Absorbed atomic

Extended x-ray absorption fine stmcture measurements (EXAFS) have been performed to iavestigate the short-range stmcture of TbFe films (46). It is observed that there is an excess number of Fe—Fe and Tb—Tb pairs ia the plane of the amorphous film and an excess number of Tb—Fe pairs perpendicular to film. The iacrease of K with the substrate temperature for samples prepared by evaporation is explained by a rearrangement of local absorbed atom configurations duting the growth of the film (surface-iaduced textuting) (47). 

A consequence of absorption of X rays is the inner shell ionization of the absorbing atoms and the subsequent generation of characteristic X rays from the absorbing atoms, called secondary fluorescence, which raises the generated intensity over that produced by the direct action of the beam electrons. Secondary fluorescence can be induced by both characteristic and bremsstrahlung X rays. Both effects are compo-sitionally dependent. 

Figure 3 Schematic illustration of the EXAFS phenomenon (A) outgoing photoelectron (solid curve) from X-ray absorbing atom (B) destructive interference at the absorbing atom between outgoing (solid curve) and backscattered (dashed curve) photoelectron from neighboring atom (C) constructhra interference at the absorbing atom between outgoing (solid curve) and backscat-tared (dashed curve) photoelectron from neighboring atom. Adapted from T. M. Hayes and J. B. Boyce. Solid State Phys. 37.173,1982.

Where, /(k) is the sum over N back-scattering atoms i, where fi is the scattering amplitude term characteristic of the atom, cT is the Debye-Waller factor associated with the vibration of the atoms, r is the distance from the absorbing atom, X is the mean free path of the photoelectron, and is the phase shift of the spherical wave as it scatters from the back-scattering atoms. By talcing the Fourier transform of the amplitude of the fine structure (that is, X( )> real-space radial distribution function of the back-scattering atoms around the absorbing atom is produced. 

Theories of EXAFS (26.30) based on the scattering of an ejected photoelectron by atoms in the coordination shells surrounding the central absorbing atom give an expression for xW of the following form ... 

In these expressions, the subscript outside the braces identifies the absorber atom, while the superscript identifies the backscattering atom. The contribution xjfK) of one type of backscattering atom to the total EXAFS function is given by the equation ... 

The copper EXAFS of the ruthenium-copper clusters might be expected to differ substantially from the copper EXAFS of a copper on silica catalyst, since the copper atoms have very different environments. This expectation is indeed borne out by experiment, as shown in Figure 2 by the plots of the function K x(K) vs. K at 100 K for the extended fine structure beyond the copper K edge for the ruthenium-copper catalyst and a copper on silica reference catalyst ( ). The difference is also evident from the Fourier transforms and first coordination shell inverse transforms in the middle and right-hand sections of Figure 2. The inverse transforms were taken over the range of distances 1.7 to 3.1A to isolate the contribution to EXAFS arising from the first coordination shell of metal atoms about a copper absorber atom. This shell consists of copper atoms alone in the copper catalyst and of both copper and ruthenium atoms in the ruthenium-copper catalyst. 

X-ray absorption spectroscopy combining x-ray absorption near edge fine structure (XANES) and extended x-ray absorption fine structure (EXAFS) was used to extensively characterize Pt on Cabosll catalysts. XANES Is the result of electron transitions to bound states of the absorbing atom and thereby maps the symmetry - selected empty manifold of electron states. It Is sensitive to the electronic configuration of the absorbing atom. When the photoelectron has sufficient kinetic energy to be ejected from the atom It can be backscattered by neighboring atoms. The quantum Interference of the Initial... 

In molecular DFT calculations, it is natural to include all electrons in the calculations and hence no further subtleties than the ones described arise in the calculation of the isomer shift. However, there are situations where other approaches are advantageous. The most prominent situation is met in the case of solids. Here, it is difficult to capture the effects of an infinite system with a finite size cluster model and one should resort to dedicated solid state techniques. It appears that very efficient solid state DFT implementations are possible on the basis of plane wave basis sets. However, it is difficult to describe the core region with plane wave basis sets. Hence, the core electrons need to be replaced by pseudopotentials, which precludes a direct calculation of the electron density at the Mossbauer absorber atom. However, there are workarounds and the subtleties involved in this subject are discussed in a complementary chapter by Blaha (see CD-ROM, Part HI). 

Sauer et al. [185] derived a weak quadmpole interaction from the asymmetry of a poorly resolved Zeeman split spectmm of in W metal versus a Ta metal absorber. They also ascribed the unexpected weak quadmpole effect to deviations from cubic symmetry at the source or absorber atom arising from either interstitial impurities or crystal defects. 

Kerma (k)—A measure of the kinetic energy transferred from gamma rays or neutrons to a unit mass of absorbing medium in the initial collision between the radiation and the absorber atoms. The SI unit is J/kg. The special name of this unit is the rad (traditional system of units) or Gray (SI). 

Pair Production—An absorption process for x- and gamma radiation in which the incident photon is absorbed in the vicinity of the nucleus of the absorbing atom, with subsequent production of an electron... 

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