X-ray Absorption Spectroscopy

Transcription

1 X-ray Absorption Spectroscopy Matthew Newville Center for Advanced Radiation Sources University of Chicago 12-Sept-2014 SES VI SES VI 12-Sept-2014 SES VI

2 What Is XAFS? X-ray Absorption Fine-Structure (XAFS) is the modulation of the x-ray absorption coefficient at energies near and above an X-ray absorption edge. XAFS is also called X-ray Absorption Spectroscopy (XAS), and is broken into 2 energy regimes: XANES EXAFS X-ray Absorption Near-Edge Spectroscopy Extended X-ray Absorption Fine-Structure which contain related, but slightly different information about an element s local coordination and chemical state. XAFS Characteristics: local atomic coordination chemical / oxidation state applies to any element works at low concentrations minimal sample requirements Fe K-edge XAFS for FeO. Introduction to X-ray Absorption SES VI 12-Sept-2014

3 X-Ray Absorption X-rays are absorbed by all matter through the photo-electric effect: photoelectron An atom absorbs an x-ray when the x-ray energy is transferred to a core-level electron (K, L, or M shell). The atom is left in an excited state with a core hole an empty electronic level. Any excess energy from the x-ray is given to an ejected photo-electron. conduction band valence band E vacuum E Fermi 3d M 4, M 5 3p M 2, M 3 3s M 1 2p L 2, L 3 2s L 1 X-ray Energy 1s K Introduction to X-ray Absorption SES VI 12-Sept-2014

4 The X-ray Absorption Coefficient: µ The intensity of an x-ray beam passing through a material of thickness t is given by the absorption coefficient µ: I = I 0e µt I0 I t where I 0 is the x-ray intensity hitting the material, and I is the intensity transmitted through the material. Introduction to X-ray Absorption SES VI 12-Sept-2014

5 The X-ray Absorption Coefficient: µ The intensity of an x-ray beam passing through a material of thickness t is given by the absorption coefficient µ: I = I 0e µt I0 I t where I 0 is the x-ray intensity hitting the material, and I is the intensity transmitted through the material. µ depends strongly on x-ray energy E atomic number Z, and also on density ρ, and Atomic mass A: µ ρz 4 AE 3 Introduction to X-ray Absorption SES VI 12-Sept-2014

6 The X-ray Absorption Coefficient: µ The intensity of an x-ray beam passing through a material of thickness t is given by the absorption coefficient µ: I = I 0e µt I0 I t where I 0 is the x-ray intensity hitting the material, and I is the intensity transmitted through the material. µ depends strongly on x-ray energy E atomic number Z, and also on density ρ, and Atomic mass A: µ ρz 4 AE 3 Plus: µ has sharp Absorption Edges corresponding to the characteristic core-level energies of the atom. Introduction to X-ray Absorption SES VI 12-Sept-2014

7 X-ray Absorption Measurements µ(e) can be measured two ways: Transmission measure what is transmitted through the sample: I = I 0e µ(e)t Appropriate for concentration samples: 10 wt.%. Fluorescence measure fluorescent x-rays from the re-filling the core hole: µ(e) I f /I 0 Appropriate for dilute elements: 2 wt.% (to ppm, or so). We need a measurement of µ(e) to 0.1%, but with an energy-tunable x-ray source, the measurements are fairly easy. X-ray Absorption Measurements SES VI 12-Sept-2014

8 X-ray Absorption Measurements µ(e) can be measured two ways: Transmission measure what is transmitted through the sample: I = I 0e µ(e)t Appropriate for concentration samples: 10 wt.%. Fluorescence measure fluorescent x-rays from the re-filling the core hole: µ(e) I f /I 0 Appropriate for dilute elements: 2 wt.% (to ppm, or so). We need a measurement of µ(e) to 0.1%, but with an energy-tunable x-ray source, the measurements are fairly easy. X-ray Absorption Measurements SES VI 12-Sept-2014

9 Absorption Edge Energies of the Elements The energies of the K shell absorption edges for the elements go roughly as E K Z 2. Elements with Z > 18 have K-, or L-edge between 2 and 35 kev, which can be accessed at many synchrotron sources. Lower Z elements (softer x-rays) can be measured as well, but may require working in vacuum. X-ray Absorption Measurements SES VI 12-Sept-2014

10 XANES: X-ray Absorption Near-Edge Spectra XANES gives chemical state and oxidation state. Cr K-edge for Cr 3+ and Cr 6+ As K-edge for As 3+ and As 5+ XANES SES VI 12-Sept-2014

11 XANES: X-ray Absorption Near-Edge Spectra XANES gives chemical state and oxidation state. Cr K-edge for Cr 3+ and Cr 6+ As K-edge for As 3+ and As 5+ Analyzing XANES: 1. Linearly combine known spectra to match measured spectra. 2. ab initio calculations to map features to electronic density of states. XANES SES VI 12-Sept-2014

12 Fe K-edge XANES Edge shifts and Heights and positions of pre-edge peaks can also determine valence state. Fe K-edge XANES for several compounds. XANES can be used to fingerprint chemical and mineral phases. XANES SES VI 12-Sept-2014

13 S K-edge XANES XANES of low-z elements are particularly sensitive to oxidation state. XANES SES VI 12-Sept-2014

14 XANES calculation: SF 6 A simple ab initio XANES calculation (from FEFF8) can model principle features and show sensitivity to structural changes: SF 6 : an octahedral coordination with bond length 1.54 Å. An off-center distortion hybridizes the d and p electron levels, giving the resonance near 2507 ev. ab initio calculations are qualitately useful, but generally not quite accurate enough for quantitative analysis. XANES SES VI 12-Sept-2014

15 EXAFS: Extended X-ray Absorption Fine Structure We re interested in the energy oscillations in µ(e), as these will tell us something about the neighboring atoms. We define the EXAFS as: µ(e) = µ 0(E)[1 + χ(e)] χ(e) = µ(e) µ0(e) µ 0(E 0) Subtract off a smooth bare atom background µ 0(E), and divide by the edge step µ 0(E 0) to get the oscillations normalized to 1 absorption event: µ(e) and smooth µ 0(E) for FeO χ(e) for FeO, with E 0 = 7122 ev. EXAFS SES VI 12-Sept-2014

16 EXAFS: χ(k) and XAFS Fourier Transforms XAFS is an interference effect, using the wave-nature of the photo-electron. We express the XAFS in terms of photo-electron wavenumber, k: 2m(E E0) k = 2 We ll also then use Fourier Transforms to convert from k to R. k 2 χ(k) for FeO Fourier Transform χ(r) for FeO. Similar to a Pair Distribution Function from scattering techniques. EXAFS SES VI 12-Sept-2014

17 The EXAFS Equation To model the EXAFS, we use the EXAFS Equation: χ(k) = j N j f j (k)e 2R j /λ(k) e 2k2 σj 2 sin[2kr j + δ j (k)] kr j 2 where f (k) and δ(k) are photo-electron scattering properties of the neighboring atom [and λ(k) is the photo-electron mean-free-path]. If we know these properties, we can determine: EXAFS SES VI 12-Sept-2014

18 The EXAFS Equation To model the EXAFS, we use the EXAFS Equation: χ(k) = j N j f j (k)e 2R j /λ(k) e 2k2 σj 2 sin[2kr j + δ j (k)] kr j 2 where f (k) and δ(k) are photo-electron scattering properties of the neighboring atom [and λ(k) is the photo-electron mean-free-path]. If we know these properties, we can determine: R distance to neighboring atom. N coordination number of neighboring atom. σ 2 mean-square disorder of neighbor distance. EXAFS SES VI 12-Sept-2014

19 The EXAFS Equation To model the EXAFS, we use the EXAFS Equation: χ(k) = j N j f j (k)e 2R j /λ(k) e 2k2 σj 2 sin[2kr j + δ j (k)] kr j 2 where f (k) and δ(k) are photo-electron scattering properties of the neighboring atom [and λ(k) is the photo-electron mean-free-path]. If we know these properties, we can determine: R distance to neighboring atom. N coordination number of neighboring atom. σ 2 mean-square disorder of neighbor distance. f (k) and δ(k) depend on atomic number Z of the scattering atom, so we can also determine the species of the neighboring atom. EXAFS SES VI 12-Sept-2014

20 Scattering Amplitude and Phase-Shift The scattering amplitude f (k) and phase-shift δ(k) depend on atomic number. f (k) extends to higher k values for higher Z elements. For very heavy elements, there is structure in f (k). EXAFS SES VI 12-Sept-2014

21 Scattering Amplitude and Phase-Shift The scattering amplitude f (k) and phase-shift δ(k) depend on atomic number. f (k) extends to higher k values for higher Z elements. For very heavy elements, there is structure in f (k). δ(k) shows sharp changes for very heavy elements. These functions can be calculated for modeling EXAFS. EXAFS SES VI 12-Sept-2014

22 Scattering Amplitude and Phase-Shift The scattering amplitude f (k) and phase-shift δ(k) depend on atomic number. f (k) extends to higher k values for higher Z elements. For very heavy elements, there is structure in f (k). δ(k) shows sharp changes for very heavy elements. These functions can be calculated for modeling EXAFS. Z can usually be determined to ±5. Fe and O can be distinguished, but Fe and Mn cannot be. EXAFS SES VI 12-Sept-2014

23 EXAFS Analysis Example: Modeling the 1st Shell of FeO FeO has a rock-salt structure. To model the FeO EXAFS, we ll calculate the scattering amplitude f (k) and phase-shift δ(k), based on a guess of the structure, with Fe-O distance R = 2.14 Å (a regular octahedral coordination). We ll use these functions to refine the values R, N, σ 2, and E 0 so our model EXAFS function matches our data. Fit results: N = 5.8 ± 1.8 R = 2.10 ± 0.02Å E 0 = -3.1 ± 2.5 ev σ 2 = ± Å 2. χ(r) for FeO data and 1 st shell fit. EXAFS Example: FeO SES VI 12-Sept-2014

24 EXAFS Analysis: 1st Shell of FeO 1 st shell fit in k space. The 1 st shell fit to FeO in k space. There is clearly another component in the XAFS! EXAFS Example: FeO SES VI 12-Sept-2014

25 EXAFS Analysis: 1st Shell of FeO 1 st shell fit in k space. The 1 st shell fit to FeO in k space. There is clearly another component in the XAFS! 1 st shell fit in R space. χ(r) and Re[χ(R)] for FeO (blue), and a 1 st shell fit (red). Though the fit to the magnitude didn t look great, the fit to Re[χ(R)] looks very good. EXAFS Example: FeO SES VI 12-Sept-2014

26 EXAFS Analysis: Second Shell of FeO Adding the second shell Fe to the model, with f (k) and δ(k) for Fe-Fe, and refining R, N, σ 2 : χ(r) data for FeO (blue), and fit of 1 st and 2 nd shells (red). These results are consistent with the known values for FeO: 6 O at 2.13Å, 12 Fe at 3.02Å. EXAFS Example: FeO SES VI 12-Sept-2014

27 EXAFS Analysis: Second Shell of FeO Adding the second shell Fe to the model, with f (k) and δ(k) for Fe-Fe, and refining R, N, σ 2 : χ(r) data for FeO (blue), and fit of 1 st and 2 nd shells (red). These results are consistent with the known values for FeO: 6 O at 2.13Å, 12 Fe at 3.02Å. Fit results: Statistics: R χ 2 ν 100. Shell N R (Å) σ 2 (Å 2 ) E 0 (ev) Fe-O 6.0(1.0) 2.10(.02) 0.015(.003) -2.1(0.8) Fe-Fe 11.7(1.3) 3.05(.02) 0.014(.002) -2.1(0.8) EXAFS Example: FeO SES VI 12-Sept-2014

28 EXAFS Analysis: Second Shell of FeO Adding the second shell Fe to the model, with f (k) and δ(k) for Fe-Fe, and refining R, N, σ 2 : χ(r) data for FeO (blue), and fit of 1 st and 2 nd shells (red). These results are consistent with the known values for FeO: 6 O at 2.13Å, 12 Fe at 3.02Å. Fit results: Statistics: R χ 2 ν 100. Shell N R (Å) σ 2 (Å 2 ) E 0 (ev) Fe-O 6.0(1.0) 2.10(.02) 0.015(.003) -2.1(0.8) Fe-Fe 11.7(1.3) 3.05(.02) 0.014(.002) -2.1(0.8) These are typical even for a very good fit on known structures. The calculation for f (k) and δ(k) are good, but not perfect! EXAFS Example: FeO SES VI 12-Sept-2014

29 EXAFS Analysis: Second Shell of FeO Other views of the data and fit: The Fe-Fe EXAFS extends to higher-k than the Fe-O EXAFS. Even in this simple system, there is some overlap of shells in R-space. The agreement in Re[χ(R)] look especially good this is how the fits are done. Of course, the modeling can get more complicated than this! EXAFS Example: FeO SES VI 12-Sept-2014

30 XANES/EXAFS Spatial and Concentration Ranges Sensitivities and time required for X-ray Spectroscopy measurements from a X-ray microprobe: Measurement Result Concentration Resolution Time µ-xrf Abundances < 1 ppm 1 µm 10 sec XRF Mapping Relative abundances 5 ppm 1 µm 50 msec µ-xanes oxidation state 10 ppm 2 µm 10 min µ-xafs 1 st neighbor distance 50 ppm 5 µm 60 min The more the energy changes, and the more time required, the worse the spatial resolution is. These are estimates of typical-to-best conditions for soil samples, and can vary greatly. MicroXAS SES VI 12-Sept-2014

31 µxanes Primary vs. diagenetic sulfur phases in bryozoan fossils Carbonate fossils have up to 1000 ppm sulfate, carrying a record of the sulfur content of the ancient. S isotope analysis are highly variable and suggest a late deposition of S. XRF map of 3mm section of a bryozoan fossil from the Ordovician era (450 Myears ago) - 5 µm pixels, 30 msec/pt, repeated at 2 incident energies to emphasize sulfide (red), sulfate (blue) and silicon (green). David Fike, Catherine Rose, Jeff Catalano (Washington Univ) S µxanes at several spots confirms localized sulfide grains - probably detrital sulfides - while most of the fossil is dominated by sulfate. MicroXAS SES VI 12-Sept-2014

32 µxafs Sr in coral aragonite Sr concentration in corals has been used as a paleothermometer. Over what lengthscale is this valid? XRF maps of 0.3mm section of a natural coral of Ca (top) and Sr (bottom) show diurnal variation in [Sr] / [Ca] ratio on a 10 micron scale. Nicola Allison, Adrian Finch (Univ St. Andrews) Sr µ-xafs shows that coral trap Sr in aragonite without precipitating SrCO 3, even when [Sr] > above the solubility limit of Sr in aragonite. MicroXAS SES VI 12-Sept-2014

33 High Energy-Resolution Fluorescence XAFS and XANES are heavily used in environmental sciences, element-specific probes of chemical state for any species. Minimal sample requirements. Work at relatively low concentrations (ppm). Require tunable, monochromatic X-rays synchrotron. MicroXAS SES VI 12-Sept-2014

34 High Energy-Resolution Fluorescence XAFS and XANES are heavily used in environmental sciences, element-specific probes of chemical state for any species. Minimal sample requirements. Work at relatively low concentrations (ppm). Require tunable, monochromatic X-rays synchrotron. High (Energy) resolution X-ray Fluorescence (K β ) give chemical information comparable to XANES. Element-specific, minimal sample constraints, as XAS. Scan/analyze emission energy with 1 ev resolution, not incident energy! Currently photon-starved measurements, so fairly high concentrations. detector/analyzer-limited, not intrinsic. Useful for environmental science? MicroXAS SES VI 12-Sept-2014