Cell-cluster development for the pair distribution function - Application to rigid disks at hight density.
Molecular pair distribution function in perfect crystalline solids, using method based on cell cluster theory
MOLECULAR STRUCTURE↗
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Hard-sphere solid - Pair distribution functions at high density.
High density form of molecular pair distribution function for rigid spheres system, using cell- cluster technique
Larsen, R. D.↗
Amorphous Analogs of Martian Global Soil: Pair Distribution Function Analyses and Implications for Scattering Models of Chemin X-ray Diffraction Data
Soils on Mars have been analyzed by the Mars Exploration Rovers (MER) and most recently by the Mars Science Laboratory (MSL) rover. Chemical analyses from a majority of soil samples suggest that there is a relatively uniform global soil composition across much of the planet. A soil site, Rocknest, was sampled by the MSL science payload including the CheMin X-ray diffractometer and the Alpha Particle X-ray Spectrometer (APXS). Che- Min X-ray diffraction (XRD) data revealed crystalline phases and a broad, elevated background, indicating the presence of amorphous or poorly ordered materials (Fig 1). Based on the chemical composition of the bulk soil measured by APXS and the composition of crystalline phases derived from unit-cell parameters determined with CheMin data, the percentages of crystalline and amorphous phases were calculated at 51% and 49%, respectively. Attempts to model the amorphous contribution to CheMin XRD patterns were made using amorphous standards and full-pattern fitting methods and show that the broad, elevated background region can be fitted by basaltic glass, allophane, and palagonite. However, the modeling shows only that these phases have scattering patterns similar to that for the soil, not that they represent unique solutions. Here, we use pair distribution function (PDF) analysis to determine the short-range order of amorphous analogs in martian soils and better constrain the amorphous material detected by CheMin.
Achilles, C. N.↗
Examination of the Atomic Pair Distribution Function (PDF) of SiC Nanocrystals by In-situ High Pressure Diffraction
Key properties of nanocrystals are determined by their real atomic structure, therefore a reasonable understanding and meaningful interpretation of their properties requires a realistic model of the structure. In this paper we present an evidence of a complex response of the lattice distances to external pressure indicating a presence of a complex structure of Sic nanopowders. The experiments were performed on nanocrystalline Sic subjected to hydrostatic or isostatic pressure using synchrotron and neutron powder diffraction. Elastic properties of the samples were examined based on X-ray diffraction data using a Diamond Anvil Cell (DAC) in HASYLAB at DESY. The dependence'of the lattice parameters and of the Bragg reflections width with pressure exhibits a ha1 nature of the properties (compressibilities) of the powders and indicates a complex structure of the grains. We interpreted tws behaviour as originating from different elastic properties of the grain interior and surface. Analysis of the dependence of individual interatomic distances on pressure was based on in-situ neutron diffraction measurements done with HbD diffractometer at LANSCE in Los Alamos National Laboratory with the Paris-Edinburgh cell under pressures up to 8 GPa (Qmax = 26/A). Interatomic distances were obtained by PDF analysis using the PDFgetN program. We have found that the interatomic distances undergo a complex, non-monotonic changes. Even under substantial pressures a considerable relaxation of the lattice may take place: some interatomic distances increase with an increase in pressure. We relate this phenomenon to: (1), changes of the microstructure of the densified material, in particular breaking of its fractal chain structure and, (2), its complex structure resembling that of a material composed of two phases, each with its distinct elastic properties.
Grzanka, E.↗
Inertial Effects in Suspension Dynamics
The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.
J. F. Brady↗
Electron-positron heating and the eclipsing millisecond pulsar PSR 1957 + 20
The companion in the eclipsing millisecond PSR 1957 + 20 appears to be strongly heated by the pulsar and may also be rapidly losing mass due to that heating. A new mechanism is presented by which the heating may be accomplished: diffusion of mildly relativistic electron-positron pairs from the pulsar's relativistic wind through a thermal wind issuing from the companion. Wave-particle scattering regulates the depth at which the pairs deposit their energy; requirements of self-consistency place bounds on the wave spectrum and pair distribution function. If the pairs carry over about 10 percent of the pulsar spin-down luminosity, and the companion's heavy element abundance is subsolar, the heating rate can be adequate to drive a wind with sufficient momentum flux to explain the eclipse geometry. Annihilation photons then heat the companion beneath its photosphere and supply a significant part of the power for the optical luminosity. This model also suggests that the eclipse duration decreases sharply above a critical photon frequency.
Krolik, Julian H.↗
Theory of droplet. Part 1: Renormalized laws of droplet vaporization in non-dilute sprays
The vaporization of a droplet, interacting with its neighbors in a non-dilute spray environment is examined as well as a vaporization scaling law established on the basis of a recently developed theory of renormalized droplet. The interacting droplet consists of a centrally located droplet and its vapor bubble which is surrounded by a cloud of droplets. The distribution of the droplets and the size of the cloud are characterized by a pair-distribution function. The vaporization of a droplet is retarded by the collective thermal quenching, the vapor concentration accumulated in the outer sphere, and by the limited percolative passages for mass, momentum and energy fluxes. The retardation is scaled by the local collective interaction parameters (group combustion number of renormalized droplet, droplet spacing, renormalization number and local ambient conditions). The numerical results of a selected case study reveal that the vaporization correction factor falls from unity monotonically as the group combustion number increases, and saturation is likely to occur when the group combustion number reaches 35 to 40 with interdroplet spacing of 7.5 diameters and an environment temperature of 500 K. The scaling law suggests that dense sprays can be classified into: (1) a diffusively dense cloud characterized by uniform thermal quenching in the cloud; (2) a stratified dense cloud characterized by a radial stratification in temperature by the differential thermal quenching of the cloud; or (3) a sharply dense cloud marked by fine structure in the quasi-droplet cloud and the corresponding variation in the correction factor due to the variation in the topological structure of the cloud characterized by a pair-distribution function of quasi-droplets.
Chiu, H. H.↗
Application of Powder Diffraction Methods to the Analysis of Short- and Long-Range Atomic Order in Nanocrystalline Diamond and SiC: The Concept of the Apparent Lattice Parameter (alp)
Two methods of the analysis of powder diffraction patterns of diamond and SiC nanocrystals are presented: (a) examination of changes of the lattice parameters with diffraction vector Q ('apparent lattice parameter', alp) which refers to Bragg scattering, and (b), examination of changes of inter-atomic distances based on the analysis of the atomic Pair Distribution Function, PDF. Application of these methods was studied based on the theoretical diffraction patterns computed for models of nanocrystals having (i) a perfect crystal lattice, and (ii), a core-shell structure, i.e. constituting a two-phase system. The models are defined by the lattice parameter of the grain core, thickness of the surface shell, and the magnitude and distribution of the strain field in the shell. X-ray and neutron experimental diffraction data of nanocrystalline SiC and diamond powders of the grain diameter from 4 nm up to micrometers were used. The effects of the internal pressure and strain at the grain surface on the structure are discussed based on the experimentally determined dependence of the alp values on the Q-vector, and changes of the interatomic distances with the grain size determined experimentally by the atomic Pair Distribution Function (PDF) analysis. The experimental results lend a strong support to the concept of a two-phase, core and the surface shell structure of nanocrystalline diamond and SiC.
Palosz, B.↗
Critical point parameters of helium
Calculations of the critical point parameters of the helium isotopes using integral equation closures for the pair distribution function are reported for two pair potentials.
Bruch, L. W.↗
Far-infrared absorption in H2 and H2-He mixtures
Collision-induced absorption in the translation-rotation band of H2 and H2-He mixtures has been measured from 20 to 900 kaysers at 77.4, 195, and 292 K. To establish the accuracy of the results, various sources of error are investigated. The zeroth and first spectral moments are evaluated from experiment and theory for H2 at the various temperatures. To obtain theoretical moments consistent with the experimental values, the quantum pair-distribution function must be used. The major portion of the experimental moments can be accounted for by quadrupole-induced dipoles in H2 pairs. The remaining portion is attributable to an anisotropic overlap interaction, although its magnitude depends on the value of the molecular parameters required to calculate the quadrupole contribution.
Birnbaum, G.↗
The polarizability of diatomic helium
The calculation of the electric dipole polarizability tensor of the He 2 dimer is described, and the results are used in the computation of several dielectric and optical properties of helium gas, at both high (322 K) and low (4 K) temperatures. The properties considered are the second dielectric virial coefficient, the second Kerr virial coefficient, and the depolarization ratio of the integrated intensities for the Raman scattering experiments. The thesis consists of five parts: the polarizability and various properties are defined; the calculation of the polarizability in the long-range region in terms of a quantum mechanical multipole expansion is described; the calculation of the He2 polarizability in the overlap region via coupled Hartree-Fock perturbation theory is described; the calculation of the quantum pair distribution function for both the He-3 and He-4 isotopes at 4 K is discussed; and the calculated values of the properties of helium gas are given.
Fortune, P. J.↗
The ground state properties of spin-aligned atomic hydrogen, deuterium, and tritium
The internal energy, pressure, and compressibility of ground-state, spin-aligned atomic hydrogen, deuterium, and tritium are calculated assuming that all pair interactions occur via the atomic triplet (spin-aligned) potential. The conditions required to obtain atomic hydrogen and its isotopes in bulk are discussed; such a development would be of value in propulsion systems because of the light mass and energetic recombination of atomic hydrogen. Results show that atomic triplet hydrogen and deuterium remain gaseous at 0 K, and that tritium forms a liquid with a binding energy of approximately -0.75 K per atom at a molar volume of 130 cu cm per mole. The pair distribution function for these systems is calculated, and the predicted superfluid behavior of atomic triplet hydrogen and tritium is briefly discussed.
Etters, R. D.↗
Scattering of electromagnetic waves from a half space of densely distributed dielectric scatterers
The scattering of a plane wave obliquely incident on a half space of densely distributed spherical dielectric scatterers is studied. The quasi-crystalline approximation is applied to truncate the hierarchy of multiple scattering equations, and the Percus-Yevick and the Verlet-Weis results are used to represent the pair distribution function. The coherent reflected wave is studied with these approximations. The incoherent scattered wave is calculated with the distorted Born approximation. In the low-frequency limit, closed-form expressions are obtained for the effective propagation constants, the coherent reflected wave, and the bistatic scattering coeficients. Results at higher frequencies are calculated numerically. The advantage of the present approach is that, in the low-frequency limit, it reproduces the effects of specular reflection, Fresnel reflection coefficient, Brewster angle, and Clausius-Mosotti relation. In addition to the classical results, the bistatic scattering coefficients are also calculated. The theory is also applied to match backscattering data from dry snow at microwave frequencies.
Tsang, L.↗
A multiple scattering theory for EM wave propagation in a dense random medium
For a dense medium of randomly distributed scatterers an integral formulation for the total coherent field has been developed. This formulation accounts for the multiple scattering of electromagnetic waves including both the twoand three-particle terms. It is shown that under the Markovian assumption the total coherent field and the effective field have the same effective wave number. As an illustration of this theory, the effective wave number and the extinction coefficient are derived in terms of the polarizability tensor and the pair distribution function for randomly distributed small spherical scatterers. It is found that the contribution of the three-particle term increases with the particle size, the volume fraction, the frequency and the permittivity of the particle. This increase is more significant with frequency and particle size than with other parameters.
Karam, M. A.↗
Nonthermal synchrotron radiation and pair annihilation in gamma-ray bursts
A self-consistent Monte Carlo simulation of quantized synchrotron emission, pair production, and pair annihilation in strong (2 x 10 to the 12th G or greater) magnetic fields is presented as a model of the production of annihilation lines in gamma-ray burst sources. The calculation determines the self-consistent photon spectrum and pair distribution functions resulting from a nonthermal injection of electrons into a region of homogeneous, strong magnetic field. The results indicate that the appearance of observable annihilation features in gamma-ray burst spectra requires isotropic or fan-beamed injection of electrons with energies of at least 5 MeV. The lines are narrow because higher energy electrons escape annihilation and do not contribute to Doppler-broadening. Injection beamed along the field did not produce observable annihilation lines in any of the cases studied. As a result, emission at energies much greater than 1 MeV produced through beaming seems to be incompatible with observable annihilation in this model. These results are discussed in relation to observed features in gamma-ray burst spectra.
Preece, Robert↗
Examination of Short- and Long-Range Atomic Order Nanocrystalline SiC and Diamond by Powder Diffraction Methods
The real atomic structure of nanocrystals determines unique, key properties of the materials. Determination of the structure presents a challenge due to inherent limitations of standard powder diffraction techniques when applied to nanocrystals. Alternate methodology of the structural analysis of nanocrystals (several nanometers in size) based on Bragg-like scattering and called the "apparent lattice parameter" (alp) is proposed. Application of the alp methodology to examination of the core-shell model of nanocrystals will be presented. The results of application of the alp method to structural analysis of several nanopowders were complemented by those obtained by determination of the Atomic Pair Distribution Function, PDF. Based on synchrotron and neutron diffraction data measured in a large diffraction vector of up to Q = 25 Angstroms(exp -1), the surface stresses in nanocrystalline diamond and SiC were evaluated.
Palosz, B.↗
High Pressure X-Ray Diffraction Studies of Nanocrystalline Materials
Experimental evidence obtained for a variety of nanocrystalline materials suggest that the crystallographic structure of a very small size particle deviates from that in the bulk crystals. In this paper we show the effect of the surface of nanocrystals on their structure by the analysis of generation and distribution of macro- and micro-strains at high pressures and their dependence on the grain size in nanocrystalline powders of Sic. We studied the structure of Sic nanocrystals by in-situ high-pressure powder diffraction technique using synchrotron and neutron sources and hydrostatic or isostatic pressure conditions. The diffraction measurements were done in HASYLAB at DESY using a Diamond Anvil Cell (DAC) in the energy dispersive geometry in the diffraction vector range up to 3.5 - 4/A and under pressures up to 50 GPa at room temperature. In-situ high pressure neutron diffraction measurements were done at LANSCE in Los Alamos National Laboratory using the HIPD and HIPPO diffractometers with the Paris-Edinburgh and TAP-98 cells, respectively, in the diffraction vector range up to 26 Examination of the response of the material to external stresses requires nonstandard methodology of the materials characterization and description. Although every diffraction pattern contains a complete information on macro- and micro-strains, a high pressure experiment can reveal only those factors which contribute to the characteristic diffraction patterns of the crystalline phases present in the sample. The elastic properties of powders with the grain size from several nm to micrometers were examined using three methodologies: (l), the analysis of positions and widths of individual Bragg reflections (used for calculating macro- and micro-strains generated during densification) [I], (2). the analysis of the dependence of the experimental apparent lattice parameter, alp, on the diffraction vector Q [2], and (3), the atomic Pair Distribution Function (PDF) technique [3]. The results of our studies show, that Sic nanocrystals have the features of two phases, each with its distinct elastic properties. and under pressures up to 8 GPa.
Palosz, B.↗
Microwave Signatures of Melting/Refreezing Snow: Observations and Modeling Using Dense Medium Radiative Transfer Theory
Microwave brightness temperatures of snow covered terrains can be modeled by means of the Dense Radiative Transfer Medium Theory (DMRT). In a dense medium, such as snow, the assumption of independent scattering is no longer valid and the scattering of correlated scatterers must be considered. In the DMRT, this is done considering a pair distribution function of the particles position. In the electromagnetic model, the snowpack is simulated as a homogeneous layer having effective permittivity and albedo calculated through the DMRT. In order to account for clustering of snow crystals, a model of cohesive particles can be applied, where the cohesion between the particles is described by means of a dimensionless parameters called stickiness (z), representing a measure of the inversion of the attraction of the particles. The lower the z the higher the stickiness. In this study, microwave signatures of melting and refreezing cycles of seasonal snowpacks at high altitudes are studied by means of both experimental and modeling tools. Radiometric data were collected 24 hours per day by the University of Michigan Tower Mounted Radiometer System (TMRS). The brightness temperatures collected by means of the TMRS are simulated by means of a multi-layer electromagnetic model based on the dense medium theory with the inputs to the model derived from the data collected at the snow pits and from the meteorological station. The paper is structured as follows: in the first Section the temperature profiles recorded by the meteorological station and the snow pit data are presented and analyzed; in the second Section, the characteristics of the radiometric system used to collect the brightness temperatures are reported together with the temporal behavior of the recorded brightness temperatures; in the successive Section the multi-layer DMRT-based electromagnetic model is described; in the fourth Section the comparison between modeled and measured brightness temperatures is discussed. We dedicate the last Section to the conclusions and future works.
Tedesco, Marco↗