An introduction to X-ray Absorption Spectroscopy Sakura Pascarelli European Synchrotron Radiation Facility, Grenoble, France 1 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Outline X-ray Absorption Spectroscopy X-ray Absorption Fine Structure (EXAFS and XANES) Major historical EXAFS breakthroughs 2 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Outline X-ray Absorption Spectroscopy X-ray Absorption Fine Structure (EXAFS and XANES) Major historical EXAFS breakthroughs 3 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Main X-ray based techniques Two fundamental X-ray-matter interactions: photoelectric absorption scattering (elastic, inelastic) Two families of experimental techniques: spectroscopy electronic structure, local structure of matter absorption emission inelastic scattering elastic diffusion microscopic geometric structure diffraction (crystalline solids) scattering (amorphous solids, liquids) 4 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
The Absorption Coefficient m I 0 I t I = I 0 exp[- m t] linear absorption coefficient m t = ln [ I 0 / I ] 5 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
The Absorption Coefficient m synchrotron incident flux transmitted flux source monitor monitor monochromator t I 0 sample I polychromatic monochromatic X-rays X-rays 1. Measure I 0 and I as a function of E X 2. Calculate: m t = ln [I 0 /I ] 6 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
The Absorption Coefficient m m / r [barns/atom] 4 depends strongly on X-ray energy E and atomic number r m Z m Z, and on the density r and atomic mass A 3 A E has sudden jumps (absorption edges) which occur at energies m characteristic of the element. 7 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
total absorption coefficient Germanium 10 6 10 4 m [cm -1 ] photoelectric absorption 10 2 10 0 10 -2 10 -4 elastic scattering 10 2 10 3 10 4 10 5 inelastic scattering E(eV) Photoelectric absorption dominates the absorption coefficient in this energy range 8 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Photoelectric Absorption X- rays (light with wavelength 0.06 ≤ l ≤ 12 Å or energy 1 ≤ E ≤ 200 keV) are absorbed by all matter through the photoelectric effect : An x-ray is absorbed by an atom when the energy of the x-ray is transferred to a core-level electron ( K , L , or M shell) which is ejected from the atom. The atom is left in an excited state with an empty electronic level (a core hole ). Any excess energy from the x-ray is given to the ejected photoelectron . 9 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
De-excitation: Fluorescence and Auger Effect When x-rays are absorbed by the photoelectric effect, the excited core-hole will relax back to a “ground state” of the atom. A higher level core electron drops into the core hole, and a fluorescent x-ray or Auger electron is emitted. X-ray Fluorescence : Auger Effect : An x-ray with energy = the difference An electron is promoted to the of the core-levels is emitted. continuum from another core-level. 3p 2p 1s K a : L K , K b : M K X-ray fluorescence and Auger emission occur at discrete energies characteristic of the absorbing atom, and can be used to identify the absorbing atom. 10 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
XAS measurements I F synchrotron source monochromator I 0 I sample XAS measures the energy dependence of the x- ray absorption coefficient μ(E) at and above the absorption edge of a selected element. μ(E) can be measured in several ways: Transmission: The absorption is measured directly by measuring what is transmitted through the sample: I = I 0 e −μ (E)t μ(E) t = − ln (I/I 0 ) Fluorescence: The re-filling the deep core hole is detected. Typically the fluorescent x-ray is measured. μ(E) ~ I F / I 0 11 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Outline X-ray Absorption Spectroscopy X-ray Absorption Fine Structure (EXAFS and XANES) Major historical EXAFS breakthroughs 12 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
What is XAFS ? X-ray Absorption Fine Structure: oscillatory variation of the X-ray absorption as a function of photon energy beyond an absorption edge. 2.40 2.20 Absorption coefficient m As K-edge in InAsP 2.00 1.80 Absorption 1.60 1.40 1.20 1.00 0.80 12000 12400 12800 13200 E(eV) E (eV) Proximity of neighboring atoms strongly modulates the absorption coefficient 13 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
EXAFS and XANES XAFS is often broken into 2 regimes: XANES X-ray Absorption Near-Edge Spectroscopy EXAFS Extended X-ray Absorption Fine-Structure which contain related, but slightly different information about an element’s local coordination and chemical state. As K-edge in InAsP 2.40 Absorption coefficient m XANES 2.20 EXAFS 2.00 Absorption 1.80 1.60 1.40 1.20 1.00 0.80 12000 12400 12800 13200 E (eV) 14 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
EXAFS and XANES XANES: transitions to unfilled bound states, nearly bound states, continuum local site symmetry, charge state, orbital occupancy EXAFS: 50 - 1000 eV after edge due to transitions to continuum local structure (bond distance, number, type of neighbors….) 2.40 XANES 2.20 Absorption coefficient m 2.00 EXAFS Absorption 1.80 1.60 1.40 1.20 1.00 0.80 12000 12400 12800 13200 E (eV) 15 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
EXAFS qualitatively condensed matter isolated atom e - E kin e - R E 0 l E The kinetic energy of the ejected photoelectron E kin is: p k 2 2 2 E kin E E = = = l = 2 p /k m m 0 2 2 16 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Where do the oscillations come from ? Due to a quantistic effect, the autointerference of photoelectron wave modifies the absorption coefficient value: p k 2 2 2 E kin E E = = = 1. As E is scanned above E 0 , E kin is m m 0 2 2 varied, and consequently k and l. 2. The outgoing and backscattered e - parts of the wave interfere either constructively or destructively, depending on the ratio between l R and R. l 3. It is the interference between outgoing and incoming waves that gives rise to the sinusoidal variation of m (E) frequency ~ distance from neighbors amplitude ~ number and type of neighbors 17 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Kr gas Rh metal 18 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Absorption coefficient photoelectron continuum continuum 4 4 3 3 2 2 1 1 ˆ 1s electron core hole in principle, all electrons are involved multi body process 2 2 ˆ m ˆ ˆ ( E ) i H r H A r I f i f I j j f f j dipole ˆ ˆ A A r 0 j 0 j j j 2 2 ˆ 1 1 ˆ N N 2 r S r i i f f 0 i f f f sudden single electron 2 2 N 1 N 1 S 0 i f 19 f S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Consequences of dipole approximation: Selection rules D l = ± 1 D s = 0 D j = ± 1 D m = 0 For 1-electron transitions: edge initial state final state K, L 1 s (l=0) p (l=1) L 2 , L 3 p (l=1) s (l=0), d (l=2) 20 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Absorption coefficient photoelectron continuum continuum 4 4 3 3 2 2 1 1 ˆ 1s electron core hole = = = E E p 1 s E i f f i i Approx: 2 m ˆ ( ) E r dipole + single electron + sudden i f f : photon polarization r : electron position | i > relatively easy ground state of atom; i.e. 1s e - wavefunction | f > very complicated final state strongly influenced by environment 21 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
Isolated atom: atomic absorption coefficient e - photoelectron free to travel away undisturbed = 0 f f outgoing spherical wave originating h from the absorbing atom m r ˆ 0 2 0 i f m ˆ * 0 2 d r r r r 0 i f overlap integral of initial and final state wavefunctions: monotonically decreases as function of E 22 S. Pascarelli – Joint ICTP-IAEA Workshop - Trieste, 2014
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