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Transmission MATTER Scattering Compton Thomson Photoelectric absorption Pair production > 1M eV X-rays Interaction X-rays - Matter Decay processes Fluorescence Auger electrons Primary competing processes and some radiative and non-radiative decay processes

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Thomson Observed data Electron positron pairs Compton Photoelectric absorption Photonuclear absorption Cross section (barns/atom) eV1 KeV1 GeV1 MeV Cu Z=29 Energy Li Z=3Ge Z=32Gd Z=64 Energy (KeV) (Barns/atom) X-ray attenuation: atomic cross section: h h sample

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Z=57 Lanthanum L L L L L L L 3, L 2, L 1 edges K edge (cm 2 /g) Photoelectric absorption coefficient

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K 1s p L 1 2s p L 2 2p 1/2 s, d L 3 2p 3/2 s, d Z dependence atomic selectivity X-ray energy range KeV h h sample Photon flux X-ray absorption spectroscopy x

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photon fluxes; x sample thickness, C depends on the detectors efficiency. Storage ring Double - crystal monochromator Sample Detectors I0I0 I EXAFS analysis Ln ( I / I 0 ) E (eV)

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XAFS measurements X-ray energy XAFS spectrum Fluorescence X-rays TEY SAMPLE Incident X-raysTransmitted X-rays Visible light XEOL h h e-e-

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Always transmission, if possible Most accurate method, best overall S/N counting statistics of about from beamlines with more than 10 8 photons/s) Always transmission, if possible Most accurate method, best overall S/N counting statistics of about from beamlines with more than 10 8 photons/s) Which method for which application? The most important criterion: The best signal to noise ratio for the element of interest e-e- I e- Fluorescence for very diluted samples A specific signal reduces the large background (but maximum tolerable detector count-rate can result in very long measuring times). Fluorescence for very diluted samples A specific signal reduces the large background (but maximum tolerable detector count-rate can result in very long measuring times). Total electron yield (TEY) for surface sensitivity and surface XAFS (adsorbates on surfaces) TEY for thick samples that cannot be made uniform. Total electron yield (TEY) for surface sensitivity and surface XAFS (adsorbates on surfaces) TEY for thick samples that cannot be made uniform. XEOL X-ray excited optical luminescence VIS/UV detection from luminescent samples XEOL X-ray excited optical luminescence VIS/UV detection from luminescent samples

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Sample = Species (A + B) Measurement sensitivity in transmission mode x A = solute, B = Solvent By changing the solute absorption coefficient Forand so that Statistically: Assuming that the solute X-ray cross section is almost equal to that of the solvent: R= Dilution Ratio

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Evaluation of the absorption coefficient n = atomic density A 0 = vector potential amplitude Transition probability if INITIAL STATEINTERACTIONFINAL STATE Ground state Core hole + excitation or ionization GOLDEN RULE (weak interaction, time dependent perturbation theory (1st order)) is the density of the final states compatible with the energy conservation principle atomic initial and final states

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Interaction Hamiltonian j = electrons; polarization unit vector; = radiation wavevector Electric dipole approximation An equivalent expression often used is: This approximation is valid if: i.e. for the K edges for energies up to K eV and for the L edges Selection rules:

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In practice one is interested to the inverse problem. Given: experimentally determined, one wants to know from XAFS, the final state But also in this case one needs to know the initial and final states or, at least, to express in parametric form the interesting structural properties. is known because it is the fundamental state of the atom. The calculation ofis complicated because the absorption process because: Many bodies interactions The final state is influenced by the environment around the absorption atom The direct and inverse problem Direct problem: Inverse problem

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One electron approximation Elastic transitions: 1 core electron excited N-1 passive electrons (relaxed) Anelastic transitions: 1 core electron excited Other electrons excited; shake up and shake off High photoelectron energy sudden approximation 1 active electronN-1 electrons TOT ( ) if S o 2 = 1= S o Evaluation of the final state!

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EXAFS XANES x X-ray photon energy (keV) a-Ge X-ray Absorption Fine Structure (XAFS) XAFS = XANES + EXAFS XANES = X-ray absorption Near Edge Structure EXAFS = Extended X-ray Absorption Fine Structure

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E E i > E f > i > E Fermi Golden rule i > E f > Arctangent curve Inflection point XANES: pre edge structure E

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Arctangent Theoretical edge Lorentian Ir metal (Experimental signal) Experimental K- edge of metallic Iridium and its simulation obtained by the superposition of an arctang function and a Lorentian 2 Energy

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Single particle binding energy (eV) 1s 2s 2p s p d EXAFS XANES EDGE X-ray edges Visible UV eV Ne K 1s p p p s np n WL Arctangent curve x 0.58 eV Energy eV Ar K Energy eV x XANES

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Double excitations (c) (c) Double excitations in the N 2 spectrum Rydberg associated to the N 1s 1 g * transition. (a) N 1s 1 g * (a) 8 vibrational levels observed in the absorpttion spectrum: N 1s 1 g * Absorption Intensity (arb. Units) Photon Energy (eV) (b) N 1s Rydberg series (b) N 1s Rydberg series K-shell photoabsorption of N 2 molecule C.T. Chen and F. Sette, Phys. Rev. A 40 (1989) K-shell photoabsorption of gas-phase N 2 Absorption Intensity (arb.units) N 1s 1 g * N 1s Rydberg series Double excitations Shape resonance x Photon energy (eV)

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XANES Chemical information: oxidation state Oxidation Numbers (formal valences) I Cu 2 O II CuO III KCuO 2 Higher transitions energy are expected for higher valence states. KCuO 2 CuO Cu 2 O Cu E (eV) Y-Ba-Cu-O (J.B. Boyce et al. Phys. Rev. B 1987)

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E X-rays 0 DOS XANES: projected density of state SbSI Sb L 1 I L 1 Absorbance (a.u.) E - E 0 (eV) Total DOS (a.u.) E - E 0 (eV) Total DOS (a.u.) Absorbance (a.u.) Sb L 3 I L 3 2s p 2p p, d (G. Dalba et al., J.of Condensed Matter, 1983)

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e-e- A B A B B BB EXAFS:phenomenological interpretation Autointerference phenomenon of the outgoing photoelectron with its parts that are backscattered by the neighboring atoms

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Kr x E (KeV) Atoms Molecules Positive interference Negative interference e-e- Outgoing wave : A A B BA EXAFS:phenomenological interpretation Br 2 XANES Photon energy (eV) x Br 2 kr f smoothly varying in the EXAFS region

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Scattering phases of the photoelectron B A BA B A B A x B A R

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1) Inelastic scattering effect:Electron mean free path 2) Thermal disorder: Standard EXAFS formula XAFS formula Approximations

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EXAFS formula For several coordination shells: Interatomic distanceCoordination number Debye Waller factor From ab-initio calculations or from reference compounds 0 1 st 2 nd 3 rd Coordination shells R

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Multiple scattering XANES: multiple scattering processes EXAFS: single scattering processes R

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B A Single scattering Double scattering Triple scattering R AB A B C A B C A B C C

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Experiment SiK-edge in c-Si Absorption Energy E-E F (eV) Comparison between the experimental Si K-edge XAFS for c-Si and calculations carried out with the FEFF code. The total multiple scattering in the first 8 shells around the absorption atom have been considered. 0 is the atomic absorption coefficient. Multiple scattering

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