Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative...
Transcript of Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative...
![Page 1: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/1.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Electron Energy-Loss Spectrometry
Walid Hetaba28.10.2016
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Max-Planck-Institut für Chemische Energiekonversion
Energy loss spectrum
Williams, Carter: Transmission Electron Microscopy, Springer 2009
![Page 3: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/3.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Energy loss spectrum
Williams, Carter: Transmission Electron Microscopy, Springer 2009
![Page 4: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/4.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Ti L2,3-edge O K-edge
NiO, WIEN2k TiO2, exp.
Hetaba et al., PRB 85 (2012), 205108
Energy loss near edge spectrum
ELNES
![Page 5: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/5.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Schrödinger equation:
Formalism
Bra-Ket formalism:
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Max-Planck-Institut für Chemische Energiekonversion
Double differential scattering cross-section
![Page 7: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/7.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Double differential scattering cross-section
![Page 8: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/8.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Double differential scattering cross-section
![Page 9: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/9.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Double differential scattering cross-section
![Page 10: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/10.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Double differential scattering cross-section
Dynamic form factor (DFF)
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Max-Planck-Institut für Chemische Energiekonversion
Demtröder, Experimentalphysik 3, Springer 2010
Interferometric EELS (the mixed DFF)
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Max-Planck-Institut für Chemische Energiekonversion
Nelhiebel, PhD thesis, 1999Demtröder, Experimentalphysik 3, Springer 2010
Kohl & Rose, 1985
Interferometric EELS (the mixed DFF)
![Page 13: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/13.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Nelhiebel, PhD thesis, 1999Demtröder, Experimentalphysik 3, Springer 2010
Kohl & Rose, 1985
Interferometric EELS (the mixed DFF)
![Page 14: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/14.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Nelhiebel, PhD thesis, 1999Demtröder, Experimentalphysik 3, Springer 2010
Kohl & Rose, 1985
Interferometric EELS (the mixed DFF)
![Page 15: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/15.jpg)
Max-Planck-Institut für Chemische Energiekonversion
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Max-Planck-Institut für Chemische Energiekonversion
The MDFF for crystals
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Max-Planck-Institut für Chemische Energiekonversion
The MDFF for crystals
![Page 18: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/18.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Experimental realisation
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Max-Planck-Institut für Chemische Energiekonversion
Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34 Ti 1.00 ± 0.000 55.66
Experimental spectra
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Max-Planck-Institut für Chemische Energiekonversion
Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.47 ± 0.067 32.01 Ti 1.00 ± 0.000 67.99
Experimental spectra
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Max-Planck-Institut für Chemische Energiekonversion
Experimental spectra
Differences in fine structure: different electronic structure
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Max-Planck-Institut für Chemische Energiekonversion
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Max-Planck-Institut für Chemische Energiekonversion
Payne et al., Rev. Mod. Phys. 64, 1045 (1992)
Calculate starting density from atomic densities:
Calculate potential from density
Solve Kohn-Sham equation:
Calculate density from gained wave functions:
New density = old density?
Input: Unit cell with atomic positions
no
yes
WIEN2k simulation
![Page 24: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/24.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Payne et al., Rev. Mod. Phys. 64, 1045 (1992)
Calculate starting density from atomic densities:
Calculate potential from density
Solve Kohn-Sham equation:
Calculate density from gained wave functions:
New density = old density?
Input: Unit cell with atomic positions
no
yes
WIEN2k simulation
![Page 25: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/25.jpg)
Max-Planck-Institut für Chemische Energiekonversion
TELNES – calculation of spectra
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Max-Planck-Institut für Chemische Energiekonversion
θ
k1k0
q
Effects of anisotropy
![Page 27: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/27.jpg)
Max-Planck-Institut für Chemische Energiekonversion
θ
k1k0
q
Effects of anisotropy
![Page 28: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/28.jpg)
Max-Planck-Institut für Chemische Energiekonversion
θ
k1k0
q
Hébert-Souche et al., UM 83 (2000), 9-16
Effects of anisotropy
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Max-Planck-Institut für Chemische Energiekonversion
Orientation: c-axis parallel to electron-beam
Anisotropy – experiment 1
![Page 30: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/30.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Orientation: c-axis perpendicular to electron-beam
Anisotropy – experiment 2
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Max-Planck-Institut für Chemische Energiekonversion
• EMCD, 2006 • Polarisation vector momentum transfer vector
Energy-loss magnetic chiral dichroism
![Page 32: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/32.jpg)
Max-Planck-Institut für Chemische Energiekonversion
kq‘
EE‘
q
• EMCD, 2006 • Polarisation vector momentum transfer vector
Energy-loss magnetic chiral dichroism
![Page 33: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/33.jpg)
Max-Planck-Institut für Chemische Energiekonversion
• EMCD, 2006 • Polarisation vector momentum transfer vector
Energy-loss magnetic chiral dichroism
![Page 34: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/34.jpg)
Max-Planck-Institut für Chemische Energiekonversion
• EMCD, 2006 • Polarisation vector momentum transfer vector
Energy-loss magnetic chiral dichroism
![Page 35: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/35.jpg)
Max-Planck-Institut für Chemische Energiekonversion
EMCD – example 1
![Page 36: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/36.jpg)
Max-Planck-Institut für Chemische Energiekonversion
EMCD – example 1
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Max-Planck-Institut für Chemische Energiekonversion
EMCD – example 2
![Page 38: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/38.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Channelling-Formalismus/Sims
ELCE, 1982
Energy losses by channelled electrons
![Page 39: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/39.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Channelling-Formalismus/Sims
Krivanek et al., Ultram 9 (1982), 249
ELCE, 1982
Energy losses by channelled electrons
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Max-Planck-Institut für Chemische Energiekonversion
Incoming wave, scattering, outgoing wave Input: crystal, exp. paramters, scattering model Output: Bloch waves, intensity maps, thickness dependence
Löffler & Schattschneider, Ultram 110 (2010), 831 Hetaba, Diploma-Thesis, 2011
ELCE simulations
![Page 41: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/41.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Incoming wave, scattering, outgoing wave Input: crystal, exp. paramters, scattering model Output: Bloch waves, intensity maps, thickness dependence
Löffler & Schattschneider, Ultram 110 (2010), 831 Hetaba, Diploma-Thesis, 2011
ELCE simulations
![Page 42: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/42.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Incoming wave, scattering, outgoing wave Input: crystal, exp. paramters, scattering model Output: Bloch waves, intensity maps, thickness dependence
Löffler & Schattschneider, Ultram 110 (2010), 831 Hetaba, Diploma-Thesis, 2011
ELCE simulations
![Page 43: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/43.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Incoming wave, scattering, outgoing wave Input: crystal, exp. paramters, scattering model Output: Bloch waves, intensity maps, thickness dependence
Löffler & Schattschneider, Ultram 110 (2010), 831 Hetaba, Diploma-Thesis, 2011
ELCE simulations
![Page 44: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/44.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Incoming wave, scattering, outgoing wave Input: crystal, exp. paramters, scattering model Output: Bloch waves, intensity maps, thickness dependence
Löffler & Schattschneider, Ultram 110 (2010), 831 Hetaba, Diploma-Thesis, 2011
ELCE simulations
![Page 45: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/45.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Ti
O
OAxis color code: x, y, z
Hetaba, Micron 63 (2014), 15
ELCE experiments & simulations
![Page 46: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/46.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Ti
O
OAxis color code: x, y, z
Hetaba, Micron 63 (2014), 15
ELCE experiments & simulations
![Page 47: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/47.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Ti
O
OAxis color code: x, y, z
Hetaba, Micron 63 (2014), 15
ELCE experiments & simulations
![Page 48: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/48.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Hetaba, Micron 63 (2014), 15
ELCE experiments & simulations
![Page 49: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/49.jpg)
Max-Planck-Institut für Chemische Energiekonversion
Hetaba, Micron 63 (2014), 15
ELCE experiments & simulations
![Page 50: Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34](https://reader031.fdocuments.us/reader031/viewer/2022021816/5a78de457f8b9a5a148ce60b/html5/thumbnails/50.jpg)
Max-Planck-Institut für Chemische Energiekonversion
• EELS comparable to XAS • Available at lower costs • Almost all TEMs have EELS-capability • Usually less energy-resolution but higher spatial resolution
• EELS is a versatile analytical methods • Information about:
• Elemental composition • Thicknes • Electronic structure • Optical properties • Magnetic properties
Summary