Identifying crystalline structure from

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Identifying crystalline structure from
Transmission electron diffraction
TED
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The geometric characteristic of electron
diffraction
Direct correspondence with the reciprocal lattice
Zone uvw
Characteristic of the projected reciprocal lattice
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Symmetry of the diffraction pattern
Arbitrarily introduce a symmetry center
Compare a trigonal and a hexagonal lattice
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6mm
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Higher order Lane zone
Origin the finite size of the Ewald sphere
R0
R1
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2q
1/l
N order (uvw)N
Therefore, if we take 001 zone, the HOLZ will
provide c parameter as
N/ruvw
1/t
O
hkl
0 order (uvw)0
Only for approximation
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Indexing the higher order Lane zone
and the reciprocal vector rn ? r1, r2
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Application of the higher order Lane zone
1 order
-2 order
2 order
Fcc 112 zone
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The dynamic effectmultiple diffractions

• reappearance of the diffractions that are not
  allowed by the structural factor or system
  reasons
• The change in the diffraction intensity

Double diffraction
Hexagonal 010 zone
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The condition for double diffraction
It looks like as long as both and
exist Double diffraction
appears
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Can we get rid of the double diffractions?
(sometimes)

• Screw axis
• Glide planes
• Non-primitive lattice no multiple diffraction
  effect

100 zone
b Glide plane (100), glide distance b/2
(-x,y1/2,z)
b
(x,y,z)
a
When k2n, F ? 0 k ? 2n, F0
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Indexing the diffraction pattern of known
crystalline structure
uvw method
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hkl method

• Calculate the length of the reciprocal lattice
  vector for all possible hkl based on crystal
  symmetry (structural factor and system absence).
  Compare them with the ones measured from the
  experimental electron diffraction patterns.
• Calculate the angles between these hkl pairs,
  and get rid of that is not consistent with
  the experimental result
• Calculate uuvw from

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Special diffraction patternstwin structures
Twin Two or more crystals in parallel, they will
overlap with each other when applying certain
symmetry operation. The symmetry operations
include mirror plane, Cn rotation
n?K1 as C2 K1 as m h1 as C2 s ? h1 as m
No center symmetry
n?K1 as C2 h1 as C2
With center symmetry
All the same
Cubic system
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Deduction of the diffraction pattern of twins
General idea Find htktlt on the (uvw) zone
from the (hkl)T
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The index transformation
HKL
To transform hklT to htktlt
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Examples
The twin plane is 111 and the h1 is lt112gt
FCC
Take HKL as (1-11)and hkl as (1-11) as an example
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Taking HKL1-11 and hkl1-1-1 as an example
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Ring pattern
Many fine particles in the illumination area,
each of them is a single crystal and orientated
randomly
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Typical polycrystalline Au diffraction pattern
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Amorphous materials
Diffused ring pattern Reflecting the short
range ordered structure Often seen at
contamination layer or on carbon support film
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Tutorial on diffraction analysis