X-ray absorption spectroscopy: principles, methods and data analysis Giuliana Aquilanti giuliana.aquilanti@elettra.eu XAS1 – smr2812 giuliana.aquilanti@elettra.eu 1
Outline • X-ray absorption • X-ray absorption fine structure • XANES • EXAFS data analysis XAS1 – smr2812 giuliana.aquilanti@elettra.eu 2
Outline • X-ray absorption • X-ray absorption fine structure • XANES • EXAFS data analysis XAS1 – smr2812 giuliana.aquilanti@elettra.eu 3
Introduction: x-rays-matter interaction XAS1 – smr2812 giuliana.aquilanti@elettra.eu 4
X-rays – matter interaction • Photoelectric absorption one photon is absorbed and the atom is ionized or excited • Scattering photons are deflected form the original trajectory by collision with an electron • Elastic (Thomson scattering): the photon wavelength is unmodified by the scattering process • Inelastic (Compton scattering): the photon wavelength is modified XAS1 – smr2812 giuliana.aquilanti@elettra.eu 5
X-ray – matter interaction XAS1 – smr2812 giuliana.aquilanti@elettra.eu 6
Main x-ray experimental techniques • Spectroscopy atomic and electronic structure of matter • Absorption • Emission • Photoelectron spectroscopy • Imaging macroscopic pictures of a sample, based on the different absorption of x-rays by different parts of the sample (medical radiography and x-ray microscopy) • Scattering • Elastic: Microscopic geometrical structure of condensed systems • Inelastic: Collective excitations XAS1 – smr2812 giuliana.aquilanti@elettra.eu 7
Spectroscopic methods • They measure the response of a system as a function of energy • The energy that is scanned can be that of the incident beam or the energy of the outgoing particles (photons in x-ray fluorescence, electrons in photoelectron spectroscopy) • In all cases, the incident radiation is synchrotron light, which is absorbed, resulting in an ejection of an electron (photoelectric effect) Photoelectric absorption An x-ray is absorbed by an atom, and the excess energy is transferred to an electron, which is expelled from the atom, leaving it ionized. XAS1 – smr2812 giuliana.aquilanti@elettra.eu 8
The absorption coefficient - 1 • Quantitatively, the absorption is given by the linear absorption coefficient 𝜈 • 𝜈𝑒𝑨 : attenuation of the beam through an infinitesimal thickness 𝑒𝑨 at a depth 𝑨 from the surface XAS1 – smr2812 giuliana.aquilanti@elettra.eu 9
The absorption coefficient - 2 The intensity 𝐽 𝑨 through the sample fulfills the condition −𝑒𝐽 = 𝐽(𝑨)𝜈𝑒𝑨 which leads to the differential equation 𝑒𝐽 𝐽(𝑨) = −𝜈𝑒𝑨 If 𝐽 𝑨 = 0 = 𝐽 0 , ( 𝐽 0 : incident beam intensity at 𝑨 = 0) then 𝐽 𝑨 = 𝐽 0 𝑓 −𝜈𝑨 XAS1 – smr2812 giuliana.aquilanti@elettra.eu 10
The absorption coefficient - 3 𝐽 𝑨 = 𝐽 0 𝑓 −𝜈𝑨 ⇒ 𝑚𝑜 𝐽 0 𝐽 = 𝜈𝑨 Experimentally, 𝜈 can be determined as the log of the ratio of the beam intensities with and without the samples (or beam intensity before and after the sample) XAS1 – smr2812 giuliana.aquilanti@elettra.eu 11
Atomic cross section mass density Avogadro’s number 𝜈 = 𝜍 𝑏𝑢 𝝉 𝒃 = 𝜍 𝑛 𝑂 𝐵 𝝉 𝒃 𝐵 Atomic number density Atomic mass 𝜏 𝑏 [cm 2 ] 𝜏 𝑏 𝑐𝑏𝑠𝑜 1 𝑐𝑏𝑠𝑜 = 10 −28 m 2 cm 2 = 𝑂 𝐵 𝜏 𝑏 cm 2 = 𝜈 𝐵 𝜏 𝑏 g 𝜍 𝑛 XAS1 – smr2812 giuliana.aquilanti@elettra.eu 12
Absorption measurements in real life I F synchrotron source I 1 I 0 monochromator sample Transmission The absorption is measured directly by measuring what is transmitted through the sample 𝐽 = 𝐽 0 𝑓 −𝜈 𝐹 𝑢 𝜈 𝐹 𝑢 = α = ln 𝐽 0 𝐽 1 Fluorescence The re-filling the deep core hole is detected. Typically the fluorescent X- ray is measured 𝛽 ∝ 𝐽 𝐺 𝐽 0 XAS1 – smr2812 giuliana.aquilanti@elettra.eu 13
XAFS at Elettra XAS1 – smr2812 giuliana.aquilanti@elettra.eu 14
𝜈 vs E and 𝜈 vs Z μ depends strongly on: • x-ray energy E • atomic number Z • density ρ • atomic mass A 𝜈 ≈ 𝜍𝑎 4 𝐵𝐹 3 In addition, μ has sharp absorption edges corresponding to the characteristic core-level energy of the atom which originate when the photon energy becomes high enough to extract an electron from a deeper level XAS1 – smr2812 giuliana.aquilanti@elettra.eu 15
Absorption edges and nomenclature XAS1 – smr2812 giuliana.aquilanti@elettra.eu 16
Absorption edge energies The energies of the K absorption edges go roughly as E K ~ Z 2 All elements with Z > 16 have either a K -, or L- edge between 2 and 35 keV, which can be accessed at many synchrotron sources XAS1 – smr2812 giuliana.aquilanti@elettra.eu 17
De-excitation process Decay to the ground state Excited state Absorption Core hole + photoelectron X-ray Fluorescence Auger Effect An x-ray with energy equal to the An electron is promoted to the difference of the core-levels is emitted continuum from another core-level X-ray fluorescence and Auger emission occur at discrete energies characteristic of the absorbing atom, and can be used to identify the absorbing atom XAS1 – smr2812 giuliana.aquilanti@elettra.eu 18
Fluorescence or Auger? XAS1 – smr2812 giuliana.aquilanti@elettra.eu 19
Core-hole lifetime ( τ h ~ 10 -15 – 10 -16 s) Total de-excitation probability per unit time The deeper the core hole and the larger the atomic number Z The larger the number of upper levels from which an electron can drop to fill the hole The shorter the core hole lifetime τ h is un upper limit to the time allowed to the photoelectron for probing the local structure surrounding the absorbing atom From the time-energy uncertainty relation: the core hole lifetime is associated to the energy width of the excited state Γ h (core hole broadening) which contributes to the resolution of the x-ray absorption experimental spectra XAS1 – smr2812 giuliana.aquilanti@elettra.eu 20
K-edge core hole broadening XAS1 – smr2812 giuliana.aquilanti@elettra.eu 21
Outline • X-ray absorption • X-ray absorption fine structure • XANES • EXAFS data analysis XAS1 – smr2812 giuliana.aquilanti@elettra.eu 22
X-ray Absorption Fine Structure 3.0 2.5 t(E) (arb. units.) 2.0 1.5 1.0 0.5 9.4 9.6 9.8 10.0 10.2 10.4 10.6 Energy (keV) What? Oscillatory behaviour of the of the x-ray absorption as a function of photon energy beyond an absorption edge When? Non isolated atoms Why? Proximity of neighboring atoms strongly modulates the absorption coefficient XAS1 – smr2812 giuliana.aquilanti@elettra.eu 23
A little history 1895 Discovery of x-rays (Röngten) (high penetration depth) 1912 First x-ray diffraction experiments (Laue, Bragg) 1913 Bohr’s atom electron energy levels 1920 First experimental observation of fine structure 1931 First attempt to explain XAFS in condensed matter (Krönig) . . 1970 Availability of synchrotron radiation sources for XAFS 1971 XAFS becomes a quantitative tool for structure determination XAS1 – smr2812 giuliana.aquilanti@elettra.eu 24
XANES and EXAFS - 1 3.0 XANES 2.5 EXAFS t(E) (arb. units.) 2.0 1.5 1.0 0.5 9.4 9.6 9.8 10.0 10.2 10.4 10.6 Energy (keV) X-ray Extended from ~ 60 eV Absorption X-ray up to ~ 60 eV to 1200 eV Absorption Near above the edge above the edge Fine Edge Structure Structure XAS1 – smr2812 giuliana.aquilanti@elettra.eu 25
XANES and EXAFS - 2 EXAFS same physical origin XANES transitions to unfilled bound states , transitions to nearly bound states , the continuum continuum • Oxidation state • Radial distribution of atoms • Coordination chemistry around the photoabsorber (tetrahedral, octahedral) (bond distance, number of the absorbing atom and type of neighbours) • Orbital occupancy XAS1 – smr2812 giuliana.aquilanti@elettra.eu 26
EXAFS qualitatively – isolated atom • X-ray photon with enough energy ejects one core (photo)electron (photoelectric effect) Kinetic energy of the p.e. wavevector of the p.e. wavelength of the p.e. • The photoelectron can be described by a wave function approximated by a spherical wave 𝜇 ∝ 1 𝐹 − 𝐹 0 E 27 XAS1 – smr2812 giuliana.aquilanti@elettra.eu 27
EXAFS qualitatively – condensed matter • The photoelectron can scatter from a neighbouring atom giving rise to an incoming spherical wave coming back to the absorbing atom • The outgoing and ingoing waves may interfere 𝜇 ∝ 1 𝐹 − 𝐹 0 E XAS1 – smr2812 giuliana.aquilanti@elettra.eu 28
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