Simo Huotari University of Helsinki, Finland European Synchrotron Radiation Facility, Grenoble, France
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1 X-ray Raman spectroscopy Simo Huotari University of Helsinki, Finland European Synchrotron Radiation Facility, Grenoble, France
2 Outline of today Part 1 Introduction Part 2 Theory Part 3 Applications I Tomorrow Instruments, applications, future Simo Huotari :33:10 2
3 X-ray interaction with matter Interaction H photoelectric absorption Incoming x-rays Transmission generic sample Simo Huotari :33:10 3
4 :33:10 Simo Huotari barn m cos 1 ˆ ˆ r r r e e r d d TH (THOMSON) Elastic scattering (wave picture) beam
5 Inelastic scattering (particle picture) Photon-electron collision can be inelastic (Arthur H. Compton Nobel prize 1927). Energy is transferred from photon to electron. 2θ Wavelength shift Δλ = h (1 cos 2θ) mc (famous Compton formula) Simo Huotari 18:33:10 5
6 Why spectroscopy? Spectroscopy electron levels and properties electron conductivity optical properties Energy levels E Structural probes (diffraction ) positions of atoms in real space elastic properties Charge density Ψ r 2 EΨ r = ħ2 2m 2 Ψ r + V r Ψ(r) Simo Huotari 18:33:11 6
7 X-ray scattering Energy transfer ħω = ħω 1 ħω 2 Momentum transfer ħq = ħk 1 ħk 2 q 2k 1 sin 2θ = 4π sin 2θ 2 λ 1 2 detector incoming x-rays 2θ ħω 1 k 1 ε 1 generic sample Simo Huotari 18:33:12 7
8 X-ray scattering Elastic x-ray scattering coherent electron state: initial = final photon energy does not change diffraction, small angle scattering, etc. (structural information) f(q) = coherent scattering factor Inelastic x-ray scattering incoherent initial final photon gives energy to the electron spectroscopy (energetic information) S(q) = incoherent scattering factor Simo Huotari 18:33:12 8
9 X-ray/matter interactions for copper (Cu, Z=29) Simo Huotari 18:33:12 9
10 History: what is x-ray Raman? Nobel prize 1930 Simo Huotari :33:12 10
11 Electron binding energy History: what is x-ray Raman? Equivalence of: Scattering Absorption Excitations optical Raman infrared absorption vibrational (mev) x-ray Raman soft x-ray absorption core-electrons (ev, kev) hole electron E core hole Simo Huotari 18:33:12 11
12 Particle probing depth photons Simo Huotari :33:13 12
13 Hard x-rays: benefits Access to extreme conditions Bulk sensitivity Almost unlimited momentum transfer Simo Huotari 18:33:13 13
14 Energy X-ray absorption edges Absorption e M 2,3,... M 1 3d 3p 3s ħω 1, I 0 ħω 1, I 0 exp ( μ ρ ρd) L 3 L 2 L 1 2p 1/2,3/2 2s K edge 1s Measure at least one of: - transmission - fluorescence yield - electron yield Simo Huotari 18:33:13 14
15 Recall from Steve Heald s lectures: from Steve Heald EXAFS: information on local structure XANES: information on chemical state and valence Simo Huotari 18:33:13 15
16 Typical spectrum D. Sokaras et al., Rev. Sci. Instrum. 83, (2012); doi: / Simo Huotari 18:33:13 16
17 Complementary techniques - Soft x-ray absorption (XAS, XANES, EXAFS) e ħω 1, I 0 ħω 1, I 0 exp ( μ ρ ρd) - Electron scattering (EELS, ELNES) e 2θ 2θ Simo Huotari 18:33:13 17
18 Outline of today Part 1 Introduction Part 2 Theory Part 3 Applications I Tomorrow Instruments, applications, future Simo Huotari :33:13 18
19 Theory Quantum mechanics: Interaction of x-rays with matter is taken into account by the transformation p p e c A(r) where A is the vector field operator. Thus the Hamiltonian becomes H = p e c A(r) 2 2m + V r H = H 0 e mc p A r + 1 2m absorption and emission e c 2 A r A(r) scattering Simo Huotari 18:33:13 19
20 Fermi s Golden Rule Transition rate w is given in the first order perturbation by w = 2π ħ f H i 2 δ(e i E f ħω) electron final state electron initial state energy transfer Simo Huotari 18:33:15 20
21 Inelastic scattering cross section d 2 σ dωdω 2 = dσ dω Th ω 2 ω 1 f f e iq r i δ E f E i ħω This gives the scattering probability to the solid angle interval [Ω, Ω + dω] and energy interval [ω 2, ω 2 + dω 2 ] Simo Huotari 18:33:15 21
22 Electron binding energy Photon absorption p A term in first order Probability for absorption process 1 exp μ ρ ρd μ/ρ [cm 2 /g] = mass absorption coefficient hole electron Photon energy ħω 1, polarisation Simo Huotari 18:33:15 22
23 Electron binding energy Inelastic scattering A A term in first order hole electron Energy transfer ω = ω 1 ω 2 Momentum transfer q = k 1 k Simo Huotari 18:33:15 23
24 Absorption vs. scattering Absorption Scattering P ω Ψ f p A Ψ i 2 δ Ei E f + ω f S Q, ω Ψ f e iq r Ψ i 2 δ Ei E f + ω f Dipole selection rule P ω ω e.g., s s (monopole, l=0) s p (dipole, l=1) s d (quadrupole, l=2) etc... Use the momentum transfer dependence of the scattering matrix element: as q 0 then e iq r = 1 + iq r q r dipole Higher order multipoles Simo Huotari, Benasque TDDFT school :33:16 24
25 Summary: most important thing X-ray Raman scattering is inelastic x-ray scattering from core electrons Powerful technique rapidly growing in popularity with 3 rd generation synchrotrons Use hard x-rays to study soft x-ray edges bulk-sensitive measurements easy access to extreme environments ω 1 ω 1 E core E core Additionally momentum-transfer dependence energy transfer E core momentum transfer q Simo Huotari 18:33:16 25
26 Outline of today Part 1 Introduction Part 2 Theory Part 3 Applications I Tomorrow Instruments, applications, future Simo Huotari :33:16 26
27 Extreme conditions pressure = force / area V.M.Giordano, T. Pylkkänen et al. ESRF ID16 photons in Experimental details 1 mm diamond tip (culet) 5 mm Be gasket 350 micron sample size sample X-ray beam µm 2 Ruby chip for P calibration Simo Huotari 18:33:16 27
28 Liquid He Cryostat (4 K) Low temperatures Liquid nitrogen cryo-jet (77 K) He sorption pump (1 K) F. Albergamo et al., ESRF Simo Huotari 18:33:16 28
29 Extremely high temperatures (thousands of deg): Laser heating and aerodynamic levitation High temperatures (up to 1000 deg C): furnaces, hot air guns Wikipedia: Aerodynamic levitation ESRF, Sample group Droplet of liquid basalt BCR-2 during levitation. The sample was heated from the top using a CO 2 -laser. The diameter of the sphere was ~2 mm. A. Pack et al., Geochemical transactions 2010, 11: Simo Huotari 18:33:16 29
30 Normalized intensity Extreme conditions: high pressure Meng et al. Nature Mat. 3, 111 (2004) vertical horizontal Mao et al. Science 302, 425 (2003) Energy loss (ev) Simo Huotari 18:33:16 30
31 Phase diagram of water Simo Huotari 18:33:16 31
32 XANES of water Wernet et al. Science 304, 995 (2004) An ongoing debate liquid water Prepeak taken as a signature of hydrogen bond distortions Difficulties in modeling signal with existing models for water NH 3 -terminated ice surface asymmetric model ice surface vs. bulk ice symmetric asymmetric Simo Huotari 18:33:17 32 Ph. Wernet et al. Science 304 (2004) 995
33 Gaining structural information by XANES spectroscopy connection? spectrum structure application? Wernet et al. Science 304, 995 (2004) Simo Huotari 17:59:14 33
34 X-Ray Raman Scattering Study of High Pressure Ices T. Pylkkänen et al. J. Phys. Chem. B, 2010, 114, g cm g cm -3 Liquid Ice VII (cubic) 0.92 g cm g cm g cm -3 Ice I h (hexagonal) Simo Huotari 18:01:36 34 Ice VI (tetragonal) Ice VIII (VII+proton order) 34
35 X-Ray Raman Scattering Study of High Pressure Ices T. Pylkkänen et al. J. Phys. Chem. B, 2010, 114, g cm g cm -3 Liquid Ice VII (cubic) 0.92 g cm g cm g cm -3 Ice I h (hexagonal) Simo Huotari 18:03:24 35 Ice VI (tetragonal) Ice VIII (VII+proton order)
36 Lithium ion batteries T. T. Fister et al., J. Chem. Phys. 135, (2011) Simo Huotari 18:33:17 36
37 X-ray Raman spectroscopy Simo Huotari Henry Moseley Summer School, Turkey, June 2012
38 Outline of today Part 1 Refresh your memory Part 2 Instrument Part 3 Novel type of 3D imaging Part 4 EXAFS Simo Huotari 17:47:23 38
39 X-ray Raman / Inelastic x-ray scattering - Not to be confused with optical Raman - Core-electron spectroscopy similar to x-ray absorption - Element specific: probes local structure around desired element - Momentum transfer vector q takes the place of polarization in x-ray absorption Simo Huotari 17:47:23 39
40 Compton line Example: diamond Core-level line T. Pylkkänen, PhD Thesis, Univ. Helsinki (2011) Simo Huotari 17:47:23 40
41 Absorption (arb. units) Energy XANES spectroscopy μ E = M E ρ l E M E is the matrix element (depends weakly on E) ρ l E = local density of states with angular symmetry l (ldos or pdos) Angular-momentum projected DOS ρ l E Carbon forms Fermi level sp 3 sp 2, in-plane sp 2, out-of-plane Energy (ev) 1s Simo Huotari 17:47:23 41
42 Examples of Gas Phase Spectra N2O CO2 O K-edge of H 2 CO Hitchcock and Brion, J. Electron Spectrosc. Relat. Phenom. 19, 231 (1980) J. Inkinen et al., in preparation Simo Huotari 17:47:23 42
43 J. Lehtola ERKALE HF/DFT from Hel Simo Huotari 17:47:23 43
44 44 Properties and specialities of ERKALE A Gaussian orbital code Supports calculation at density-functional theory and Hartree-Fock level LDA, GGA, hybrid GGA and meta-gga functionals supported Basis sets of arbitrary angular momentum supported X-ray absorption and x-ray Raman scattering through the transition potential approximation (TPA) Valence excitations through time-dependent DFT with Casida formalism Ground-state electron momentum density and Compton profile Simo Huotari 17:47:23 44
45 Vibrational modes effect on CO2 300 K 850 K J. Inkinen et al. in preparation Simo Huotari 17:47:23 45
46 Calculations of core-level spectra Neglecting vibrations: f> unoccupied occupied i> Simo Huotari 17:47:23 46
47 Including vibrations: Calculations of core-level spectra Franck-Condon overlap integral Simo Huotari 17:47:23 47
48 Absorption vs. scattering Absorption Scattering P ω Ψ f p A Ψ i 2 δ Ei E f + ω f S Q, ω Ψ f e iq r Ψ i 2 δ Ei E f + ω f Dipole selection rule Use the momentum transfer dependence of the scattering matrix element: as q 0 then e iq r = 1 + iq r q r e.g., s s (monopole, l=0) s p (dipole, l=1) s d (quadrupole, l=2) etc... dipole Higher order multipoles Simo Huotari, Benasque TDDFT school :47:23 48
49 Higher-Z materials: 4d-4f (N 4,5 edge) transitions in LaPO 4 4f0 4f1 R. A. Gordon et al. EPL 81, (2008) Simo Huotari 17:48:05 49
50 Higher-Z materials: 4d-4f (N 4,5 edge) transitions in LaPO 4 4f0 R. A. Gordon et al. EPL 81, (2008) Simo Huotari 17:47:23 50
51 Outline of today Part 1 Refresh your memory Part 2 Instrument Part 3 Novel type of 3D imaging Part 4 EXAFS Simo Huotari 17:47:23 51
52 Energy resolution Best solid-state detectors (e.g., silicon drift diodes) offer ~150 ev energy resolution Darwin width of a reflection from a Si crystal is <1 ev: Crystal optics! Bragg s law: nλ = 2d sinθ Simo Huotari 17:47:23 52
53 Darwin width Bragg s law: nλ = 2d sinθ Si(660) θ B = 89 Simo Huotari 17:47:23 53
54 Diffuse scattering from point source? Crystal diffraction OK when beam nearly parallel Diffuse scattering from a point source not OK for flat crystal: alternative solution required Simo Huotari 17:47:23 54
55 Concept of Rowland circle Simo Huotari 17:47:23 55
56 Concept of Rowland circle bending radius R ~ m Simo Huotari 17:47:23 56
57 Concept of Rowland circle Simo Huotari 17:47:23 57
58 Johann approximation Simo Huotari 17:47:23 58
59 Johann approximation R ~ m Simo Huotari 17:47:23 59
60 Crucial element: Analyser crystal Spherically bent analyser crystals for medium energy resolution ( mev) Diced analyser crystals for high energy resolution (1-200 mev)
61 Taupin (1964) Takagi (1962,1969) Simo Huotari 17:47:23 61
62 Summary: Rowland circle -Offers simultaneous focusing and energy analysis of scattering from a point source -Requirement: crystal surface needs to be cylindrical (n=1) or spherical (n=2) and align with the Rowland circle -Bending causes elastic deformations that enlargen the bandwidth 2 E E l R cot n B Taupin (1964) Takagi (1962,1969) θ B Sample R Analyzer Detector Rowland-circle geometry
63 First instruments Nothing like this... These are experiments! Simo Huotari 17:47:23 63
64 First instruments Nothing like this... These are experiments! Simo Huotari 17:50:43 64
65 Increasing solid angle SSRL ( ) ESRF ID16 (9) SPring-8 (15) APS LERIX (19) 65
66 ESRF UPBL6 (G. Monaco, R. Verbeni, L. Simonelli, K. Martel, C. Henriquet, et al.) 6 movable chambers: 12 analyzers each K-B mirrors Simo Huotari 17:47:23 66
67 Instrumental setup for (non-resonant) IXS α = sample Detector High-resolution monochromator e.g. Si(444) High heat load monochromator e.g. Si(111) ΔE/E ~ tan α Incident beam monitor 62 m Focusing mirror 56 m 54 m 50 m Synchrotron radiation source distance from source ~ 0.2 ev Beam mirror ~ 1 sample ~ 50 µm Bandwidth ~ 1 ev 10 kev photons: momentum transfer ~ 1.4 a.u. Typical incident photon energy ~ 5 15 kev Typical energy transfers ~ 0.2 ev 1 kev Typical momentum transfers ~ a.u.
68 Instrumental setup for (non-resonant) IXS α = sample Detector High-resolution monochromator e.g. Si(444) High heat load monochromator e.g. Si(111) ΔE/E ~ tan α Incident beam monitor 62 m Focusing mirror 56 m 54 m 50 m Synchrotron radiation source distance from source ~ 0.2 ev Beam mirror ~ 1 sample ~ 50 µm Bandwidth ~ 1 ev 10 kev photons: momentum transfer ~ 3.4 a.u. Typical incident photon energy ~ 5 15 kev Typical energy transfers ~ 0.2 ev 1 kev Typical momentum transfers ~ a.u.
69 Instrumental setup for (non-resonant) IXS α = sample Detector High-resolution monochromator e.g. Si(444) High heat load monochromator e.g. Si(111) ΔE/E ~ tan α Incident beam monitor 62 m Focusing mirror 56 m 54 m 50 m Synchrotron radiation source distance from source ~ 0.2 ev Beam mirror ~ 1 sample ~ 50 µm Bandwidth ~ 1 ev 10 kev photons: momentum transfer ~ 5.2 a.u. Typical incident photon energy ~ 5 15 kev Typical energy transfers ~ 0.2 ev 1 kev Typical momentum transfers ~ a.u.
70 Outline of today Part 1 Refresh your memory Part 2 Instrument Part 3 Novel type of 3D imaging Part 4 EXAFS Simo Huotari 17:47:23 70
71 Special techniques: imaging R ~ m Simo Huotari 17:47:23 71
72 X-ray imaging: need for contrast Absorption contrast Phase contrast F. Pfeiffer et al., Nature Physics 2, 258 (2006)
73 Chemical contrast: elemental and chemical mapping U. Bergmann et al., PNAS 107, 9060 (2010)
74 Simo Huotari 17:47:23 74
75 How to identify different carbon bonds with IXS? amorphous graphite crystalline graphite armophous diamond crystalline diamond Simo Huotari 17:47:23 75
76 Carbon mystery sample Carbon composite from fusion reactor sp 2 vs. sp 3? Crystalline vs. amorphous?
77 Result: periodic sp 2 bond orientation variation Huotari, Pylkkänen, Verbeni, Monaco, and Hämäläinen Nature Mater. 10, 489 (2011) Simo Huotari 17:47:23 77
78 Detector: photon-counting hybrid pixel detector TimePix Simo Huotari 17:47:23 78
79 Outline of today Part 1 Refresh your memory Part 2 Instrument Part 3 Novel type of 3D imaging Part 4 EXAFS Simo Huotari 17:47:23 79
80 EXAFS EXAFS = Extended x-ray absorption fine structure Oscillations due to photoelectron scattering with surrounding atoms -> intereference effects -> access to local neighbouring structure XAS Carbon K-edge: ~280 ev Oxygen K-edge: ~540 ev XRS Simo Huotari 17:47:23 80
81 Special techniques: EXAFS Recall: - x-ray Raman spectroscopy is a bulk-sensitive alternative to x-ray absorption of soft-x-ray edges ( ev) - x-ray Raman varying the magnitude of momentum transfer (q) can access non-dipole transitions Simo Huotari 17:47:23 81
82 EXAFS of water U. Bergmann et al., J.. Chem. Phys. 127, (2007) Simo Huotari 17:47:23 82
83 EXAFS of diamond: raw data S. Huotari et al., J. Synchrotron Radiat. 19, 106 (2012) Simo Huotari 17:47:23 83
84 EXAFS of diamond: K edge FEFFq is XRS-extension to FEFF (available in FEFF 9, through the NRIXS keyword) A. Soininen et al., Phys. Rev. B 72, (2005) Simo Huotari 17:47:23 84
85 EXAFS of diamond: result FEFFq is XRS-extension to FEFF (available in FEFF 9, through the NRIXS keyword) A. Soininen et al., Phys. Rev. B 72, (2005) Simo Huotari 17:47:23 85
86 Backscattering path Path leg angle 70 degrees Simo Huotari 17:47:23 86
87 Helsinki Group and Collaborators Helsinki: K. Hämäläinen, M. Hakala, C. Sahle, S. Galambosi, A. Sakko, T. Pylkkänen, J. Lehtola, I. Juurinen, K. Ruotsalainen, J. Inkinen, A. Kallonen, A. Rintala, J. Koskelo ESRF: G. Monaco, R. Verbeni, L. Simonelli, V. M. Giordano et al. Dortmund: Ch. Sternemann, M. Tolan et al. Computations: E. Shirley, J. Rehr, A. Rubio, L. G. M. Pettersson Simo Huotari 17:47:23 87
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