Download Synchrotron X-ray Absorption Spectroscopy

Synchrotron X-ray Absorption
Spectroscopy
Near-edge Spectra (I)
Graham N. George
Ingrid J. Pickering
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Today…
Near-edge spectra
Nomenclature
Selection rules and spectra
What are near-edge spectra sensitive to?
Pseudo Voigt peak fitting analysis
I. J. Pickering and G. N. George
GEOL 498.3/898.3
X-ray Absorption Spectroscopy
EXAFS oscillations (k3-weighted)
Near-edge spectrum
I. J. Pickering and G. N. George
GEOL 498.3/898.3
1
Nomenclature
There are a large number of names and acronyms in use –
they all refer to the same thing or are closely related…
Edge Spectra
Near-Edge Spectra
Near-Edge X-ray Absorption Fine Structure (NEXAFS)
X-ray Absorption Near-Edge Structure (XANES)
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Nomenclature
Sometimes, but not always, “XANES” is used to refer to the region
just above the edge, which is more readily calculable using multiple
scattering theory.
}
near-edge
}
XANES
EXAFS
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Nomenclature
What is a “White Line”?
The term “white line” refers to an intense absorption in the near-edge. The
nomenclature dates from the days when spectra were recorded on strips of
photographic film, and such intense absorption peaks showed up as a heavily
exposed line on the developed film.
White Line
photographic film
White Line
I. J. Pickering and G. N. George
spectrum
GEOL 498.3/898.3
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X-ray absorption near-edge spectra
Intense features arise due excitation of transitions from the core level
to vacant levels, close to the highest occupied molecular orbital.
nucleus
vacant orbital
electron
2p, l=1
hν
electron-hole
1s,
l=0
2s, l=0
I. J. Pickering and G. N. George
GEOL 498.3/898.3
What is a near-edge spectrum
The photoelectron is excited to a variety of bound states lying
below the threshold energy.
Transitions to
bound states
observed spectrum
Core level
Threshold, E0
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Near-edge spectra
X-ray absorption is given by Fermi’s Golden Rule:
µ (E ) = ∑ ψ i H ψ f
2
ψi - the initial state wavefunction
ψf - the final state wavefunction
H
- the interaction
If we wish to quantify spectra, we have two alternatives – evaluate the
integral as completely as possible (molecular orbital approach) or use
multiple scattering theory.
Molecular orbital approach. A chemistry perspective – the X-ray excites
transitions between the core level and a molecular orbital. Quantification is
non-trivial, but this approach is highly successful in understanding spectra.
Multiple scattering approach. A physics perspective – the X-ray excites a lowenergy photo-electron which undergoes extensive multiple scattering by nearby
atoms. This success of this approach is limited (to date). It usually cannot
model features due to low-lying bound-state transitions.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
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What is a near-edge spectrum?
Molecular orbital approach - transitions to boundstate molecular orbitals.
σ*
S1s → σ*
LUMO+1
S1s →π*
S
O
OH
π*
LUMO
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Spectral linewidths
Two components contribute to the spectral linewidth – the core-hole
lifetime and the optical resolution.
Core-hole lifetime.
Heisenberg’s uncertainty principal states that:
∆E∆t ≥
1
h
2
Thus, comparing high and low energy edges, we expect the higher
energy edge to have shorter core hole lifetimes (∆t) and
correspondingly broader experimental linewidth (∆E) (assuming that
the spectroscopic resolution is not limiting).
This adds a Lorentzian component to the lineshape.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Spectral linewidths
Example – aqueous solution of molybdate [MoO4]2- measured at the K-edge (1s
excitation) and the LI edge (2s excitation). These are very similar ground
states, and no significant differences in the nature of the near-edge
transitions are expected. The spectra have been offset by 20008.70 eV and
2869.95 eV, respectively. The K edge is has a much shorter core-hole
lifetime than the LI edge, and has corresponding broader linewidths.
LI edge
K edge
I. J. Pickering and G. N. George
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Spectral linewidths
Spectrometer Resolution
In a modern EXAFS beamline this is usually only a function of the
monochromator. Each monochromator material has an inherent energy
resolution - the Darwin width of the crystal.
This adds a Gaussian component to the overall experimental lineshape
function.
The experimental lineshape is expected to be approximated by a convolution
of a Gaussian and a Lorenztian due to monochromator and lifetime broadening,
respectively. This is known as a Voigt lineshape function – in practice it can be
approximated by the sum of a Gaussian and Lorenztian – a pseudo Voigt
lineshape function.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Near-edge Spectra
We can write Fermi’s Golden Rule as:
µ ∝ ∑ ψ i (e ⋅ p)e i (k ⋅r ) ψ f
If we use a series expansion of
the exponential, and examine
just the first term, we get what
is called the “dipole-allowed”
transitions. These are the most
intense transitions observed, and
can be thought of as being
stimulated by an oscillating
electric field.
2
ψi
ψf
e
p
k
- the initial state wavefunction
r
- the transition operator (x, y or z)
in the molecular axis system
- the final state wavefunction
- the X-ray electric vector
- the electron momentum vector
- the X-ray forward propagation
vector
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Dipole and Quadrupole Transitions
Dipole transitions are described by:
µ D ∝ ∑ ψ i (e ⋅ p) ψ f
2
These are the most intense transitions observed, and can be thought of as
being stimulated by an oscillating electric field, and have ∆l= ±1.
Including the next term in the series expansion gives “quadrupole
transitions”, which have ∆l= ±2, and these are described by:
µQ ∝ ∑ ψ i (e ⋅ p)(k ⋅ r ) ψ f
2
Quadrupole transitions are of low intensity and can be thought of as being
stimulated by the electric field gradient, which is significant due to the
short wavelength of the X-radiation being used.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
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Selection Rules for X-ray absorption
near-edge spectra
Transition
Selection rule
LIII-edge
Strength K-edge
Dipole
∆l=±1
Intense
1s →np
2p →nd
Quadrupole
∆l=±2
Weak
1s →nd
2p →nf
MIV, MV
Transition
K, LI, MI
LII, LIII, MII, MIII
Dipole
ns →n´p
np →n´d
nd →n´f
Quadrupole
ns →n´d
np →n´f
nd →n´g
I. J. Pickering and G. N. George
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Tungsten L-edges – Selection Rules
XAS L-edge spectra of Na2WO4 – W(VI) is 5d0, so we expect strong dipole
allowed transitions to the 5d manifold at the LIII and LII edges from the
2p3/2 and 2p1/2, respectively. No such intense transitions are expected at
the LI near-edge (2s excitation).
W LIII
W LII
W LI
I. J. Pickering and G. N. George
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Uranium M-edges – Selection Rules
XAS M-edge spectra of UO2(CH3CO2)2(H2O)2 – U(VI) is 5f0, so we expect
strong dipole-allowed transitions to the 5f manifold at the MV and MIV edges
from the 3d3/2 and 3d1/2, respectively. No such intense transitions are
expected at the MIII, MII (3p3/2 and 3p1/2 excitation, respectively) or MI (3s
excitation) near-edges.
O
O O OH
2
O
U
H2O
O
O
MI
MIV
MIII
MII
MV
I. J. Pickering and G. N. George
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Dipole and Quadrupole transitions
Cu K-edge spectrum of [Cu(Imidazole)4](NO3)2 is 3d9. Spectra arise from 1s excitation,
so we expect strong dipole allowed transitions to orbitals with a lot of 4p character, and
a single weak quadrupole allowed transition to the half-filled 3d level.
Quadrupole 1s→3d transition
Dipole 1s→4p transitions
x20
I. J. Pickering and G. N. George
GEOL 498.3/898.3
What do we expect about near-edge
spectra?
•
Intense features due to dipole-allowed ∆l=±1 transitions
•
Weak features due to quadrupole-allowed ∆l=±2 transitions
•
For hard X-ray spectra (i.e. E > 1500 eV) the core-hole lies deep
within the atom. One consequence of this is that the final state of an
absorber with atomic number Z approximates to that of Z+1 – i.e. the
next element in the periodic table. This can be important when
comparing splittings measured from UV-visible electronic spectroscopy
with X-ray near-edge spectra – e.g splittings of Co2+ K near-edge
spectra correspond optical spittings observed in the iso-structural
Fe2+ compound.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
What do we expect about near-edge
spectra?
•
For hard X-ray spectra (i.e. E > 1500 eV) the ejection of a core
electron will cause the outer orbitals to relax to lower energies (e.g.
by about 10 eV for Cu K-edge spectra). This causes a corresponding
shrinkage of the wave function, and thus reduction in the overlap
integrals for molecular orbitals. We therefore expect the spectra to
be very “atomic” in some of their properties.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
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Influence of core hole on electronic structure
Ejection of metal core-electron causes outer metal orbitals to relax to
lower energies.
4p
4p
3d
3p
3p
3d
metal
1s
ligand
Ground state
metal
1s
ligand
Final state
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GEOL 498.3/898.3
What are near-edge spectra sensitive to?
Oxidation State
Pyrococcus furiosus rubredoxin
Fe2+
Fe3+
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What are near-edge spectra sensitive to?
Nature of the Ligands
Ferric ions with sulfur and oxygen donors
[Fe3+(SR)4]-
[Fe3+(OR)4]-
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What are near-edge spectra sensitive to?
Nature of the Ligands
P4O10 and P4S10 are isostructural, both with P(V) oxidation state
P4S10
P4O10
Covalency of sulfur means that phosphorus appears more reduced than its
formal oxidation state
I. J. Pickering and G. N. George
GEOL 498.3/898.3
What are near-edge spectra sensitive to?
Coordination Geometry
Oxygen coordinated ferric ions – octahedral vs. tetrahedral
octahedral
1s→3d region
tetrahedral
I. J. Pickering and G. N. George
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Transition metal MO4 anions
Similar chemical environments give rise to similar spectra
VO42K
K
K
LI
K
K2CrO4
KMnO4
K2FeO4
Na2WO4
Edge energy
K
Na2MoO4
Spectra have been offset to align the lowest energy transition
I. J. Pickering and G. N. George
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What are near-edge spectra sensitive to?
Trigonal vs. Digonal cuprous thiolate compounds
Inspection of the chemical literature indicates that Cu(I) prefers two
distinct coordination environments – linear two-coordinate (digonal)
and planar three-coordinate (trigonal) coordination geometries, e.g.
with thiolate ligands:
SR
-
SR
RS
Cu
2-
Cu
SR
SR
Cuprous thiolate metalloproteins form a very large group of diverse
function. Both two and three coordinate examples are known.
I. J. Pickering and G. N. George
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Ligand Field Splitting
Isolated atom – degenerate
p-orbital energies
Molecule – ligand-field splitting,
p-orbital degeneracy lifted
pz
px
py
energy
energy
atom
pz
px
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py
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What are near-edge spectra sensitive to?
Trigonal vs. Digonal cuprous thiolate compounds
Cu(I) is 3d10, so we expect no quadrupole transitions to the 3d
manifold, and the lowest energy features in the near-edge should be
1s→4p transitions. Let us consider the ligand field splitting of the 4p
orbitals.
digonal
SR
z
y
x
Cu
SR
trigonal
pz
px
py
I. J. Pickering and G. N. George
SR
RS
distorted trigonal
SR
pz
py
RS
Cu
SR
px
Cu
SR
pz
py
px
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Cu K near-edge spectra of digonal and
trigonal cuprous thiolates
Cu 1s→4px,y
digonal
trigonal
Cu 1s→4px
I. J. Pickering and G. N. George
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Cu K near-edge spectra of digonal and
trigonal cuprous thiolates
Trigonal vs. Digonal cuprous thiolate compounds
The ~8983 eV peak is diagnostic of digonal Cu(I)
coordination. It can be used as a fingerprint of this kind
of metal coordination.
SR
Cu
SR
I. J. Pickering and G. N. George
SR
RS
Cu
SR
GEOL 498.3/898.3
1s→3d transitions of transition metal ions
Octahedral Fe3+ with oxygen coordination – a small quadrupoleallowed, dipole-forbidden 1s→3d peak is observed.
The transition has structure is due to the ligand field splitting of the
3d manifold.
1s→3d
1s→3d
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Ligand Field Splitting
Octahedrally coordinated
metal atom
Ligand atom
Those d-orbitals with lobes
directed towards the ligand atoms
will possess higher energies than
those with lobes directed in
between the ligands.
Energy
dz2
d x2 − y2
∆
d xy
d xz
d yz
The energy separation of the orbitals ∆ is known as the ligand field splitting
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GEOL 498.3/898.3
1s→3d transitions of transition metal ions
The size of the ligand field splitting ∆ (remember this is an excited
state splitting) can tell us about the nature of the metal site.
∆
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High-Spin vs. Low-Spin Ferrous
d x2 − y2 d z2
eg
d xy d xz d yz
t2g
d x2 − y2 d z2
eg
d xy d xz d yz
t2g
Low spin, Rion=0.92 Å
High spin, Rion=0.75 Å
Low-spin Fe2+ occurs with larger ∆, and gives rise to one peak of
relatively increased intensity.
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GEOL 498.3/898.3
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1s→3d transitons – octahedral vs.
tetrahedral geometry
Centrosymmetric (e.g. octahedral
symmetry) mixing of metal 4p and
3d orbitals forbidden, and the
transition is pure quadrupole.
Non-centrosymmetric (e.g.
tetrahedral symmetry) mixing of
metal 4p and 3d orbitals allowed,
and the transition is quadrupole,
plus dipole-allowed intensity from
admixture of metal 4p levels.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Analysis by peak deconvolution
The experimental spectrum is fitted to a calculated spectrum
comprised of a sum of pseudo Voigt peaks (IV) plus a step function
for the edge (I0). This is usually done by iteratively minimizing the
sum-of-squares of the differences between calculated and
measured spectra. Each peak should comprise a single transition
(or group of transitions) to a particular bound state (or states).
µ calc (E ) = a0 I 0 (E ) + ∑ ai IVi (E )
i
IVi
I0
a0
ai
- psudo-Voigt peak i
- edge function
- amplitude for edge function
- amplitude for peak i
This method allows quantitative analysis of quite subtle changes in
near-edge spectra.
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Analysis by peak deconvolution
IV = mI G + (1 − m )I L
 − ln 2(E − Em )2 

I G = exp

 [(W + (E − Em )η )ξ ] 
IL =
[W + (E − Em )η ]2
[W + (E − Em )η ]2 + (E − Em )2
I. J. Pickering and G. N. George
IV - the psudo-Voigt function
IG - Gaussian peak-shape function
IL - Lorentzian peak-shape function
m - mixing factor
Em - peak position
W – half-width of peak
η - peak skew
ξ - ratio of Gaussian to Lorentzian
widths
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Analysis by peak deconvolution
I. J. Pickering and G. N. George
GEOL 498.3/898.3
Sulfur K-edge X-ray
absorption near-edge
spectra
SO42RSO3-
Sulfur K Near-edge spectra of
biological model compounds.
SO32RSO2RS=O
The spectra are very sensitive
to the chemical form of sulfur
and can be used to “fingerprint”
forms of sulfur present.
R3S+
x2
x2
x2
x2
x2
I. J. Pickering and G. N. George
RS-Me
RS-H
RS-SR
S8
Fe4S4
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