X-ray absorption Spectroscopy
Dr. Gavin Mountjoy, University of Kent, UK
Nell'ambito del programma "Visiting Professor",
finanziato dalla Regione Sardegna.
Outline
1) Introduction
2) Theory of X-ray Absorption Spectroscopy
3) Experimental Method
4) EXAFS Theory
Experimental Method
Data Analysis
Examples
5) XANES Theory
Experimental Method
Data Analysis
Examples
6) Conclusions
1) Introduction
X-ray Absorption Spectroscopy (XAS)
• is a structural characterisation technique
• uses X-rays as a "probe" of structure
• spectroscopy = measure the energy of an interaction
Two methods:
• EXAFS FS = Fine Structure
• XANES NE = Near Edge
Structural characterisation techniques
• study the interaction of a "probe" with a sample
• knowledge of interaction → information about structure
• different types of probes → different types of interactions
• different types of probes
– electromagnetic radiation
– particles
– physical contact
→ different energy
– used for spectroscopy
different wavevector
– used for scattering
X-rays
• a type of electromagnetic radiation
– higher energy compared to UV light
• energy E in electron volts (eV) or kilo eV (keV)
– where1 eV = 1.6 10-19 J, and blue light has E = 3 eV
• energy E from 120 eV (soft) to 120 keV (hard) E (keV ) = 12.4keV
• wavelength λ from 100 Å to 0.1 Å ()
λ A
Sources of X-rays
• natural sources of high energy rays
– radioactive isotopes (gamma rays)
– cosmic rays
• artificial processes which produce X-rays
– excitation of core electrons in atoms (energy from 100s eV to 10s keV)
– acceleration of electrons causes emission of electromagnetic radiation
• artificial sources of X-rays
– X-ray tube (cost €1k) by excitation of core electrons
– synchrotron (cost €500M) by acceleration of electrons
Alternative X-ray sources
• rotating anode
– lab-based source based similar to X-ray tubes
• energy dispersive X-ray absorption spectroscopy
– simultaneously measures X-rays of different energies
Encountering X-rays
• X-rays are harmful to human tissue
– require sheilding using heavy elements, e.g. Pb
• in everyday life
– "box" television: uses accelerated electrons to make picture
– airport security: X-rays are penetrating
– medical imaging: X-rays are penetrating
• in laboratory
– electron microscope: uses accelerated electrons to make picture
– X-ray diffraction: X-ray wavelength ~ atom size
– X-ray fluorescence: X-rays are unique to each element
Interaction of X-rays with atoms
• X-rays interact with electrons in atoms
(i) elastic scattering (no energy transfer)
– used in X-ray diffraction
(ii) inelastic scattering (some energy transfer)
– called "Compton scattering"
– similar to Raman spectroscopy
(iii) absorption (all energy transferred)
– similar to infrared spectroscopy
elastic
inelastic
* absorption
Not to be confused with
• Energy-Dispersive X-ray Spectroscopy (EDX or EDS)
• X-ray Fluorescence Spectroscopy (XRF or XRS)
• no word "Absorption"
• completely different techniques! EDX
XRF
2) Theory
• Transmission of X-rays is given by IT=I0exp(-µt)
– Beer-Lambert law for infrared spectroscopy
– t is thickness
– µ is linear absorption coefficient
– µ increases with atomic number Z (more electrons)
• Absorption coefficient is defined µt=ln(I0/IT)
• spectroscopy: measure µt as a function of energy E
– t is constant
– µ decreases with E (X-ray more penetrating)
absorption µt
sample
X-ray
detector detector
X-ray energy E
X-ray absorption edges
• Absorption edges occur for each shell of core electrons
– when E ~ binding energy of core electron
• X-ray absorption edges are labelled after core electrons
K: 1s1/2 L1: 2s1/2 L2: 2p1/2 L3: 2p3/2 (nj notation)
– note that emitted X-rays
have slightly different labels
Kα, Kβ
• energy of absorption edge E0
is unique for each element
– element-specific technique
Absorption edge energies
• difficult for light elements, e.g. Z57 (La)
100
X-ray absorption edge energy (keV)
40 keV
K-edge
10 L3-edge
4 keV
1
10 20 30 40 50 60 70 80
atomic number (Z)
Element-specific technique
• sample contains several elements
• each element has several X-ray absorption edges
• measurement of a single X-ray absorption edge
• other edges form a uniform background
whole sample single edge of element X
total
absorption µt
absorption µt
background
element X from X
element Y background
element Z from Y& Z
X-ray energy E X-ray energy E
The excited atom
• atom which absorbs X-ray is "excited"
• core electron which absorbs X-ray is ejected from core shell
– sometimes involves "many-electron" effects
• core shell is now has a "core hole"
– other electrons are less shielded from nucleus and "relax"
• another atomic electron drops down in to fill core hole
– timescale for this is called core-hole "lifetime"
• this releases energy similar to X-ray energy
– new X-ray released (X-ray fluorescence)
– additional atomic electron ejected (Auger electron)
The photo-electron
• core electron undergoes transition to a higher energy state
– called a photo-electron
– energy of new state = X-ray energy E - binding energy ionisation
photo-electron
• higher energy state must be:
– unoccupied
– around the excited atom
– obey the dipole selection rule, ∆= 1, e.g. s → p
• molecular orbital approach: → LUMO
• band structure approach : → conduction band
binding
X-ray energy E energy
core electron
Regions of the absorption edge
E0=absorption edge energy Ti K-edge
-5.6
1) pre-edge region (E57 (La)
100
X-ray absorption edge energy (keV)
L1-edge
L2-edge
40 keV
L3-edge
K-edge
10 L3-edge
4 keV
L3 is limited to kmax=11Å-1
due to overlap with L2 and L1 1
50 60 70 80
atomic number (Z)
EXAFS: Examples
Fe-Co alloy nanocrystals
Fe K-edge Co K-edge
Fe Co
k3χ(k)
k3χ(k)
BCC (a=2.87Å) FCC (a=3.51Å)
N R(Å) N R(Å)
8 2.49 12 2.48
6 2.87 6 3.51
12 4.06 24 4.26
k(Å-1) k(Å-1)
samples ?
Fe K-edge Co K-edge
FT
FT
Fe Co
BCC (a=2.87Å) FCC (a=3.51Å)
N R(Å) N R(Å)
8 2.49 12 2.48
6 2.87 6 3.51
12 4.06 24 4.26
R(Å) samples = BCC R(Å)
samples ≠ FCC
CoFe2O4 Nanocrystals
c a
CoFe2O4 is a partially inverted spinel
normal spinel: A2+[Tet](B3+2)[Oct]O4
inverse spinel: B3+[Tet](A2+B3+)[Oct]O4
z x
y
degree of inversion x:
(Co1-xFex)[Tet][CoxFe2-x][Oct]O4
b
distance site [Oct] site
[Tet]
M[Tet]-O 4xO -
M[Oct]-O - 6xO
M[Oct]-M[Oct] - 6xM[Oct]
M[Tet]-M[Oct] 12xM[Oct] 6xM[Tet]
M[Tet]-O 12xO -
Co K-edge
15 (A)
20 (B)
(b)
EXAFS results
FT
0
k3χ(k)
10wt% 900 C
k χ(k)
FT
(b)
(a)
3
0
degree of inversion x=0.69
0
(a)
0 metal cation Co2+/Fe3+
4 6
k(Å-1)
8 10 12 1 2
r(Å)
3 4 5 occupancy
k(Å-1) R(Å) [Tet] site 31%/35%
Fe K-edge [Oct] site 69%/65%
20
(D)
20
distances R (Å)
(b)
M[Tet]-O 1.89/1.84
kk χ(k)
0
M[Oct]-O 2.06/1.98
FT
χ(k)
(b)
3
3
(a) 0
M[Oct]-M[Oct] 2.96
0
(a) M[Tet]-M[Oct] 3.48
0
M[Tet]-O 3.50
1 2 3 4 5
4 6 k(Å-1) 8 10 12
r(Å)
k(Å-1) R(Å)
Nanocrystalline TiO2 materials for Li ion battery applications
studied by Ti K-edge EXAFS in situ
U. Lafont, E. Kelder, D. Carta, G. Mountjoy, et al
Nanocrystalline TiO2
– nanocrystalline TiO2 used in Li ion battery materials
– during charging cycle TiO2 (Ti4+) → Li:TiO2 (Ti3+)
– Ti K-edge EXAFS was measured in situ
structural
changes
charging cycle
– EXAFS results show progression
– three different structures depending on Li content
Anatase TiO2 I41/amd Li0.5TiO2 Imma LiTiO2 I41/amd
15 % Li 40 % Li 100% Li
R(Å) N 2σ 2 R(Å) N 2σ2 R(Å) N 2σ2
O 1.93 6.0 0.010 O 1.93 3.0 0.010 O 2.01 6.0 0.017
Ti 3.03 4.0 0.015 O 2.01 3.0 0.026 Ti 3.13 4.0 0.032
O 3.82 8.0 0.010 Ti 3.12 4.0 0.025 O 3.80 8.0 0.032
Ti 3.82 4.0 0.025 O 3.50 4.0 0.036 Ti 4.14 4.0 0.030
Rfit =39% O 3.78 4.0 0.028 Rfit = 47%
Ti 3.94 4.0 0.017
R fit = 39
5) XANES
X-ray Absorption Near Edge Structure (XANES)
or Near Edge X-ray Absorption Fine Structure (NEXAFS)
XANES: Theory
• photo-electron excited to low energy state
– several eV below or above ionisation level
ionisation
photo-electron
-5.6 Ti K-edge
µt (arbitrary offset)
-6
-6.4
binding
X-ray energy E energy
-6.8
4800 5000 5200 5400
E (eV) core electron
Peaks in XANES spectra
• 10s eV above the absorption edge multiple scatt. peak
– like EXAFS but very strong scattering (start of EXAFS)
• the absorption edge absorption edge peak:
– beginning of conduction band 1s→np continuum states
~ ionisation level 1.5
• a few eV below the absorption edge
– non- or anti-bonding states
1
1 + χ(E)
0.5
pre-edge peak: Zr K-edge
due to 1s→pd mixing at
non-centrosymmetric sites 0
17960 18000 18040
E(eV)
Describing low energy states
• Molecular orbital approach → LUMO
(Lowest Unoccupied Molecular Orbital)
– around the excited atom
– obey the dipole selection rule, ∆= 1, e.g. s → p (for K edge)
• Band structure approach → conduction band
Note: also called "Electronic structure", valence band is full
– site-symmetry projected density of states
• Multiple scattering approach → resonant wavefunction
– photo-electron has very low kinetic energy
– strongly scattered by neighbouring atoms (can't use EXAFS equation)
• Carbon K-edge XANES
– Carbon K-edge is at 284eV
– transition is 1s->np
– XANES depends on
density of unoccupied p states
– see strong peak for π* states
– XANES is difficult to use
for light elements
Effect of oxidation state on XANES
• higher oxidation state → higher energy of XANES
– higher (+) charge on the excited atom → electron states more tightly bound
• XANES is very good for measuring oxidation state
– typically +1 oxidation state → +3 eV energy
Mn K-edge
L-edge XANES
• X-ray absorption edges are labelled after core electrons
K: 1s1/2 L1: 2s1/2 L2: 2p1/2 L3: 2p3/2 (nj notation)
• L1 edge
– involves s→p transitions, so is similar to K-edge XANES
• L2 and L3 edges
– involve p → d transitions
– transition metals show strong peaks due to empty d-states
• for heavy elements use L edge, e.g. Z>57 (La)
– but core-hole lifetime makes resolution worse than ~3 eV
XANES: Experimental method
• near edge region
– scan X-ray energy from -25eV to +50eV above E0
• need good energy calibration
– to measure oxidation state and pre-edge peak
– use a metal foil as a reference
• need good energy resolution
– to measure pre-edge peak Ti K-edge
– typically 1 eV resolution
-5.6
• typical measurement time 15 mins
µt (arbitrary offset)
– faster (10 sec) for a good sample and beamline -6
-6.4
-6.8
4800 5000 5200 5400
E (eV)
XANES: Data analysis
µtsample − µt post −edge
• only fit background to pre-edge χ (E ) =
and post-edge regions µt post −edge − µt pre−edge
• spectra is function of E and has no kn weighting
– spectra can be shown as function of E or E-E0
– where E0 = absorption edge energy of the metal
1.5
post-edge fit
2
pre-edge fit
normalised absorption
absorption µt
1
1
0 0.5
Ti K-edge Ti K-edge
µt(E) 1+χ(E)
-1 0
4700 4900 5100 5300 5500 -20 0 20 40 60 80 100 120
E (eV) E-E0 (eV)
Interpreting XANES spectra
• The pre-edge peak
– a well-defined peak before the absorption edge
– due to known molecular orbitals with p-type symmetry
– can provide semi-quantitative comparison
• The "Fingerprint" approach
– qualitative comparison with XANES spectra of reference samples
– sample and reference are the same → XANES spectra are the same
• Comparison with simulated XANES spectra
– simulations using Band Structure or Multiple Scattering calculations
– quantitative comparison with sample spectra
XANES: Examples
• Ti oxidation state absorption edge position
– nanocrystalline TiO2 used in Li ion battery materials
– during charging cycle TiO2 (Ti4+) → Li:TiO2 (Ti3+)
– Ti K-edge XANES was measured in situ
1.5 14.0
0%
5%
10%
normalised absorbance
13.0
15%
edge position (eV)
1
40%
70%
12.0
100%
100%
0.5
11.0
0 10.0
-5 0 5 10 15 20 25 30 35 40 45 0 20 40 60 80 100
E-E0 (eV)
% charge/discharge
Ti K-edge pre-edge peak
Ti-O coordination
1.5
anatase
[4]Ti ZrTiO4
4
[5]Ti Na2SiTiO5
1/4 Ba2TiO4
1.0
pre-edge peak
absorbance
least
centrosymmetric 0.5
[6]Ti
4/2 6 0.0
-10 0 10 20 30
E(eV)
Note: E is set to zero at 4966eV
most
centrosymmetric
Ti pre-edge peak in TiO2-SiO2 xerogels
[Greegor et al, J. Non-Cryst.
1 Solids 55, 27 (1983)]
[Farges et al, Geoch. et Cosmoch.
[4]Ti
Acta 60, 3023 (1996)]
[5]Ti
relative peak height
TiO2-SiO2 glass
reference
reference
TiO2-SiO2 xerogel
[6]Ti TiO2-SiO2 xerogel
[Chem. Phys. Lett. 304, 150 (1999)]
0
3.5 4.5 5.5
relative peak position (eV)
Zr K-edge XANES
reference compounds (ZrO2)x(SiO2)1-x xerogels
3 3
ZrSiO4
tetrag. ZrO2 750°C
cubic ZrO2
mono. ZrO2 2 2
Zr(OH)4
1+χ(E)
1+χ(E)
RT
zirconolite
BaZrO3
Zr propox. 1 1
x=0.1
[Farges et al, Am. x=0.2
Mineral. 70, 838 (1994)] x=0.3
x=0.4
0 0
-20 0 20 40 -20 0 20 40
E (eV) E(eV)
CoFe2O4 Nanocrystals
• precursor phases studied by XANES
• Fe K-edge • Co K-edge
• 10wt% 450 C is like FeOOH • 10wt% 450 C is like Co(OH)2
• 5wt% 450 C is like Fe[Tet] silicate • 5wt% 450 C is like Co[Oct] silicate
10wt% 450°C ferrihydrite 10wt% 450°C Co Silicate
5wt% 450°C Fe:MCM 5wt% 450°C
2 2.0
1.5 1.5
1 1.0
0.5 0.5
0 0.0
0 10 20 30 40 50 0 10 20 30 40 50
E(eV) E(eV)
• identifying Fe and S compounds using the Fingerprint method
Magnus Sandström,1 Farideh Jalilehvand,2 Emiliana Damian,1 Yvonne Fors,1 Ulrik
Gelius,3 Mark Jones,4 and Murielle Salomé5
6) Conclusions
• X-ray absorption spectroscopy
– can be routinely performed at Synchrotrons
– is an element-specific technique
• EXAFS
– photo-electron is scattered by the neighbouring atoms
– Fourier Transform analysis gives structural parameters R, N and A
• XANES
– photo-electron goes to states near ionisation energy
– analysis gives oxidation state, site-symmetry, and compound identification
• detailed structural information which is difficult to obtain
from other techniques
Acknowledgements
• collaborators:
– A. Corrias, D. Carta, M.F. Casula, D. Loche, G. Navarra, U. Lafont,
E. Kelder, R.J. Newport, D.M. Pickup
• synchrotrons:
– L. Olivi (Elettra), S. Fiddy, F. Mosslemanns, L. Murphy (SRS)
• funding organisations:
– Marie Curie Fellowship (EU), Royal Society Fellowship (UK), EPRSC (UK)