X-ray absorption spectroscopy.
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1 X-ray absorption spectroscopy
2 X-ray absorption spectroscopy Frank de Groot PhD: solid state chemistry U Nijmegen (91) Post-doc: LURE, Orsay (93-94) Post-doc: solid state physics U Groningen (95-98) U Utrecht since 1999 Synchrotron and theoretical spectroscopy of catalytic nanomaterials (inorganic chemistry and catalysis)
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4 Interaction of x-rays with matter Interaction of x-rays with matter Intensity (log) XAFS studies photoelectric absorption Elastic scattering (Thompson) Photoelectric Thompson Mn Inelastic scattering (Compton) 1 Compton 100 1k 10k 100k Energy (ev)
5 X-ray absorption of an atom XAS of an atom
6 X-ray absorption of a solid XAS of a solid
7 X-ray absorption of a solid XAS of a solid
8 X-ray absorption of a solid XAS of a solid Fe 4p - Fe 3d 0 O 2p 5 O 2s 20 Fe 3p 50 Fe 3s 85 O 1s 530 Fe 2p 700 Fe 2s 800 Fe 1s 7115
9 X-ray absorption of a solid XAS of a solid
10 X-ray absorption and X-ray photoemission XAS and XPS Excitation of core electrons to empty states. Spectrum given by the Fermi Golden Rule I XAS ~ T f f 1 i 2 E f E i
11 X-ray absorption and X-ray photoemission XAS and XPS
12 X-ray absorption and X-ray photoemission XAS and XPS
13 X-ray absorption spectroscopy Excitations of core electrons to empty states The XAS spectrum is given by the Fermi Golden Rule I XAS ~ f f eˆ r i 2 E f E i
14 X-ray Absorption Spectroscopy Excitations of core electrons to empty states The XAS spectrum is given by the Fermi Golden Rule 2 I ~ M XAS site, symmetry
15 X-ray Absorption Spectroscopy Density of States (DOS) is the integral over k-space of the band structure. Core states have no dispersion. XAS preserves momentum (k)
16 X-ray Absorption Spectroscopy 2p 2s Phys. Rev. B.40, 5715 (1989)
17 X-ray Absorption Spectroscopy oxygen 1s > p DOS Phys. Rev. B.40, 5715 (1989); 48, 2074 (1993)
18 Electronic Structure; TiO 2 Density of States of TiO 2 Phys. Rev. B. 40, 5715 (1989); 48, 2074 (1993)
19 Electronic Structure: TiO 2 Density of States of TiO 2 Phys. Rev. B. 40, 5715 (1989); 48, 2074 (1993)
20 X-ray absorption: core hole effect XAS: core hole effect TiSi 2 Final State Rule: Spectral shape of XAS looks like final state DOS Initial State Rule: Intensity of XAS is given by the initial state Phys. Rev. B. 41, (1991)
21 X-ray absorption X-ray Absorption Spectroscopy Excitation of core electrons to empty states. Spectrum identifies with the empty Density of States Works well for K edges (1s) Calculate with DFT (LDA+U, DMFT, BSE)
22 Metal 1s XAS 2p 2s
23 Metal 1s XAS 2p 2s Cr 3+ in MgAl 2 O 4 Juhin et al., Phys. Rev. B. 78, (2008)
24 Pre-edges structures in 1s XAS 1s 1 3d N 4p 1 edge 3d N 4p 0
25 Pre-edges structures in 1s XAS 1s 1 3d N 4p 1 edge 3d N 4p 0 1s 1 3d N+1 4p 0 pre-edge
26 Pre-edge and edge Pre-edges structures in 1s XAS Co III (acac) low-spin Co III 3d 6 [ 1 A 1 ] T 2g full E g empty
27 K pre-edge of TM oxides (LiCoO 2 ) Pre-edges structures in 1s XAS 1 Co K edge of LiCoO 2 edge 0 preedge? Energy (ev) low-spin Co III 3d 6 [ 1 A 1 ] T 2g full E g empty
28 X-ray absorption X-ray absorption spectroscopy Excitation of core electrons to empty states. Spectrum identifies with the empty Density of States Works well for K edges Metal K edges: quadrupole 1s3d transitions
29 X-ray absorption X-ray absorption spectroscopy Fermi Golden Rule: I XAS = < f dipole i > 2 [ E=0] Single electron (excitation) approximation: I XAS = < empty dipole core > 2
30 Quiz: Calculate the 2p XAS spectrum of Fe atom
31 X-ray absorption of an Fe atom XAS of an iron atom Fermi Golden Rule: I XAS = < f dipole i > 2 [ E=0] i =1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 f =1s 2 2s 2 2p 5 3s 2 3p 6 4s 2 3d 7 i =2p 6 3d 6 f =2p 5 3d 7
32 X-ray absorption XAS of an iron atom Fermi Golden Rule: I XAS = < f dipole i > 2 [ E=0] i =2p 6 3d 6 f =2p 5 3d 7 Single electron (excitation) approximation: I XAS = < empty dipole core > 2 core = 2p empty = 3d Neglect 2p-3d interactions (in the final state)
33 Multiplet Effects in XAS XAS of an iron atom 3d Overlap of core and valence wave functions <2p3d 1/r 2p3d> 2p 3/2 2p 1/2
34 Multiplet Effects in XAS XAS of atoms and solids 3d <2p3d 1/r 2p3d> Direct 2p3d Coulomb interaction (= core hole potential) is screened in molecules and solids. 2p 3/2 2p 1/2 Higher order terms (Coulomb and exchange) are NOT screened in molecules and solids
35 Multiplet Effects in XAS XAS of atoms and solids 3d <2p3d 1/r 2p3d> Single Particle model breaks down 2p 3/2 2p 1/2 PRB 42, 5459 (1990)
36 XAS XAS of molecules and solids Single Particle: 1s edges (WIEN, FEFF, PARATEC,..) Multiplets: 2p, 3s, 3p edges (TT-MULTIPLETS)
37 XAS XAS of molecules and solids No Unified Interpretation! Single Particle: 1s edges (WIEN, FEFF, ORCA, PWSCF, etc.) Multiplets: 2p, 3s, 3p edges (TT-MULTIPLETS)
38 Charge transfer multiplet program Used for the analysis of XAS, EELS, Photoemission, Auger, XES, ATOMIC PHYSICS GROUP THEORY MODEL HAMILTONIANS
39 CTM4XAS program
40 CTM4XAS version 5.2 CTM4XAS program
41 Atomic Multiplet Theory Atomic Multiplet Theory =E H N p 2 Ze i ( r 2m r r N i 2 pairs e 2 ij N i ) l i s i Kinetic Energy Nuclear Energy Electron-electron interaction Spin-orbit coupling
42 Atomic Multiplet Theory =E H Ze i X ( r 2m X ri rij N p 2 N 2 pairs e 2 N Kinetic Energy Nuclear Energy Electron-electron interaction Spin-orbit coupling i ) l i s i
43 N i i i pairs r e ATOM s l r H ij ) ( 2 k k k k k k J S r e J S G g F f L L Electron Correlation of Valence States [5 ev] Valence Spin-orbit coupling [0.1 ev] Atomic Multiplet Theory (ground state)
44 N i i i pairs r e ATOM s l r H ij ) ( 2 k k k k k k J S r e J S G g F f L L Core Valence Overlap [5 ev] Core Spin-orbit coupling [15 ev] Atomic Multiplet Theory (core hole)
45 2p XAS of ScF 3 2p XAS of a Ca atom Ground state is 3d 0 Dipole transition 3d 0 2p 5 3d 1 Dipole selection rules: S=1 and L=±1 Core hole spin-orbit coupling large L and S are no good quantum numbers J=±1 or 0 (J=J 0)
46 Term Symbols Term symbols Term Symbol 2S+1 L J L=0,1,2,3,4 > S, P, D, F, G LS quantum numbers not useful for XAS due to large spin-orbit coupling of the core hole. Use only J quantum numbers Degeneracy of each J-state: 2J+1
47 Term Symbols Term symbols Term symbols of a 1s electron S=1/2, L=0 J=1/2 2 S 1/2 Term symbols of a 3d electron S=1/2, L=2 J=3/2 or J=5/2 2 D 3/2 or 2 D 5/2
48 Term Symbols Term symbols 2p3d-configuration (6x10 = 60 states) all combinations are possible: In short: 2 P 2 D = 1,3 P,D,F Add J-quantum numbers: 1 P 1, 1 D 2, 1 F P 0, 3 P 1, 3 P D 1, 3 D 2, 3 D 3, + 3 F 2, 3 F 3, 3 F 4,
49 2p XAS of ScF 3 2p XAS of a Ca atom Ground state is 3d 0 : symmetry: 1 S 0 Dipole transition 3d 0 2p 5 3d 1 Selection rule: J=±1 or 0 (and J=J 0) J =1
50 Term Symbols 2p XAS of a Ca atom Term symbols of a 2p 5 3d 1 configuration 3 P 0 1 P 3 1 P 1, 3 P 2 3 D 1 1 D 3 2 D 2 3 D 3 3 F 2 1 F 3 3 F 3 3 F 4 [ ] 1 3x3 4x5 3x7 1x9 Ground state: 3d 0 : L=S=J=0 1 S 0 Selection rule: Final state must have J =1
51 2p XAS of a Ca atom 2p XAS of a Ca atom Ground state is 3d 0
52 e g states Crystal Field Effects 2p XAS of ScF 3 : crystal fields t 2g states
53 2p XAS of ScF 3 : crystal fields Octahedral crystal field splitting metal ion in free space in symmetrical field in octahedral ligand field x 2 -y 2 z 2 e g t 2g x 2 -y 2 yz z 2 xz xy yz xz xy
54 Comparison with Experiment 2p XAS of ScF 3
55 CTM4XAS version 5.2 Calculations with CTM4XAS
56 2p XAS of transition metal ions 2p XAS of transition metal ions Ground state is 3d N : determine symmetry Hunds rule: High-spin ground states max S, max L, max J Effect of crystal field splitting High spin or low spin Effect of 3d spin-orbit coupling Charge transfer effects
57 Effect of 10Dq on XAS:3d N 2p XAS of VF 3
58 High-spin or Low-spin High-spin or low-spin 10Dq > 3J (d 4 and d 5 ) 10Dq > 2J (d 6 and d 7 )
59 High-spin or Low-spin High-spin or low-spin High-spin: 10Dq = 1.2 Low-spin: 10Dq = 3.0
60 High-spin or Low-spin High-spin or low-spin
61 3d spin-orbit coupling 3d spin-orbit coupling
62 3d spin-orbit coupling 3d spin-orbit coupling
63 Charge Transfer Effects Charge transfer effects Ground state of a transition metal system 3d N at every site Charge fluctations
64 Charge Transfer Effects Charge transfer effects Hubbard U for a 3d 8 ground state: U= E(3d 7 ) + E(3d 9 ) E(3d 8 ) E(3d 8 ) Ligand-to-Metal Charge Transfer (LMCT): = E(3d 9 L) E(3d 8 )
65 Charge transfer effects in XAS and XPS Charge transfer effects Transition metal oxide: Ground state: 3d 5 + 3d 6 L Energy of 3d 6 L: Charge transfer energy XPS 2p 5 3d 5 -Q 2p 5 3d 6 L 3d 6 L 3d 5 Ground State XAS 2p 5 3d 7 L +U-Q 2p 5 3d 6
66 Charge Transfer effects High valent oxides (Cu 3+ ) Systems with π-bonds
67 =10 Charge Transfer Effects in XAS Charge Transfer effects in XAS 3d 8 + 3d 9 L =5 NiO =0 La 2 Li ½ Cu ½ O 4 =-5 =-10 J. Elec. Spec.67, 529 (1994)
68 =10 Charge Transfer Effects in XAS Charge Transfer effects in XAS 3d 8 + 3d 9 L 30% 3d 8 =5 NiO 1 A 1 =0 =-5 La 2 Li ½ Cu ½ O 4 30% 3d 8 3 A 2 =-10 Chem. Phys. Lett. 297, 321 (1998)
69 LMCT and MLCT: - bonding Fe III : Ground state: 3d 5 + 3d 6 L M C N M C N empty empty d or p d-orbital (i) - 3d 6 L 3d 5 filled - orbital (i) donation filled d-orbital +U-Q empty *-orbital 2p 5 3d 7 L (ii) back-donation C?C?N distance 2p 5 3d 6 with Ed Solomon (Stanford) JACS 125, (2003), JACS 128, (2006), JACS 129, 113 (2007)
70 LMCT and MLCT: - bonding Fe III : Ground state: 3d 5 + 3d 6 L + 3d 4 L 2p 5 3d 5 L 3d 4 L 3d 6 L 3d 5 -U+Q + 2 +U-Q - 2 2p 5 3d 7 L 2p 5 3d 6 with Ed Solomon (Stanford) JACS 125, (2003), JACS 128, (2006), JACS 129, 113 (2007)
71 Normalized Absorption LMCT and MLCT: - bonding Fe III (CN) 6 Fit X Series2 Fe III (tacn) with Ed Solomon (Stanford) JACS 125, (2003), JACS 128, Energy (2006), (ev) JACS 129, 113 (2007)
72 Time resolved XAS Huse et al. JACS 132, 6809 (2010); JPCL 2, 880 (2011)
73 XAS: multiplet effects Single Particle: 1s edges (DFT + core hole (+U)) 2-particle: (TDDFT, BSE) + L edges of 3d 0 Multiplets: 2p, 3s, 3p edges (CTM4XAS)
74 Why X-ray absorption? Element specific Low concentrations ( wt%) local electronic & magnetic structure valence, spin-state, symmetry hybridization, MO energies / density of states crystal field, charge transfer, spin-orbit, moments Time: excited states in fs/ps/ns range Pressure: 1 bar/500 ºC flowing gas Space: 0.5 nm (STEM), 20 nm (STXM)
75 Quiz: Calculate the 2p XAS spectrum of Fe atom
76 Quiz: Calculate the 2p XAS of NiF2 and NiCl2
77 X-MCD Magnetic circular dichroism
78 Quiz: Calculate the X-MCD of ferromagnetic Ni 2+ [Ni II Cr III (CN) 6 ] 1- Arrio et al. JPC 100, 4679 (1996)
79 Charge transfer effects in XAS and XPS Charge transfer effects Transition metal oxide: Ground state: 3d 5 + 3d 6 L Energy of 3d 6 L: Charge transfer energy XPS 2p 5 3d 5 -Q 2p 5 3d 6 L 3d 6 L 3d 5 Ground State XAS 2p 5 3d 7 L +U-Q 2p 5 3d 6
80 Quiz: Calculate the 2p XPS of NiF2 and NiCl2
81 XAS XAS experiments
82 Core Hole Decay XAS experiments: using the core hole decay Fluorescence Auger 2p3/2 2p1/2 2s 2p3/2 2p1/2 2s 1s fluorescent radiation 1s
83 XAS XAS experiments Quiz: How to measure XAS of a solid
84 XAS XAS experiments
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