Transcript Chapter 12
XII. Electron diffraction in TEM
Newest TEM in MSE 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.
12-1. Electron radiation (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
2
(
pc
)
2
(
m
0
c
2
)
2
p
E
(
KE
mc
2
m
0
c
2
)
2
KE
(
m
0
c
2
pc
)
2
(
pc
)
pc
2
(
m
0
c
2
)
2
(
KE KE
2
KE
2
m
0
2
c
2
)
2
KEm
0
c
2
(
m
0
c
2
m
0 2
)
c
2 4 2
KEm
0
c
2
m
2 0
c
4 Massless particle:
p
KE
/
c p
2
m
0
KE
KE
2
c
2 2
m
0
KE
1
KE
2
m
0
c
2
h p
2
m
0
KE h
1
KE
2
m
0
c
2
KE
e
voltage
h m
0 = 6.62606957×10 -34 = 9.10938291
10 -31 m 2 kg/s Kg
c
= 299792458 m/s
e
= 1.60217657×10 -19 coulombs 1eV = 1.602176565
10 -19 J (Kg m 2 /s 2 )
For 200 KV electrons
KE
200 keV 3 .
204 10 14 J(Kg m 2 /s 2 )
h
2
m
0
KE
1
KE
2
m
0
c
2 1 2 9 .
109 3 .
204 10 31 10 14 ( 2 .
998 10 8 ) 2 1 6 0 .
.
1956 626 1 .
10 34 0934 m 2 Kg/s 6 2 .
626 9 .
109 10 34 10 31 m 2 Kg Kg/s 3 .
204 2 .
74 2 .
416 10 22 mKg/s 10 14 Kg 10 12 m m 2 / s 2
h
2
m
0
KE
1 1
KE
2
m
0
c
2 2 .
506 10 12 m
For 20 KV electrons
KE
20 keV 3 .
20436 10 15 J(Kg m 2 /s 2 ) 2
m
0
c
2 (
e
V ) 2 9 .
109 10 31 ( 2 .
998 10 8 ) 2 1 .
602 10 19 1 .
022 10 6 1
KE
2
m
0
c
2
h
2
m
0 1 20000 1 .
022 10 6 1 0 .
01957 1 .
00973 2 1 .
22 9 .
109 10 9 6 .
626 10 34 m 2 Kg/s 10 31 Kg 1 .
60217 10 19 J/eV 1 .
22 10 9
KE
1 .
22 10 9 20000 8 .
6 10 12 (m)
For X-ray Wavelength = 1.542 Å
h p
hc pc
hc E E
hc
E
6 .
626 10 34 (m 2 kg/s) 2 .
998 10 8 (m/s) 1 .
542 10 10 (m) 1 .
288 10 15 (m 2 kg/s 2 ) J
E
1 .
288 10 15 (J) 1 .
60217 10 19 (J/
e
V) 8 .
04 10 3 (eV)
E
(eV) 1 .
2399 10 6 (eV/m) (m) ~ 1240 (eV/nm) (nm)
(ii) electrons can be focused c.f. x-ray is hard to focus (iii) easily scattered
f e
10 4
x f e
and
f x
: form factor for electron and x-ray, respectively Form factor for electron includes nucleus scattering!
(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
2 2 sin = 2Å 0 .
037 sin 0 .
0925
0 .
0925
for 200Kev 0 .
0625
0 .
0925
180
0 .
53
o
0 .
025 A
0 .
0625 180 0 .
34 o
12-3.
d
spacing determination is not good 2
d
sin
hkl
For fixed
d
2
d
d
sin
/
d
2 sin 2
d
sin cot
d
cos sin 2
d
cos sin ( (brevity) 2 cot ) 90 o ; cot 0 ;
d
0 we can get more accurate d at higher angle!
In TEM
0 .
5
o 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 ZrO 2 http://www.microscopy.ethz.ch/BFDF-TEM.htm
Diffraction Bright-Field Dark-Field pattern Image 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.