Seminar - 4th year

Resonant X-ray Emission Spectroscopy

Author: Bor Marolt

Adviser: dr. Matjaž Kavčič

Co-Adviser: dr. Matjaž Žitnik

Ljubljana, November 2010

AbstractResonant x-ray emission spectroscopy is a powerful method for studying electronic structure of atoms, molecules, and solid materials. In this seminar the main characteristics of the RXES method and its advantages over other methods will be presented. The basic aspects of core level spectroscopies together with fundamentals of interaction of x-rays with matter are described leading to the Kramers-Heisenberg equation which governs the x-rays scattering. The experimental requirements for the RXES spectroscopy will be outlined and the high resolution RXES spectrometer of Jožef Stefan Institute will be presented in more details.

Table of Contents1 Introduction.......................................................................................................................................22 Core Level Spectroscopies................................................................................................................23 RXES.................................................................................................................................................4

3.1 Interaction of X-rays with Matter..............................................................................................53.1.1 Electromagnetic field.........................................................................................................53.1.2 Interaction Hamiltonian ....................................................................................................63.1.3 Golden Rule.......................................................................................................................6

3.2 The Kramers- Heisenberg Equation...........................................................................................73.3 RXES plane................................................................................................................................9

4 High Resolution X-ray Spectroscopy..............................................................................................104.1 Plane-Crystal Spectrometers....................................................................................................104.2 Focusing Crystal Diffraction Spectrometers............................................................................114.3 High resolution x-ray spectrometer of the J. Stefan Institute..................................................12

5 RXES experimental example..........................................................................................................146 Conclusion.......................................................................................................................................157 References.......................................................................................................................................15

1 IntroductionSynchrotron sources provide the intense beams of monochromatic x-rays in the keV energy range. With its wavelength on the 0.1 nm scale comparable to the size of atoms, x-rays offer a possibility to study the fundamental properties of atoms and molecules and characterize different materials on the atomic level [1]. The development of the new high-brilliant x-ray sources stimulated also the development of x-ray spectroscopic methods. Two basic x-ray spectroscopy methods used today at the synchrotron sources are the x-ray absorption and x-ray emission spectroscopy, respectively [1,2]. With the advent of the third generation high-brilliance synchrotron sources and new modern x-ray spectrometers with increased efficiency and resolution, a new spectroscopic technique has emerged. This is a resonant x-ray emission spectroscopy combining both standard techniques, absorption and emission [1]. Within this seminar some general basic aspects concerning resonant x-ray spectroscopy are discussed from the theoretical and experimental point of view.

2 Core Level SpectroscopiesWhen atoms condense into solids, the valence electron states (VES) are strongly affected depending on the atomic species and their arrangement in solids. The properties of solids are determined by the characteristic features of VES. Therefore the study of VES is the main object of solid state physics. On the other hand, core electrons of atoms are deeply bound inside atoms and are almost unchanged even when atoms condense into solids. In core level spectroscopy a core electron is excited by incident x-rays and the VES are detected with the core electron state (or core hole state, depends on whether we observe absorption or emission) as a probe. In order to excite core electrons, incident photons with energies larger than the core level binding energies are needed. These energies are in the x-ray range and go from 1 keV for K-hole excitation of Na up to several tens of keV for core excitation of heavier atoms. Recently, the development of core level spectroscopy has been remarkable, especially with high-brilliance third generation synchrotron radiation sources. There are various kinds of core level spectroscopies. Two of the most important are x-ray absorption spectroscopy (XAS) and x-ray emission spectroscopy (XES). This two methods are in a sense complementary, because XES provides the information about occupied valence states whereas XAS provides the information about unoccupied valence states.

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In Figure 1 these spectroscopic processes are shown schematically for a simple case, where the VES consists of a filled valence band and an empty conduction band. In Figure 2 this schematic representation is replaced by the measured data for three different sulphide samples.In the case of XAS, a core electron is excited near to the excitation threshold, which corresponds to the conduction band in this example, by the incident x-ray through the electric dipole transition (and sometimes the electric quadrupole transition in the hard x-ray region). XAS is a first-order optical process that includes only one photon, but XES is a second order process where a core electron is excited by the incident x-ray and the excited state of the system decays radiatively by emitting x-rays. When the core electron is excited by the incident x-ray to the high energy continuum (ionization), this is called normal XES (NXES), but when the core electron is excited near to the threshold – when the incident x-ray energy resonates with the excitation into the bound state below the threshold, it is called resonant XES (RXES). It is important to understand that as soon as core hole creation takes place, decay occurs. This implies that close to the XAS absorption edge, the decay processes will be different from the decay of excitations above the resonance. The follow-up of excitation and decay process implies that in case of resonant excitations one is studying the spectra (two dimensional spectral maps) which are functions of both the excitation and decay energies. RXES is a second order optical process, where the excitation and de-excitation amplitudes are coupled by the second-order quantum formula, the so called Kramers-Heisenberg formula. RXES can be applied equally to metals and insulators. It gives us bulk-sensitive, element-specific, and site-selective information. The intermediate state of RXES is the same as the final state of XAS,

but the information obtained is much more valuable since the occupied valence states are also involved in the emission process. However, the intensity of the RXES is much weaker than XAS, so

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Figure 2: S K-edge near edge absorption spectra and the Kβ (K-M) normal XES spectra for three different sulphur compounds. [8]

Figure 1: Schematic representation of XAS, NXES, RXES. [1]

that high-brilliance x-ray sources are required to obtain precise experimental data. The recent development of the RXES studying is due to the implementation of undulator radiation from third-generation synchrotron radiation sources as well as highly efficient detectors.

3 RXESIn RXES an excitation of a core electron to an unoccupied valence state and subsequent decay take place. Depending on the electronic levels participating in the electron transition leading to the x-ray emission, RXES can be divided into two categories. If the initial and final electronic states are the same than also, the incident and emitted x-ray energies are the same and this corresponds to the resonant elastic x-ray scattering. This can be described as a two step process, the energy left in the system by the incident and emitted photons in each step is given by:

0 XAS

Ew−E c XES

0 (1)

and the final energy transfer is equal to zero. This is schematically shown in the middle frame of

Figure 3 for a case of an oxide, where the energy of the O 1s core level measured from the Fermi energy is Ec=−530 eV , and the 2p states are split into a filled valence band with energy E v and an empty conduction band with energy Ew .If the initial and final state are not the same, the process is called resonant inelastic x-ray scattering (RIXS). This can be further divided into two subcategories. In the first subcategory the decay occurs from a valence state Ev after the excitation of a core electron to a higher valence state Ew . Similar as for the case of resonant elastic scattering the energy can be written as:

0 XAS

Ew−Ec XES

Ew−E v (2)

In this case the energy transfer is finite and it actually corresponds to the energy of elementary excitations of valence electrons. In other words, it measures all valenece band-conduction band excitations. The second subcategory of RIXS is the case where the radiative decay occurs from a higher core state with energy E c ' to a lower core state with energy E c :

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Figure 3: Schematic representation of the resonant elastic (middle) and resonant inelastic (bottom) x-ray scattering. [1]

0 XAS

Ew−E c XES

Ew−E c' (3)

In this case the energy transfer is much higher and we can no more measure the valence electrons elementary excitation. The main advantage of this particular case is the longer lifetime of the shallow core-hole in the final state (τ ~ several fs) compared with the intermediate core hole state (τ ~ fs). Since the width of the measured RXES spectrum depends only on the final state lifetime broadening this kind of RXES measurements can be applied to record absorption spectrum free from lifetime broadening provided that our esxperimental reolution is high enough (smaller than the width of the core hole intermediate state). In this case weak core electron excitations can be detected, which can not be resolved in conventional XAS experiment.

In Figure 4 experimental 2D RXES maps for the Na2MoO4 are shown. Excitation energy in the measurements was around the Mo 2p absorption edge. The left picture represents the case of the valence-core electron transition with energy transfer of only few eV, while the right picture corresponds to the core-core transition resulting in larger energy transfer but much narrower RXES spectra.

3.1 Interaction of X-rays with Matter

The RXES spectrum is described by the Kramers-Heisenberg equation [1, 4, 5]. In order to introduce the formula and discuss it in detail, we first need to discuss the the fundamentals of interaction of x-rays with matter. Generally x-rays are defined as electromagnetic radiation with wavelengths smaller than UV radiation. The border between UV radiation and x-rays is not clearly defined, but is usually set at around 10 nm. This defines the low-energy limit of ~ 100 eV .

3.1.1 Electromagnetic field

Classicaly, the electromagnetic field can be represented by a complete set of plane waves. First, consider a single plane wave propagating in the x direction. Its wavevector k is along x, its electric field E is along y, perpendicular to x and its magnetic field B is along z, perpendicular to x and y. The central object is the vector potential, which is given by:

A r ,t =A0 e y e i k x− tA0

* e y e−ik x−t , r=r x , y , z (4)

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Figure 4: RXES maps of valence-core (left) and core-core (right) transitions for the Na2MoO4

sample. Recorded at the ID26 beamline of the ESRF synchrotron with the J. Stefan high-resolution x-ray spectrometer. [10]

The electric field E r , t and the magnetic field B r ,t , are given in terms of the vector potential. After rewriting the exponentials as cosin functions, this gives:

E r , t =− ∂∂ t

A r , t =2i A0 e y cos k x− t ,

B r ,t =∇×Ar , t =2 i k A0 e z cos k x− t (5)

The transition to quantum mechanics implies the change of the classical vector potential to a quantum mechanical operator. We can write operator A r with the use of creation an annihilation operators [11]. A creation operator bk

+ increases the number of photons by one (with wavevector k and polarization λ). Similarly, an annihilation bk operator lowers the numbers of photons by one. The operator A r is now written as [11]:

A r =∑k

A0 e k bkeik rbk

+ e−ik r , (6)

where A0=ℏ /2k0 V , with k=c∣k∣ and the normalization volume V.

3.1.2 Interaction Hamiltonian

The overall Hamiltonian, describing the atomic electrons interacting with x-rays, can be written as:

H=H radiationH atomH interaction , (7)

Where the radiation field Hamiltonian and the Hamiltonian of atomic electrons are given with

H radiation=∑k

ℏknk 12 and H atom=∑

i

[p i

2

2mV r i]

(8)

Hatom consists of a kinetic term and the central potential, which contains the Coulumb interaction with the nucleus, repulsion between electrons, and the spin-orbit interaction, which is not described explicitly in the equation. The interaction Hamiltonian is treated as a small perturbation. The first-order perturbation terms of the interaction Hamiltonian are:

H int 1=em∑i

p i⋅A r ieℏ2m∑i

i⋅∇×A r i . (9)

The first term describes the electric field acting on the electron moments. The second term describes the magnetic field acting on the electron spin σ. In the second order of perturbation, a new type of term appears:

H int 2=e2

2m∑

i

A2r i . (10)

3.1.3 Golden Rule

The central role in the interaction of x-rays with matter is played by the Golden Rule. The Golden

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Rule states that the transition probability W between a system in its initial state Φ i and final state Φf

by absorbing the incident photon with energy ℏ is given by:

W fi=2ℏ∣⟨ f ∣T∣ i ⟩∣

2E f−E i−ℏ (11)

The initial and the final state wave functions i , f consist of an electron part and a photon part, but the two can be dealt with separately and thus in the following, we will not include the photon part explicitly in the discussion, since we are intereseted in the electron part [11]. The delta function takes care of the energy conservation. The squared matrix element gives the transition rate. The transition operator T is related to the interaction Hamiltonian with the Lippmann-Schwinger equation:

T=H intH int1

E i−Hi/ 2T . (12)

Γ is the lifetime broadening of an excited state and H is the Hamiltonian of the unperturbed system. The Lippmann-Schwinger equation is solved iteratively and in first order T 1=H int 1 , which describes one-photon transitions (x-ray absorbtion, x-ray emission). Two photon phenomena (x-ray scattering), are described with the transition operator in second order [1]:

T 2=H int 2H int 11

E i−Hi/2H int1 (13)

The first term in this equation describes the elastic scattering process, and the second term describes the absorption into an intermediate state and its subsequent decay into the final state.

3.2 The Kramers- Heisenberg Equation

RXES is a second order optical process, where the excitation and de-excitation processes are coherently correlated by the second order quantum formula - the so called Kramers-Heisenberg formula. Let us consider the RXES process, where an x-ray photon with energy ℏ (wavevector k1) and polarization λ1 is incident on a material and then an x-ray photon with energy ℏ(wavevector k2) and polarization λ2 is emitted as a result of the electron-photon interaction in the material. This is a two photon phenomena, therefore the transition operator T2 must be taken into account. The differential cross section of the photon scatering (with respect to the solid angle k2

and energy ℏ ) is expressed as [1]:

d2

dk2d ℏ

=Vc

W 12 , (14)

where the transition rate W12 is given by [1]:

(15)

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W 12=r 02 cV∑j

Egℏ−E j−ℏ

∣[ ⟨ j∣k1−k2∣g ⟩ e1e2

1m∑

i

⟨ j∣pk2⋅e2∣i ⟩ ⟨i∣p−k1⋅e1∣g ⟩

Ei−Eg−ℏ

⟨ j∣p k1⋅e1∣i ⟩ ⟨i∣p−k2⋅e2∣g ⟩Ei−Egℏ

]∣2

Here ∣g ⟩ , ∣i ⟩ , and ∣ j ⟩ are initial, intermediate, and final states of the material system, respectively, Eg, Ei, and Ej are their energies, e1 and e2 are polarization directions (unit vectors) of incident and emitted photons ( e1=ek 11

), and r0 is the classical radius of the electron. We define:

r0=e2

40 mc2 , pk =∑n

pn exp −i k rn , k=∑n

exp−i k r n (16)

The three terms in square brackets of W12 are shown in Figure 5.

The first term is the elastic scattering process, also called Thomson scattering. If we are not interested in this term we can make it negligible by selecting the right geometry . The angle between incident and emitted x-rays is fixed at 90° and the emission is observed in the direction of the incident polarization. Since the polarization of the emitted x-rays is then necessarily perpendicular to the polarization of the incident x-rays, the e1⋅e2 term will vanish. When the incident photon energy is close to the core excitation threshold, as in the case of RXES, the contribution of the second term becomes dominant. When the excitation energy is chosen so that

Ei−Eg−ℏ=0 , the second order perturbation breaks down, as written, because the denominator becomes zero. However, if we take into account that the intermediate state has a finite

lifetime i~ℏ i~1 fs becouse of the lifetime of a core hole, then the energy Ei is replaced by a

complex number Ei−i i

2 and the divergence is removed [1]. Removing unimportant factors in

Equation 15, we can describe the most essential part of the spectrum of RXES in the form

F ,=∑j∣∑

i

⟨ j∣T e∣i ⟩ ⟨ i∣T i∣g ⟩Egℏ−E iii /2∣

2

Egℏ−E j−ℏ (17)

where Ti and Te represent the radiative transitions by incident and emitted photons, respectively, and i represents the spectral broadening due to the core-hole lifetime in the intermediate state. If we

take into account the finite j lifetime of the final state (a core-hole in a higher core state) the delta function in F , is replaced by a Lorentzian [4]:

F ,=∑j∣∑

i

⟨ j∣T e∣i ⟩ ⟨ i∣T i∣g ⟩Egℏ−E iii /2∣

2 j /2

Eg−E jℏ−ℏ2 j

2/4

(18)

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Figure 5: Schematic representation of three scattering terms. [1]

3.3 RXES plane

In a typical RXES experiment we record with high energy resolution the x-ray emission spectrum corresponding to either valence-core or core-core electron transition while the excitation energy is scanned across the absorption edge of the corresponding element in the sample. The recorded intensity is proportional to F , given by the Kramers-Heisenberg equation and is thus plotted versus a two-dimensional grid with ℏ (excitation energy) on horizontal and ℏ (emitted energy) on vertical axis. Figure 6 represents such a RXES spectral plane for a model system with two resonant intermediate states. As indicated in the figure 6 (left) the lower intermediate state can decay into two different final states with different transition probabilities. The

energy transfer is defined as a difference between the excitation and emission energy, − . Within the RXES plane we can clearly distinguish two separate types of spectral contributions. The contributions along the diagonal lines correspond to resonant excitations into discrete (bound) intermediate states. As the energy of the intermediate state electron configuration increases along the excitation energy axis in the RXES plane the final state energy (energy transfer) decreases along the emission energy axis. The diagonal lines therefore correspond to the constant energy transfer characteristic for excitation into discrete intermediate sates. The emitted x-ray energy follows the change in the excitation energy, a typical (Raman-like) linear dispersion characteristic for the RXES process. As the excitation energy is raised above the ionization threshold another type of spectral contribution is observed following the horizontal line in the RXES plane. In this case the inner-shell electron is excited into a continuum and the photoelectron is emitted from the system. As a consequence the emitted x-ray spectrum does not depend any more on the excitation energy and we are reaching the region of normal (non-resonant) x-ray emission (NXES). It is useful to introduce several cuts within the 2D RXES plane. The most important are vertical and horizontal cuts, which can be realized experimentally in a straight forward way. A scan in the vertical direction means that the emission spectrum is recorded at fixed excitation energy. Along such scan the intermediate state is kept fixed while the final states are varied, so that different decay channels from the same intermediate sate are being observed. Such a scan shows all those final states that are reached via one particular resonance. Especially interesting is the horizontal cut. In this case the analyzer of the spectrometer is fixed to particular emission energy, usually on the top of the emission line, while the excitation energy is scanned across the ionization edge. Since in this case the energy difference between the intermediate and final state (or ) is kept constant, such scan shows all the resonances that decay with this particular energy ℏ . As seen from Equation (18) the broadening of the RXES spectrum at fixed excitation energy depends only on the broadening j of a shallow core hole in the final state which is usually much smaller than the broadening i due to a deeper core hole intermediate state, which determines the broadening of

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Figure 6: Model system with two resonant intermediate states (left) and RIXS plane (right) [5]

the XAS spectrum. As a consequence, a horizontal cut through the RXES plan enables us to probe the x-ray absorbtion near edge structure (XANES) with a resolution much higher than the natural width of the decay and thus provide the spectrum free from lifetime broadening. This can be used in the study of unknown compounds, because the local electronic configuration of the observed element is reflected in the near-edge region. The near-edge spectral features are sensitive to the oxidation state, site symmetry and other effects.

4 High Resolution X-ray SpectroscopyIn order to perform successfully RXES experiments, an intese source of tunable monochromatic x-ray radiation is required (resolution of the monochromator at the ID26 beamline of the ESRF

synchrotron in Grenoble is EE~1.45⋅10−4

). This is provided at the undulator beamlines of the

high-brilliance, third generation synchrotron sources. In addition, a high energy resolution as well as good efficiency is required also in the detection channel. While in x-ray spectroscopy solid state energy dispersive detectors in which electric signals are proportional to the incident photon energy are commonly used, the high-resolution x-ray spectroscopy employs wavelength dispersive spectrometers. In this case the x-rays are analyzed according to their wavelength using the Bragg diffraction on the crystal plane. In wavelength dispersive spectroscopy x-rays emitted from the target propagate to the analysator crystal in the spectrometer, where they scatter on the crystallographic planes and propagate onwards to the detector. Scattering is described by the Bragg's law, which states that rays incident on the crystal lattice will interfere constructively only if

2dsinB=n , (19)

where is the wavelength of the incident x-ray, d is the spacing between the planes in the atomic lattice, B is the angle between the incident ray and scattering planes, and n is the order of diffraction. For short wavelengths, x-rays can be detected in the so-called open or short-wave spectrometers. For longer wavelengths where signicificant transmission losses during the transmission through air are characteristic, the spectrometer is operated under vacuum. In this case one speaks about the so-called vacuum or long-wave spectrometers.

4.1 Plane-Crystal Spectrometers

The simplest example of a crystal spectrometer is when the analysator crystal is flat (Figure 7 right). The beam travels from the target through a slit (to define the angle) to the crystal, where it is reflected and than passes through another slit to the detector. X-rays that hit the detector have the energy determined by the Bragg's law. If the angle B is then varied, which will normally involve rotating the crystal through controllable angle and the detector by twice this amount, the detector will receive radiation over a range of energies and spectrum will be obtained. Beacuse only a small zone of the crystals always contributes to the diffraction process such spectrometers have low luminosity. An improvement of the plane crystal spectrometer can be made, by the use of position sensitive detectors, where measurements in the multi channel mode can be made, and thus the efficiency increased. The resolution of such a system is determined by the aperture of the slits and the quality of the crystal. At any one setting, a small range of angles will be available and any wavelength for which the appropriate Bragg angle lies within this range will be reflected and recorded. A further limit is imposed by the intrinsic resolution of the crystal. If the incident radiation were truly monoenergetic, the peak obtained in the spectrum would have a finite width determined by the effect of the crystal. This is known as the crystal rocking curve. If the crystal has too many impurities the experimental resolution will be effected, however high quality is usually

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guaranteed by the manufacturer, therefore the resolution is determined mostly by the aperture of the slits.

4.2 Focusing Crystal Diffraction Spectrometers

In order to obtain a high resolution in a plane crystal spectrometer, the slits must be as narrow as possible. Narrower slits means less intensity on the detector. To obtain increased intensity in a crystal spectrometer a focusing arrangament using a crystal with its surface bent into an arc of a circle is devised. This has been applied to different geometries where the focusing can take place within the diffraction plane (Johann and Johansson geometries), or in the plane perpendicular to the diffraction plane (Von Hamos geometry).

Johann GeometryIf a flat crystal is simply bent to a radius ON, as seen in Figure 8 (a), where source of x-rays lies in point P, and the detector in point Q, it is clear that this will not be satisfactory, because, although the angles PNQ and PMQ are the same, the reflecting planes at M are not perpendicular to the bisector MO' of PMQ, so Bragg reflection will not take place. The required radius of the lattice planes is NO' (radius R ~ 1 m), therefore the most straight forward solution is to simply bent a flat crystal to a radius R. However it is seen from Figure 8 (b), that this focussing is not exact, but it is sufficient for many uses if the operation is restricted to small crystal apertures.

Johansson GeometryAn improvement of the Johann geometry system can be made by bending a flat crystal to radius R as before and then grinding the crystal so that the ground surface assumes radius R/2, and the lattices assume radius R. This arrangement provides exact point to point focusing and is seen in Figure 8 (c). The circle with radius R/2 is called the Rowland circle. By altering the position of the source P on the Rowland circle, different wavelengths can be brought to a focus at the symmetrical

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Figure 7: Scattering on crystal planes (left) [9]; Spectrometer with a flat crystal (right)

Figure 8:Bragg reflection can not take place if the crystal is simply bent to a radius of a circle (a), the crystals in Johann geometry (b) and Johansson geometry (c) enable point to point focusing. Target moved to the interior of the Rowland circle in order to record a finite spectrum (d) [2]

position of Q, and a spectrum is obtained. The geometry described is called Johansson geometry. Spectrometers utilizing Johann and Johansson geometry focus a small point-like source on the Rowland circle to a point image on the Rowland circle (point to point focusing), which implies the use of a detector operating in single channel mode. However it is often useful to move the source point P (the target of interest in the experiment) to the interior of the Rowland circle. The corresponding point Q still lies on the Rowland circle, however, now the Bragg condition holds for all points between P and P' (Figure 8 d), which are focused to points between Q and Q'. In this case the implementation of position sensitive detector is useful, because this way a finite spectrum can be taken without moving the source and the detecor.

Von Hamos GeometryIn the von Hamos Scheme, a crystal is bent into a cylindrical surface. The x-ray source and the detector plane lie on the cylinder axis (Figure 9). The crystall diffracts x-rays with different

wavelengths according to the Bragg law. Each wavelength, after diffraction from the crystal arc is focused to a point lying on the spectrometer axis.The width of the spectral band depends on the length of the crystal in the dispersion direction. For a long crystal, the wavelength band can be wide. Each wavelength in this band is focused to a unique spot on the axis of the crystal – hence, high efficiency. Because all the wavelengths within the band satisfy the bragg law simultaneously, the entire spectrum lies on the axis of the system. The use of position sensitive detector enables the recording of this spectrum without moving the source or the detector. The resolution of the Von Hamos spectrometer is defined only by the size of the photon source, which is smiliar to the simple case of flat crystal spectrometer.

4.3 High resolution x-ray spectrometer of the J. Stefan Institute

Within this chapter the high resolution spectrometer designed and built witihn the mircroanalytical center at the J. Stefan Institute will be presented. The spectrometer employs a cylindrical bent crystal in the Johanssongeometry with the Rowland radius of 50 cm. The mechanical /2 stagecovers the 30°-65° angular range. Within this range of Bragg angles that can be reached mechanically within the spectrometer the x-ray energy range of 0.5-6.5 keV is covered by using different crystals for the diffraction of analyzed x-rays (See the table in Figure 10). In order to simultaneously collect certain range of emission energies at fixed crystal detector position the sample is positioned within the Rowland circle. The x-rays diffracted by the analyzing crystal are

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Figure 9: Spectrometer in the Von Hamos geometry. [3]

Figure 10: The table describing the crystals that are used in the spectrometer with the photo of one of the crystals. [10]

detected by a two dimensional position sensitive x-ray detector, a back illuminated CCD camera. The detector chip consists of 770×1152 pixles with the pixel size of 22.5×22.5 m2 . In order to reduce the thermal noise the camera is cooled by a four stage Peltier cooler. A typical temperature is -40˚ C. After a short exposition to the diffracted x-rays the charge accumulated in the pixels is read at the 1 MHz reading frequency. The signal from the on-chip amplifier signal is than digitized by the 16 bit AD converter. The diffracted x-rays form a 2D image (diffraction pattern) on the CCD. The final x-ray spectrum is produced by projecting the image on the horizontal axis representing the dispersion axis. The vertical dimension of the CCD therefore serves mainly to increase the collection efficiency. Figure 11 presents the CCD image measured after photoexcitation of the sulfur target with the 2.5 keV photons. The intense double stripe in the middle of the image corresponds to the Kα1,2 (K-L2,3) spectral line of sulfur. The final energy resolution is ~ 0.3 – 0.4 eV being below the natural linewidth of the measured spectral line. As a consequence of such high resolution the spectrum exhibits almost pure Lorentzian natural shape. The whole spectrometer is enclosed within the 1.6×1.3×0.3 m3 stainless steel vacuum chamber equipped with its own

pumping system (turbo molecular pump, 1200 l/s) in order to reach the working pressure 10-6 mbar. Such a high vacuum is needed to operate the CCD detector at low temperatures. At the same time the chamber of the spectrometer can be installed directly to the beamline of a scynchrotron or another kind of particle accelerator. Direct installation to the beamline without any additional windows to separate the spectrometer chamber from the spectrometer enables efficient measurements of low energy x-rays which are otherwise heavily absorbed in window foils or even air.

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Figure 11: The 2D x-ray image on the CCD camera corresponding to the Kα1,2 photons of the photoexcited S target. The final spectrum is obtained by projection on the dispersion axis. [10]

Figure 12: The vacuum chamber of the IJS spectrometer (left). The view inside the spectrometer chamber installed at the ID26 beamline of the ESRF synchrotron. [10]

5 RXES experimental exampleIn order to perform RXES measurements the spectrometer is installed at the ID26 undulator beamline of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The beamline is equipped with a double Si(111) crystal monochromator with a theoretical resolution ofE/E~1.45×10−4 (0.44 eV at 3 keV). The beamline provides us with the high photon flux on

the target in the order of 1012 photons /s . The most important characteristics for the RXES experimental set-up is the overall energy resolution incorporating resolutions in both channels, excitation and emission. This resolution can be determined observing the FWHM of the peak corresponding to the elastic scattering. In Figure 13 the measured signal of the incoming beam at

4720 eV energy scattered elastically on the Xe atoms can be seen. The 1.0 eV width corresponds to the experimental resolution of the RXES setup and is determined by the resolution of the beam and the spectrometer. The two contributions are usually nearly equal, since high resolution in one channel is pointless if the resolution in the other channel is low. RXES measurements for the Na2MoO4 sample around the Mo L3 absorption edge ere performed with the high resolution x-ray spectrometer of the Microanalytical Center (J. Stefan Institute). At this energy the overall resolution of the set-up was ~ 0.6 eV being significantly below the L3 lifetime width, whereas the XAS spectrum of the same absorption edge is smeared out by the Mo L3 lifetime width which is close to 2 eV. The spectrometer was tuned to the Lα1,2 x-ray line corresponding to the L3 – M4,5 core-core

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Figure 14: The Mo L2,3 RXES spectrum around the L3 absorption edge measured for the Na2MoO4

compound (left). Projection on the horizontal axis - XAS (right, black), horizontal cut through the RXES (right, red)

Figure 13: The signal of the incoming beam at 4720 eV scattered elastically on the Xe atoms. [10]

electron transition. The width of the final state determining the theoretical width of the RXES spectrum is around 0.1 eV being practically negligible in comparison with the L3 lifetime width as well as the experimental resolution. The measured RXES plane is presented in the left part of Figure 14 exhibiting nicely the crystal field splitting. If the measured signal is projected on the horizontal axis we reproduce the regular XAS spectrum (Figure 14 right, black line). However if we make a horizontal cut of the RXES plane at the 2293 eV emission energy corresponding to the maximum signal (top of the Lα1 line) the lifetime broadening is removed from the spectrum (red line in Figure 17 right). RXES measurements therefore overcome the intrinsic lifetime broadening limitation and as a consequence enhance drastically the sensitivity to the local coordination of the neighboring atoms.

6 ConclusionRXES provides us with information about both, the x-ray absorption and emission. Its main advantage over XAS is the narrowing effect, which bypasses the broadening of the fast decaying intermediate core-hole state. The development of RXES was made possible by the third generation high-brilliance synchrotrons and new high-resolution spectrometers, relying on focusing of bent analysator crystals in different geometries. RXES can be used in the study of unknown compounds, because the local electronic configuration of the observed element is reflected in the near-edge region. The near-edge spectral features are sensitive to the oxidation state, site symmetry and other effects. It is expected that this method will be used much more in the future to study electronic structure of various materials in the near-edge region of the RXES spectrum.

7 References[1] Frank de Groot, Akio Kotani, Core Level Spectroscopy of Solids, CRC Press, 2008

[2] N. A. Dyson, X-rays in Atomic and Nuclear Physics, Second edition, Cambridge University Press, 1990

[3] Günter Zschornack, Handbook of X-ray Data, Springer-Verlag Berlin Heidelberg, 2007

[4] Pieter Glatzel, Uwe Bergmann, High resolution 1s core hole X-ray spectroscopy in 3d transition metal complexes-electronic and structural information, Coordination Chemistry Reviews, Elsevier B.V., 2004

[5] P. Glatzel, M. Sikora, M. Fernandez-Garcia, Resonant X-ray spectroscopy to study K absorption pre-edges in 3d transition metal compounds, The European Physical Journal, Springer-Verlag, 2009

[6] A. Shevelko, A. Antonov, I Grigorieva, Yu. Kasyanov, O. Yakushev, X-ray Focusing Crystal Von Hamos Spectrometer With a CCD Linear Array as a Detector, Advances in X-ray analysis, International Centre for Diffraction Data, 2002

[7] E. J. Lede, F. G. Requejo, B Pawelec, and J. L. Fierro, XANES Mo L-Edges and XPS Study of Mo Loaded in HY Zeolite, Journal of Physical Chemistry B, 2002

[8] R. Alonso Mori, E. Paris, G. Giuli, S. G. Eeckhout, M. Kavčič, M. Žitnik, K. Bučar, L. G. M. Pettersson, and P. Glatzel, Sulfur-Metal Orbital Hybridization in Sulfur-Bearing Compounds Studied by X-ray Emssion Spectroscopy

[9] http://www.farmfak.uu.se/farm/farmfyskem-web/instrumentation/saxs.shtml, October 2010

[10] http://www.rcp.ijs.si/mic/our_work/hrxrs.php, October 2010

[11] J. J. Sakurai, Advanced Quantum Mechanics, Addison-Wesley publishing company, 1967

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