Radial electron distribution

The quantity p2 as a function of the coordinates is interpreted as the probability of the corresponding microscopic state of the system in this case the probability that the electron occupies a certain position relative to the nucleus. It is seen from equation 6 that in the normal state the hydrogen atom is spherically symmetrical, for p1M is a function of r alone. The atom is furthermore not bounded, but extends to infinity the major portion is, however, within a radius of about 2a0 or lA. In figure 3 are represented the eigenfunction pm, the average electron density p = p]m and the radial electron distribution D = 4ir r p for the normal state of the hydrogen atom. 

View the electron density plots for the noble gases helium, neon, and argon in the Radial Electron Distribution movie (eChapter 5.8). 

Figure 4. Radial electron distribution of Pt/Gex (a) experimental distribution obtained by Fourier transform of X-ray scattering data (b) model distribution calculated for spherical clusters.

The effect of metal loading on the reducibility was examined with PdNaY (71). For samples calcined at 500°C, the TPR peak maximum shifts from 190 to 150°C the Pd loading increases from 2.0 to 6.7 wt%. This has been attributed to the formation of ion pairs in sodalite cages. The reduction conditions are important for the resultant metal dispersion. TEM and radial electron distribution (RED) evidence shows that reduction of Ir ions in an H2 flow results in much smaller Ir aggregates than reduction under static H2 (173). 

There are two very general X-ray techniques for study of the metal particle size distribution the line-broadening analysis (LBA) and the small angle X-ray scattering (SAXS) (lb, 170). Other methods include the radial electron distribution (RED) and the extended X-ray absorption fine structure (EXAFS), which are aimed primarily at studying the structure of catalysts (Section IV,G). 

The EXAFS results indicate that the lattice parameter of small particles is contracted as compared with that of the bulk metal (23). This fact is confirmed by radial electron distribution data obtained from X-ray experiments (257a,b) and also by electron diffraction measurements (257c). Both this contraction and the anomalous pentagonal symmetry can be eliminated in the case of Pt particles onto which hydrogen is adsorbed. These relaxation effects, which are found to be reversible, will not be... 

These methods have been seldom used but are potentially quite valuable as they provide quantitative structural data. The diffraction method involves determination of a radial electron distribution (RED) function which gives a distribution of distances and coordination numbers of atoms surrounding a metal atom. This method has been used to characterize the formation of rhodium [79] and iridium [39] carbonyl clusters in NaY zeolite. 

The predominant feature of the radial electron distribution pattern of a sample inferred to contain [Ir6(CO)i6] in NaY zeolite [39] is a strong peak at 2.78 A, which is typical of the first neighbor Ir-Ir distance of the hexanuclear iridium carbonyl in the crystalline state. Peaks observed at atomic distances exceeding 8 A in the RED pattern of the crystalline form of the cluster were not observed with the zeolite sample and suggest that [Ir (CO)i6] is isolated in separate cages. 

The radial electron distribution (RED) determined from X-ray diffraction data has been frequently used to characterize the structures of encaged metal clusters. In contrast to EXAFS spectroscopy, the RED gives only metd-metal distances, not metal-support and metal-adsorbate distances. 

The optimum effective atomic number Zeff 1. 69 minimizes the energy predicted by the Schrodinger equation and gives the result i(ls He) = —2.85 h, with the radial electron distribution shown in Fig. 4.12. This answer is reasonable eff < Z as predicted, but the second electron does not completely cancel the charge of one of the protons, so Zgff > 1. 

Because rhodium oxide species, probably located in supercages, were obtained following calcination treatments, subsequent H2-reduction yielded homogeneously distributed, very small rhodium clusters in supercages. This was confirmed by TEM measurements [20,192] as well as by radial electron distribution (RED) [143] showing no Rh-Rh peaks at distances larger than 7 A in samples calcined at 620 K and reduced at 470 K (Fig. 9, curve a). 

Fig. 9. Radial electron distribution of Rh/NaY zeolite (from [143]). a After calcining in O2 at 623 K and reducing in H2 at 473 K b after contacting with CO at 300 K and c after contacting with CO/H2O at 300 K (treatments carried out successively)...

The nuclearity of platinum clusters in Y-type zeolite has been studied by comparing the distribution of interatomic distances obtained experimentally with the Radial Electron Distribution (RED) technique [6,7] and various distributions calculated from model clusters with an f.c.c. structure. Fig. 2 shows that the experimental distribution... 

Figure 5. Radial electron distribution. Curve a distribution characterizing Ir Y zeolite (no Ir-Ir distances can be observed). Curve b distribution obtained after treatment of the sample with a CO+H2 mixture (the large peak at 2.78 A corresponds to Ir6(C0)i5 clusters).

RDA (radial distribution of atoms) 132, 133, 148 RED (radial electron distribution) 144, 148, 149 characterization of Rh clusters by 148, 149 nuclearity of Pt clusters by 144 reforming catalysts 130 rhenium... 

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