Nuclear density distribution

A somewhat more sophisticated approach to the problem of defining the nuclear size and density is to assume the nuclear density distribution, p(r), assumes the form of a Fermi distribution, that is,... 

Figure 2.10 Nuclear density distribution (a) in a schematic view and (b) in an artist s conception from R. Mackintosh, J. Al-Khalili, B. Jonson and T. Pena, Nucleus A Trip into the Heart of Matter. Copyright 2001 by The Johns Hopkins University Press, 2001 reprinted by permission of Johns Hopkins. (Figure also appears in color figure section.)...

An example of the distribution of the interatomic vectors density function in the uOw plane of CeRhGea is illustrated in Figure 2.61. When compared with the electron and nuclear density distributions Figure 2.59), there are many more peaks in the two Patterson maps. Similar to the results shown in Figure 2.59, both Patterson functions are nearly identical except for the distribution of peak intensities, which is expected due to the differences in the scattering ability of Ce, Rh and Ge using x-rays and neutrons. 

Table 6.25. The three-dimensional nuclear density distribution in the symmetrically independent part of the unit cell of CeRhGea calculated using the observed structure factors determined from Le Bail s extraction (Table 6.23) and phase angles determined by Ge in 4(b)...

Table 6.27. The three-dimensional nuclear density distribution in the symmetrically independent part of the unit cell of CeRhGea calculated using the observed structure factors determined from Le Bail s extraction Table 6.23) and phase angles determined by Ge in 4(b) with z = 0.000, Ge in 2(a) with z = 0.355, Ce in 2(a) with z = 0.754, and Rh in 2(a) with z = 0.113 in the space group I4mm (Rp = 16.3 %). ...

The first analysis performed for the Lio,6FeP04 solid-solution phase at 620 K was the Rietveld refinement for the neutron diffraction profile and the resultant pattern is summarized in Fig. 14.12b. To evaluate the dynamic disorder of lithium, maximum entropy method (MEM) was applied to estimate the neutron scattering length density distribution, which corresponds to the nuclear density distribution. 

Fig. 14.14 The 010 plane slice of difference Fourier scattering length density plot of LiFeP04 with contours in 0.05 fin steps. The map was calculated by Fo(Li) = Fo( LiFeP04) - caic.(LioFeP04), where F and Fcaic. ste the observed and calculated structure factors, respectively, and LioFeP04 expresses the FeP04 framework having identical structural parameters with LiFeP04. The nuclear density distribution of lithium itself is anisotropic with the same direction as the refined thermal vibration...

The problem is to find the flux, temperature, and nuclear-density distributions in this reactor and its power-generating capacity as a function of the reactor size Rq, the surface temperature To, the pressure p, and the various nuclear and physical constants of the gas. 

Figure 1.3 Temperature dependence of (a) unit-cell parameter a and (b) atomic displacement parameters of the cubic fluorite-type Ce02- Reprinted with permission from Yashima et aV Copyright 2003 Elsevier, (c) Nuclear-density distribution of the fluorite-type Ce02 at 1770 K. Reprinted with permission from Yashima et aP Copyright 2004 American Institute of Physics.

We studied the nuclear density distributions of Ceo.5Zro.5O2 at 1832 K and of Ce02 at 1826 K by in situ neutron diffraction and MEM (Fig. 1.31). The nuclear density distribution of oxide ions in Ceo.5Zro.5O2 (Fig. 1.31(a)) indicates the large positional disorder of oxide ions, spreading over a wide area and a shift to the <111> directions. Possible diffusion paths of the oxide ions can be seen along the... 

Figure 1.31 Nuclear density distributions on the (110) planes of (a) cubic CeQ jZro jOj at 1832 Kand (b) CeOjat 1826 Kwith black contours in the range from 0.7 to 5.0 fm A" (steps of 0.5 fm The dotted lines (A) and (B) with arrows...

The experimental diffraction data were analyzed by a combined technique involving Rietveld analysis, the maximum entropy method (MEM), and MEM-based pattern fitting (MPF) [10-15]. Rietveld analysis, which is used to refine the crystal structure from the powder diffraction data by a least squares method, was carried out using the RIETAN-2000 program [27], which yields structure factors and their errors after structural refinement. It is known that MEM can be used to obtain a nuclear density distribution map based on neutron structure factors and their errors [5, 6, 8, 10-15, 26-29] any type of complicated nuclear density distribution is allowed so long as it satisfies the symmetry requirements. MEM calculations were carried out using the PRIMA program [29]. To reduce the bias imposed by the simple structural model in the Rietveld refinement, an iterative procedure known as the REMEDY cycle [29] was applied after MEM analysis (Fig. 6.3). In this procedure, structure factors... 

Fig. 6.8 Nuclear density distribution in the ab plane atz = 0.2 (0 < jc, y < 2 ) of double perovskite-type PAjmmm Lao.64(Tio.92Nbo.o8 02.99 at (a) 1631 K, (b) 1281 K, and (c) 769 K [11]. Contours are in the range 0.05-0.35 fm A with steps of 0.05 ftnA. The solid line in (a) denotes the curved diffusion path of the oxide ions, and the dotted line denotes the direct path between ideal positions. At low temperature (769 K), oxide ions are localized near the equilibrium position (see (c)) at high temperature (1631 K), the oxide ions are dispersed over a wide area between the regular positions (see (a))...

Fig. 6.10 Nuclear density distribution in the (100) plane for Lao.6Sro.4Co03 measured at 1531 K, with black contours in the range from 2 to 10 fm A (2 fm A steps) [12]. The color scale of 100% corresponds to the maximum density of 46.4 fm A The dotted circles indicate possible oxide-ion diffusion paths. The dashed straight line indicates the edge of the CoOg octahedron. The solid straight lines indicate the unit cell. The figure shows four unit cells...

MPF analysis of LSCF6482 was conducted using diffraction data taken at 1533 K in the 20 range from 20° to 153°, with the structure factors obtained from Rietveld analysis. The R factors for the structure factors, Rjrwas improved from 3.20% in the Rietveld analysis to 2.32% in the MPF. To visualize the structural disorder, the MEM nuclear density distribution map on the (100)... 

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