Pair Structure Factors Research Articles

Investigation of the Structures of Sodium Borophosphate Glasses by Reverse Monte Carlo Modeling to Examine the Origins of the Mixed Glass Former Effect

We present new results for the Reverse Monte Carlo modeling of 0.35Na2O + 0.65[xB2O3 + (1 – x)P2O5] glasses based on previously reported X-ray diffraction (XRD) data. Structural models have been generated that accurately reproduce the pair correlation functions and structure factors determined by XRD while maintaining nearly perfect charge neutrality between the positively charged cations and the negatively charged phosphate and borate oxyanion groups and while maintaining appropriate bond distances between the various atom pairs. These models, however, are not successful in accounting for the concentrations of network forming units (NFUs), as predicted by recent theoretical modeling and by magic-angle spinning nuclear magnetic resonance (MAS NMR) data for sodium borate glasses with similar stoichiometry. By a further refinement of the modeling, the NFU concentrations can be successfully reproduced as well. For the optimized structures, we investigate the question if the conductivity activation energy cor...

Spatial Organization and Correlations of Cell Nuclei in Brain Tumors

Accepting the hypothesis that cancers are self-organizing, opportunistic systems, it is crucial to understand the collective behavior of cancer cells in their tumorous heterogeneous environment. In the present paper, we ask the following basic question: Is this self-organization of tumor evolution reflected in the manner in which malignant cells are spatially distributed in their heterogeneous environment? We employ a variety of nontrivial statistical microstructural descriptors that arise in the theory of heterogeneous media to characterize the spatial distributions of the nuclei of both benign brain white matter cells and brain glioma cells as obtained from histological images. These descriptors, which include the pair correlation function, structure factor and various nearest neighbor functions, quantify how pairs of cell nuclei are correlated in space in various ways. We map the centroids of the cell nuclei into point distributions to show that while commonly used local spatial statistics (e.g., cell areas and number of neighboring cells) cannot clearly distinguish spatial correlations in distributions of normal and abnormal cell nuclei, their salient structural features are captured very well by the aforementioned microstructural descriptors. We show that the tumorous cells pack more densely than normal cells and exhibit stronger effective repulsions between any pair of cells. Moreover, we demonstrate that brain gliomas are organized in a collective way rather than randomly on intermediate and large length scales. The existence of nontrivial spatial correlations between the abnormal cells strongly supports the view that cancer is not an unorganized collection of malignant cells but rather a complex emergent integrated system.

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.

Pair-structure matrix of random collection of particles: Implications for light scattering

Scattering of light fields from random collections of particles of different types is considered. A new matrix called pair-structure matrix characterizing the correlations between particles of the same and of different types is introduced. This matrix reduces to the pair-structure factor of scattering collection [Opt. Lett. 34 , 1762 (2009)] in the case when the particles in the collection are all of the same type. For illustration of the importance of the new matrix the formula for the degree of coherence of a polychromatic plane wave scattered from a collection of particles of different types is derived.

Molecular dynamics of liquid alkaline-earth metals near the melting point

Results of the studies of the properties like binding energy, the pair distribution function g(r), the structure factor S(q), specific heat at constant volume, velocity autocorrelation function (VACF), radial distribution function, self-diffusion coefficient and coordination number of alkaline-earth metals (Be, Mg, Ca, Sr and Ba) near melting point using molecular dynamics (MD) simulation technique using a pseudopotential proposed by us are presented in this article. Good agreement with the experiment is achieved for the binding energy, pair distribution function and structure factor, and these results compare favourably with the results obtained by other such calculations, showing the transferability of the pseudopotential used from solid to liquid environment in the case of alkaline-earth metals.

Atomistic comparison of volume-dependent melt properties from four models of aluminum

With the increasing use of simulations in materials research and design, it is important to quantify the differences between, and accuracy of, models used in these simulations. Here we present the results of such a comparison for four embedded-atom models of aluminum that were optimized to have good liquid properties, particularly the melting temperatures. The effects of temperature and volume are systematically examined in the melts for bulk thermodynamic quantities, pair correlation functions and structure factors and diffusion coefficients for each interatomic potential. Where possible, these are then compared with experimental values. We find quantitative differences in the properties determined from the various interatomic potentials despite the fact that they were fit with similar sets of data.

Microstructure of the solid phase in fluidized beds for non-Stokes regimes

Experiments on two-dimensional fluidized beds of glass beads are presented for two fluids of typical Reynolds numbers of about 1 and a few hundred. The presence of inertial effects leads to the formation of wakes behind the particles and consequently to an anisotropy of the microstructure. The microstructures, studied by video imaging, are characterized by pair probability distribution functions and structure factors.

Molecular dynamics of liquid alkali metals near melting temperature

In the present research article we report a study of certain properties like binding energy, pair distribution function g(r), structure factor S(q), velocity auto correlation function (VACF) and its spectral density, radial distribution function (RDF), self-diffusion coefficient, and coordination number of liquid alkali metals (Li, Na, K, Rb, and Cs) near the melting temperature using molecular dynamics (MD) simulation technique with a pseudopotential proposed earlier by us. Good agreement with the experiment is observed for the binding energy, pair distribution function, structure factor, and self-diffusion coefficient and these results also compare favorably with the results obtained by other theoretical calculations. This confirms the transferability of the pseudopotential formalism from solid to liquid environment in the case of alkali metals.

Determination of pair-structure factor of scattering potential of a collection of particles

The method of determination of the pair-structure factor of a collection of particles has been discussed. It is shown that the pair-structure factor of scattering potential of the collection of particles can be determined from the cross-spectral density function of the scattered field.

Structure and Inter-Diffusion Coefficients of Liquid Na x K1−x Alloys

Structure and atomic transport properties of liquid Na-K alloys are reported. Inter-diffusion coefficients of liquid NaxK1−x, alloys are calculated using scaling law proposed by Samanta et al. following Dzugutov 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. The partial pair distribution functions and structure factors are calculated from the solution of Ornstein-Zernike integral equation with Rogers-Young closure. The evaluation with the composition of static structure and inter-diffusion properties are discussed.

Effect of the pair-structure factor of a particulate medium on scalar wave scattering in the first Born approximation

Using scattering matrices and the angular spectrum representation of waves, we develop the analytical theory of scattering of random scalar waves from random collections of particles, valid under the first Born approximation. We demonstrate that in the calculation of far-field statistics, such as the spectral density and the spectral degree of coherence, the knowledge of the pair-structure factor of the collection is crucial. We illustrate our analytical approach by considering a numerical example involving scattering of two partially correlated plane waves from a random distribution of spheres.

Pair Correlations of a Spin-Imbalanced Fermi Gas on Two-Leg Ladders

We study the pair correlations of a spin-imbalanced two-leg ladder with attractive interactions, using the density matrix renormalization group method. We identify regions in the phase diagram spanned by the chemical potential and the magnetic field that can harbor Fulde-Ferrell-Larkin-Ovchinnikov- (FFLO-)like physics. Results for the pair structure factor, exhibiting multiple pairing wave vectors, substantiate the presence of FFLO-like correlations. We further discuss phase separation scenarios induced by a harmonic trap, which differ from the case of isolated chains.

Disordered two-dimensional superconductors: Roles of temperature and interaction strength

We have considered the half-filled disordered attractive Hubbard model on a square lattice, in which the on-site attraction is switched off on a fraction $f$ of sites, while keeping a finite $U$ on the remaining ones. Through quantum Monte Carlo simulations for several values of $f$ and $U$ and for system sizes ranging from $8\ifmmode\times\else\texttimes\fi{}8$ to $16\ifmmode\times\else\texttimes\fi{}16$, we have calculated the configurational averages of the equal-time pair structure factor ${P}_{s}$ and, for a more restricted set of variables, the helicity modulus ${\ensuremath{\rho}}_{s}$, as functions of temperature. Two finite-size scaling Ans\atze for ${P}_{s}$ have been used: one for zero temperature and the other for finite temperatures. We have found that the system sustains superconductivity in the ground state up to a critical impurity concentration ${f}_{c}$, which increases with $U$, at least up to $U=4$ (in units of the hopping energy). Also, the normalized zero-temperature gap as a function of $f$ shows a maximum near $f\ensuremath{\sim}0.07$ for $2\ensuremath{\lesssim}U\ensuremath{\lesssim}6$. Analyses of the helicity modulus and of the pair structure factor led to the determination of the critical temperature as a function of $f$ for $U=3$, 4, and 6: they also show maxima near $f\ensuremath{\sim}0.07$, with the highest ${T}_{c}$ increasing with $U$ in this range. We argue that, overall, the observed behavior results from both the breakdown of charge-density-wave-superconductivity degeneracy and the fact that free sites tend to ``push'' electrons toward attractive sites; the latter effect being more drastic at weak couplings.

Structural characterization of Mg 65Cu 25Y 10 metallic glass from ab initio molecular dynamics

Ab initio molecular dynamics simulation (AIMD) was performed on the structural evolution of Mg65Cu25Y10 alloy from 2000 K to 300 K. Pair correlation functions (PCFs), coordination numbers (CNs) and structure factors (SFs) of this glassy alloy were characterized. With the temperature decreased, the first peaks of both PCF and SF become narrower and higher, and shift to higher displacement or higher scattering vector. At the room temperature, the second peaks of both PCF and SF curves occur splitting, and the height of first peak of partial PCF for heterogenic atomic pairs is larger than that for homogenic atomic pairs. The generalized coordination numbers in this alloy are in good agreement with the results calculated by using efficient atomic packing model, which approves the atomic configuration of this alloy is in terms of dense packing. It was also found that the shape of both PCF and SF, and the CNs occur distinct change around 750 K.

Structure of strongly coupled multicomponent plasmas

We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification.

Simulation of liquid Rb by the methods of classical and first-principle molecular dynamics and statistical geometrical analysis of the atomic structure models using the Voronoi-Delaunay method

The atomic structures of liquid rubidium were simulated by classical and first-principle Molecular Dynamics methods for a range of temperatures. The pair potentials necessary for the Classical Molecular Dynamics calculations were obtained using diffraction data by the Schommers iterative method. In all cases simulated pair correlation functions and structure factors correctly reproduced the experimental ones. A Delaunay simplex, comprised by four atoms, is the simplest element of the structure. All atomic aggregates in an atomic structure consist of them. The structure factor of the simplicial voids system is additional structural characteristic which allows seeing distinction in structures with almost similar pair correlation functions.

Short-to-medium-range order in Mg 65Cu 25Y 10 metallic glass

The atomic configurations of liquid and glassy Mg65Cu25Y10 alloy have been simulated in the temperature range of 300 K to 2000 K via ab initio molecular dynamics. The variations of pair correlation function (PCF), structure factor (SF), coordination number (CN) and bond pairs with the temperature for this alloy are characterized. It has been shown that the atoms are near densely packed and icosahedral type of short-range order (SRO) is predominant in the glass state. Icosahedral medium range order (MRO) can be formed by vertex or intercross connection of icosahedral SROs. In this work, an icosahedral MRO which is composed of 55 atoms has been found. It has been also clarified that Mg and Cu occupy the centre or vertex, and Y atoms only occupy the vertex of the icosahedron in this glassy alloy. It is believed that these findings have implication for understanding the glass forming mechanism of magnesium based metallic glasses.

On the Microheterogeneity in Neat and Aqueous Amides: A Molecular Dynamics Study

A molecular dynamics study of three amides, namely, formamide, N-methyl formamide, and dimethyl formamide, and their mixtures with water is conducted to sort out the nature of the local microstructure of both the pure amides and the aqueous mixtures. For pure amides, both the cluster distribution and pair structure factors are investigated. The former reveals no specific cluster formation for all three amides, while the latter shows that formamide has a weak prepeak at about k ≈ 1.32 Å-1 reminiscent of that observed for water, thus enforcing the puzzle of the nature of the hydrogen-bonding self-clustering in this type of liquids. The analysis of aqueous mixtures shows that all three mixtures are strongly microheterogeneous at the nanometer/nanosecond scales. This is confirmed in two ways: the direct visual observation and through the analysis of the pair distribution functions. The observation of microheterogeneity through usually measured quantities, namely the Kirkwood−Buff integrals, is discussed in light of the present analysis, and these latter quantities are shown to be weak indicators of microheterogeneity mainly because all three aqueous amides have nearly ideal such integrals in contrast to displaying strong microheterogeneity. As a direct consequence of this fact two features are reported. First, the Kirkwood−Buff integrals of the amide−amide correlations are obtained in relatively good agreement with the experimental ones, and second, those involving correlations with water are considerably affected by the microheterogeneity beyond the 15 Å range and need prohibitively larger statistics despite the large system sizes used in this study.

First-principle molecular dynamics study of the structural and electronic properties of liquid and amorphous Ni–Al alloys

Abstract Atomic and electronic structures of liquid and rapidly quenched Ni–Al (NiAl 3 , NiAl, and Ni 3 Al) alloys were studied by ab initio molecular dynamics simulation. Pair correlation function, structure factor, bond pair, electron population, and density of states were calculated. It is found that amorphous Ni–Al alloys can be prepared by rapid quenching of liquid alloys, with the former bearing similar structures to the latter, although amorphous alloys have a more ordered structure. Bond pair analysis indicates that both the liquid and amorphous Ni–Al alloys consist mainly of 1441, 1431, 1421, and 1422 pairs of tetrahedral local order. The positions of the first peaks of the Al–Ni pair correlation functions are lower than the sum of the metallic radii of Ni and Al, suggesting the occurrence of chemical bonding between Ni and Al in Ni–Al alloys. Electronic structure analysis further revealed that the interaction between the d-electrons of Ni and the p-electrons of Al is responsible for the bonding. The main peak positions of the total DOS of amorphous Ni–Al alloys become more and more positive when the content of Ni in the alloys increases.

Pair distribution function and structure factor of spherical particles

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.