Partial Structure Factors Research Articles

Anomalous X-ray scattering studies on semiconducting and metallic glasses

In order to explore local- and intermediate-range atomic structures of several semiconducting and metallic glasses, anomalous X-ray scattering (AXS) experiments were performed using an improved detecting system suitable for third-generation synchrotron radiation facilities, and the obtained data were analyzed using reverse Monte Carlo (RMC) modelling to obtain partial structure factors and to construct three-dimensional atomic configurations of these glasses. Examples of GeSe2 semiconducting and Pd40Ni40P20 metallic glasses are demonstrated to exhibit the feasibility of the combination of AXS and RMC techniques. Importance of an additional combination with neutron scattering is also described for alloys containing light elements.

Structure of near-eutectic Bi-Zn liquid alloys

The structure of near-eutectic Bi1 − xZnx melts (x = 0.04–0.25) has been studied by X-ray diffraction. We have analyzed structure factors, calculated pair correlation functions, and evaluated partial structure factors using reverse Monte Carlo simulation. The results demonstrate that the composition dependences of structural parameters are nonlinear around the eutectic point. Bismuth-rich melts have a random atomic distribution, whereas zinc enrichment leads to the formation of Zn clusters.

Structure and Electrical Resistivities of Liquid Al and Ga Metals and Their Binary Alloys

The ionic and electronic properties of liquid Al and Ga metals and Al1-xGax alloys have been investigated self-consistently. Partial structure factors have been calculated from the solution of the Ornstein–Zernike equation with the hybridized mean spherical approximation closure, and the transferable electron–ion potential of Fiolhais et al. has been used as the input pseudopotential. Two different formulas are used in the electrical resistivity calculation, namely, the Faber–Ziman formula and the modified Ziman’s formula suggested by Ferraz–March. The results are compared with each other and experimental values.

Neutron Scattering and X-ray Investigation of the Structure and Dynamics of Poly(ethyl methacrylate)

We present a study on the structure and dynamics of poly(ethyl methacrylate) (PEMA), one of the polymers with shortest side-group in the poly(n-alkyl methacrylate)s (PnMAs) series. The contributions to the structure factor have been unveiled by combining T-dependent X-ray and neutron diffraction with polarization analysis on samples with different deuteration labelings, accessing thereby different partial structure factors of PEMA. We find clear hints for strong structural ordering with anticorrelated side-groups and main-chain locations, fitting thus in the general scenario of nanosegregation of main chains and side groups found in higher order PnMAs members. Backscattering measurements on a PEMA sample with deuterated side-group have revealed the dynamics of main-chain and α-methyl group hydrogens. The characterization of the rotations of the latter indicates highly disordered environments in the glassy state. Above the glass transition, the incoherent scattering function related to segmental relaxation shows stretching and clear deviations from Gaussian behavior in the accessed window. We also present results on the dynamic structure factor (collective dynamics) at the peaks characteristic (i) for the intermain-chain and interside-group-domain correlations and (ii) for the side-group/side-group atomic correlations within the domains. Viscosity dictates the temperature dependence in both cases, and also that of the dielectric spectroscopy results at high temperatures. However, the α-process followed by dielectric relaxation deviates from the rheological behavior when approaching the calorimetric glass-transition, indicating a strong influence of the faster side-group motions on the dynamics of the dielectric probes.

A polymer in an ionic liquid: Effect of the length of the cationic nonpolar tail on the character of interchain correlations

On the basis of the integral equation theory, we examine spatial correlations of flexible polymer chains dissolved in an ionic liquid. The effect of the concentration of a polymer on its structural properties is studied for different lengths of the nonpolar tail of the solvent cation. The structure of a polymer-containing ionic liquid is analyzed in the reciprocal space on the basis of calculated partial structure factors. In a wide range of polymer concentrations, for all the selected values of length of the cationic nonpolar tail, long-range liquid ordering and intermediate-range liquid ordering of polymer chains are observed. The dependences of the characteristic scale of ordering of macromolecules on their number density in solution are different for ionic liquids with different lengths of the cationic nonpolar tail.

Analytical static structure factors for the restricted primitive model

The mean static structure for the restricted primitive model formed by m ionic species is presented. Explicit expressions for the partial static structure factors are obtained from the Blum’s solution for the primitive model, which depend on an accumulative parameter, γ, expressed in terms of the Debye length. Additionally, the number–number, number–charge and charge–charge structure factors are provided. An equation to calculate the radial distribution functions which tends to the contact values when r→σ+ is also given. Finally, molecular dynamics simulation is performed to assess the accuracy of the theoretical results.

Multiscale Structure, Interfacial Cohesion, Adsorbed Layers, and Thermodynamics in Dense Polymer-Nanoparticle Mixtures

We establish the existence and size of adsorbed polymer layers in miscible dense nanocomposites and their consequences on microstructure and the bulk modulus. Using contrast-matching small-angle neutron scattering to characterize all partial collective structure factors of polymers, particles, and their interface, we demonstrate qualitative failure of the random phase approximation, accuracy of the polymer reference site interaction model theory, ability to deduce the adsorbed polymer layer thickness, and high sensitivity of the nanocomposite bulk modulus to interfacial cohesion.

A study for structure and inter-diffusion coefficient of liquid K1− x Cs x metal alloys

Inter-diffusion coefficients of liquid K1− x Cs x metal alloys are calculated using scaling law proposed by Samanta et al. [A. Samanta, Sk.M. Ali, and S.K. Ghosh, Phys. Rev. Lett. 87, 245901 (2001)] following Dzugutov [M. Dzugutov, Nature 381, 137 (1996)], which express the possible relationship between the excess entropy and diffusion coefficient. The interatomic interactions are described from the individual version of the electron–ion potential proposed by Fiolhais et al. [C. Fiolhais, J.P. Perdew, S.Q. Armster, J.M. McLaren, and M. Brajczewska, Phys. Rev. B 51, 14001 (1995)]. The partial pair distribution functions and structure factors are calculated from the solution of Ornstein–Zernike integral equation with Rogers–Young closure. The evaluations with the composition of static structure and the inter-diffusion properties are discussed.

Long- and Intermediate-Range Correlations in Polymer-Containing Ionic Liquids

Structure on long- and intermediate-length scales in polymer-containing ionic liquids is investigated on the basis of the polymer integral equation method. The structural features of flexible homopolymer chains and the ions of the solvent are analyzed in reciprocal space using partial structure factors. There is a range of polymer concentrations at which the long-range correlations of polymer chains are observed. When these correlations are pronounced, the decrease of the characteristic scale of the long-range polymer ordering with increasing polymer concentration fits a power law. The effect of adding polymer chains upon the ordering of the ions of the solvent is also considered. Upon addition of a polymer, it is shown that long-range correlations of ions can arise, although the intermediate-range ordering typical of pure ionic liquids remains dominant and stable. The dependence of the characteristic scale of the long-range ordering of the ions of the solvent on the polymer concentration also fits a power law.

Recent developments of anomalous X‐ray scattering for non‐crystalline materials with help of reverse Monte Carlo modeling: The example of GeSe2 glass

AbstractAnomalous X‐ray scattering (AXS) experiments on glassy GeSe2 were carried out at energies close to the Ge and Se K absorption edges in order to explore the atomic structure in the short‐ and intermediate‐ranges. The partial structure factors, Sij(Q), and the corresponding partial pair‐distribution functions, gij(r), obtained with help of reverse Monte Carlo (RMC) modeling, are in good agreement with the experimental results from neutron diffraction employing isotopic substitution (NDIS), and with the theoretical data from ab initio molecular dynamics simulation. The prepeak in the total structure factor, S(Q), indicating the existence of intermediate‐range order (IRO), does not only result from Ge–Ge atomic correlations, but also contains Ge–Se correlations. From the atomic configuration obtained from RMC modeling, several structural parameters are discussed, such as partial coordination numbers, connections of the Ge(Se1/2)4 tetrahedra, and bond angle distributions.

Partial pair correlation functions and viscosity of liquid Al–Si hypoeutectic alloys via high-energy X-ray diffraction experiments

The liquid structure of Al–Si hypoeutectic binary alloys was characterized by diffraction experiments using a high-energy X-ray (synchrotron) beam source. The diffraction experiments were carried out for liquid pure Al, Al–3 wt% Si, Al–7 wt% Si, Al–10 wt% Si and Al–12.5 wt% Si alloys at several temperatures. The salient structure information such as structure factor (SF), pair distribution function (PDF), radial distribution function (RDF), coordination number (CN) and atomic packing densities (PD) were quantified as a function of Si concentration and melt temperatures. Reverse Monte Carlo (RMC) analysis was carried out using the diffraction experimental data to quantify the partial pair correlation functions, such as partial structure factor, partial pair distribution function (PPDF) and partial radial distribution function. Furthermore, the partial pair distribution function and the liquid atomic structure information were used in a semi-empirical model to evaluate the viscosity of these liquid alloys at various melt temperatures. The results show that the viscosity determined by semi-empirical methods using the atomic structure information is in good agreement with the experimentally determined viscosity values.

Anomalous x-ray scattering study of GexSe1−xglassy alloys across the stiffness transition composition

Anomalous x-ray scattering experiments on glassy Ge${}_{x}$Se${}_{1\ensuremath{-}x}$ were carried out at energies close to the Ge and Se $K$ absorption edges at concentrations between $x=0.15$ and $0.333$ in order to explore the correlation between the atomic structures in short and intermediate ranges and the stiffness transition which appears at approximately $x=0.20$ in this glassy system. The partial structure factors ${S}_{ij}(Q)$ and the corresponding partial pair-distribution functions ${g}_{ij}(r)$ were obtained using reverse Monte Carlo modeling. Although the ${S}_{ij}(Q)$ and ${g}_{ij}(r)$ spectra seem to gradually change with $x$, some indications are found related to the stiffness transition, in particular in the intermediate-range structure. First, the preshoulder position in ${S}_{\mathrm{SeSe}}(Q)$ largely shifts toward lower $Q$ values in the intermediate phase concentration region of the stiffness transition, while the prepeak positions in ${S}_{\mathrm{GeGe}}(Q)$ and ${S}_{\mathrm{GeSe}}(Q)$ remain almost unchanged. Second, the Ge-Se-Se bond angles are distributed at $\ensuremath{\sim}$90${}^{\ensuremath{\circ}}$ when the transition region is approached with decreasing $x$. No appreciable portions of the Ge-Se-Se-Ge sequences, i.e., Ge(Se${}_{1/2}$)${}_{4}$ tetrahedra connected by the Se${}_{2}$ dimer, are found in the Ge${}_{0.20}$Se${}_{0.80}$ glass. Instead, there is experimental evidence for a phase-separation tendency between directly connected Ge(Se${}_{1/2}$)${}_{4}$ tetrahedra and Se${}_{n}$ ($n\ensuremath{\geqslant}3$) chains in the intermediate phase concentration region of the stiffness transition. This may be due to avoid large stress in the Se${}_{2}$ dimer bonds of the Ge-Se-Se bond angle.

Radial distribution functions of non-additive hard sphere mixtures via Percus’ test particleroute

Using fundamental density functional theory we calculate the partial radial distribution functions,gij(r), of a binary non-additive hard sphere mixture using either Percus’ test particle approachor inversion of the analytic structure factor obtained via the Ornstein–Zernike route. Wefind good agreement between the theoretical results and Monte Carlo simulation data forboth positive and moderate negative non-additivities. We investigate the asymptotic,, decay of the gij(r) and show that this agrees with the analytic analysis of the contributions to the partialstructure factors in the plane of complex wavevectors. We find the test particle densityprofiles to be free of unphysical artefacts, contrary to earlier reports.

On the application of structure-specific bulk-solvent models

It is often discussed, mainly in connection with the rather high macromolecular R factors, that the treatment of bulk solvent in macromolecular refinement may lack the detail needed for modelling the solvent environment of molecules as complex as proteins and nucleic acids. This line of thought directly leads to the hypothesis that improvements in the modelling of the bulk solvent may substantially improve the agreement between the experimental data and the crystallographic models. Here, part of this hypothesis is being tested through the construction, via molecular-dynamics simulations, of a highly detailed, physics-based, structure-specific and crystallographic data-agnostic model of the bulk solvent of a known crystal structure. The water-distribution map obtained from the simulation is converted (after imposing space-group symmetry) to a constant (but scalable) partial structure factor which is then added in a re-refinement of the crystal structure. Compared with the simple Babinet-based correction, a reduction of the totally cross-validated free R value by 0.3% is observed. The implications and possible interpretations of these results are discussed.

Ion Specific Effects on the Structure of Molten AF-ZrF4 Systems (A+ = Li+, Na+, and K+)

The structure of AF-ZrF(4) system (A(+) = Li(+), Na(+), K(+)) compounds in the liquid state is studied using an approach combining EXAFS spectroscopy with molecular dynamics simulations. A very good agreement is observed between the two techniques, which allows us to propose a quantitative description of the liquids. From the Zr(4+) solvation shell point of view, we observe a progressive stabilization of the 7-fold and then of the 6-fold coordinated complexes when passing from Li(+) to Na(+) and K(+) as a "counterion". Particular attention is given to the systems consisting of 35 mol % of ZrF(4). At that particular composition, the ZrF(6)(2-) complex predominates largely whatever the nature of the alkali. The calculated vibrational properties of this complex are in excellent agreement with a previous Raman spectroscopy experiment on molten KF-ZrF(4). The most important differences are observed for the lifetime of these octahedral units, which increases importantly with the size of the monovalent cation. On a larger scale, an intense first sharp diffraction peak is observed for the Zr(4+)-Zr(4+) partial structure factor, which can be attributed to the correlations between the octahedral units formed.

Determination of two-particle structure factors from elemental maps

The structure of crystals can be described by defining size and shape of a unit cell and the positions of the atoms within it. Many materials, however, exhibit a glassy or amorphous structure. Such disordered structures are described by structure factors. These are usually determined by small angle scattering experiments. The angular distribution recorded in these experiments is related to the structure factor. In this work we present an alternative approach using elemental maps obtained in an energy filtering transmission electron microscope. In this way we can even obtain chemically resolved partial structure factors giving additional information on the specimen.

Medium-range correlation of Ag ions in superionic melts ofAg2Se and AgI by reverse Monte Carlo structural modelling—connectivity and voiddistribution

High-energy x-ray diffraction measurements on moltenAg2Se were performed. Partial structure factors and radial distribution functionswere deduced by reverse Monte Carlo (RMC) structural modelling on thebasis of our new x-ray and earlier published neutron diffraction data. Thesepartial functions were compared with those of molten AgI. Both AgI andAg2Se have a superionic solid phase prior to melting. New RMC structural modellingfor molten AgI was performed to revise our previous model with a bond-anglerestriction to reduce the number of unphysical Ag triangles. The refined model ofmolten AgI revealed that isolated unbranched chains formed by Ag ions are thecause of the medium-range order of Ag. In contrast with molten AgI, moltenAg2Se has ‘cage-like’ structures with approximately seven Ag ions surrounding aSe ion. Connectivity analysis revealed that most of the Ag ions in moltenAg2Se are located within 2.9 Å of each other and only small voids are found, whichis in contrast to the wide distribution of Ag-void radii in molten AgI. Itis conjectured that the collective motion of Ag ions through small voidsis required to realize the well-known fast diffusion of Ag ions in moltenAg2Se, which is comparable to that in molten AgI.

Acousto-spinodal decomposition of compressible polymer solutions: Early stage analysis

The structure and dynamics of early stage kinetics of pressure-induced phase separation of compressible polymer solutions via spinodal decomposition is analyzed using a linear Euler-Cahn-Hilliard model and the modified Sanchez Lacombe equation of state. The integrated density wave and Cahn-Hilliard equations combine the kinetic and structural characteristics of spinodal decomposition with density waves arising from pressure-induced couplings. When mass transfer rate is slower that acoustic waves, concentration gradients generate density waves that cycle back into the spinodal decomposition dynamics, resulting in oscillatory demixing. The wave attenuation increases with increasing mass transfer rates eventually leading to nonoscillatory spinodal demixing. The novel aspects of acousto-spinodal decomposition arise from the coexistence of stable oscillatory density dynamics and the unstable monotonic concentration dynamics. Scaling laws for structure and dynamics indicate deviations from incompressible behavior, with a significant slowing down of demixing due to couplings with density waves. Partial structure factors for density and density-concentration reflect the oscillatory nature of acousto-spinodal modes at lower wave vectors, while the single maximum at a constant wave vector reflects the presence of a dominant mode in the linear regime. The computed total structure factor is in qualitative agreement with experimental data for a similar polymer solution.

Multiscale study of the influence of chemical order on the properties of liquid Li-Bi alloys

The static structure and diffusion properties of Li-Bi liquid alloys at three compositions are investigated by molecular dynamics simulations. Due to the strong chemical order shown by these alloys, a multiscale approach is applied, fitting empirical pair potentials to data from ab initio molecular dynamics simulations to subsequently perform large-scale classical simulations. In this way, the partial structure factors as well as the self-diffusion and interdiffusion coefficients can be computed with sufficient accuracy to be discussed quantitatively. This approach is validated by comparing our predictions with experimental structure factor measurements. A marked heterocoordination is observed, which strongly influences the diffusion properties. These observations are consistent with an evolution toward ionic bonding at the Li${}_{75}$-Bi${}_{25}$ composition.

Molecular dynamic investigation of atomic distribution in molten Al-Al2Cu eutectic alloy

Structure of Al0.83Cu0.17 eutectic alloy has been studied in liquid state by means of X-ray diffraction and molecular dynamic methods. The total and partial structure factors are analyzed. These functions were used in order to calculate pair correlation functions and partial correlation functions, whose analysis allowed us to conclude that Al2Cu-like atomic groups are distributed in Al-matrix.