Introduction to X-ray Spectroscopy. Pieter Glatzel

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2 Introduction to X-ray Spectroscopy Pieter Glatzel

3 Books J. J. Sakurai: Advanced Quantum Mechanics Addison Wesley, 1967 G. Bunker: Introduction to XAFS Cambridge Press, 2010 F.M.F. de Groot and A. Kotani: Core level spectroscopy of solids Taylor and Francis, 2008 W. Schülke: Electron Dynamics by Inelastic X-ray Scattering Oxford University Press, 2007 Michel van Veenendaal: Theory of Inelastic Scattering and Absorption of X-rays Cambridge University Press, 2015

4 Reminder: The photon E h hc 0 1 ev 5 ev 100 ev 1000 ev ev Energy p k, k 2 Linear momentum 4

5 Photon intrinsic angular momentum 5 Wikipedia

6 Spectroscopy The response of the system that is probed by photons depends on the photon energy. Infrared Raman UV-Vis VUV Soft X-ray Hard X-ray 0 1 ev 5 ev 100 ev 1000 ev ev Energy Vibration Valence shell Core levels 6

7 What may happen in the sample? A simplified view: An electron is excited to an unoccupied orbital. h E F 3d 2p 1s A single electron energy diagram is simple and qualitative.

8 Why X-ray Spectroscopy Electronic and atomic structural information XAS XES Element specific Bulk sensitive; compatible with in-situ and extreme conditions

9 Soft and hard X-rays to study electronic structure Ideal for electronic structure studies Ideal for in situ studies Soft X-Rays Improve in situ conditions Hard X-Rays Develop new techniques to study electronic structures Tender X-rays

10 L- and K-edges in 3d transition metals Soft X-rays Hard X-rays 2p 3d 1s np 10 Gilbert et al., J. Phys. Chem. A, Vol. 107, No. 16, 2003

11 Why X-ray spectroscopy? Spectroscopy does not require long range order. Ideal tool for e.g. catalysis, environmental sciences, biology, Identify Cr(V) 11 J. Bagar et al., SSRL

12 Electromagnetic radiation A A ˆ e 0 i kr t

13 Interaction of X-rays with matter, k, ˆ in in ( in ) (,, ˆ out k out out) q q q: scattering angle k in -k out =q (momentum transfer) in - out (energy transfer) Describe photon with vector field: A Perturbation Theory In first order, a term in A 2 is retained. In second order, a term in A p is retained.

14 Perturbation Theory: Two scattering terms (,, ˆ out k out out) A 2 n (, k, in in in) p A ˆ

15 The A 2 term and the dynamic structure factor (,, ˆ out k out out) Thomson scattering: in = out, k, ˆ in in ( in ) q Bragg scattering: Raman scattering: in = out out < in Compton Scattering: out < in F(, in out ) out in 2 * in out f Oˆ g f E f E g in out with Oˆ iq r i e ; q i k in k out Dynamic Structure Factor

16 THE RESONANT SCATTERING TERM: XES, RXES, RIXS, RXRS, HERFD

17 Perturbation Theory: Two scattering terms (,, ˆ out k out out) A 2 n (, k, in in in) p A ˆ

18 The A p term Kramers and Heisenberg F KH (, in out ) out in f n E n f Oˆ E g n n O g ˆ in i n 2 E f E g in out, k, ˆ in in ( in ) (,, ˆ out k out out) q ik rj O ˆ p je j ˆ r ( ˆ r )( k r)... (resonant) X-ray emission (RXES, RIXS, fluorescence, XAS)

19 Total Energy Transition schemes 1s 1 3d n p E F 3d 3d 3p 2p nkb rkb 1s 1 3d n+1 Kb 3p 5 3d n p 3p 5 3d n+1 1s 1s 2 3d n One-electron diagram Many body diagram

20 Energy scheme and spectroscopy Total Energy E total Hˆ n> 1s 1 3d 5 (p) 1 1s 1 3d 6 Ka <n Ô g> 2 Kb 2p 5 3d 5 (p) 1 2p 5 3d 6 in out L-edge 3p 5 3d 5 (p) 1 3p 5 3d 6 g> M-edge UV-Vis Valence-to-core 3d 6 MO n-1 Fe III [Ar 3d 5 ]

21 Photon-in/photon out spectroscopy ( ) I E i 2 E i, I 1 E i, I 0 ( E i ) ln I I 0 1 Sample E e, I 2 Single crystal monochromator Fluorescence

22 Photon-in/photon-out spectroscopy ( ) I E i 2 E i, I 1 E i, I 0 ( E i ) ln I I 0 1 Sample E e, I 2 Single crystal monochromator Fluorescence Analyzer crystal X-ray Emission

23 ,, ˆ ) (, k, ˆ in in in) ( out kout out ESRF ID26

24 What can inner-shell spectroscopy do? Inner-shell spectroscopy probes electronic transitions and thus the electron density or electron configuration. This may tell you about: The chemical environment o bond distances o bond angles o type and number of ligands The spin-orbit term of the ground state: The measured spectrum represents excited states that are linked to the ground state via the transition matrix element. The transition probability depends on the ground state symmetry, e.g. the spin state, formal oxidation state 2S+1 L DS=0 DL=0;±1 1 P n> 1 S g>

25 What is oxidation state: Atoms and electron density 2 r(r) and MO in a Ni complex When measuring oxidation state we often ask what is the charge per atom? Is that the right question to ask?

26 The idea of an atom Wikipedia: Noumenon: An object knowable by the mind or intellect, not by the senses; a noumenon in the sense of Kant. an experimentalist has no doubt that he or she is measuring the properties of a single atom

27 Orbital relaxation The potential experienced by all electrons changes after photoexcitation. All electrons will adjust after excitation with X-rays: Always consider ALL electrons when describing the energy levels.

28 Two-electron excitation Valence Orbital Empty Orbital The orbitals may adjust non-adiabatically, i.e. electrons are excited to higher orbitals upon orbital relaxation (additionally to the electron that is photo-excited).

29 The inner-shell absorption proces Energy n 1s 1 3d 6 4p 1 T abs n O g Approximate multielectron effects by scaling factor S S0 a O c 2 r l 1s 4p h Many-electron wavefunction One-electron wavefunction g 3d 6

30 Electronic structure calculations and inner-shell spectroscopy Ligand field multiplet theory Electron density calculations Start with ion in spherical symmetry Start with structure 1 (r 1 ) 1 ( r 2 ) 1 (r N ) 1 2 ( r ) 1 N! N ( r 1) N ( r N ) Branch to real symmetry (e.g. to O h ) Include covalency using configuration interaction (CI) empirical approximative Include core hole Include multi-electron excitations Good treatment of core hole effect and multi-electron excitation Good treatment of ligands/long range order

31 Multi-electron excitations Experiment: Ce L 3 (2p 3/2 ) edge Single impurity Anderson model One-electron calculation Multi-electron excitation ~f 1 ~f 0 Multi-electron excitations Empirical crystal field splitting No multi-electron excitations Correct crystal field splitting

32 EXPERIMENTAL ARTEFACTS

33 Secondary process detection The goal is to determine (E) by recording the intensity of the scattered X-rays I XES I 0 K ( E) sin 1 e A A d t t A t t ( E) t ( EF ) sin sin K J f 4 fs cs ds ls J f fs cs ds ls jumping ratio PE of shell of interest fluorescence yield per shell fractional yield per subshell fraction of line measured with spectrometer crystal efficiency detector efficiency losses due to absorption (windows, beam path in air)

34 Selective fluorescence detection in CoFe 2 O 4 The total absorption appears in the denominator I XES I 0 K ( E) 1 e sin A A d t t Total fluorescence yield Fe fluorescence yield

35 TFY and HERFD on CoFe 2 O 4 Experiment Total fluorescence yield Fe fluorescence yield after edge before edge Calculation using tabulated values J. Synchrotron Rad. (2012). 19,

36 Incident Beam Self Absorption Incident Beam Self Absorption compresses the intensity of a spectrum Incident beam self absorption (IBSA) arises from a similar mechanism as the dip seen in the previous slides but for the same element. 36

37 RADIATION DAMAGE

38 Photosynthesis If a leaf can do it, we can do it too! Lubitz and Messinger, Energy and Environmental Science, 2008

39 The Sample Spinacia oleracea

40 Photosystem II Multi-protein complex Photosystem-II

41 Damage of the Mn cluster Incident Energy [ev]

42 Dealing with radiation sensitive samples on ID26 Spectral change at fixed energy as function of time. beam size: 700 x 100 m; ~2*10 13 photons/second Page 42

43 Dealing with radiation sensitive samples Each energy point measured in different position of beam on sample. Take map of metal fluorescence response. Page 43 l Title of Presentation l Date of Presentation l Author

44 Detect and Destroy at a free electron laser Science 316, (2007); Nature 406, (2000)

45 PSII and the free electron Laser Kern et al. Science 340 (2012) 491

46 Kern et al. Science 340 (2012) 491 XFEL provides correct Kb spectra VS 3p 2p 1s

47 THE ENERGY LEVELS OF LOCALIZED ORBITALS

48 3d orbitals in a crystal field atomic e g t 2g 10Dq Oh 48

49 Octahedral and tetrahedral coordination 49 UC Davis

50 3d orbitals in a crystal field UC Davis 50

51 MULTIPLET THEORY

52 An open shell 3d orbitals E t = E rest + E 3d E t =E rest +? How can we treat open shells? MULTIPLET THEORY

53 Treating electron-electron interactions two-electron operator: N i 1 g ij g( r i, r j ) i 2 j1 i j Matrix element for two-electron operator: ij g ij ij g ji i> j i> j g ij "direct term" > 0 "exchange term" > 0 Slater integrals or Racah parameters

54 An open shell: 3d 2 L L l 1 L Angular momentum coupling l l l 1 l 1 2 l l 1 l (Total Angular Momentum) 2 (for d-electrons) (S,P,D,F,G) d 2 Notation: 2S+1 L 1 S 1 G 3 P 1 D 3 F The Racah parameters determine the magnitude of the splitting.

55 Crystal Field Splitting: Tanabe-Sugano diagram Atom O h coordination 3d d 2 t 2g e g Additional splitting due to orbital hybridization (ligand field theory) The spectra become very very complex already for d 2

56 Inner-shell spectra are often very complex Intra-valence shell electron-electron interactions Core hole valence electron interactions 3d 5 Multi-electron excitations 2p 5 56

57 RESONANT INELASTIC X-RAY SCATTERING: RIXS, HERFD

58 Hard X-ray Photon-in/Photon-out spectroscopy I 2 ~ (E i ) CeO 2 L 3 -edge E i, I 1 E i, I 0 ( E i ) ln I I 0 1 Sample E e, I 2 Single crystal monochromator Incident Energy (E i ) [ev] 5d 4f 3d 5d 4f 3d Second order process E i E e 2p 2p Correctly treated with Kramers-Heisenberg equation

59 Hard X-ray Photon-in/Photon-out spectroscopy I 2 ~ (E i ) XAS E i, I 1 E i, I 0 ( E i ) ln I I 0 1 Sample E e, I 2 Single crystal monochromator Incident Energy (E i ) [ev] Analyzer crystal 5d 4f 3d 5d 4f 3d XES E i E e 2p 2p Energy Transfer (E i -E e ) [ev]

60 Hard X-ray Photon-in/Photon-out spectroscopy I 2 ~ (E i ) XAS E i, I 1 E i, I 0 ( E i ) ln I I 0 1 Sample E e, I 2 Single crystal monochromator Incident Energy (E i ) [ev] Analyzer crystal Energy Transfer (E i -E e ) [ev]

61 High resolution XANES CeO 2 XAS Conventional TFY TFY HERFD

62 High resolution XANES CeO 2 XAS Fine structure of 5d band 5d Conventional TFY High resolution (HERFD-XAS) 4f Resolve fine structure in 5d band (crystal field splitting) Resolve 4f orbitals

63 3d hole 2p3d (La) RIXS plane in CeO 2 The 3d and 2p core hole potentials are similar. Weak interaction of core hole with photoexcited electron z 3d Spectral features appear along diagonal streak. 2p 3/2 hole Hämäläinen et al., Phys. Rev. Lett (1991) Carra et al. PRL (1995) Glatzel et al., J. Electr. Spectr. Relat. Phenomena 188 (2013) Kotani et al., J. Electr. Spectr. Relat. Phenomena 184 (2011)

64 Direct study of the valence shell Ce 2p 4f excitations Kvashnina et al., JAAS (2011)

65 Total Energy Lifetime broadening and continuum excitations Intermediate (absorption) State 2 p 2 p Emitted Energy XES Incident Energy XAS 3d 3d Energy transfer Final State Ground State

66 Energy Transfer Total Energy The RIXS plane Energy transfer Incident Energy

67 Energy Transfer Energy Transfer The RIXS/RXES plane n f f n Incident Energy

68 Simplifying the Kramers-Heisenberg Formula F KH (, in out ) out in f n E n f Oˆ E g n n O g ˆ in i n 2 E f E g in out Interference changes intensities but not energies. n>, E n in out f>, E f g>, E g Ignore Interference and simplify: Does the scattered photon forget? F KH (, in out ) out in f n f ( E n Oˆ E g n 2 n Oˆ g ) in n E f E g in out

69 Simplifying the Kramers-Heisenberg Formula F KH (, in out ) out in f n E n f Oˆ E g n n O g ˆ in i n 2 E f E g in out Interference changes intensities but not energies. n>, E n f>, E f g>, E g Ignore Interference and simplify: XES XAS F KH (, in out ) out in f n f ( E n Oˆ E g n 2 n Oˆ g ) in n E f E g in out

70 Total Energy Total Energy Atomic multiplet model calculations for 4f 0 No 3d 4f interaction With 3d 4f interaction 4f 0 2p 5 4f 1 2p 5 4f 1 3d 9 4f 1 3d 9 4f 1 4f 0 4f 0

71 Total Energy Total Energy Atomic multiplet model calculations for 4f 1 No 3d 4f interaction With 3d 4f interaction 4f 1 2p 5 4f 2 2p 5 4f 2 3d9 4f 2 3d 9 4f 2 4f 1 4f 1 Kvashnina et al., JAAS (2011)

72 Total Energy Total Energy Atomic multiplet model calculations for 4f 1 No 3d 4f interaction Interference With 3d 4f interaction No Interference 4f 1 2p 5 4f 2 2p 5 4f 2 3d9 4f 2 3d 9 4f 2 4f 1 4f 1 Kvashnina et al., JAAS (2011)

73 Comparison with Experiment Experiment 4f 0 4f 1 Theory Interference No Interference Kvashnina et al., JAAS (2011)

74 A little history of Ceria The Relevance of Ceria The Spectroscopy on Ceria The Theory applied to Ceria The Confusion around Ceria The Defects in Ceria

75 The Relevance of CeO 2 CeO 2 CeO 2- + /2 O 2 PNAS 2006;103: Labeling of cancerous cells Solid oxide fuel cell

76 Have we understood bulk CeO 2?

77 Atomic Structure of Ceria CeO 2 Formally: Ce IV 4f 0 Cubic One Ce site

78 Bulk Ceria during the 80 s f 0 Ce 4f and O 2p mix 4f levels are populated in ground state n 4f ~ 0.5 Homogeneous mixed valence

79 Bulk Ceria during the 80 s 3d XPS Homogeneous mixed valence 2p 3/2 XAS 4f 0 Fujimori, PRB (1983) Bianconi et al., PRB (1987)

80 Bulk Ceria during the 80 s Wuilloud et al. PRL (1984) «a mixed valence can be definitely excluded» 4f 0 Nakano et al. JPSJ (1987) «The number of 4f electrons is between 0.36 and 0.54 «Homogeneous mixed valence 4f 0

81 Bulk Ceria in the 21 st century RIXS: Sham et al. Phys Rev B 72, (2005): CeO 2 in the initial state is Ce 4+ (4f 0 )... Hybrid DFT: Graciani et al. J. Chem. Theory and Comp (2011) All valence Ce states, including the 4f states, are empty 4f 0 Almost all publications presenting DFT calculations Bond Valence Method: Shoko et al. Phys Rev B 79, (2009): we conclude that CeO 2 is a mixed-valent compound... RIXS: Kvashnina, Kotani, Butorin, Glatzel J. Electr. Spectr. Relat. Phenomena 184 (2011) f 0 Sadly, very little new insight over the past 30 years.

82 Can we determine the charge per atom? Cococcioni et al. (PRB (2005)) : there is no unique or rigorous way to define occupation of localized atomic levels in a multiatom system Ce d-dos Ce f-dos O p-dos

83 The Single Impurity Anderson Model Ground State Gunnarsson and Schönhammer, PRB (1983) photoexcitation Excited State Metal ion + e - Ligand Metal ion + e - e - Ligand e b Non-screened e a screened g b cos b 4 f 0 sin b 4 f 1 L

84 Multi-electron excitations in CeO 2 ~f 1 L Total fluorescence yield ~f 0 High resolution XAS One-electron calculations

85 Surface reduction observed using TEM-EELS Turner et al., Nanoscale (2011)

86 CeO2 on Pt (111) under vacuum with L. Amidani, F. Pagliuca, F. Boscherini

87 In-situ study of CeO 2 nanoparticle synthesis 10 mm ACS Nano, 2013, 7 (12), pp

88 IN-SITU STUDY OF CEO 2 NANOPARTICLE SYNTHESIS Intensity/a.u Ce(NO 3 ) 3.6H 2 O Weight franction Intensity/a.u Pre-edge 2p 4f Ce 4+ CeO 2 NP Ce(NO Ce 3+ 3 ) Reaction Energy time/h /ev CeO 2 Reaction time/hr ACS Nano, 2013, 7 (12), pp Energy /ev 60 seconds one scan

89 Normalized intensity (a.u.) BLURRING OF 5D BAND STRUCTURE 5d band NPs 25 nm NPs belt NPs 15 nm NPs 10 nm NPs 3.2 nm 3 nm Incident energy (kev) Paun et al., J. Phys. Chem. C 2012, 116,

90 SPIN MULTIPLICITY AND ORBITAL MOMENT CeO 2 CeO 2- Ce ion Ligand Ce ion Ligand e - e - g b cos b 4 f 0 sin b 4 f 1 L g b 4 f 1 1 S 2S+1 L 2 F

91 DIRECT STUDY OF THE VALENCE SHELL Kvashnina et al., JAAS (2011) 2 F 1 S

92 Normalized intensity (a.u.) THE CE 4F LEVEL IN NANOPARTICLES NPs 25 nm 1 S NPs belt NPs 15 nm NPs 10 nm NPs 3.2 nm Ce(NO 3 ) 3 2 F Incident energy (kev) No Ce 2 F in nanoparticles Are they chemically active?

93 CHEMICAL ACTIVITY: ADDING H 2 O 2 Balancing ROS levels Celardo et al., Nanoscale (2011)

94 CHEMICAL ACTIVITY: ADDING H 2 O f 1 L f f-occupancy 4f-occupancy Time/hrs Time/ hrs 3nm, 25 nm Intensity/a.u H 2 O 2 25nm CeO 2 3nm CeO CeO 2 NPs (3nm) Energy/eV 4.5 ph CeO 2 NPs (3nm) + H 2 O Days Reduction

95 IS THERE ANY CE 3+ 2 F? 2p 4f nm CeO f-occupancy f-occupancy nm, 25 nm Intensity/a.u Time/hrs Time/ hrs 3nm CeO Energy/eV Consistent with initial increase of electron density on Ce and subsequent oxidation ACS Nano, 2013, 7 (12), pp Electron Sponge No observation of Ce 3+ 2 F

96 Total Energy Core-to-core RIXS Intermediate (absorption) State Emitted Energy XES Incident Energy XAS Final State Energy transfer ~900 ev Ground State

97 Total Energy Core-to-valence RIXS Intermediate (absorption) State No core hole in the final state! Incident Energy XAS Emitted Energy XES Ground State ~1 ev Final State

98 Photon-in/photon-out spectroscopic techniques Non-resonant Resonant E F 3d L, (3d) 3p 2p Kb vtc rkb rvtc 1s

99 Titanium in Silicalite TS-1 TS-1 NH 3

100 DFT calculations Exp. Theory 1 2 NH 3 ChemPhysChem 14, (2013)

101 DFT and vtc XES Ti silicalite Use Kohn-Sham orbitals: MO ˆ r 1s MO VB E. Gallo and P. Glatzel, Advanced Materials (2014)

102 Application of RIXS: Combine with magnetic circular dichroism

103 3d TM X-ray Magnetic Circular Dichroism L-edge MCD is a great success because of sum rules to determine spin and orbital angular moments. In situ experiments at the L-edge very challenging or impossible. Hard X-rays at the K-edge probe the p-dos very weak MCD effect K-edge MCD difficult to interpret (no spin-orbit split edge) Compatible with in situ experiments

104 Magnetic circular dichroism Energy B n Dm 1 Dm 1 Different final states are reached following the selection rules. B g Derive sum rules using ligand field multiplet theory. XMCD arises from removing the degeneracy with respect to the magnetic quantum number m by more than kt and macroscopically orienting the moments.

105 The RIXS-MCD Energy Scheme Magnetite (Fe 3+ ) tetra (Fe 3+ ) octa (Fe 2+ ) octa O 4

106 RIXS-MCD Experimental Setup

107 The first RIXS-MCD plane Experiment Theory M. Sikora, A. Juhin, et al. PRL 105, (2010)

108 Constant emission energy scans Sharpening of spectral features (decreased lifetime broadening) XMCD enhanced by factor of ~10-20 CEE

109 APPLICATION OF RIXS-MCD Mn MCD signal! Direct evidence for the existence of an intermediate interdiffused layer A. Juhin, A. Lopez Ortega, M. Sikora,, J. Nogues, under review

110 Kb X-RAY EMISSION SPECTROSCOPY (XES)

111 The K fluorescence lines in 3d transition metals Kb VS 3p x 500 2p x 8 1s

112 The exchange interaction For 3d transition metals the strong chemical sensitivity of core levels does NOT arise from screening! VS 3p E total Fluorescence Exchange energy lowers total energy Acts only between electrons with parallel spins and lowers the total Energy Mn 4+ Mn 3+ Chemically sensitive!!

113 Chemical sensitivity of Kb Emission MnF 4 : S=3/2 Screening effect very small (unlike Sulfur!!). (3p,3d) interactions are dominating. Kb 1,3 MnF 3 : S=2 Kb MnF 2 : S=5/2 Wang et al. Phys. Rev. B 56, 4553 (1997)

114 Model systems and multiplet theory Experiment LS Fe 2 O 3 S=5/2 K 3 Fe(CN) 6 S=1/2 K 4 Fe(CN) 6 S=0 HS Crystal field multiplet model

115 Mn-Mg pairs in GaN Th. Devillers, M. Rovezzi, et al. Scientific Reports (2012)

116 Mn-Mg pairs in GaN Kb Th. Devillers, M. Rovezzi, et al. Scientific Reports (2012)

117 XAS and XES in a layered Mn perovskite The La 1-x Sr 1+x MnO 4 series: doping dependence in powders x XANES Kb (Mn 3+ ) (Mn 4+ ) Absorption Energy [ev] Emission Energy [ev] Replace La 3+ by Sr 2+ Formally: Mn 3+ Mn 3.5+

118 Linear Dichroism in XES E i, I 1 Sample E i, I 0 Single crystal monochromator e E e, I 2 E i, I 1 Sample E i, I 0 Single crystal monochromator e E e, I 2

119 VALENCE-TO-CORE X-RAY EMISSION SPECTROSCOPY (VTC XES)

120 Valence-to-Core X-Ray Emission in 3d Transition Metals VS 3p x 500 2p x 8 1s

121 Mn(V)N XES and XAS: Complementary Techniques Occupied states XES Fermi Energy Unoccupied states E F VS 3p 2p XAS 1s

122 Fine structure of valence-to-core emission lines Transitions from: Mainly sensitive to orbitals that are centered on ligands. Ligand 2p M Ligand 2s M ungerade symmetry with respect to metal center Bergmann et al., Chem. Phys. Lett (1999) Safonov et al., J. Phys. Chem. B (2006)

123 Degree of ligand protonation ID26 Lassalle-Kaiser et al., Inorg. Chem. 2013, 52,