Calculated Structure Factors Research Articles

Theoretical Investigations and Comparisons of the Amorphous Structures of Adamantane-like Cluster Materials Utilizing Molecular Dynamics Simulations.

Cluster materials of the composition AdR4 (Ad = adamantane, R = organic substituent) and [(RT)4E6] (R = organic substituent; T = Si, Ge, Sn; and E = S, Se, Te) exhibit directional white light emission or produce second harmonics when irradiated with a continuous wave infrared laser source. The nature of the nonlinear optical properties correlates with the macroscopic structures of the cluster materials. The desired white light emission predominantly occurs in amorphous materials. It is therefore crucial to understand the geometric structures of the materials and the order within the materials. Here, we investigate the geometric structures of 12 different adamantane-like cluster materials by molecular dynamics simulations using a nonperiodic particle approach. The comparison of the calculated structure factors for two cluster materials with the corresponding experimental data obtained from diffraction and EXAFS measurements shows very good agreement. Our computations revealed that, on the one hand, larger, more flexible core structures (Ad < {Si4S6} < {Ge4S6} < {Sn4S6}) tend to lead to amorphous solids. On the other hand, larger substituents (methyl < phenyl < naphthyl) lead to more defined nearest neighbor interactions, with a tendency toward crystalline solids. Overall, our results show that a beginning order in the material results from a combination of the degree of flexibility of the core structure and the variation of the nearest neighbor interaction determined by the substituents.

Three-dimensional Heisenberg model with Dzyaloshinskii-Moriya interaction: A Monte Carlo study.

The three-dimensional classical Heisenberg model on a simple cubic lattice with Dzyaloshinskii-Moriya (DM) interactions between nearest-neighbors in all directions has been studied using Monte Carlo simulations. The Metropolis algorithm, combined with single histogram reweighting techniques and finite-size scaling analyses, has been used to obtain the thermodynamic behavior of the system in the thermodynamic limit. Simulations were performed with the same set of interaction parameters for both shifted boundary conditions (SBC) and fluctuating boundary conditions (FBC). Because of an incommensurability caused by the DM interaction, the SBC incorporated a fixed shift angle at the boundary which varies as a function of the DM interaction and lattice size. This SBC method decreases the simulation time significantly, but the distribution of states is somewhat different than that obtained with FBC. The ground state for nonzero DM interaction is a spiral configuration where the spins are restricted to lie in planes perpendicular to the DM vector. We found that this spiral configuration undergoes a conventional second-order phase transition into a disordered, paramagnetic state with the transition temperature being a function of the magnitude of the DM interaction. The limiting case with only DM interaction in the model has also been considered. The critical exponent ν, the critical exponent ratios α/ν, β/ν, γ/ν, as well as the critical temperature T_{c} and fourth-order cumulant of the order parameter U_{4}^{*} at T_{c} have been estimated for different magnitudes of DM interaction. The critical exponents and cumulants at the transition are different from those for the three-dimensional Heisenberg model, but the ratios α/ν, β/ν, γ/ν, U_{4}^{*}/ν are the same, implying that weak universality is valid for all values of DM interaction. Structure factor calculations for particular cases have been performed considering SBC and FBC in the simulations with different lattice sizes at the critical temperatures.

Structure Factors for Hot Neutron Matter from AbInitio Lattice Simulations with High-Fidelity Chiral Interactions.

We present the first abinitio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The abinitio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with abinitio lattice calculations.

Calculating structure factors of protein solutions by atomistic modeling of protein-protein interactions

We present a method, FMAPS(q), for calculating the structure factor, S(q), of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function gC(R). At low protein concentrations, gC(R) can be approximated as e−βW(R), where W(R) is the potential of mean force along the center-center distance R. We calculate W(R) using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203–8215]. For higher protein concentrations, we obtain S(q) by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.

Photoinduced shortening of metallic bond in 1T′-ReS2 revealed by femtosecond electron diffraction

Rhenium disulfide with a distorted crystal structure has recently attracted tremendous attention for its excitonic and highly anisotropic properties. While ultrafast spectroscopies have extensively probed the carrier response to photoexcitation, the associated lattice response has remained elusive. In this study, we utilize MeV femtosecond electron diffraction to unravel the intricate dynamics of lattice responses and energy flow post-photoexcitation. Combining with structure factor calculations, our investigation reveals the dominance of photoinduced shortening in the Re–Re metallic bond, driven by the strong electron–phonon coupling via the Ag8 mode, resulting in an anisotropic intensity change of Bragg reflections within the initial 0.2 ps. Subsequent stretching of the metallic bond, coupled with the concurrent lattice thermalization, enables the system to reach a new equilibrium within 20 ps. This comprehensive understanding of lattice responses in a nonequilibrium state provides unique insights into photoinduced dynamics in 1T′-ReS2 from a structural perspective.

Concentration-Dependent Diffusion of Monoclonal Antibodies: Underlying Mechanisms of Anomalous Diffusion.

The development, storage, transport, and subcutaneous delivery of highly concentrated monoclonal antibody formulations pose significant challenges due to the high solution viscosity and low diffusion of the antibody molecules in crowded environments. These issues often stem from the self-associating behavior of the antibody molecules, potentially leading to aggregation. In this work, we used a dissipative particle dynamics-based coarse-grained model to investigate the diffusion behavior of IgG1 antibody molecules in aqueous solutions with 15 and 32 mM NaCl and antibody concentrations ranging from 10 to 400 mg/mL. We determined the coarse-grained interaction parameters by matching the calculated structure factor with the computational and experimental data from the literature. Our results indicate Fickian diffusion for antibody concentrations of 10 and 25 mg/mL and anomalous diffusion for concentrations exceeding 50 mg/mL. The anomalous diffusion was observed for ∼0.33 to 0.4 μs, followed by Fickian diffusion for all antibody concentrations. We observed a strong linear correlation between the diffusion behavior of the antibody molecules (diffusion coefficient D and anomalous diffusion exponent α) and the amount of aggregates present in the solution and between the amount of aggregates and the Coulomb interaction energy. The investigation of underlying mechanisms for anomalous diffusion revealed that in crowded environments at high antibody concentrations, the attractive interaction between electrostatically complementary regions of the antibody molecules could further bring the neighboring molecules closer to one another, ultimately resulting in aggregate formation. Further, the Coulomb attraction can continue to draw more molecules together, forming larger aggregates.

Femtosecond Electron Diffraction Reveals Local Disorder and Local Anharmonicity in Thermoelectric SnSe.

In addition to long-range periodicity, local disorder, with local structures deviating from the average lattice structure, dominates the physical properties of phonons, electrons, and spin subsystems in crystalline functional materials. Experimentally characterizing the 3D atomic configuration of such a local disorder and correlating it with advanced functions remains challenging. Using a combination of femtosecond electron diffraction, structure factor calculations, and time-dependent density functional theory molecular dynamics simulations, the static local disorder and its local anharmonicity in thermoelectric SnSe are identified exclusively. The ultrafast structural dynamics reveal that the crystalline SnSe is composed of multiple locally correlated configurations dominated by the static off-symmetry displacements of Sn (≈0.4 Å) and such a set of locally correlated structures is termed local disorder. Moreover, the anharmonicity of this local disorder induces an ultrafast atomic displacement within 100 fs, indicating the signature of probable THz Einstein oscillators. The identified local disorder and local anharmonicity suggest a glass-like thermal transport channel, which updates the fundamental insight into the long-debated ultralow thermal conductivity of SnSe. The method of revealing the 3D local disorder and the locally correlated interactions by ultrafast structural dynamics will inspire broad interest in the construction of structure-property relationships in material science.

Engineering Ultrasoft Interactions in Stiff All-DNA Dendrimers by Site-Specific Control of Scaffold Flexibility.

A combined experimental and theoretical study of the structural correlations in moderately concentrated suspensions of all-DNA dendrimers of the second generation (G2) with controlled scaffold rigidity is reported here. Small-angle X-ray scattering experiments in concentrated aqueous saline solutions of stiff all-DNA G2 dendritic constructs reveal a novel anomalous liquid-like phase behavior which is reflected in the calculated structure factors as a two-step increase at low scattering wave vectors. By developing a new design strategy for adjusting the particle's internal flexibility based on site-selective incorporation of single-stranded DNA linkers into the dendritic scaffold, it is shown that this unconventional type of self-organization is strongly contingent on the dendrimer's stiffness. A comprehensive computer simulation study employing dendritic models with different levels of coarse-graining, and two theoretical approaches based on effective, pair-potential interactions, remarkably confirmed the origin of this unusual liquid-like behavior. The results demonstrate that the precise control of the internal structure of the dendritic scaffold conferred by the DNA can be potentially used to engineer a rich palette of novel ultrasoft interaction potentials that could offer a route for directed self-assembly of intriguing soft matter phases and experimental realizations of a host of unusual phenomena theoretically predicted for ultrasoft interactingsystems.

A Composite Ansatz for Calculation of Dynamical Structure Factor

We propose an ansatz without adjustable parameters for the calculation of a dynamical structure factor. The ansatz combines the quasi-particle Green’s function, especially the contribution from the renormalization factor, and the exchange-correlation kernel from time-dependent density functional theory together, verified for typical metals and semiconductors from a plasmon excitation regime to the Compton scattering regime. It has the capability to reconcile both small-angle and large-angle inelastic x-ray scattering (IXS) signals with much-improved accuracy, which can be used as the theoretical base model, in inversely inferring electronic structures of condensed matter from IXS experimental signals directly. It may also be used to diagnose thermal parameters, such as temperature and density, of dense plasmas in x-ray Thomson scattering experiments.

Order-disorder (OD) polytypism of K3FeTe2O8(OH)2(H2O)1+x.

K3FeTe2O8(OH)2(H2O)2 was synthesized under hydrothermal conditions from Te(OH)6, FeSO4·7H2O and 85 wt% KOH in a 1:2:6 molar ratio. The crystal structure is built of a triperiodic network. One disordered water molecule per formula unit is located in a channel and can be partially removed by heating. Systematic one-dimensional diffuse scattering indicates a polytypic character, which is best described by application of the order-disorder theory. The major polytype is monoclinic with pseudo-orthorhombic metrics. It is interrupted by fragments of an orthorhombic polytype. The diffraction intensities are analyzed using structure factor calculations.

Large bi-axial tensile strain effect in epitaxial BiFeO3 film grown on single crystal PrScO3

A BiFeO3 film is grown epitaxially on a PrScO3 single crystal substrate which imparts ~ 1.45% of biaxial tensile strain to BiFeO3 resulting from lattice misfit. The biaxial tensile strain effect on BiFeO3 is investigated in terms of crystal structure, Poisson ratio, and ferroelectric domain structure. Lattice resolution scanning transmission electron microscopy, precession electron diffraction, and X-ray diffraction results clearly show that in-plane interplanar distance of BiFeO3 is the same as that of PrScO3 with no sign of misfit dislocations, indicating that the biaxial tensile strain caused by lattice mismatch between BiFeO3 and PrScO3 are stored as elastic energy within BiFeO3 film. Nano-beam electron diffraction patterns compared with structure factor calculation found that the BiFeO3 maintains rhombohedral symmetry, i.e., space group of R3c. The pattern analysis also revealed two crystallographically distinguishable domains. Their relations with ferroelectric domain structures in terms of size and spontaneous polarization orientations within the domains are further understood using four-dimensional scanning transmission electron microscopy technique.

Applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. Chemical bonding and binding features in the crystal and dimer of 1,3-bis(2-hydroxyethyl)-6-methyluracil.

We considered it timely to test the applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. The procedure was carried out on the crystal of 1,3-bis(2-hydroxyethyl)-6-methyluracil, and some derived properties of the scalar potential and vector force fields were compared with those obtained from the experimental multipole model and from the aspherical pseudo-atom model with parameters fitted to the calculated structure factors. The procedure was shown to accurately replicate the general vector-field behavior, the peculiarities of the quantum potentials and the characteristics of the force-field pseudoatoms, such as charge, shape and volume, as well as to reproduce the relative arrangement of atomic and pseudoatomic zero-flux surfaces along internuclear regions. It was found that, in addition to the quantum-topological atoms, the force-field pseudoatoms are spatially reproduced within a single structural fragment and similar environment. In addition, the classical and nonclassical hydrogen bonds in the uracil derivative crystal, as well as the H...O, N...O and N...C interactions in the free π-stacked dimer of the uracil derivative molecules, were studied using the potential and force fields within the concepts of interatomic charge transfer and electron lone pair donation-acceptance. Remarkably, the nitrogen atoms in the N...O and N...C interactions behave rather like a Lewis base and an electron contributor. At the same time, the hydrogen atom in the H...O interaction, being a Lewis acid, also participates in the interatomic electron transfer by acting as a contributor. Thus, it has been argued that, when describing polar interatomic interactions within orbital-free considerations, it makes more physical sense to identify electronegative (electron occupier) and electropositive (electron contributor) atoms or subatomic fragments rather than nucleophilic and electrophilic sites.

Calculation of Second Virial Coefficient of DNA

In this work, a new calculate method has been presented to calculate second virial coefficient with structure factor. The second virial coefficient for DNA have been defined using the calculated structure factor and the programmed fitting technique of Mathematica Software 7.0. The obtained results have been compared with theoretical data and shown in good agreement with literature.

A continuum model for morphology formation from interacting ternary mixtures: Simulation study of the formation and growth of patterns

Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume–Capel-type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar qualitative features (e.g. general shape and approximate coarsening rates) which have been observed in previous works on the stochastic Blume–Capel model with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.

On the absence of structure factors in concentrated colloidal suspensions and nanocomposites.

Small-angle scattering is a commonly used tool to analyze the dispersion of nanoparticles in all kinds of matrices. Besides some obvious cases, the associated structure factor is often complex and cannot be reduced to a simple interparticle interaction, like excluded volume only. In recent experiments, we have encountered a surprising absence of structure factors (S(q) = 1) in scattering from rather concentrated polymer nanocomposites (Genix et al. in ACS Appl Mater Interfaces 11(19):17863-17872, 2019). In this case, quite pure form factor scattering is observed. This somewhat "ideal" structure is further investigated here making use of reverse Monte Carlo simulations in order to shed light on the corresponding nanoparticle structure in space. By fixing the target "experimental" apparent structure factor to one over a given q-range in these simulations, we show that it is possible to find dispersions with this property. The influence of nanoparticle volume fraction and polydispersity has been investigated, and it was found that for high concentrations only a high polydispersity allows reaching a state of S = 1. The underlying structure in real space is discussed in terms of the pair-correlation function, which evidences the importance of attractive interactions between polydisperse nanoparticles. The calculation of partial structure factors shows that there is no specific ordering of large or small particles, but that the presence of attractive interactions together with polydispersity allows reaching an almost "structureless" state.

Cyclo-hexane plastic phase I: single-crystal diffraction images and new structural model.

The plastic phase of cyclohexane (polymorph I) was studied by Kahn and co-workers, without achieving a satisfactory determination of the atomic coord-inates [Kahn et al. (1973). Acta Cryst. B29, 131-138]. The positions of the C atoms cannot be determined directly as a consequence of the disorder in a high-symmetry space group, an inherent feature of plastic materials. Given this situation, the building of a polyhedron describing the disorder was the main tool for determining the molecular structure in the present work. Based on the shape of reflections {111}, {200} and {113} in space group Fm 3 m, we assumed that cyclohexane is disordered through the action of rotation group 432. The polyhedral cluster of disordered molecules is then a rhombic dodecahedron centred on the nodes of an fcc Bravais lattice. The vertices of this polyhedron are the positions of C atoms for the cyclohexane molecule, which is disordered over 24 positions. With such a model, the asymmetric unit is reduced to two C atoms placed on special positions, and an acceptable fit between the observed and calculated structure factors is obtained.

Local Structure of Molten Lithium Fluoride. II. Structure Factor Calculation by Ab Initio and Classical Molecular Dynamics Methods

Local Structure of Molten Lithium Fluoride. II. Structure Factor Calculation by Ab Initio and Classical Molecular Dynamics Methods

Photoinduced Ultrafast Transition of the Local Correlated Structure in Chalcogenide Phase-Change Materials.

Revealing the bonding and time-evolving atomic dynamics in functional materials with complex lattice structures can update the fundamental knowledge on rich physics therein, and also help to manipulate the material properties as desired. As the most prototypical chalcogenide phase change material, Ge_{2}Sb_{2}Te_{5} has been widely used in optical data storage and nonvolatile electric memory due to the fast switching speed and the low energy consumption. However, the basic understanding of the structural dynamics on the atomic scale is still not clear. Using femtosecond electron diffraction, structure factor calculation, and time-dependent density-functional theory molecular dynamic simulation, we reveal the photoinduced ultrafast transition of the local correlated structure in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5}. The randomly oriented Peierls distortion among unit cells in the averaged rocksalt phase of Ge_{2}Sb_{2}Te_{5} is termed as local correlated structures. The ultrafast suppression of the local Peierls distortions in the individual unit cell gives rise to a local structure change from the rhombohedral to the cubic geometry within ∼0.3 ps. In addition, the impact of the carrier relaxation and the large number of vacancies to the ultrafast structural response is quantified and discussed. Our Letter provides new microscopic insights into contributions of the local correlated structure to the transient structural and optical responses in phase change materials. Moreover, we stress the significance of femtosecond electron diffraction in revealing the local correlated structure in the subunit cell and the link between the local correlated structure and physical properties in functional materials with complex microstructures.

Formulation of the partial structure factors and of the order parameters for the liquid or amorphous multicomponent alloy – Application to the quinternary and hexa-component alloys

Thanks to the extension of the results of our four previous works (B. Grosdidier 2018, 2019, 2021, 2022), we now study the structure and the order parameters of the multicomponent alloy in two conceptualizations by working in a “physical basis”. In this basis, all the structural quantities and the order parameters are formulated by very concise equations, in which the number of components does not explicitly appear. These equations allow a fast calculation of the total structure factors and also the investigation of properties valid for any number of species for several “toy models” having specific behavior of their atomic species. Some of our results are confirmed by studying the atom exchanges in several iso-stoichiometric multicomponent alloys. From these equations, we provide a protocol of the calculation for all partial and total structure factors of the hexa-component alloy, which can be reduced to a quinternary, quaternary and finally ternary system.

Calculating temperature-dependent X-ray structure factors of α-quartz with an extensible Python 3 package.

The design of X-ray optics based on diffraction from crystals depends on the accurate calculation of the structure factors of their Bragg reflections over a wide range of temperatures. In general, the temperature dependence of the lattice parameters, the atomic positions and the atomic thermal vibrations is both anisotropic and nonlinear. Implemented here is a software package for precise and flexible calculation of structure factors for dynamical diffraction. α-Quartz is used as an example because it presents the challenges mentioned above and because it is being considered for use in high-resolution X-ray spectroscopy. The package is designed to be extended easily to other crystals by adding new material files, which are kept separate from the package's stable core. Python 3 was chosen as the language to allow the easy integration of this code into existing packages. The importance of a correct anisotropic treatment of the atomic thermal vibrations is demonstrated by comparison with an isotropic Debye model. Discrepancies between the two models can be as much as 5% for strong reflections and considerably larger (even to the level of 100%) for weak reflections. A script for finding Bragg reflections that backscatter X-rays of a given energy within a given temperature range is demonstrated. The package and example scripts are available on request. Also discussed, in detail, are the various conventions related to the proper description of chiral quartz.