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Topics Interaction of X-rays with matter Overview of core level - - PowerPoint PPT Presentation

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Topics Interaction of X-rays with matter Overview of core level spectroscopies XAS analysis of spectral features Interpretation of X-ray absorption Interaction of X-rays with matter Interaction of x-rays with matter 1 The photon

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SLIDE 1

Topics

  • Interaction of X-rays with matter
  • Overview of core level spectroscopies
  • XAS analysis of spectral features
  • Interpretation of X-ray absorption
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SLIDE 2
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SLIDE 3
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SLIDE 4

Interaction of X-rays with matter

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SLIDE 5

Interaction of x-rays with matter 1

The photon moves towards the atom

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SLIDE 6

Interaction of x-rays with matter 1

The photon meets an electron and is annihilated

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SLIDE 7

Interaction of x-rays with matter 1

The electron gains the energy of the photon and is turned into a blue electron.

Beyond the one-electron model: von Almbladh and Hedin, Handbook of synchrotron radiation 1, chapter 8, pages 607-900 (1983)

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SLIDE 8

Interaction of x-rays with matter 1

The blue electron (feeling lonely) leaves the atom and scatters of neighbors

  • r escapes from the sample
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SLIDE 9

Interaction of x-rays with matter 1

The probability of photon annihilation determines the intensity of the transmitted photon beam

I0 I Ek

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SLIDE 10

Overview of core level spectroscopies

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SLIDE 11

Mn 4p

  • Mn 3d

O 2p

5

O 2s

20

Mn 3p

45 Mn 3s 80 O 1s 530 Mn 2p 650 Mn 2s 770 Mn 1s 6540 MnO 3d5

Ground State

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SLIDE 12

Mn 4p

  • Mn 3d

O 2p

5

O 2s

20

Mn 3p

45

Ground State

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SLIDE 13

Mn 4p

  • Mn 3d

O 2p

5

O 2s

20

Mn 3p

45

X-ray absorption

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SLIDE 14

X-ray absorption

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SLIDE 15

X-ray absorption

The life of a core hole is rather short: ~few femtoseconds

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SLIDE 16

X-ray emission after x-ray absorption

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SLIDE 17

X-ray emission after electron excitation

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SLIDE 18

Auger

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SLIDE 19

XAS and XPS

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SLIDE 20

XPS (PES) and Inverse PES

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X-ray emission decay

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SLIDE 22

Auger electron decay

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SLIDE 23

Resonant Auger decay (resonant PES)

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Resonant X-ray emission decay

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SLIDE 25

Binding Energies

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Label Orbital eV [literature reference] K 1s 6539 [1] L I 2s 769.1 [3] L II 2p1/2 649.9 [3] L III 2p3/2 638.7 [3] M I 3s 82.3 [3] M II 3p1/2 47.2 [3] M III 3p3/2 47.2 [3]

X-ray absorption edges

Manganese Electron binding energies http://www.webelements.com/

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SLIDE 27

Bohr frequency condition:

h h

Rydberg formula

Atomic binding energies in hydrogen

13.6 eV

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SLIDE 28

Bohr frequency condition:

h h

Rydberg formula

Atomic binding energies in oxygen

640 eV

*Z2

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SLIDE 29

Bohr frequency condition:

h h

Rydberg formula

Atomic binding energies in oxygen

*Zeff2

530 eV

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SLIDE 30

… simple laws have been found which […] make it possible to predict with confidence the position of the principal lines in the spectrum of any element from aluminum to gold.

Atomic binding energies

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Label Orbital eV [literature reference] K 1s 6539 [1] L I 2s 769.1 [3] L II 2p1/2 649.9 [3] L III 2p3/2 638.7 [3] M I 3s 82.3 [3] M II 3p1/2 47.2 [3] M III 3p3/2 47.2 [3]

X-ray absorption edges

Manganese Electron binding energies http://www.webelements.com/

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SLIDE 32

Qualitative XAS analysis

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SLIDE 33

X-ray absorption: XANES and EXAFS

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XANES: qualitative analysis

Edge position gives valence

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SLIDE 35

Wong et al.

  • Phys. Rev. B. 30, 5596 (1984)

XANES: qualitative analysis

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SLIDE 36

XANES: qualitative analysis

Edge position gives valence Pre-edge gives valence Different slopes

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SLIDE 37

XANES: qualitative analysis

Pre-edge intensity gives site symmetry

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SLIDE 38

XANES: qualitative analysis

L edge of 4d-systems > number of empty 4d states

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SLIDE 39

XANES: qualitative analysis

L edge of 5d-systems > number of empty 5d states

Difference between metal and oxide

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SLIDE 40

Quantitative XAS interpretation

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SLIDE 41

  

   

i f

E E i f f XAS

r e I

2

ˆ ~

Excitation of core electrons to empty states. Spectrum given by the Fermi Golden Rule (name Golden Rule given by Fermi; rule itself given by Dirac)

X-ray absorption

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SLIDE 42

X-ray Absorption Spectroscopy

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SLIDE 43

2p 2s

X-ray Absorption Spectroscopy

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SLIDE 44

Electronic Structure; TiO2

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SLIDE 45

Electronic Structure: TiO2

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SLIDE 46
  • Final State Rule:

Spectral shape of XAS looks like final state DOS TiSi2

  • Initial State Rule:

Intensity of XAS is given by the initial state

X-ray absorption: core hole effect

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SLIDE 47

  

   

i f

E E i f f XAS

r e I

2

ˆ ~

Excitation of core electrons to empty states. Spectrum given by the Fermi Golden Rule (name Golden Rule given by Fermi; rule itself given by Dirac)

X-ray absorption

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SLIDE 48

Fermi Golden Rule: IXAS = |<f|dipole| i>|2 [E=0] Single electron (excitation) approximation: IXAS = |< φempty|dipole| φcore>|2 

X-ray absorption

2 2

ˆ ˆ

i q i i q f

r e c r e        

2

ˆ ?? c r eq   

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SLIDE 49

2p3/2 2p1/2 Overlap of core and valence wave functions

 Single Particle model breaks down

3d

<2p3d|1/r|2p3d>

XAS: multiplet effects

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SLIDE 50

Single Particle:

1s edges

(DFT codes)

Multiplets:

2p, 3s, 3p edges

(CTM4XAS)

XAS

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SLIDE 51

Single Particle: 1s edges (DFT + core hole (+U)) 2-particle: (TDDFT, BSE) + L edges of 3d0 Multiplets: 2p, 3s, 3p edges (CTM4XAS)

XAS: multiplet effects

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SLIDE 52

X-ray absorption: core hole effect

XAS: recent first principle developments for L edges

  • DFT + projection to cluster multiplet (Haverkort, Uozumi)
  • Restricted-Active-Space (Odelius, Broer, Kuhn, Neese)
  • ab-initio multiplets [DFT+CI] (Ikeno, Uldry)
  • extended BSE (Rehr, Shirley, Joly, Laskowski)
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SLIDE 53

Single Particle: 1s edges (DFT + core hole (+U)) 2-particle: (TDDFT, BSE) + L edges of 3d0 Multiplets: 2p, 3s, 3p edges (CTM4XAS)

XAS: multiplet effects

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SLIDE 54

Charge Transfer Multiplet program

XAS, EELS, Photoemission, Auger, XES, Resonant PES, RIXS

ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS

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SLIDE 55

CTM4XAS (semi-empirical)

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SLIDE 56

   

    

 N i i i pairs r e N r Ze N m p

s l r H

ij i i

) (

2 2 2

2

Atomic Multiplet Theory

=E

  • Kinetic Energy
  • Nuclear Energy
  • Electron-electron interaction
  • Spin-orbit coupling
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SLIDE 57

   

    

 N i i i pairs r e N r Ze N m p

s l r H

ij i i

) (

2 2 2

2

Atomic Multiplet Theory

X X

=E

  • Kinetic Energy
  • Nuclear Energy
  • Electron-electron interaction
  • Spin-orbit coupling
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SLIDE 58

 

  

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

1 2 1 2

| |

12 2

Atomic Multiplet Theory

Electron-electron interactions of Valence States Valence Spin-orbit coupling

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SLIDE 59

CTM4XAS version 5.2

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SLIDE 60

 

  

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

1 2 1 2

| |

12 2

Atomic Multiplet Theory

Core Valence Overlap Core Spin-orbit coupling

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SLIDE 61
  • Term symbols with maximum spin S are lowest in energy,
  • Among these terms:

Term symbols with maximum L are lowest in energy

  • In the presence of spin-orbit coupling, the lowest term has
  • J = |L-S| if the shell is less than half full
  • J = L+S if the shell is more than half full

Hunds rules

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SLIDE 62

max S > max L > max J (if more than half full) What is the Hund’s rule ground states for 3d2 ?

Hunds rules

2  1  0 

  • 1 
  • 2 

2  1  0 

  • 1 
  • 2 
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SLIDE 63

max S > max L > max J (if more than half full) What is the Hund’s rule ground states for 3d2 ?

Hunds rules

2  1  0 

  • 1 
  • 2 

2  1  0 

  • 1 
  • 2 

L=3, S=1 J=2 Term symbol = 3F2

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SLIDE 64

max S > max L > max J (if more than half full) What is the Hund’s rule ground states for 3d2 ?

Hunds rules

2  1  0 

  • 1 
  • 2 

2  1  0 

  • 1 
  • 2 

See the slides EXTRA Slater Integrals for more information

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SLIDE 65

What is the Hund’s rule ground states for 3d2 ?

Hunds rules

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SLIDE 66

Charge Transfer Multiplet program

Used for the analysis of XAS, EELS,

Photoemission, Auger, XES,

ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS

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SLIDE 67

t2g states

Crystal Field Effects

eg states

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SLIDE 68

Crystal Field Effects: Tanabe-Sugano

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Crystal Field Effects: branching rules

S P F G D

A1 T2 T1 E A2

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Crystal Field Effects: branching rules

S P F G D

A1 T2 T1 E A2 A1 B2 A2 B1 E

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SLIDE 71

Crystal Field Effects: branching rules

S P F G D

A1 T2 T1 E A2 A1 B2 A2 B1 E

Dipole & Quadrupole

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SLIDE 72

Crystal Field Effects: branching rules

S P F G D

A1 T2 T1 E A2 A1 B2 A2 B1 E

Hamiltonian (atomic, 10Dq, Ds, Dt)

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Effect of 10Dq on XAS:3d0

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SLIDE 74

Comparison with Experiment

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SLIDE 75

2p XAS of Mn2+

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SLIDE 76

Charge Transfer Multiplet program

Used for the analysis of XAS, EELS,

Photoemission, Auger, XES,

ATOMIC PHYSICS  GROUP THEORY  MODEL HAMILTONIANS

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SLIDE 77

Ground state of a transition metal system 3dN at every site Charge fluctations

Charge Transfer Effects

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SLIDE 78

Hubbard U for a 3d8 ground state: U= E(3d7) + E(3d9) – E(3d8) – E(3d8) Ligand-to-Metal Charge Transfer (LMCT):

= E(3d9L) – E(3d8) Charge Transfer Effects

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SLIDE 79

6 7 8 9 10 5 10 15

3U-2 U- 2+U

 Energy (eV) 3d count

Charge Transfer Effects

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SLIDE 80

6 7 8 9 10 5 10 15 Energy (eV) 3d count

 +U-Q

Charge Transfer Effects in XAS

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3d6L 3d5

MnO: Ground state: 3d5 + 3d6L Energy of 3d6L: Charge transfer energy 

2p53d7L 2p53d6

+U-Q  

Charge Transfer Effects

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SLIDE 82

6 7 8 9 10 5 10 15 Energy (eV) 3d count

 -Q

Charge Transfer Effects in XPS

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SLIDE 83

3d6L

  • Transition metal oxide: Ground state: 3d5 + 3d6L
  • Energy of 3d6L: Charge transfer energy 

XAS 2p53d7L

+U-Q   

2p53d6 3d5 2p53d6L XPS 2p53d5

-Q

Ground State

Charge transfer effects in XAS and XPS

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SLIDE 84

Spectral shape: (1) Multiplet effects (2) Charge Transfer

  • J. Elec. Spec.

67, 529 (1994)

X-ray Absorption Spectroscopy

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=10 NiO La2Li½Cu½O4 30% 3d8

1A1

30% 3d8

3A2

=-5 =5 =0 =-10

3d8 + 3d9L Charge Transfer effects

  • Chem. Phys. Lett. 297, 321 (1998)
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SLIDE 86

3d6L 3d5

2p53d7L 2p53d6

+U-Q  

FeIII: Ground state: 3d5 + 3d6L

C N M

filled empty 

M C N

filled - empty d or p

C N M

filled empty 

M C N

filled - empty d or p

C N M

filled empty 

M C N

filled - empty d or p

C N M

filled empty 

M C N

filled - empty d or p

 

empty filled 

LMCT and MLCT:  - bonding

with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)

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SLIDE 87

3d4L 3d6L 3d5

FeIII: Ground state: 3d5 + 3d6L + 3d4L

2p53d5L 2p53d7L 2p53d6

+U-Q   - 2  -U+Q   + 2

with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)

LMCT and MLCT:  - bonding

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SLIDE 88
  • 2

2 4 6 8 10 700 705 710 715 720 725 730

Energy (eV) Normalized Absorption

Fit X Series2

FeIII(tacn)2 FeIII(CN)6

with Ed Solomon (Stanford) JACS 125, 12894 (2003), JACS 128, 10442 (2006), JACS 129, 113 (2007)

LMCT and MLCT:  - bonding

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SLIDE 89

resonant inelastic x-ray scattering

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SLIDE 90

Ψ0

a.k.a. resonant x-ray Raman

3 2 1 0

resonant inelastic x-ray scattering

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SLIDE 91

resonant inelastic x-ray scattering

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SLIDE 92
  • Measure optical spectra with x-rays

>> in-situ, element/valence specific

  • dd-transitions > electronic structure
  • Magnetic excitations
  • Select specific states (active sites)

Why RIXS?

(only soft x-ray RIXS)

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SLIDE 93

dd

spin-flip ‘spin-flip’ MS S

2p3d RIXS and magnetic excitations (NiO)

[Phys. Rev. B. 57, 14584 (1998)]

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2p3d RIXS of CoO

eV 2-electron integrals crystal field charge transfer MCD, spin, angles polarization, angular-dependence (in, sample, out) meV spin-orbit, magnetic distortions vibrations

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2p3d resonant XES of Co-carboxylates

(1) (2) (3) (4)

van Schooneveld et al., Angew. Chem. 52, 1170 (2012)

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2p3d RIXS of CoO

4.2 nm

[van Schooneveld, J. Phys. Chem. C. 116, 15218 (2012)]

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SLIDE 97

2p3d RIXS of CoO

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SLIDE 98

Select specific states in 2p3d RIXS (Fe3O4)

Incident photon energy (eV)

  • 6.0
  • 5.0
  • 4.0
  • 3.0
  • 2.0
  • 1.0

0.0

Energy loss (eV)

703 703.5 704 704.5 705 705.5 705.9 706.3 706.7 707.2 50 40 30 20 10

Intensity (arb. units)

  • 1.0
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.2 0.4

Energy loss (eV)

703 703.5 704 704.5 705 705.5 705.9 706.3

exchange spin-orbit + exchange

[Huang et al. arXiv:1512.07957 ]

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SLIDE 99

Select specific states in 2p3d RIXS (Fe3O4)

Incident photon energy (eV)

  • 6.0
  • 5.0
  • 4.0
  • 3.0
  • 2.0
  • 1.0

0.0

Energy loss (eV)

703 703.5 704 704.5 705 705.5 705.9 706.3 706.7 707.2 50 40 30 20 10

Intensity (arb. units)

  • 1.0
  • 0.8
  • 0.6
  • 0.4
  • 0.2

0.0 0.2 0.4

Energy loss (eV)

703 703.5 704 704.5 705 705.5 705.9 706.3

exchange spin-orbit + exchange

Interference shows that lifetime broadening (fwhm) is only 100 meV, not 200 meV 20 fs >>> 40 fs

[Huang et al. arXiv:1512.07957 ]

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SLIDE 100

2p3d resonant XES of metal Co nanoparticles

[van Schooneveld, J. Phys. Chem. Lett 4, 1161 (2013)]

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SLIDE 101

Van Schooneveld et al., submitted

101

2p3d resonant XES of metal Co nanoparticles

CoO

[van Schooneveld, J. Phys. Chem. Lett 4, 1161 (2013)]

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SLIDE 102

van Schooneveld et al., J. Phys. Chem. Lett. 4, 1161 (2013)

2p3d resonant XES of metal Co nanoparticles

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SLIDE 103

Van Schooneveld et al., submitted

103

2p3d resonant XES of metal Co nanoparticles

van Schooneveld et al., J. Phys. Chem. Lett. 4, 1161 (2013)

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SLIDE 104

2p3d resonant XES of metal Co nanoparticles

van Schooneveld et al., J. Phys. Chem. Lett. 4, 1161 (2013)

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SLIDE 105

2p3d resonant XES of metal Co nanoparticles

van Schooneveld et al., J. Phys. Chem. Lett. 4, 1161 (2013)

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SLIDE 106

2p3d resonant XES of metal Co nanoparticles

van Schooneveld et al., J. Phys. Chem. Lett. 4, 1161 (2013)

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SLIDE 107

Removing the silent majority

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SLIDE 108