Simulated Pair Distribution Function Research Articles

Correlated Anion Disorder in Heteroanionic Cubic TiOF2.

Resolving anion configurations in heteroanionic materials is crucial for understanding and controlling their properties. For anion-disordered oxyfluorides, conventional Bragg diffraction cannot fully resolve the anionic structure, necessitating alternative structure determination methods. We have investigated the anionic structure of anion-disordered cubic (ReO3-type) TiOF2 using X-ray pair distribution function (PDF), 19F MAS NMR analysis, density functional theory (DFT), cluster expansion modeling, and genetic-algorithm structure prediction. Our computational data predict short-range anion ordering in TiOF2, characterized by predominant cis-[O2F4] titanium coordination, resulting in correlated anion disorder at longer ranges. To validate our predictions, we generated partially disordered supercells using genetic-algorithm structure prediction and computed simulated X-ray PDF data and 19F MAS NMR spectra, which we compared directly to experimental data. To construct our simulated 19F NMR spectra, we derived new transformation functions for mapping calculated magnetic shieldings to predicted magnetic chemical shifts in titanium (oxy)fluorides, obtained by fitting DFT-calculated magnetic shieldings to previously published experimental chemical shift data for TiF4. We find good agreement between our simulated and experimental data, which supports our computationally predicted structural model and demonstrates the effectiveness of complementary experimental and computational techniques in resolving anionic structure in anion-disordered oxyfluorides. From additional DFT calculations, we predict that increasing anion disorder makes lithium intercalation more favorable by, on average, up to 2 eV, highlighting the significant effect of variations in short-range order on the intercalation properties of anion-disordered materials.

Integrated analysis of X-ray diffraction patterns and pair distribution functions for machine-learned phase identification

To bolster the accuracy of existing methods for automated phase identification from X-ray diffraction (XRD) patterns, we introduce a machine learning approach that uses a dual representation whereby XRD patterns are augmented with simulated pair distribution functions (PDFs). A convolutional neural network is trained directly on XRD patterns calculated using physics-informed data augmentation, which accounts for experimental artifacts such as lattice strain and crystallographic texture. A second network is trained on PDFs generated via Fourier transform of the augmented XRD patterns. At inference, these networks classify unknown samples by aggregating their predictions in a confidence-weighted sum. We show that such an integrated approach to phase identification provides enhanced accuracy by leveraging the benefits of each model’s input representation. Whereas networks trained on XRD patterns provide a reciprocal space representation and can effectively distinguish large diffraction peaks in multi-phase samples, networks trained on PDFs provide a real space representation and perform better when peaks with low intensity become important. These findings underscore the importance of using diverse input representations for machine learning models in materials science and point to new avenues for automating multi-modal characterization.

DeepStruc: towards structure solution from pair distribution function data using deep generative models.

Structure solution of nanostructured materials that have limited long-range order remains a bottleneck in materials development. We present a deep learning algorithm, DeepStruc, that can solve a simple monometallic nanoparticle structure directly from a Pair Distribution Function (PDF) obtained from total scattering data by using a conditional variational autoencoder. We first apply DeepStruc to PDFs from seven different structure types of monometallic nanoparticles, and show that structures can be solved from both simulated and experimental PDFs, including PDFs from nanoparticles that are not present in the training distribution. We also apply DeepStruc to a system of hcp, fcc and stacking faulted nanoparticles, where DeepStruc recognizes stacking faulted nanoparticles as an interpolation between hcp and fcc nanoparticles and is able to solve stacking faulted structures from PDFs. Our findings suggests that DeepStruc is a step towards a general approach for structure solution of nanomaterials.

New insights into the application of pair distribution function studies to biogenic and synthetic hydroxyapatites

Biogenic and synthetic hydroxyapatites are confounding materials whose properties remain uncertain, even after years of study. Pair distribution function (PDF) analysis was applied to hydroxyapatites in the 1970’s and 1980’s, but this area of research has not taken full advantage of the relatively recent advances in synchrotron facilities. Here, synchrotron X-ray PDF analysis is compared to techniques commonly used to characterise hydroxyapatite (such as wide angle X-ray scattering, Fourier-transform infrared spectroscopy and thermogravimetric analysis) for a range of biogenic and synthetic hydroxyapatites with a wide range of carbonate substitution. Contributions to the pair distribution function from collagen, carbonate and finite crystallite size were examined through principal component analysis and comparison of PDFs. Noticeable contributions from collagen were observed in biogenic PDFs when compared to synthetic PDFs (namely r < 15 Å), consistent with simulated PDFs of collagen structures. Additionally, changes in local structure were observed for PDFs of synthetic hydroxyapatites with differing carbonate content, notably in features near 4 Å, 8 Å and 19 Å. Regression models were generated to predict carbonate substitution from peak position within the PDFs.

X-ray scattering study of water confined in bioactive glasses: experimental and simulated pair distribution function.

Temperature-dependent total X-ray scattering measurements for water confined in bioactive glass samples with 5.9 nm pore diameter have been performed. Based on these experimental data, simulations were carried out using the Empirical Potential Structure Refinement (EPSR) code, in order to study the structural organization of the confined water in detail. The results indicate a non-homogeneous structure for water inside the pore, with three different structural organizations of water, depending on the distance from the pore surface: (i) a first layer (4 Å) of interfacial pore water that forms a strong chemical bond with the substrate, (ii) intermediate pore water forming a second layer (4-11 Å) on top of the interfacial pore water, (iii) bulk-like pore water in the centre of the pores. Analysis of the simulated site-site partial pair distribution function shows that the water-silica (Ow-Si) pair correlations occur at ∼3.75 Å. The tetrahedral network of bulk water with oxygen-oxygen (Ow-Ow) hydrogen-bonded pair correlations at ∼2.8, ∼4.1 and ∼4.5 Å is strongly distorted for the interfacial pore water while the second neighbour pair correlations are observed at ∼4.0 and ∼4.9 Å. For the interfacial pore water, an additional Ow-Ow pair correlation appears at ∼3.3 Å, which is likely caused by distortions due to the interactions of the water molecules with the silica at the pore surface.

First-principles study on the effect of Sn doping in Cu2S—Acanthite phase as a substitute to low chalcocite for modeling complex doping

The major challenge in the application of Cu2S, as a solar absorber for photovoltaic, is its excessive Cu-vacancy formation tendency within the crystal structure that makes it a degenerate semiconductor. A recent study on Ag alloyed Cu2S acanthite phase has shown a reduced Cu-vacancy formation and a high Cu diffusion barrier. Though low chalcocite is the experimentally known ground state phase at room temperature, its low crystallinity makes it computationally expensive for complex doping modeling. In this work, we first establish the structural correspondence between a newly predicted acanthite and experimentally known low chalcocite phases of Cu2S. This study shows that the acanthite crystal structure of Cu2S can be used to model complex doping in the low chalcocite. The simulated pair distribution functions and diffusions of Cu at room temperature in acanthite and low chalcocite phases of Cu2S show that they have similar structural behavior. Pristine band structures and density of state plots of these two phases also show similarity. Next, we report density functional theory based first-principles investigations of Cu2−xSnxS systems for x = 0 to 0.31 in the acanthite phase for thermodynamic, electronic, and optical properties. We have found that Sn doping coupled with Cu vacancies creates charge-neutral defects and results in higher photoabsorption in the visible light spectra. It was found from these detailed studies that a low concentration of Sn doping is preferable. Then, Sn doping and Cu-vacancy related defects in low chalcocite Cu2S are also studied. Ab initio molecular dynamics simulations show that these compound defects in Cu2S do not negatively affect Cu diffusion inside the crystal. We propose a possible route to synthesize Sn doped acanthite like Cu2S.

Hydration for the Alite mineral: Morphology evolution, reaction mechanism and the compositional influences

Hydration of minerals, playing fundamental role in many technological applications, involves multi-stage chemical reactions, morphology changes and compositional variations. For the first time, the hydration mechanism for the tricalcium silicate was investigated by the combination of C3S hydration experimentally and polymerization of silicate monomers via molecular dynamics simulation. Tricalcium silicate was self-synthesized and utilized to hydrate with water at the water/solid ratio of 50. Samples hydrated from one day to one year were obtained and characterized by XRD, IR, SEM, NMR and TEM techniques. Based on SEM observation, the morphology of hydrated C3S transformed from small localized to foil-like wrinkled clusters with fibrillar-like wrinkles distributed randomly. Wrinkled product of C-S-H possessed poor-crystallined or amorphous feature based on XRD and TEM analysis. Such was also evidenced by the fact that no layered crystal phase was observed in simulated calcium silicate gel clusters. Besides, the simulated pair distribution function of C-S-H gel demonstrating the structure feature of short range order and long range disorder, also confirmed glassy structural nature for the C-S-H gel. Furthermore, based on NMR and SEM results C/S ratio changed to 1.2 and the mean silicate chain length in C-S-H was obtained at around 4 after hydration for one year with Q1 and Q2 species representing linear silicate chain structure present dominantly. The molecular dynamics helped illuminate the hydration mechanism that the morphology of C-S-H gel was closely related with C/S ratio. At C/S ratio of 1, solid branched 3-dimmensional cluster was segregated from the solution while ellipsoid colloid particle with the size of 4nm×4nm×8nm was formed at C/S ratio of 1.75. It was also found that calcium ions prevented the polymerization reaction of silicate monomers and silicate chains were shortened significantly at high Ca/Si ratio, amplifying the predominate percentage of Q1 species in the C-S-H gel.

Structural analysis of lignin-derived carbon composite anodes

The development of novel lignin-based carbon composite anodes consisting of nanocrystalline and amorphous domains motivates the understanding of the relationship of the structural properties characterizing these materials, such as crystallite size, intracrystallitedspacing, crystalline volume fraction and composite density, with their pair distribution functions (PDFs), obtained from both molecular dynamics simulation and neutron scattering. A model for these composite materials is developed as a function of experimentally measurable parameters and realized in 15 composite systems, three of which directly match all parameters of their experimental counterparts. The accurate reproduction of the experimental PDFs using the model systems validates the model. The decomposition of the simulated PDFs provides an understanding of each feature in the PDF and allows for the development of a mapping between the defining characteristics of the PDF and the material properties of interest.

Distinguishing Types of Disorder in Diffuse Scattering: A Numerical Simulation Study

Using numerical simulation tools such as DISCUS and ZMC, the signatures in simulated pair distribution function (PDF) and single-crystal diffuse scattering (SCDS) of various types of disorders in a range of model systems are explored by observation of the evolution of calculated PDF and SCDS. Disordered crystalline materials may show a variety of types of short-range correlations in occupancies, displacements, and (if a molecular system) orientations of constituents. Further, the correlation between occupancy and displacement (the size effect) will often also be present. This work provides some insight into the abilities of the two data types to distinguish and quantify these different aspects of disorder in materials, with a view to guide the analysis of real systems.

Fine Structure Evaluation of the Pair Distribution Function with Molecular Models of the Argonne Premium Coals

The pair distribution function (PDF) is one means of evaluating the atomic spatial arrangements of coals. Analysis of PDF based on X-ray diffraction data provides structural information on turbostratic crystalline parameters that can be utilized to further characterize coal structure. With coalification, expectations are of limited growth in aromatic stacking and a slight growth in the aromatic cluster size over the lignite to medium-volatile bituminous range. The PDF can be also used to construct and validate atomistic representations for carbonaceous materials including coal. Here, the PDF was evaluated with molecular slice models of several Argonne Premium coals (Beulah-Zap, Illinois No. 6, Upper Freeport, Pocahontas No. 3), also a non-Argonne Hon Gai anthracite, and compared to experimental observations. Atomistic representations were generated directly from high-resolution transmission electron microscope (HRTEM) lattice fringe images. The Fringe3D approach populates aromatic moieties matching the distributions of fringe: length, layers per stack, interlayer spacing, and orientations to produce an aromatic slice model of limited depth. Perl scripts incorporated appropriate aliphatic and heteroatom components. This approach creates atomistic representations with greater ease, improved accuracy, and reduced computational expense than other construction approaches. The constructed coal models were partially geometry-optimized to achieve realistic bond lengths but without displacement of coal molecules enabling the distribution of fringe length, stacking, and orientations to be duplicated in 3D modeling space. The resulting coal slice models, devoid of cross-links, captured a distribution of turbostratic crystalline dimensions with an average cluster size of about 1 nm, an average interlayer spacing ranging between 0.37 and 0.39 nm, and an average stacking number of ∼2–3 in accordance with HRTEM and XRD data for Argonne coals. These structural models were used to predict PDFs and to evaluate the fine detail of the frequency spectra via examination of intermolecular and intramolecular contributions. There was good agreement between predicted and experimental observations. Analysis of the simulated intermolecular PDF contribution showed strong intensities with increasing coal rank in agreement with the growth in the stacking number and stack height observed from low- to high-rank coals. The simulated intramolecular PDF contribution showed shorter peak amplitudes for low-rank coals in comparison to high-rank coals in agreement with the increase in stack width as coal rank increases. To further examine these contributions, lattice models composed of pyrene molecules were also constructed via Fringe 3D and manipulated to directly investigate the effect of aromatic orientation distributions and stacking on the simulated PDF. Peak intensities of simulated intermolecular PDFs at the average interlayer spacing increased with the degree of alignment (ϕ) according to g(r)interd002 = 0.0014ϕ2 + 0.0107ϕ + 4.2784. This result was consistent with the slight increase in the stacking number observed from low- to high-rank coals with a more dramatic transition for anthracite.

Atomic packing and short-to-medium range order evolution of Zr-Pd metallic glass

A larger-scale Zr70Pd30 alloy system has been simulated using molecular dynamics (MD) to investigate structure evolution in Zr70Pd30 metallic glass. The simulated pair distribution function of Zr70Pd30 metallic glass agrees well with the experimental results. Voronoi polyhedron analysis indicates that the icosahedra are not randomly distributed in space, but form characteristic intercrossed icosahedral clusters with medium-range order. Intercrossed icosahedral clusters are the dominant local configurations in Zr70Pd30 metallic glass and probably cause the quasicrystalline phase discovered in Zr70Pd30 metallic glass.

Icosahedral medium-range order formed in Mg70Zn30 metallic glass: a larger-scale molecular dynamics simulation

A larger-scale Mg70Zn30 alloy system including 100000 atoms has been simulated by using the molecular dynamics method to investigate the icosahedral medium-range order (IMRO) formed in the Mg70Zn30 metallic glass. It is found that the simulated pair distribution function of Mg70Zn30 metallic glass is in good agreement with the experimental results. The glass transition temperature Tg is near 450 K under the cooling rate of 1×1012 K/s. The icosahedral local structures play a critical role in the formation of metallic glass, and they are the dominant local configurations in the Mg70Zn30 metallic glass. The IMRO in the Mg70Zn30 metallic glass is characterized by certain types of extended icosahedral clusters combined by intercross-sharing atoms in the form of chains or dendrites. The size distributions of these IMRO clusters present a magic number sequence of 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, …, and the magic clusters can be classified into three types according to their compactness. The IMRO clusters grow rapidly in a low-dimensional way with cooling, but this growth is limited near Tg.

Calculation of elementary diagrams using a Metropolis-like simulation method

A method for the evaluation of higher order elementary diagrams is proposed. It utilizes symbolic algebra programming and automatic code generation. The method is used to calculate elementary diagrams for hard spheres up to the fifth. The obtained values are fitted to suitable functions of interparticle distance. The resulting truncated density expansion is compared with recent values of the bridge function calculated directly from the simulated pair distribution function. The method can be straightforwardly extended to hard-body systems and their mixtures.

COORDINATION AND STRUCTURAL ENERGETICS OF VARIOUS PHASES OF Ni

Nickel is one of the most versatile metals in the transition series of the periodic table. We have investigated the coordination and the cohesion of Ni corresponding to its various phases. The neighboring distances and the coordination numbers are estimated from the observed and simulated pair distribution functions (PDF) g(r) relevant to the various phases. Since the profiles of these functions are not symmetric, we have used the concept of minimum-to-minimum positions of the PDFs to estimate the successive coordination numbers for the solid amorphous and microcrystalline phases. The approximate values of the pseudo-lattice vectors estimated from the peak positions of the PDFs are employed to calculate the total energies for the amorphous and the microcrystalline phases of Ni in terms of the pseudopotential theory. The roles of the s- and d-electrons in the cohesion of Ni have been investigated by calculating the free energies for the relevant phases. The calculated energetics reveal the relative stability of the various phases in a qualitative manner. It is noted that the d-electrons play the dominant role in predicting the stability of the various phases; the s-electrons merely supplement the d-electron trend. Since the formalism corresponds to very low temperature, the lattice vibrations [Einstein model] do not seem to play any visible role in the prediction.

Molecular dynamics simulations on specific heat capacity and glass transition temperature of liquid silver

The embedded-atom method is adopted to simulate the specific heat capacity of liquid silver. The relationship between the specific heat capacity and the temperature above and below melting point is derived. The results show that there exists an anormaly of the specific heat capacity of liquid silver near 950 K. Simulated pair distribution functions show that the liquid-to-glass transition takes place at this temperature.

The decay of pair correlation functions in ionic fluids: A dressed ion theory analysis of Monte Carlo simulations

We analyze the decay of structural correlation functions for 1:1, 1:2, and 2:2 electrolyte solutions obtained from Monte Carlo simulations. It is found that by the use of dressed ion theory and a simple Picard iteration scheme one can extract the leading decay parameters with high accuracy, even from simulations with a rather limited number of ions in the simulation cell. The extraction scheme consists of replacing in a self-consistent manner the tails of the simulated pair distribution functions by analytical expressions evaluated by residue analysis of short-ranged parts of the correlation functions. Numerical results in this work are restricted to primitive model electrolytes where the solvent only enters as a dielectric continuum. The leading decay parameters of the simulated correlation functions are compared to results obtained from the hypernetted chain (HNC) approximation. For 1:1 and 1:2 electrolytes in aqueous solution the simulation results confirm predictions from the HNC approximation. For 2:2 electrolytes the HNC results agree qualitatively with the simulations but deviate quantitatively. To investigate artifacts induced by boundary conditions used in the simulations we analyze correlation functions obtained from simulations in a spherical cell as well as with cubic periodic boundary conditions. The results and method of analysis presented are restricted to electrolyte concentrations at which the leading decay terms of the pair distribution functions exhibit monotonic exponential decay.

Analysis of occupational and displacive disorder using the atomic pair distribution function: a systematic investigation

Many disorderd crystalline materials show chemical short range order and relaxation of neighboring atoms. Local structural information can be obtained by analyzing the atomic pair distribution function (PDF). The viability of reverse Monte Carlo (RMC) simulations to extract quantitative information about chemical ordering as well as displacements is investigated. The method has been applied to simulated PDFs of disordered structures showing chemical disorder alone as well as in combination with displacements.