Transmission electron microscopy (TEM) is important tools for surface and interface study. Electron Energy Loss Spectroscopy (EELS) belongs to the TEM family, I added some know-how about DFT simulation of EELS spectrum. I showed some tricks and caution which I found important. Please send me a note for questions and comments

1. By
Shruba Gangopadhyay
Email: shruba@gmail.com

2. Basics of EELS
 Material exposed to a beam of electrons with a
known, narrow range of kinetic energies
 Electrons will undergo inelastic scattering, which
means that they lose energy
 Inelastic interactions include
 phonon excitations,
 inter and intra band transitions
 plasmon excitations
 inner shell ionizations
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3. Atomic & Electronic Structure
 STEM + EELS makes
essential connection
between physical &
electronic structure,
both at atomic
resolution
Electron Energy
Loss Spectrometer
Annular Dark Field
(ADF) detector
y
x
Atomic Diameter
Electron Probe
Increasing
energyloss
 We can have an estimate of beam energy ranges from
 http://people.ccmr.cornell.edu/~davidm/WEELS/index.html
 http://pc-web.cemes.fr/eelsdb/index.php?page=search.php

4. EELS …(Theory)
THEORY OF EELS :
The EELS (and XAS) spectral shape is given by the Fermi golden rule.
The core electron is excited to an empty state, where at the edge the lowest empty
state (allowed by the selection rules) is reached.
As such, one essentially probes the empty density of states in the presence of the
core hole. Calculations to obtain a quantitative picture of the empty states can be
performed with DFT based codes.
A double differential scattering cross-section is calculated by
summing over all possible transitions between initial and final
states, each described by a Fermi’s golden rule.
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5. 5

6. When we need core hole approximation
 When you have good energy resolution (<1 eV)
 When screening is poor
 Metals (small), semiconductors(medium), ionic (huge)
 The effect is larger on anions than cations
 More noticeable in nanoparticles and clusters than bulk
 Batson’s Rule: core hole effects are more pronounced when
 The excited electron is confined near the core hole. (It shouldn’t work, but it
does.)
 Atoms surrounded by strong scatterers (often nodeless valence wavefunctions
1s, 2p, 3d…) (e.g Si in SiOx, Al in NiAl, TiB2 out of plane)
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In Wien 2k we can only simulate electron loss near-
edge structure (ELNES) ”: features in the spectrum with
energy loss E = Ec to Ec + 50 eV (by definition). It contains
information on local density of empty states,
oxidation state.

7. How to simulate Core Hole in Wien2k
No core hole (= ground state, sudden approximation)
􀂄 Z+1 approximation (e.g., replace C by N)
􀂄 Remove 1 core electron, add 1 electron to conduction band
􀂄 Remove 1 core electron, add 1 electron as uniform background
charge
More localized the core hole, the bigger the error
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8. How to simulate EELS in in Wien2k
(TELNES)
Construct a supercell and perform an SCF
(need good amount of K points)
If excited states required prepare another input by
reseting energy range and recalculate valence bands
Compute Valence electron densities from eigenvectors
Calculate eigenvalues and corresponding partial charges
Prepare input for EELS
use of beam energy and other angular parameters
This results : The differential cross section is either a function of energy (ELNES ( the output of
Wien2k) integrated over impulse transfer); or a function of impulse transfer (ELNES integrated
over energy loss E), which shows the angular behavior of scattering.
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9. Available softwares and pros and cons
Wien2k Quantum ESPRESSO
(External suite SaX)
Telnes (code) SaX external code
Double differential
scattering cross
section on a
grid of energy loss
Macroscopic
dielectric tensor
within the Random
Phase Approximation
with or without
excitonic effects as a
function of energy
Computationally
less expensive
Very expensive
Applied to various
systems
Not too many
published papers
Band structure codes
PARATEC (Cabaret et al.,2007;Gaudryetal.,2005),
PWSCF(Cabaret et al.,2010;Juhin et al.,2010),
CASTEP(Gao et al.,2008)
WIEN2K(Schwarz et al., 2002),
Real space multiple scattering codes
FDMNES (Joly, 2003)
FEFF(Rehr andAlbers,2000)
Molecular DFT codes
STOBE(Kolczewski andHermann,2005)
ORCA (George etal.,2008)
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10. Literature Review
As per my understanding the advantages of Wien2k is
Can handle large system
No need to worry about core hole pseudopotentials
Applied to TM and Lanthanide including Magnetic transitions
Parallel implementation
Option of using relativistic correction
User friendly interface for generating input files
Extremely active user forum
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Wien2k VO2 (crystal), LiMn2O4, TiO2, ZrO2, Nb1-xMgxB2, LixTiP4 (x=2-
11), LiK edge in Li, Li2O, and LiMn2O4 , Si layers
ferroelectric transition in BaTiO3
………………………………………… TiC , TiN
Quantum
ESPRESSO
Boron, Nitrogen doped graphene, different phases of Al2O3
VASP No direct implementation (derived from DOS), C60

11. Simulated EELS for K edge EELS of
Carbon in TiC using (2x2x2) supercell
1000 k points
100 k points
I did not use any core hole approximation in
this calculation
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12. Sources
 Wien2k manual, Tutorial from 2007 PSU
workshop
 SaX manual
 Presentation from David Mullers summer
school pdf
 Calculations are performed in NERSC using
Wien2k v10.1 and Telnes2
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