Radial structure plot

An example of the type of information that can be derived from XAFS is shown in Figure 3.3-4 which presents a radial structure plot (RSP) for an... 

Figure 3.3-4 An XAFS radial structure plot weighted) 0.2 m Ni " in H20(1) and scHzO. The vertical axis represents the probability of finding an oxygen (from water) or a Br counterion at distance away from the central Ni atom. The plot is uncorrected for phase shifts.

Figure 3.3-6 An XAFS radial structure plot weighted) for 0.2 M cymantrene (CpMn(CO)3) (a) in liquid hexane under ambient conditions (b) in SCCO2 at 60 °C and 129 bar. The doublet at 1.6 A is from the carbons on the carbonyl and the cyclo-pentadiene moieties. The peak at 2.4 A is for the carbonyl oxygens. The plotted distances are not corrected for XAFS phase shifts.

FiO. 7,3. Schematic representation of the profile of — for the krypton atom along a radial line. Unlike a radial distribution plot, which is a one-dimensional function, the Laplacian distribution displays shell structure in three-dimensional space. 

It is useful to understand the microstructure of soft particle dispersions before discussing the predictions of their elastic properties and the comparison of these with experimental data. The radial distribution function is a convenient form for characterizing the microstructure since one expects radial symmetry at nearequilibrium conditions. In Fig. 7, the radial distribution function computed for the undeformed system has been plotted against the scaled radial distance. But for the first peak (Fig. 7a), this radial structure is very similar to that observed for jammed hard-sphere packings [139]. For hard spheres, g r shows a sharp rise from zero at the hard-sphere diameter, i.e., r = IR. Here, since the soft-sphere packing is... 

Figure 10.2. Plot of the positions (x,y) of peak maxima extracted on radial rays in a moderately oriented SAXS fiber pattern according to BRANDT RULAND [265], A microscopical draw ratio Xj = 1.41 of the structural entities is determined from the slope... 

In Fig. 18, flow path lines are shown in a perspective view of the 3D WS. By displaying the path lines in a perspective view, the 3D structure of the field, and of the path lines, becomes more apparent. To create a better view of the flow field, some particles were removed. For Fig. 18, the particles were released in the bottom plane of the geometry, and the flow paths are calculated from the release point. From the path line plot, we see that the diverging flow around the particle-wall contact points is part of a larger undulating flow through the pores in the near-wall bed structure. Another flow feature is the wake flow behind the middle particle in the bottom near-wall layer. It can also be seen that the fluid is transported radially toward the wall in this wake flow. 

Fig. 24. Contour plot of the structure factor (the kinematic LEED intensity) of a x y/i monolayer in a triangular lattice gas with nearest-neighbor repulsion, at a temperature k TIi = 0.355 (about 5% above T ) and a chemical potential // = 1.5 (0c = 0.336 at the transition temperature.) Contour increments are in a (common) logarithmic scale separated by 0.1, starting with 3.2 at the outermost contour. Center of the surface Brillouin zon is to the left k, and k the radial and azimuthal components of kH, are in units of nlXla, a being the lattice spacing. Data are based on averages over 2x10 Monte Carlo steps per site. (From Bartelt et...

Fig. 3. Theoretical density profile of dendritic structures of generations 2-7 [12]. The radial volume fraction properly normalized to unity at the center of the molecule is plotted against the radial distance to the origin. All data has been calculated assuming a realistic excluded volume parameter of the segments of the dendrimer. Reproduced with permission from [12]...

As is described in Abrahams (1997), plotting the radial distribution of the intensity of the interference function G(h), most of the intensity is around the origin. Thus, when you convolute the structure factors F with the interference function G, each structure factor will mainly be recombined with structure factors that are close by. 

The calculations of g(r) and C(t) are performed for a variety of temperatures ranging from the very low temperatures where the atoms oscillate around the ground state minimum to temperatures where the average energy is above the dissociation limit and the cluster fragments. In the course of these calculations the students explore both the distinctions between solid-like and liquid-like behavior. Typical radial distribution functions and velocity autocorrelation functions are plotted in Figure 6 for a van der Waals cluster at two different temperatures. Evaluation of the structure in the radial distribution functions allows for discussion of the transition from solid-like to liquid-like behavior. The velocity autocorrelation function leads to insight into diffusion processes and into atomic motion in different systems as a function of temperature. 

In order to determine the constant 7, we computed the radial distribution functions for the two types of the Sierpinski gaskets under consideration. In Fig. 6.6 these functions are plotted, as averaged over all sites of the finite gaskets at the 11th stage. Due to the finite size of the structures, deviations... 

Considerable evidence exits of the survival of Zintl ions in the liquid alloy. Neutron diffraction measurements [5], as well as molecular dynamics simulations [6, 7], give structure factors and radial distribution functions in agreement with the existence of a superstructure which has many features in common with a disordered network of tetrahedra. Resistivity plots against Pb concentration [8] show sharp maxima at 50% Pb in K-Pb, Rb-Pb and Cs-Pb. However, for Li-Pb and Na-Pb the maximum occurs at 20% Pb, and an additional shoulder appears at 50% Pb for Na-Pb. This means that Zintl ion formation is a well-established process in the K, Rb and Cs cases, whereas in the Li-Pb liquid alloy only Li4Pb units (octet complex) seem to be formed. The Na-Pb alloy is then a transition case, showing coexistence of Na4Pb clusters and (Pb4)4- ions and the predominance of each one of them near the appropiate stoichiometric composition. Measurements of other physical properties like density, specific heat, and thermodynamic stability show similar features (peaks) as a function of composition, and support also the change of stoichiometry from the octet complex to the Zintl clusters between Li-Pb and K-Pb [8]. 

Figure 157 Radial plots of outer emission intensity from a microcavity (a) and microcavity-free (b) structures from Fig. 141 at different emission wavelengths as indicated in the figure. After Ref. 550. Copyright 1993 American Institute of Physics.

In Fig. 4.3 we plot the density dependence of the resulting exchange potentials. The relevant range of density values for electronic structure calculations is indicated by the j8-values at the origin and the expectation value of the radial coordinate of the lSl/2-orbital for the Kr and Hg atoms. One finds that relativistic effects are somewhat more pronounced for than for and are definitely relevant for inner shell features of high Z-atoms. 

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