the eutectic ternary chloride salt MgCl 2 –NaCl–KCl is modeled using ab-initio molecular dynamics simulations (AIMDs) in the liquid phase. Using the simulated data, the thermophysical and transport properties of eutectic chloride salt can be calculated: density, viscosity, heat capacity, diffusion coefficient, and ionic conductivity. For an initial model validation, experimental pair-distribution function data were obtained from X-ray total scattering techniques and compared to the theoretical pair-distribution function. Additionally, theoretical viscosity values are compared to experimental viscosity values for a similar system. The results provide a starting foundation for a MgCl 2 –NaCl–KCl model that can be extended to predict other fundamental properties.
38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
ATOMIC AND MICROSTRUCTURAL ORIGINS OF STORED ENERGY RELEASE IN NEUTRON-IRRADIATED SILICON CARBIDE
Here, we employ a combination of advanced synchrotron-based scattering characterization techniques to understand and unravel the atomic origins of the colossal stored energy release in neutron irradiated silicon carbide. The quantification of the neutron irradiation-induced defects, and their impact on the structureproperty relationship is important for the design and safe operation of advanced fission and fusion reactors. Our experimental results show that the atomic structure in the as irradiated samples is significantly perturbed due to a large fraction of vacancy and interstitial type defects that lead to complex microstructures and additional components in the x-ray diffraction and pair distribution function results. We directly correlate the stored energy release to the recovery of the sub-lattices, with pair distribution function analysis highlighting that the carbon interstitial and vacancy-type defects contribute to stored energy more than those of silicon. We find these results to be striking and believe our discoveries to be timely and noteworthy given the technological importance of silicon carbide to the nuclear fission and fusion communities.
Sprouster, D.J.↗