What is electron crystallography?

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What is Electron Crystallography?
Xiaodong Zou
Structural Chemistry, Arrhenius Laboratory,
Stockholm University
The Royal Swedish Academy of Sciences
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http//www.crystalerice.org/
Crystallography is a technique for investigating
the structure of matter in the ordered solid
state, scientifically defined "crystalline
state".
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X-ray
Crystallography
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What is Electron Crystallography?

• Electron crystallography is the quantitative use
  of different information by electron scattering
  to study perfect crystal structures as well as
  defects and interfaces.

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Why electrons?

• 104-5 times stronger interaction with matter
  compared with X-ray
• - single crystal data on powder sample
• - short data collection time

• Phases are present in high resolution
  electron microscopy (HREM) images

- for nano- and micro-sized crystals
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Transmission electron microscopy

• Diffraction selected area, nano- and
  convergent beam electron diffraction
• Imaging conventional, high resolution
• Chemical analysis EDS and EELS

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SAED Selected Area Electron Diffraction CBED
Convergent Beam Electron Diffraction
Different electron diffraction techniques

• CBED makes use of dynamical efftects
• SAED requires near kinematic conditions
• CBED for unit cell dimensions lt10Å
• SAED for unit cell dimensions gt10Å
• CBED for thick specimens gt200 Å
• SAED for thin specimens lt 200 Å

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Determine unit cell parameters and space group by
SAED
080
800
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Determine unit cell parameters and space group by
CBED
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Lattice Imaging 1972

• 4Å EM image showed details within unit cell
• Image simulation invented
• Contrast reversal by defocusing

Iijima, S., J. Appl. Phys. 42 (1971) 5891 Ijima,
S., OKeefe, M.A. and Buseck, P., Nature 274
(1978) 322
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Structure Determination by Electron
Crystallography
Exit Wave Phase
Structure Factors F(hkl) Amplitude Phase
Amplitudes are obtained from ED Phases are
determined by direct methods or Patterson method.
Both amplitudes and phases are obtained from
images
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A crystal structure determination contains two
steps solving and refining the structure

• Solving finding a rough model of at
• least the most important (heaviest) atoms
• within about 0.25 Å. Use EM-images.
• 2Å resolution, few reflections, phases.
• Refine by least-squares methods find
• all atoms within about 0.02 Å.
• Use SAED or CBED data. 1Å resolution,
• many reflections, only amplitudes.

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Images or diffraction patterns?

• Images have lower resolution but phases
• SAED gives more amplitudes but no phases
• HREM for solving structures
• SAED and CBED for refining structures
• SAED milder for radiation sensitive materials

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The different phases in EM
Property Crystallographic structure factor phases Wave front phases
Wave length The waves are Phases relative to Phase information Physical entity Method of retrieval Interrelations ?1 - 20 Å Stationary standing waves symmetry elements in crystal present in EM images electron density or potential Fourier transform of EM image modulates the wave front ? 0.03 Å moving - propagating incident electron wave front lost in EM images electromagnetic wave holography, focal series EM records the structure factor
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History of electron crystallography

• Pinsker, Vainshtein and Zvyagin (1940-50s) solved
  inorganic crystal structures from electron
  diffraction patterns
• Cowley Moodie (1957) developed n-bean
  dynamical diffraction - fear of dynamical effects
  caused by strong interaction between electrons
  and matter
• Klug (1968) crystallographic structure factor
  phases from in EM images
• Unwin and Henderson (1975) solved first membrane
  proteins
• Dorset Hauptmann (1976) applied direct methods
  on electron diffraction data, organic crystals
• Hovmöller, Li, Fan (1980s) - inorganic atomic
  co-ordinates from EM images

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Main breakthrough of electron crystallography was
in 1990

• Direct methods
• Maximum entropy likelihood
• Crystallographic image processing
• Electron holography
• Exit wave reconstruction
• Structure determination by CBED
• ...

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n-beam dynamical diffraction theory
Structure analysis by electron diffraction from
oblique textures
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Aron Klug - Nobel Prize in Chemistry 1982

"for his development of crystallographic electron
microscopy and his structural elucidation of
biologically important nucleic acid-protein
complexes

• 3D reconstruction
• Phases from the FT
• Virus structures

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Solving structures from electron diffraction data
Zr2Se
in a similar way as from X-ray diffraction ...
Ti9Se2
Dynamic
kinematic
Weirich, Zou, Hovmöller et al. Acta Cryst. A56
(2000) 29-35
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Atomic coordinates to 0.2 Å accuracy solved from
EM image
(-1 1)
(1 1)
(1 1)

• Hovmöller, et al. Nature 311 (1984) 238

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Unknown Structure Solved and Refined by Electron
Crystallography
C2/m a 25.52, b 3.448, c 19.20Å, ?
117.84?
Ti11Se4
HREM
All 23 unique atoms found from HREM after image
processing

• Ti

Se
Refined to 0.02 Å precision using ED data
Model
ED
Weirich, Ramlau, Simon, Hovmöller, Zou et al.
Nature 382 (1996) 144 -146
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Intergrowth of zeolite beta polymorph A, B C
(here pure SiO2)
Electron crystallography on Zeolites
The structure of the new polymorph C could be
determined by combining HREM and ED.
Liu, Ohsuna, Terasaki, et al., J. Am. Chem.
Soc., 123 (2001), 5370-5371.
Ohsuna, Liu, Terasaki, et al. J. Phys. Chem. B106
(2002), 5673-5678.
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3D reconstruction of ?-Al81Cr11Fe8
P63/m a 40.687, c 12.546 Å
1176 atoms, of which 129 unique, are found in the
unit cell
Zou, Mo, Hovmöller, Li, Kuo Acta Cryst. A59
(2003) 526-539
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Imaging oxygen - spherical aberration corrector
Haider et al. Nature 392 (1998) 768-769 Batson et
al. Nature 418 (2002) 617-620
Jia, Lentzen, Urban Science 299 (2003)
870-873 Jia and Urban Science 303 (2004) 2001-2004
Atomic-Resolution and Measurement of Oxygen
Concentration
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Structure refinement using dynamical diffraction
Exit wave reconstruction Multi-slice least
square (MSLS) refinement
Mg5Si6 Particles in Al
A rough structure model was obtained from exit
waves reconstructed from images. The structure
was refined with electron nanodiffraction data (R
3.1)
Zandbergen, Andersen, Jansen, Science 277 (1997)
1221 Jansen, Tang, Zandbergen, Schenk, Acta
Cryst. A54 (1998) 91
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Direct Atom-Resolved Imaging of Oxides and Their
Grain Boundaries using ultra high voltage TEM
(1250 kv) Zaoli Zhang, Wilfried Sigle, Fritz
Phillipp, Manfred Ruhle
Science 299 (2003) 870-873
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Copper-Oxygen Bond in Cuprite determined by CBED
Measured surface of constant charge density
difference in Cu2O
Red excess electrons Blue holes
Zuo, Kim, OKeefe, Spence, Nature 401 (1999) 49
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Phasing electron diffraction by over-sampling
Miao, Charalambous, Kirz Sayre Nature 400
(1999) 342 Miao Sayre, Acta Cryst. A56, (2000)
596-605
Atomic Resolution Imaging of a Carbon Nanotube
from Diffraction Intensities
J. M. Zuo et al. Science 300 (2003) 1419-1421
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Ultrafast Electron Crystallography Transient
Structures and Phase Transitions
Ahmed Zewail, Nobel Prize in Chemistry 1999 for
his contribution on femtosecond chemistry
Ruan, Zewail et al. Science 304 (2004) 80-84
http//www.its.caltech.edu/femto/
Ihee, Zewail et al. Science 291 (2001) 458-462
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Transient Structures and Phase Transitions
Interfacial Water
Ihee, Zewail et al. Science 291 (2001) 458-462
Ruan, Zewail et al. Science 304 (2004) 80-84
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Solid-liquid state transition in polycrystalline
Al
Siwick, Dwyer, Jordan, Miller, Science 302 (2003)
1382-1385
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Electron Crystallography Schools

• 1990 Erice (workshop)
• 1993 Stockholm, Beijing (IUCr)
• 1994 Stockholm
• 1995 Stockholm
• 1996 Stockholm (EUCHEM conference)
• 1997 Erice Katowice
• 1998 Stockholm
• 1999 Nantes
• 2000 Aachen
• 2001 Barcelona
• 2002 Tampere
• 2003 Moscow
• 2004 Erice

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• 2011 Erice?