### Chapter 12

```XII. Electron diffraction in TEM
JEOL
JEM-ARM200FTH
Spherical-aberration
Corrected Field
Emission Transmission
Electron Microscope
Other TEM in MSE
JEOL JEM-3000F
JEOL JEM-2100
Simple sketch of the
beam path of the
electrons in a TEM
Diffraction pattern: scattered in the same
direction; containing information on the angular
scattering distribution of the electrons
Image plane (bottom)
The diffraction pattern and the image are related
through a Fourier transform.
(i) ~ hundreds Kev
 
h
p
highly monochromatic than X-ray
Typical TEM voltage: 100 – 400 KV
Relativistic effect should be taken into
account!
SEM typically operated at a potential of 10
KV  v ~ 20% c (speed of light)
TEM operated at 200 kV  v ~ 70% c.
 
h
E  ( pc )  ( m 0 c )
2
p
 E  mc
2
2
 KE  m 0 c
2
2
( KE  m 0 c )  ( pc )  ( m 0 c )
2
( pc )  ( KE  m 0 c )  ( m 0 c )
2
2
2
2
2
2
 KE
pc 
2
2
2
2
2
 2 KEm 0 c  m 0 c  m 0 c
2
KE  2 KEm 0 c
2
2
4
2
2
Massless particle: p  KE / c
p
2 m 0 KE 
KE
c
2
2

2 m 0 KE
1
KE
2m 0c
2
4
 
h
p
h

2 m 0 KE
1
KE
2m 0c
2
KE  e  voltage
h = 6.62606957×10-34 m2kg/s
m0 = 9.1093829110-31 Kg
c = 299792458 m/s
e = 1.60217657×10-19 coulombs
1eV = 1.60217656510-19 J (Kgm2/s2)
For 200 KV electrons
 14
KE  200 keV  3 . 204  10
1
KE
2 m 0c
h
2
3 . 204  10

1

1  0 . 1956  1 . 0934
2  9 . 109  10
6 . 626  10

2 m 0 KE
J(Kg  m /s )
2
 31
 34
 31
2
 14
 ( 2 . 998  10 )
8
2
2
m Kg/s
 14
2  9 . 109  10 Kg  3 . 204  10 Kg  m / s
 34
2
6 . 626  10 m Kg/s
 12

 2 . 74  10 m
 22
2 . 416  10
mKg/s
 
h
2 m 0 KE
1
1
 2 . 506  10
KE
2 m 0c
2
 12
2
m
2
For 20 KV electrons
KE  20 keV  3 . 20436  10
2 m 0c (eV ) 
2
1
KE
2 m 0c
h
2m0

2
2  9 . 109  10
 31
 15
J(Kg  m /s )
2
 ( 2 . 998  10 )
8
2
 19

1 . 602  10
20000
1

6
1 . 022  10
6 . 626  10
2  9 . 109  10
 1 . 22  10
1 . 22  10
KE
 31
 34
2
 1 . 022  10
1  0 . 01957  1 . 00973
2
m Kg/s
Kg  1 . 60217  10
 19
9
9

1 . 22  10
20000
9
 8 . 6  10
 12
(m)
J/eV
6
For X-ray
 
h
p
E 

hc

hc
pc
6 . 626  10
E
 34
2
8
2
 10
 15
 19
1 . 2399  10
(m)
2
(m kg/s )
1 . 288  10
E (eV) 

(m kg/s)  2 . 998  10 (m/s)
 15
1 . 60217  10
hc
E 
1 . 542  10
 1 . 288  10
E 
Wavelength = 1.542 Å
(J)
J
 8 . 04  10 (eV)
3
(J/ e V)
6
 (m)
(eV/m)
~
1240 (eV/nm)
 (nm)
(ii) electrons can be focused
c.f. x-ray is hard to focus
(iii) easily scattered
f e  10 f x
4
: form factor for electron and
x-ray, respectively
Form factor for electron includes nucleus
scattering!
f e and f x
(iv) need thin crystals
＜1000Å, beam size  m
12-2. Bragg angle is small
2 d hkl sin   

for 100 KeV    0 . 037 A
Assume d = 2Å
sin   0 . 0925
2  2 sin   0 . 037
  0 . 0925  0 . 0925 
180

 0 . 53

o
   0 . 025 A
180
o
  0 . 0625  0 . 0625 
 0 . 34
for 200Kev

12-3. d spacing determination is not good
2 d hkl sin   
2d sin    (brevity)
For fixed 

d
  cos  
d 




2
2   sin  
2 sin 

d
  cos  



  d (  cot  )

2 sin    sin  
  d / d   cot   
  90 ; cot   0 ;  d  0
o
we can get more accurate d at higher angle!
o
In TEM   0 . 5
Not good for d determination!
12-4. Electron diffraction pattern from a single
crystalline material
Example: epitaxial PtSi/p-Si(100)
Ewald sphere construction:
 is very small k is very large
compared to the lattice spacing in the
reciprocal space
(1) An electron beam is usually incident
along the zone axis of the electron
diffraction pattern.
The sample can be tuned along another zone
axis [xyz] . All the spots in the diffraction
pattern belongs the zone axis [xyz].
12-5. Electron diffraction pattern from a
polycrystalline material
Example: polycrystalline PtSi/p-Si(100)
Ewald sphere constructions for powders and
polycrystalline materials
12-6. diffraction and image (bright field, dark field)
(a) Bright field image
http://labs.mete.metu.ed
u.tr/tem/TEMtext/TEMt
ext.html
(b) Dark filed image
http://labs.mete.metu.edu.tr/tem/TEMtext/TEMtext.html
Example: microcrystalline ZrO2
http://www.microscopy.ethz.ch/BFDF-TEM.htm
Diffraction
pattern
Bright-Field
Image
Dark-Field
Image
BF image: some crystals appear with dark contrast since
they are oriented (almost) parallel to a zone axis (Bragg
contrast).
DF image: some of the microcrystals appear with bright
contrast, namely such whose diffracted beams partly
pass the objective aperture.
```