Metal radial distribution functions

Fig. 7. Pt—Re on alumina catalysts at the reduced step compared to the metal. Radial distribution functions (uncorrected from phase shifts) at the Lj edges of Pt and Re for two reduction temperatures...

In this paper we have endeavored to present a review of some characterization methods of metal nanoclusters, focusing, among the extremely vast array of methods and techniques, on two of them, XRD and TEM, on which we have direct experience, and emphasizing also some recent developments, like the radial distribution function in XRD and EH in TEM. 

The structure of the adsorbed ion coordination shell is determined by the competition between the water-ion and the metal-ion interactions, and by the constraints imposed on the water by the metal surface. This structure can be characterized by water-ion radial distribution functions and water-ion orientational probability distribution functions. Much is known about this structure from X-ray and neutron scattering measurements performed in bulk solutions, and these are generally in agreement with computer simulations. The goal of molecular dynamics simulations of ions at the metal/water interface has been to examine to what degree the structure of the ion solvation shell is modified at the interface. 

It is found that the atomic arrangement, or a vacancy network, in a depleted zone in a refractory metal or a dilute alloy of a refractory metal, created by bombardment of an ion can be reconstructed on an atomic scale from which the shape and size of the zone, the radial distribution function of the vacancies, and the fraction of monovacancies and vacancy clusters can be calculated. For example, Wei Seidman108 studied structures of depleted zones in tungsten produced by the bombardment of 30 keV ions of different masses, W+, Mo+ and Cr+. They find the average diameters of the depleted zones created by these ions to be 18,25 and 42 A, respectively. The fractions of isolated monovacancies are, respectively, 0.13,0.19and0.28,andthe fractions of vacancies with more than six nearest neighbor vacancies (or vacancy clusters) are, respect-... 

Figure 1 shows Fourier transforms of EXAFS spectra of a few samples prepared. The radial distribution functions of these samples are different from that of nickel oxide or cobalt oxide [7]. All the Fourier transforms showed two peaks at similar distances (phase uncorrected) the peak between 1 and 2 A is ascribed to the M-0 bond (M divalent cation) and the peak between 2 and 3 A is ascribed to the M-O-M and M-O-Si bonds. The similar radial distribution functions in Figure 1 indicate that the local structures of X-ray absorbing atoms (Ni, Co, and Zn) are similar. No other bonds derived from metal oxides (nickel, cobalt and zinc oxides) were observed in the EXAFS Fourier transforms of the samples calcined at 873 K, which suggests that the divalent cations are incorporated in the octahedral lattice. 

Schlesinger and Marton (15) studied the nucleation and growth of electrolessly deposited thin nickel (Ni-P) films. These studies were later extended and complemented by the studies performed by Cortijo and Schlesinger (19, 20) on radial distribution functions (RDFs). RDF curves were derived from electron diffraction data obtained from similar types of films as well as electrolessly deposited copper ones. Those studies, taken together, have elucidated the process of crystallization in the electroless deposition of thin metal films. 

The conduction electrons are scattered by the alkali atoms, the coherence implicit in the radial distribution function. Unlike the case of the scattering of a single electron in a plane wave state by a liquid, discussed previously, in this case the structure factor S(k) must be known up to the Fermi energy (which is 0.5 e.v. — 1 e.v. in saturated metal ammonia solutions). 

Korsunsky, V.I. (2000) The investigation of structure of heavy metal clusters and polynuclear complexes in powder samples with the radial distribution function method. Coord. Chem. Rev., 199, 55. 

Figure 12. Radial distribution functions between the metal ions and the oxygen atoms. (02, OH, OS and OW stand for the oxygen atoms in the carboxylic, alcoholic, ester groups and water, respectively).

Figure 18. Radial distribution functions between the metal ions, the oxygen atoms in the PGA network and the water oxygens. 02 and OH are the carboxyl and hydroxyl oxygen atoms of the PGA chains, respectively. OW is the water molecule oxygen.

Figure 3 Two-dimensional radial distribution function of Na ions in the active site for the activated precursor simulation without Mg2 present in the active site (dRT-Na). The lower panels show results for cluster A that contains population members that are in active in-line conformations, and the upper panels show results for cluster B that are not in-line (see Table 2). The axes are the distances (in A) to different metal coordination sites. The green lines indicate the regions where Na ions have distances less than 3.0 A to both sites indicated by the axes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this book.)...

Fig. 5.4 Generic radial distribution functions gMO for the metal ion in water for cases of (a) strong coordination and (b) weak coordination. Tmo is the optimum metal ion-oxygen distance in the solvated species. The coordination number is estimated by integrating the distribution function out to the minimum at rg. (From reference 8, with permission.)...

Germanium(iv) bromide has been reinvestigated by electron diffraction. Constraining the molecule symmetry to afforded a value of 2.272(1) The electronic radial distribution functions for germanium(iv) and tin(iv) chlorides in the liquid state at 23 °C have been calculated from X-ray diffraction intensity distributions obtained by use of theta-theta reflection diffractometry. Both liquids show intermolecular effects at distances equivalent to the Cl—Cl intermolecular distance. Values of 0.9 D (Si—Cl), 1.5 D (Ge—Cl), and 2.7 D (Sn—Cl) have been derived for the bond dipole moments of these bonds in the metal(iv)... 

X-ray scattering studies often lead to ambiguous answers concerning the local structure, especially in the case of multicomponent glasses. As EXAFS provides a partial radial distribution function, this method becomes very powerful when the distribution relative to each atomic species can be joined up. This situation is often encountered in metallic glasses. 

---