Vij D.R. Handbook of Applied Solid State Spectroscopy

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14.5 Applications

The calculations reproduce all of the spectral structures very well,

especially the enhancement of the peak at about 1.2 eV with increasing

excitation energies. The growth of the peak is due to enhanced transitions into

the

state. Changes in absolute intensities of inelastic scattering structures

corresponding to the transitions are reproduced on going from spectrum

to spectrum b. For spectra c and d, such changes in calculated intensities

are about three times higher as compared to those in the experiment.

The discrepancy may originate from the normalization procedure for the

experimental spectra to account for variations in the incident photon flux. The

intensity of the elastic peak was used as a reference in this procedure.

However, the elastic peak contains some contribution of diffuse scattering,

which may vary with varying excitation energies.

RIXS profiles, corresponding to the fof excitations, are found to be very

sensitive to the chemical state of U in different systems [114]. For example, it

is a matter of the presence or absence of these excitations when going from

to U

compounds. Therefore, RIXS measurements near the U 5d

threshold provide good fingerprints for the chemical state of U in different

systems in contrast to X-ray absorption spectra, which show only small

differences at the U 5d edge.

One interesting example concerns the chemical state of U in U

and

reduced UO

. In particular, for U

, it was discussed in the literature that the

chemical state of U is described as either U

V,2

or U

VI,2

. To our

knowledge there is no clear and convincing answer to this question and it is

still under debate. Thus, core level photoemission [115, 116, 117] and

electron spin resonance [118, 119] data have been interpreted in favor of

either situation by different groups, and therefore these techniques cannot

really provide an unambiguous answer. It turns out that the RIXS technique

can. RIXS spectra of fof excitations are a good indicator of whether uranium

is in the U(IV), U(V) or U(VI) state. The data are easy to interpret and not

very difficult to calculate. Establishing the real chemical state of U in oxides

is important for applied, environmental and fundamental science (e.g., a

development of the theory of nonstoichiometry is a fundamental problem).

Figure 14.33 displays RIXS spectra of transitions for a number of U

oxides. Close similarity of the transitions profile in U

to those in UO

and UF

, as well as to that calculated for the U(IV) ion (see Figure 14.32),

unambiguously indicates the presence of the U(IV) fraction in U

, thus

favoring the U

VI,2

description of the uranium chemical state in this

oxide. Furthermore, a similar pattern is observed for reduced UO

, thus

indicating that oxygen deficiency leads to the creation of U(IV) species in the

compound.

643

fof

Figure 14.33 Resonant inelastic X-ray scattering spectra of U oxides recorded at the incident

photon energy of 99.9 eV.

Charge-transfer effects are expected to be significant in actinide

compounds as a result of metal 5f-ligand 2p hybridization. The analysis of our

data [114] obtained at the U 3d

5/2

threshold shows that the ligand 2p

U 5f

charge-transfer plays an important role in uranium compounds, such as UO

(NO

)

u 6H

O, and even in UF

This is also supported by theoretical studies. Molecular orbital calculations

by several research groups [120, 121, 122, 123] gave values for the 5f

occupancy, which range from 2.3 to 2.9 electrons, while this occupancy was

estimated at about 2.3 electrons from the analysis of X-ray absorption and

photoemission data within an Anderson impurity model [124, 125]. These

results indicate a significant degree of covalency for U–O chemical bonds in

. For UF

, a 5f contribution of a0.3 electron to the bonding orbitals was

also predicted from relativistic Dirac-Slater local density calculations [126].

For compounds containing U

, the degree of covalency for metal-ligand

bonds is expected to be even higher than that for U

systems. For example,

molecular orbital calculations yielded the 5f occupancy of a2.6 electrons for

the uranyl ion UO

2+,2

[127, 128]. Although the values for the 5f occupancy

obtained from molecular orbital calculations seem to be overestimated [129],

one cannot rule out the importance of the U 5f-ligand 2p hybridization even in

a compound with “ionic” bonds such as UF

644

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

Intensity (arb. units)

-4 -3 -2 -1

0 1 2

Energy loss (eV)

(reduced)

U 5d RIXS

14.5 Applications

The consequence of high covalency and hybridization in the ground state

is an appearance of charge-transfer satellites in high energy spectroscopic

data. Figure 14.34 illustrates the dependence of the RIXS spectra on the

chemical environment of U atoms in various compounds.

Figure 14.34 Resonant inelastic X-ray scattering spectra of a number of U compounds

recorded at the incident photon energy of 115.0 eV.

The spectra were measured under conditions when the inelastic RIXS

cross-section is enhanced for the ligand 2p → U 5f charge-transfer transitions,

in particular, when the energy of the incident photon beam is tuned to the

main edge of the U 5d X-ray absorption spectrum (see Figure 14.31). At these

energies, the charge-transfer excitations dominate RIXS spectra, thus defining

the RIXS profile. The profiles can be clearly divided into three groups: (i)

, (ii) UO

and UO

3–d

, (iii) U

and UO

. The differences between profiles

are determined by the character of the bonding and the local geometrical

arrangement of ligands, i.e., local crystal structure.

14.5.3.7 Molecular Systems and Liquids

Free Molecules: During the last decade, it became possible to measure sub-

keV X-ray emission of molecules in gas phase using excitation by

monochromatized synchrotron radiation. This was demonstrated by [130],

which presented resonant X-ray spectra of free molecular oxygen [130],

where the results gave conclusive proof that parity is conserved in the two-

photon, absorption-emission X-ray process. Cases where vibronic coupling

can lower the symmetry upon core excitation have been observed, notably

. It has been demonstrated that by detuning the excitation energy down

Intensity (arb. units)

-15 -10

-5

0 5

Photon energy (eV)

(reduced)

U 5d RIXS

645

from resonance one effectively restores the symmetry by virtue of an effective

shortening of the X-ray scattering time [131]. Further, the symmetry-selective

character of this spectroscopy, spectator shifts, angular anisotropy, vibronic

coupling leading to symmetry breaking, and different types of interference

effects in the resonant and nonresonant spectra of molecular N

, CO, CO

have been studied. Some of the molecular studies serve as illustrative

examples of the properties of resonant soft X-ray emission spectroscopy.

Figure 14.35 shows the nitrogen K emission spectra recorded at various

excitation energies, which resonantly promote a core electron to various

unoccupied levels of different symmetry. The top spectrum represents the

nonresonant case where continuum states above the ionization threshold are

excited. These are infinitely degenerate with respect to all symmetries. The

spectrum shows three bands, representing emission from the three outermost

valence orbitals of both gerade (g)andungerade (u) symmetry. When, on the

other hand, the excitation is to a level with a defined symmetry the emission

spectrum appears different, not showing emission from all three levels.

Instead, two, or even a single band, are observed in this case. When exciting

to a Rydberg state of ungerade symmetry, the 3S

, only emission from the

two ungerade levels are observed. The 3sσ

excitation leads to a single

emission band, which corresponds to the 3σ

state. This also KROGVIRUWKH

excitation where the 3σ

–1



final state is seen. In that spectrum, the high

energy band at ~400.5 eV is the so-called participator transition, where the

excited electron fills the core hole. One can note energy shifts of the 3σ

related emission in these spectra that are caused by the presence of the excited

electron in the intermediate and final state. The solid lines in Figure 14.35

represent simulations based on potential energy curves taken from the

literature and lifetime vibrational interference theory describing the

vibrational bands [132].

For molecules having inversion symmetry experimental spectra obey a g

→

g selection rule with respect to unoccupied (respectively, occupied) orbitals

[130, 132, 133, 134, 135, 136]. In a molecular orbital picture describing also

the core orbitals this comes out naturally because the dipole nature of the

transitions implies that the parity has to change at the absorption or the

emission of a photon, e.g., g

→

u or u

→

g, as described earlier. In the full

absorption-emission transition we have a g

→

g or u

→

u rule, which

explains the observations for N

. For polyatomic molecules, where vibrations

of non-total symmetry are possible, selection rules are observed to relax

because of dynamical (vibronic) symmetry breaking in the intermediate core

state. This effect can be observed in one of the simplest molecules of this

kind, CO

, where only two non-totally symmetric vibrations are present [131].

646

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

14.5 Applications

Figure 14.35 X-ray emission spectra of molecular N

. From the top, nonresonant spectrum,

resonantly excited to the Rydberg 3S

level, 3sσ

andtothe1

valence level, respectively.

Note the g-g selection rule, which holds for the resonant spectra.

The strict symmetry selection rules appropriate for a particular molecule

as described above can in some cases be broken [137]. For larger molecules

symmetry-forbidden transitions have been observed [131, 138]. As these

molecules possess a vast number of vibrations, the results are difficult to

describe in detail. Just as N

or O

are good cases for demonstrating that the

parity selection rule is valid, CO

is as good a candidate to study the effect of

symmetry breaking. The central carbon atom between the two oxygen atoms

adds an antisymmetric stretch mode that can couple the gerade and ungerade

oxygen core excited states and therefore break the parity selection rule [137].

of CO

and O

. The resonant excitations are to the first empty molecular

orbitals, 2

and 1

respectively. In the O

case only symmetry-allowed

transitions are observed [130], in a similar way as was described for N

[132],

i.e., only transitions that give gerade final states. The resonant O

spectrum

consists of only two bands, a spectator and a single participator. Especially

the absence of the

–

final state proves the validity of the selection rules.

647

Figure 14.36 shows resonant and nonresonant oxygen K emission spectra

Intensity (arb. units)

404

402

400

398

396

394

392

390

388

Emission ener

(eV)

N1s -3s

Non-resonant

N1s -1

(v=0)

Resonant

N1s -3p

-1

N-K emission

(spectator)

(participator)

Figure 14.36

-excited and nonresonant oxygen K emission spectra of CO

and O

illustrating

the effect of symmetry-breaking in the intermediate core excited states of CO

. Symmetry-

forbidden transitions in ground state symmetry are given intensity by non-totally symmetric

vibrational excitations lowering the symmetry of the intermediate state. The resonant O

spectrum only shows intensity from symmetry-allowed transitions similar to the case of N

In contrast to how different the nonresonant and resonant spectra of O

are

the two CO

spectra are rather similar. Here, intensity from all valence

orbitals is observed in both spectra, despite the symmetry-selective excitation

to an ungerade state, providing proof that the symmetry of the intermediate,

core-excited state is broken. In particular, the appearance of the high energy

spectator transition involving the outer valence orbital, 1

, would be strictly

forbidden if the inversion symmetry would be retained in the core-excited

state. The relative intensities between the high and low energy bands are not

648

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

Intensity (arb. units)

540535530525520515

Ener

(eV)

Nonresonant

Resonant

O1s

- 1

Resonant

O1s

- 2

-1

(participator)

(spectator)

Nonresonant

-1

14.5 Applications

the same in the nonresonant and resonant spectra. The deviation can give

information about the strength of the vibronic coupling and hence how strong

the symmetry breaking is [131]. The fact that some effect of the selection rule

pertains can be used in the determination of the parity of specific empty states

probed by resonant excitation [138]. The effect of symmetry-breaking is very

clear for CO

but observations of “forbidden” lines in other molecular systems

have been made, like in C

[136], and C

[133], which can also be

explained by the vibronic coupling.

It has been observed that the symmetry selection rule in polyatomic

molecules is more strict when the narrow bandpass excitation is detuned

below the first resonance [135, 136]. This is discussed in more detail for the

molecule [131] where the above discussed forbidden high energy band

decreases monotonically with the detuning energy. Figure 14.37 shows the

detuning spectra referring to resonant excitation to the first unoccupied level,



,ofCO

giving the forbidden |g 〉 =1σ

–1



andallowed|g〉 =

1σ

–1



core-excited states.

Figure 14.37 Oxygen K 2

resonant X-ray emission spectra of CO

with different detuning

energies below the 2

resonance.

The spectra consist of two peaks; the high energy peak derives from

transitions to the forbidden |f(u) 〉 =|1

–1

〉



final state, and the low

energy peak to the allowed |f(g) 〉 =|1

–1

〉



final state (configuration

state splitting and contribution from the weak 4σ

emission can be neglected).

As seen in the figure, the high energy peak receives significant intensity in

649

Intensity (arb. units)

540535530525520515510

Energy (eV)

-1

O-K emission

resonant O1s-2

535.0 eV

-1.0 eV

-1.5 eV

-1.75 eV

-2.0 eV

-2.3 eV

Nonresonant

551 eV

violation of the selection rule and appears quite like the nonresonant X-ray

emission spectrum of CO

. Thus, the core-excited state cannot be described as

a pure |1

–1

〉



state, but must be mixed with the |1

–1

〉



state. By

detuning the energy it is clear that the spectrum becomes symmetry-purified.

In a time-dependent picture this can be seen as an effective shortening of the

scattering time, allowing sub-femtosecond study of dynamics.

Liquids: Our microscopic understanding of a liquid is very much based on the

study of spatial and spatio-temporal correlation functions. The study of

correlations allows us to appreciate the local organization of one molecule

surrounded by others, and to unravel the microscopic dynamics. Neutron

diffraction and scattering have played and continue to play a major role in

these studies. X-ray diffraction is important as well, and recently X-ray

inelastic scattering has become available. Using X-ray absorption and

selectively excited X-ray emission spectroscopy to probe unoccupied and

occupied electronic states, one can establish a firm interpretation for the

unusual thermodynamic properties of molecular liquids. Furthermore, one can

elucidate finer details of the structural properties of molecular liquids. XAS

and XES spectra reflect the local electronic structure of various

conformations; in this case, the oxygen X-ray absorption and emission line-

shapes are sensitive to the hydrogen bonding configurations.

Water is a very abundant substance on our planet, and it is the principal

constituent of all living organisms. Chemical reactions taking place in liquid

water are essential for many important processes in electrochemistry,

environmental science, pharmaceutical science, and biology in general. Many

models have been proposed to view the details of how liquid water is

geometrically organized by hydrogen bond networks. The hydrogen bond is

an attractive interaction forming a link of a hydrogen atom with a highly

electronegative and nonmetallic element that contains a lone pair of electrons.

Although H-bonds are much weaker than conventional chemical bonds, they

have important consequences on the properties of water. Diffraction of X-rays

[139] and neutrons [140] provide strong evidence that tetrahedral hydrogen-

bond order persists beyond the melting transition, but with substantial

disorder present [141]. Important questions remain about the precise nature of

the disorder and how it is spatially manifested.

The local structure of liquid water is still under debate. It has been

demonstrated that soft X-ray emission spectra, emanating from the radiative

decay, subsequent to core excitation, can be useful in assigning structures in

X-ray absorption spectra [138, 142, 143]. Especially, it has been shown that

the resonantly excited SXE measurements on liquid water are compatible with

the traditional view that three and four hydrogen bonds dominate the structure

[142].

650

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy

14.5 Applications

An X-ray absorption study of liquid water [144] suggests that the four

hydrogen-bonding networks mainly contribute to a single broad feature, while

a shoulder located at 534.7 eV suggests the presence of broken hydrogen

bonds. Indeed, recent theoretical simulations assign this pre-edge structure to

a particular three-hydrogen bond structure with one missing hydrogen bond at

the hydrogen site.

This assignment is fully confirmed by X-ray emission spectra, excited on

this particular pre-edge shoulder (Figure 14.38). Different local structures

provide different nonresonant spectra because of their different valence band

structures. The nonresonant spectrum should be a sum of the ones from all

different structures. However, since the SYM structure is the dominating

structure in the liquid water, its nonresonant spectrum is close to the

experimental one. Compared to the nonresonant spectrum we observe a

substantial narrowing of the 1b

peak at 526 eV, and a further attenuation of

the 3a

-associated structure at 524.5 eV. This is in excellent agreement with

the predictions for the DASYM configuration.

Figure 14.38 The sharp structures in the X-ray absorption spectrum of the water molecule

(inset) are smeared out in the liquid water due to the diffuse nature of the corresponding

molecular orbitals. A pre-peak is resolved at 534.7 eV in the spectrum of liquid water. The

arrows indicate the photon energies used for resonantly and normally excited X-ray emission

spectra. The resonantly excited spectrum is in good agreement with the prediction for the three-

bonded D-ASYM configuration.

Intensity (arb. units)

530525520515

Energy (eV)

Normal

Resonant

SYM

A-ASYM

D-ASYM

Experiment

540

536532

O 1s

gas water

liquid water

651

The early hypothesis of cyclic structures by Pauling [145] has been both

supported [146] and contested [147] by neutron diffraction analysis, the

competing interpretation being that the majority of liquid molecules are

ordered in chains with up to 10 members [147, 148] or linear trimer-tetramer

chains [149]. This uncertainty is accentuated when one considers alcohol-

water solutions. The observed entropy increase upon mixing alcohol and

water is much smaller than expected for an ideal solution. Early neutron

diffraction data provide structure information of water cages around

hydrophobic headgroups in solution [150, 151, 152, 153]. Recently, a new

neutron diffraction analysis demonstrated that incomplete mixing at the

molecular level is essential to understanding the smaller than expected

entropy increase [154]. This contrasts with the prevailing view that a

rearrangement of the water network around hydrophobic methyl groups of the

methanol clusters is the main feature behind the unusual thermodynamic

properties [155].

A comparison of the theoretical and experimental X-ray emission spectra

(in Figure 14.39) associated with possible molecular arrangements makes it

obvious that both rings and chains are present in liquid methanol. The maxima

at 526 eV and 527 eV can be assigned to ring and chain structures,

respectively. In addition, we find that the measured spectra are typical for

rings and chains consisting of 6 and 8 molecules. Configurations with fewer

than 6 molecules do not give representative predictions, and odd-numbered

configurations yield an unobserved high energy feature at 528 eV. Chains

with more than 10 molecules are unlikely in light of neutron diffraction data

[147, 148]. Therefore, the 6- and/or 8-membered rings and chains provide the

predominant structures in liquid methanol. From the excitation energy-

dependence we can state that the pre-shoulder in the XA spectrum is due to

ring structures (A); that the onset of absorption in the chains is located at the

main absorption band (B); from the emission spectrum corresponding to high

energy excitations (C) we estimate that the relative abundance of chains and

rings in liquid methanol is equal.

Details in the water-methanol interaction are revealed in the X-ray

emission spectra generated at excitation energies near threshold. The X-ray

emission spectra that are excited in this region (Figure 14.40) are significantly

different from the emission spectra of the pure liquids. The 0.8-eV linewidth

of the main peak is narrower than any X-ray emission feature of either liquid

phase: for water (1.0 eV), for methanol (1.9 eV). The main peak E

shifts

towards higher energy as the excitation energy is lowered from 532.5 eV to

531.5 eV and 530.6 eV. We also note that the spectrum excited at 530.6 eV

shows depletion of intensity in the region around 525 eV. One can conclude

that specific bonded structures involving water as well as methanol are

responsible for this spectral behavior.

652

14. Soft X-Ray Emission and Resonant Inelastic X-Ray Scattering Spectroscopy