Download Introduction to X-ray Absorption Spectroscopy, Extended X

• Mini-school X-ray Absorption Spectroscopy
Introduction to X-ray Absorption
Spectroscopy, Extended X-ray
Absorption Fine Structure
Martin C. Feiters, IMM, HG 03.021
Institute for Molecules and Materials, Radboud University
Heijendaalsweg 153, 6525 AJ Nijmegen, NL
( 024-3652016, [email protected]
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Programme
• 9.00 Martin Feiters (RU) - Introduction to X-ray Absorption
Spectroscopy, Extended X-ray Absorption Fine Structure
• 9.45 Frank de Groot (UU) - X-ray absorption spectroscopy near the
edge. (aka XANES)
• 10.30 Coffee Break
• 11.00 Dipanjan Banerjee (DUBBLE-ESRF) – X-ray sources, optics,
and detectors for absorption spectroscopy beamlines
• 11.45 Alessandro Longo (DUBBLE-ESRF) - Introduction to EXAFS
data analysis
• 12.30 Lunch Break
• 13.30 Martin Feiters (RU) - Coordination Chemistry and Trace
Element Biology
• 14.10 Florian Meirer (UU) - X-ray micro-spectroscopy, tomography,
and operando conditions • 14.55 Coffee Break
• 15.20 Mario Delgado (UU) - Holistic data analysis with Blueprint
XAS
• Institute
15.50
Frank and
de Materials
Groot (UU) - The future of X-ray absorption
for Molecules
• Spectroscopy,
16.30 Drinks
Mini-school X-ray Absorption
SyNeW Utrecht, June 2, 2015
spectroscopy
2
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
X-ray spectrometer: schematic representation
Ø Monochromation by diffraction of a set of parallel Si crystals, following
Bragg’s law
n l = 2 d sin q
Ø Wavelength l selected by varying angle q of Si crystal with respect to beam
Ø Higher order reflections (n > 1) are rejected by making the crystals slightly
non-parallel
Ø Transmitted intensity It depends on incident intensity I0, sample thickness x,
and absorption coefficient m(E) by Lambert-Beer law
It = I0 exp(-mx)
Ø The X-ray absorption spectrum is represented in the dimension of the
energy dependent X-ray absorption coefficient m(E)
ln(I0/It) = mx
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
4
X-ray Absorption Spectroscopy (XAS)
• EXAFS = Extended X-ray Absorption Fine Structure
• XANES = X-ray Absorption Near Edge Structure
• XAFS = X-ray Absorption Fine Structure
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
X-ray fluorescence for dilute samples
•
•
•
The hole created by inner electron excitation can be filled by electrons from
higher orbitals, which give rise to fluorescence
The total fluorescence yield is more intense for K than for L-excitation
The X-ray absorption spectrum can be measured as mf = If / I0
Institute for Molecules
andFeiters
Materials
M. C.
and W. Meyer-Klaucke, in Practical Approaches
to Biological
Mini-school
Inorganic
X-ray Absorption
ChemistrySpectroscopy,
(R. R. Crichton
SyNeW
and Utrecht,
R. Louro,
June
Editors;
2, 20152013)
6
X-ray excitation energies
Tuning into any edge in the Periodic Table
120000
K edges, 1s;
L3, 2p3/2
Excitation Energy (eV)
100000
80000
60000
40000
20000
0
0
10
20
30
40
50
60
70
80
90
100
Atomic Number
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
7
Fine Structure in X-ray Absorption Spectra
• Type of experiment:
Measurement of the X-ray absorption (or fluorescence)
at wavelengths around the edge of an element of
interest (= spectroscopy)
• Type of phenomena:
Edge and fine structure: interference effects due to
wave character of electron (= diffraction)
XANES, XES also transitions (= spectroscopy)
• Type of data treatment:
Energy calibration,
normalization,
background subtraction, simulation
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
8
Fe X-ray Absorption K edge (XANES) of Haems
Normalized X-ray fluorescence
1.4
1.2
1.0
0.8
0.6
Mb
0.4
OxyMb
0.2
0.0
continuum
1s
4p
4s
3d
7105
7120
7135
7150
• Position and structure of Fe K
absorption edge of O2-binding
protein myoglobin depend on
oxygenation state
• Both oxidation state (valence, Fe(II)
vs. Fe(III)-O2-) and average ligand
distance (‘Natoli rule’) affect edge
position (= energy where the
absorption is ½ of the maximum)
• ‘Pre-edge’ absorptions are due to
excitation of 1s electron to empty
orbitals like 3d, 4s, 4p as indicated
• Intensity pre-edge features depends
on symmetry of coordination geometry around absorber atom (Fe)
7165
Energy (eV)
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
9
X-ray induced electron diffraction:
Pebble in a pond
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Extended X-ray Absorption Fine Structure
(EXAFS) of a porphyrin first shell
X-ray energy > edge: photoelectronic
effect at the absorber atom
Photoelectronic wave
backscattered by
surrounding atoms
Interference of incoming and outcoming waves
at absorber atom: variations in electron density
as energy is scanned, kinetic energy/electron
wavelength varied
Energy-dependent variations in
electron density give variations in
X-ray absorption coefficient
Institute for Molecules and Materials
S. P. Cramer
& K. O. Hodgson,
Prog.SyNeW
Inorg. Utrecht,
Chem. June
25 (1979)
Mini-school
X-ray Absorption
Spectroscopy,
2, 20151-39.
11
Type of information - Relation with other techniques
Type of information:
• EXAFS: number, type, and distance of ligand atoms
• XANES: valence, coordination geometry
Relation with other techniques:
• EXAFS: refinement of distance information from crystallography
• XANES: combine with other spectroscopic techniques
EXAFS/XANES can be used, together with other spectroscopic
techniques, to construct a ‘spectroscopically effective model’ of a
metal site
XAS is applicable to any element, in any valence or spin state, in
samples in any physical state (solution, frozen solution, powder,
single crystal, crystalline slurry, gas)
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
12
Wherefrom …. Whereto with XAS
• Starting from
¬ simplified physics, mathematics
• Going to ®
understanding of chemical parameters
(important in a biological context) like:
number, type, and distance of
surrounding atoms;
valence state, ligand geometry
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Physical/Mathematical
Foundations
Wilhelm Conrad
Röntgen
(1845-1923)
X-rays
Christiaan
Huygens
(1629-1695)
wave theory
of light
Institute for Molecules and Materials
Louis de Broglie
(1892-1987)
wave character
of electrons
Ralph de L. Kronig
(1904-1995)
early theories
of X-ray absorption
fine structure
Joseph Fourier
(1768-1830)
transformation,
analysis of sum
of oscillations
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
14
Fine structure above the edge: EXAFS
c(E)
0.4
•
The X-ray absorption spectrum m
has a fine structure (EXAFS,
Extended X-ray Absorption Fine
Structure) extending a few 100 –
1000 eV above the edge, starting 50
– 100 eV above the edge
•
From the experimental X-ray
absorption (fluorescence) spectrum
m the EXAFS or c(k) can be
extracted by c(k) = (mA – mo)/mo
with mA = m – m’, where m’ =
hypothetical spectrum with no Fe;
m0 = hypothetical spectrum with no
surrounding atoms
•
It is convenient to convert the
energy axis to the wave vector k:
k2 = 2me (E – Eo)/ħ2
c
0.2
//
Normalized fluorescence counts
0.0
0.6
0.4
m0
m
0.2
m’
0.0
pre-edge
XANES
E X A F S
6920 7020
7120 7220 and
7320Materials
7420 7520 7620 7720 7820
Institute
for Molecules
Energy X-ray
(eV) Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Mini-school
15
Comparison of mono- and diatomic molecule
Kr
Br-Br
Quantitative
rationalization of
the absence and
presence,
respectively, of
EXAFS in a
monatomic gas
such as Kr (a and
c) and a diatomic
gas such as Br2
(b and d)
Institute for Molecules and Materials D. C. Koningsberger and R. Prins, X-ray Absorption Spectroscopy
Wiley-Interscience,
New
York
(1988)
16
Mini-school X-ray Absorption Spectroscopy,
SyNeW Utrecht,
June
2, 2015
Background subtraction, extraction of fine structure
Fluorescence
0.7
m0
m
m’
c(E)
0.0
0.4
• m, experiment; m’, no Fe;
m0, no surrounding
atoms; mA = m – m’
• EXAFS or
c(k) = (mA – mo)/mo
mA = m – m’
k2 = 2me (E – Eo)/ħ2
0.0
-0.4
6920
7220
7520
7820
Institute for
Molecules
and Materials
Energy
(eV)
Mini-school
X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
17
Background subtraction, extraction of fine structure
• m, experiment; m’,
no Fe; m0, no
surrounding atoms;
mA = m – m’
• EXAFS or
c(k) = (mA – mo)/mo
mA = m – m’
k2 = 2me (E – Eo)/ħ2
0.5
c(k)
Fluorescence
0.7
m0
0.0
m
m’
-0.5
c(E)
c(k) * k3
10
0.0
0.4
0
0.0
-0.4
-10
6920
7220
7520
7820 2
Institute for
Molecules
and Materials
5
8
11
k (Å-1)
Energy
(eV)
Mini-school
X-ray Absorption Spectroscopy,
SyNeW Utrecht, June 2, 2015
18
Founders of Modern EXAFS Theory
Joseph Fourier
(1768-1830)
transformation,
analysis of sum
of oscillations
•
Edward Stern, Dale Sayers, and Farrel Lytle accept the American
Crystallographic Association’s Bertram Warren Award in 1979, for
their development of EXAFS
Institute for Molecules and Materials
Mini-school
X-ray
SyNeW Utrecht, 27
June
2, 20151204
D. L. Sayers,
E.Absorption
A. Stern, Spectroscopy,
F. W. Lytle, Phys.Rev.Lett.
(1971)
19
EXAFS interpretation by Fourier transformation
60
c(k)
0.5
40
/FT/ of k3-weighted EXAFS
0.0
-0.5
c(k) * k3
10
0
20
0
-20
-40
-10
2
5
8
Institute for Molecules and Materials
k (Å-1)
11
0
1
2
3
4
5
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, JuneR2,(Å)
2015
6
7
8
20
Golden Rule and Plane Wave approximation
•
•
•
•
Separate atomic and scattering contributions:
m(E) = Slm m0lm(E) x (1 + clm(E))
Summed over all allowed final states lm
Atomic contribution given in dipole approximation by ‘Golden
Rule’:
• m0(E) = (1/h) <|ψf| e.r | ψi|>2 D(E)
• With e the electric vector of the photon, r the position with
respect to the nucleus, and D(E) the energy density of final
states
• Plane wave approximation for c, with
k, electron wave vector (Å-1) defined as:
2 2
-2k
s j . e -2rj/l. sin(2kr + f (k))/kr2
c(k) = jS Nj. Si(k). Fj(k). e
j
j
j
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Plane wave/single scattering approximation of EXAFS
c is a sum of j (resolved) shells of backscatters of type i
k, electron wave vector (Å-1) defined as k =
2me (E-E0)
h2
Fj backscattering amplitude of each of the
Nj backscattering atoms of type i with
sj Debye-Waller-type factor
rj distance
fj total phaseshift
Si amplitude reduction factor
l electron mean free path (D)E0 threshold energy
The (bio)chemist is interested in the type of atom (choose Fj)
and its number Nj and distance rj (refine in simulation).
Unfortunately, refinement of (and correlation with !) the DebyeInstitute for Molecules and Materials
Waller-type
factor and DE0 cannot
be avoided.
Mini-school X-ray Absorption
Spectroscopy, SyNeW Utrecht, June 2, 2015
22
Calculation of Backscattering
Amplitude and Phase Shift
Ø ‘Phase shift calculations’ in EXCURVE based on a
Muffin-Tin
Potential
Ø Backscattering amplitude Fi and phase shift fj can be
accurately calculated for absorber-backscatterer
• In modern phase shift calculations, we do not adjust the
amplitude reduction factor Sj
nor the electron mean free path lj
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
23
Calculation of Backscattering
Amplitude and Phase Shift
Ø ‘Phase shift calculations’ in EXCURVE based on a
Muffin-Tin
Potential
Ø Backscattering amplitude Fi and phase shift fj can be
accurately calculated for absorber-backscatterer
• In modern phase shift calculations, we do not adjust the
amplitude reduction factor Sj
nor the electron mean free path lj
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
24
Fourier Transformation:
Radial Distribution Function
Ø Fourier transformation of EXAFS results in radial distribution
function:
Ø Peak position: distance after correction for ‘phase shift’
(extract from reference compound, or calculate)
Ø Amplitude: coordination number, occupancy of shell
Ø The (bio)chemist is interested in the type of atom i (choose
a calculated Fj) and its number Nj and distance rj (refine
simulation with calculated fj)
Ø Unfortunately, correlation of Nj with the Debye-Waller-type
factor sj, and of rj with the threshold energy E0 (or EF),
cannot be avoided.
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
25
Effect of Atom Types
Ø Phase relation EXAFS/Fourier transform
dependent on nature of atom
Ø EXAFS of S ligand is p out of phase with those
of C, N, and O
Ø EXAFS of C, N, and O virtually indistinguishable
(‘low-Z’ ligands);
Ø It is possible that waves of different phases
interfere destructively; it may be difficult to
unravel contributions of opposite phase at
similar distances
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
26
Backscattering amplitude and phase
characteristic for element
W
I
EXAFS * k3
10
0
Mo
-10
2
Br
3
4
5
6
7
8
9
I
Br
Zn
F
O
N
C
Cl
Cr
10 11 12 13 14 15 16
k (Å-1)
100
/FT/
Backscattering amplitude envelope
100
Cl
S
F
H
0
2 3 4for5Molecules
6 7 8 and
9 10Materials
11 12 13
Institute
(Å-1)
14 15 16
0
0
1
2
3
4
k
R2,(Å)
Mini-school
X-ray Absorption Spectroscopy, SyNeW Utrecht, June
2015
5
6
27
Resolution of FT techniques
Compared to NMR, FT-MS, or FT-IR, the resolution of EXAFS is poor because
the Fourier transform is typically taken over only a few oscillations
EXAFS * k 3
10
0
-10
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
k (Å-1)
60
Ion Cyclotron MS
Resolution: DR = p / 2 Dk (Å)
Institute for Molecules
and Materials
Dk
= 14 Å-1: DR
= p / 2 * 14 = 0.11 Å
/FT/
Pulsed NMR
Total simulation:
2 S, 2 N (imidazole)
2 S 2.25, 2 N 2.00 Å
0
0
1
2
3
4
5
6
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
R (Å)
7
8
9
10
28
Debye-Waller(-type) factor (1)
•
Debye-Waller factor describes effects of thermal and static disorder.
•
Distance rj accurately (± 0.02 Å) determined. Typical data range (10
Å-1): distances within 0.15 Å not resolved (DR = p / 2 Dk (Å)); average
distance determined.
•
Increased disorder in shell composed of non-resolved contributions
(static disorder) noted as more rapid decline of EXAFS amplitude at
high k, and peak broadening in the Fourier transform, described by
larger value for Debye-Waller factor.
•
High value for Debye-Waller factor can be caused by variance in
ligand distances (static disorder).
•
It can also be caused by disorder due to thermal effects: probe by
temperature variation.
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
•A model for elemental Fe
(body-centered cubic, a-Fe):
• Are all Fe-Fe distances the
same (static disorder) ?
• Are all Fe-Fe bonds rigid
(thermal disorder) ?
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Debye-Waller factor and resolution
4
0
0
-4
-4
EXAFS * k3
4
2
4
6
8
10
12
14
16
2
4
6
k (Å-1)
10
12
14
16
k (Å-1)
60
60
2 N at 2.0 Å
from Zn, DR
0, increasing
DW-factor
/FT/
8
2s
0.00
0.06
0.10
0.14
0.18
DR
0.00
0.06
0.10
0.14
0.18
2 N at 2.0 Å
(average)
from Zn, DR
increasing,
DW-factor
0.02 Å
0
0
0
1
2
Institute
for Molecules
and Materials
3
4
0
1
2
R (Å)
R (Å)
Mini-school
X-ray Absorption Spectroscopy, SyNeW Utrecht, June
2, 2015
3
4
31
Multiple Scattering
Important in the EXAFS of rigid ligand systems where the angle
A-B-R-A approaches 180 o (> 140 o):
• Coordinating carbon monoxide
• Coordinating rigid heteroatomic ligand:
e. g. pyridine,
imidazole,
• Metal at center of unit: octahedral, square planar
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
32
EXAFS summary (1)
• XAS can be applied to samples irrespective of physical
(solution, powder, frozen solution) or chemical (oxidation,
spin) state
• Crystals and other oriented systems can be studied, but be
aware of the polarization of the synchrotron beam
• Even whole organisms can be studied but preferentially
the element under study is homogeneous with respect to
its chemical environment
• Because long acquisition times may be needed, radiation
damage should be monitored, in particular photoreduction
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
EXAFS summary (2)
•
XANES gives information on oxidation state and
coordination geometry; simulated on the basis of 3dimensional information
•
EXAFS (1-, 2-dimensional) gives accurate metal-ligand
distances, and an indication of ligand type and coordination
number; combine with XANES and Bond Valence Sum
Analysis for more accurate coordination number
•
Validation of ligand geometries from other structural
(crystallographic, NMR) and computational studies
•
Combine with other spectroscopic techniques to construct a
‘spectroscopically effective model’ of a metal site
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015
Institute for Molecules and Materials
Mini-school X-ray Absorption Spectroscopy, SyNeW Utrecht, June 2, 2015