X-ray Spectroscopy Röntgen s experment n 1895 Lecture 1: Introducton & expermental aspects Lecture : Atomc Multplet Theory Crystal Feld Theory CTM4XAS program Lecture 3: Charge Transfer Multplet Theory Resonant Inelastc X-ray Scatterng X-ray Spectroscopy on nanomaterals Röntgen s experment Röntgen s experment Interacton of x-rays x wth matter x-rays Wavelength: 10-10 m Frequency: C/λ= 3 10 18 Hz 1
mm 1.1 The µm Characterstcs nm of Electromagnetc Radaton pm Interacton of x-rays x wth matter XAFS studes photoelectrc absorpton Thompson scatterng (Dffracton) Compton scatterng Intensty (log) 100 10 1 Photoelectrc Thompson Compton Mn mev ev kev MeV 100 1k 10k 100k Energy (ev) Interacton of x-rays x wth matter 1 Interacton of x-rays x wth matter 1 The photon moves towards the atom The photon meets an electron and s annhlated Interacton of x-rays x wth matter 1 Interacton of x-rays x wth matter 1 The electron gans the energy of the photon and s turned nto a blue electron. The blue electron (feelng lonely) leaves the atom and scatters of neghbors or escapes from the sample
Interacton of x-rays x wth matter 1 XPS machne The probablty of photon annhlaton determnes the ntensty of the transmtted photon beam I 0 I E k XPS machne X-ray photoemsson X-ray photoemsson X-ray photoemsson: workfuncton E vac E F Vacuum level Work functon Ferm level sp-band onzaton energy ε a core level 1 core level metal adsorbed atom free atom Fgure 6.11 3
XPS and the photo-electrc effect Photo-electrc effect XPS Bndng Energy: defned versus hghest occuped state E vac conducton band conducton band E F valence band d-band band gap sp-band sp-band sp-band free electron metal transton metal nsulator hν=e k + Φ hν=e L + E k + Φ Fgure 6.17 X-ray photoemsson Atomc bndng energes THE HIGH FREQUENCY SPECTRA OF THE ELEMENTS (1913) Moseley (1887-1915) Atomc bndng energes smple laws have been found whch [ ] make t possble to predct wth confdence the poston of the prncpal lnes n the spectrum of any element from alumnum to gold. Atomc bndng energes ν =.5 10 15 (Z-α) Hz Moseley. Phl. Mag. 6, 156(1913); onlne lnk at webste 4
Atomc bndng energes Atomc bndng energes Transton from 1s to p n hydrogen: Bohr frequency condton: h h = 13.6 * (1/1-1/4) ~ 10 ev Transton from 1s to p n oxygen: h h h h Z Rydberg formula = 10 * 8 = 10 * 64 = 640 ev Atomc bndng energes X-ray photoemsson Transton from 1s to p n oxygen: 58 ev; Calculated as 640 ev Screenng of charge: hc*(z eff ) =58 ev, wth Z eff =7. hc*(z-α), wth α=0.8 X-ray photoemsson edges X-ray photoemsson Paladum Electron bndng energes M I M II M III M IV M V N I N II N III 3s 3p1/ 3p3/ 3d3/ 3d5/ 4s 4p1/ 4p3/ 671.6 559.9 53.3 340.5 335. 87.1 55.7 50.9 3s 3p 1/ 3p 3/ 3d http://www.webelements.com/ http://www.webelements.com/ 5
Interacton of x-rays x wth matter 1 X-ray absorpton and X-ray X photoemsson I 0 I I(ω FIXED ) E k X-ray absorpton and X-ray X photoemsson X-ray absorpton and X-ray X photoemsson Jump at bndng energy Peak at bndng energy I(ω FIXED ) X-ray absorpton and X-ray X photoemsson X-ray absorpton experments 6
X-ray absorpton and X-ray X photoemsson X-ray Absorpton Spectroscopy Phys. Rev. B. 40, 5715 (1989); 48, 074 (1993) X-ray Absorpton Spectroscopy Electronc Structure; TO p s Phys. Rev. B. 40, 5715 (1989); 48, 074 (1993) Phys. Rev. B. 40, 5715 (1989); 48, 074 (1993) Electronc Structure: TO SOLID STATE >> delocalsed ATOMIC >> localsed Phys. Rev. B. 40, 5715 (1989); 48, 074 (1993) 7
I Exctaton of core electrons to empty states. Spectrum gven by the Ferm Golden Rule (name Golden Rule gven by Ferm; rule tself gven by Drac) XAS ~ Σ X-ray absorpton f Φ f eˆ r Φ δ E f E hω X-ray absorpton Ferm Golden Rule: I XAS = <Φ f dpole Φ > δ [ E=0] Φ f eˆ q r Φ Sngle electron (exctaton) approxmaton: I XAS = <Φ empty dpole Φ core > ρ = =?? ε eˆ q r c Φ cε eˆ q r Φ X-ray absorpton: core hole effect X-ray absorpton: core hole effect TS Fnal State Rule: Spectral shape of XAS looks lke fnal state DOS ground state Intal State Rule: Intensty of XAS s gven by the ntal state Mg p core holed state Mg 1s core holed state Phys. Rev. B. 41, 11899 (1991) Tanaka et al, J. Am. Ceram. Soc. 88, 013 (005). Mn 4p - Mn 3d 0 O p 5 O s 0 Ground State MnO 3d 5 Mn 4p - Mn 3d 0 O p 5 O s 0 Oxygen 1s XAS MnO 3d 5 Mn 3p 45 Mn 3s 80 O 1s 530 Mn p 650 Mn s 770 Mn 1s 6540 Mn 3p 45 Mn 3s 80 O 1s 530 Mn p 650 Mn s 770 Mn 1s 6540 8
Mn 4p - Manganese 1s XAS Mn 3d 0 O p 5 O s 0 MnO 3d 5 Mn 4p - Manganese 1s XAS Mn 3d 0 O p 5 O s 0 MnO 3d 5 Mn 3p 45 Mn 3s 80 O 1s 530 Mn p 650 Mn s 770 Mn 1s 6540 Mn 3p 45 Mn 3s 80 O 1s 530 Mn p 650 Mn s 770 Mn 1s 6540 Quadrupole transton The lfe of a Core Hole Auger spectroscopy Hesenberg uncertanty relaton Γτ ħ(~ 10-16 ev s). Broadenng of XAS: ~0.1 ev Lfetme = 1 femtosecond Oxygen 1spp Auger Mn 4p - Mn 3d 0 MnO 3d 5 X-ray emsson O p 5 O s 0 Mn 3p 45 Mn 3s 80 O 1s 530 Mn p 650 Mn s 770 Mn 1s 6540 9
Mn 4p - Mn 3d 0 O p 5 O s 0 Mn 1s3p XES MnO 3d 5 Resonant X-ray X emsson spectroscopy Mn 3p 45 Mn 3s 80 O 1s 530 Mn p 650 Mn s 770 Mn 1s 6540 Kβ 1,3 Kβ' Mn 3p Kβ'' O s 6460 6480 6500 650 6540 6560 Energy [ev] Kβ,5 O p X-ray absorpton Ferm Golden Rule: I XAS = <Φ f dpole Φ > δ [ E=0] Φ f eˆ q r Φ = Φ cε eˆ q r Φ =?? ε eˆ q r c Sngle electron (exctaton) approxmaton: I XAS = <Φ empty dpole Φ core > ρ Multplet Effects n XAS Multplet Effects n XAS 10
Multplet Effects n XAS Multplet Effects n XAS Overlap of core and valence wave functons 3d Sngle Partcle model breaks down <p3d 1/r p3d> p 3/ p 1/ PRB 4, 5459 (1990) XAS XAS Sngle Partcle: 1s edges (DFT codes) Multplets: p, 3s, 3p edges (CTM4XAS) No Unfed Interpretaton! Sngle Partcle: 1s edges (DFT codes) Multplets: p, 3s, 3p edges (CTM4XAS) Bethe-Salpeter calculatons (Erc Shrley): Excted state = lnear superposton of all states produced by a sngle electron exctaton. XAS: multplet XAS effects Sngle Partcle: 1s edges (DFT + core hole (+U)) E el In each such electron-hole par state, electron n band n, wth crystal momentum k+q. -partcle: (TDDFT, BSE) + L edges of 3d 0 momentum hole n [band or core-level] n, wth crystal momentum k, Many-partcle: p, 3s, 3p edges (CTM4XAS) Phys. Rev. Lett. 80, 794 (1998); PRB 8, 05104 (010) 11
XAS: multplet XAS effects X-ray absorpton and X-ray X photoemsson Sngle Partcle: 1s edges (DFT + core hole (+U)) -partcle: (TDDFT, BSE) + L edges of 3d 0 No Unfed Interpretaton! I(ω FIXED ) Many-partcle: p, 3s, 3p edges (CTM4XAS) X-rays from synchrotrons Lnear Accelerator Storage Rng c=99 79,4581 km/s 1.7GeV synchrotron gves 0.9999999c 1
Magnets n the storage rng a X-rays from synchrotrons Magnetc Force F = q v B Perpendcular to Feld and propagaton drecton X-rays from synchrotrons Bendng Magnets Inserton Devces: Wggler Undulator 13
X-rays from synchrotrons X-rays from synchrotrons X-ray absorpton beamlne (transmsson) Beamlne 18ID at the APS Whte X-ray Bocat Homepage I II III IV V VII VIII Mrrors Monochromator I Entrance slts II Monochromator IIIExt slts IV Ionsaton chamber V Sample VI Ionsaton chamber VII Reference materal VIII Ionsaton chamber ALS http://www-als.lbl.gov/als/ 14
Energy: tunable source Intensty: 10 6-10 1 hgher than x-ray tube Space: spot-sze 1x1 mm (unfocussed) down to 0x0 nm (focussed) Tme: pulse 50 ps, slced down to 50 fs. Polarzaton: Why a synchrotron? Angular dependence & Crcular dchrosm: NOT coherent (no laser) XAS: multplet XAS effects Sngle Partcle: 1s edges (DFT + core hole (+U)) -partcle: (TDDFT, BSE) + L edges of 3d 0 Many-partcle: p, 3s, 3p edges (CTM4XAS) Charge Transfer Multplet program The CTM4XAS program Used for the analyss of XAS, EELS, Photoemsson, Auger, XES, ATOMIC PHYSICS GROUP THEORY MODEL HAMILTONIANS 15