Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative...

Max-Planck-Institut für Chemische Energiekonversion

Electron Energy-Loss Spectrometry

Walid Hetaba28.10.2016

Energy loss spectrum

Williams, Carter: Transmission Electron Microscopy, Springer 2009

Energy loss spectrum

Williams, Carter: Transmission Electron Microscopy, Springer 2009

Ti L2,3-edge O K-edge

NiO, WIEN2k TiO2, exp.

Hetaba et al., PRB 85 (2012), 205108

Energy loss near edge spectrum

Schrödinger equation:

Formalism

Bra-Ket formalism:

Double differential scattering cross-section

Dynamic form factor (DFF)

Demtröder, Experimentalphysik 3, Springer 2010

Interferometric EELS (the mixed DFF)

Nelhiebel, PhD thesis, 1999Demtröder, Experimentalphysik 3, Springer 2010

Kohl & Rose, 1985

The MDFF for crystals

Experimental realisation

Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.80 ± 0.113 44.34 Ti 1.00 ± 0.000 55.66

Experimental spectra

Relative quantification: Elem. Atomic ratio (/Ti) Percent content N 0.47 ± 0.067 32.01 Ti 1.00 ± 0.000 67.99

Differences in fine structure: different electronic structure

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

WIEN2k simulation

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

WIEN2k simulation

TELNES – calculation of spectra

Effects of anisotropy

Hébert-Souche et al., UM 83 (2000), 9-16

Orientation: c-axis parallel to electron-beam

Anisotropy – experiment 1

Orientation: c-axis perpendicular to electron-beam

Anisotropy – experiment 2

• EMCD, 2006 • Polarisation vector momentum transfer vector

Energy-loss magnetic chiral dichroism

EMCD – example 1

EMCD – example 2

Channelling-Formalismus/Sims

ELCE, 1982

Energy losses by channelled electrons

Channelling-Formalismus/Sims

Krivanek et al., Ultram 9 (1982), 249

ELCE, 1982

Energy losses by channelled electrons

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

OAxis color code: x, y, z

Hetaba, Micron 63 (2014), 15

ELCE experiments & simulations

• 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

Electron Energy-Loss · PDF fileElectron Energy-Loss Spectrometry ... Relative...

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