xii. electron diffraction in tem jeol jem-arm200fth spherical-aberration corrected field emission...
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XII. Electron diffraction in TEM
JEOLJEM-ARM200FTH
Spherical-aberration Corrected Field Emission Transmission Electron Microscope
Newest TEM in MSE
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Other TEM in MSE
JEOL JEM-3000F
JEOL JEM-2100
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Diffraction pattern: scattered in the same direction; containing information on the angular scattering distribution of the electronsImage plane (bottom)
Simple sketch of the beam path of the electrons in a TEM
The diffraction pattern and the image are related through a Fourier transform.
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12-1. Electron radiation
(i) ~ hundreds Kevp
h
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.
highly monochromatic than X-ray
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p
h
2
0
02
2
0 2122
cm
KEKEm
c
KEKEmp
22
0
22 )()( cmpcE
2
0
2 cmKEmcE 22
0
222
0 )()()( cmpccmKE 22
0
22
0
2 )()()( cmcmKEpc 42
0
42
0
2
0
2 2 cmcmcKEmKE 2
0
2 2 cKEmKEpc
Massless particle: cKEp /
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2
0
0 212
cmKE
KEm
h
p
h
voltageeKE
h = 6.62606957×10-34 m2kg/sm0 = 9.1093829110-31 Kgc = 299792458 m/se = 1.60217657×10-19 coulombs1eV = 1.60217656510-19 J (Kgm2/s2)
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For 200 KV electrons)/smJ(Kg 10204.3keV 200 2214 KE
2831
14
20 )10998.2(10109.92
10204.31
21
cm
KE
0934.11956.01
221431
234
0 s/mKg10204.3Kg10109.92
Kg/sm10626.6
2
KEm
h
m1074.2mKg/s10416.2
Kg/sm10626.6 1222
234
m 10506.2
21
1
212
20
0
cmKEKEm
h
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For 20 KV electrons)/smJ(Kg 1020436.3keV 20 2215 KE
619
28312
0 10022.110602.1
)10998.2(10109.92)V(2
ecm
(m) 106.820000
1022.11022.1 1299
KE
00973.101957.0110022.1
200001
21
620
cm
KE
J/eV1060217.1Kg10109.92
Kg/sm10626.6
2 1931
234
0
m
h
91022.1
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For X-ray Wavelength = 1.542 Å
E
hc
pc
hc
p
h
hc
E
(m) 10542.1
(m/s) 10998.2kg/s)(m 10626.610
8234
E
)kg/s(m 10288.1 2215
(eV) 1004.8V)(J/ 1060217.1
(J) 10288.1 319
15
eE
J
(nm)
(eV/nm) 1240~
(m)
(eV/m) 102399.1(eV)
6
E
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(ii) electrons can be focusedc.f. x-ray is hard to focus
(iii) easily scattered
xe ff 410
: form factor for electron and x-ray, respectively
xe ff and
Form factor for electron includes nucleus scattering!
(iv) need thin crystals
< 1000Å, beam size m
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12-2. Bragg angle is small
sin2 hkld
for 100 KeV
A 037.0 Assume d = 2Å
037.0sin22 0925.0sin o53.0
1800925.00925.0
for 200Kev
A 025.0 o34.0
1800625.00625.0
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12-3. d spacing determination is not good
sin2 hkld sin2d (brevity)
For fixed
sin2d
2sin
cos
2
d
)cot(sin
cos
sin2
dd
cot/ dd
0 ;0cot ;90o dwe can get more accurate d at higher angle!
o5.0In TEM
Not good for d determination!
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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
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(1) An electron beam is usually incident along the zone axis of the electron diffraction pattern.
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The sample can be tuned along another zone axis [xyz] . All the spots in the diffraction pattern belongs the zone axis [xyz].
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12-5. Electron diffraction pattern from a polycrystalline material
Example: polycrystalline PtSi/p-Si(100)
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Ewald sphere constructions for powders and polycrystalline materials
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12-6. diffraction and image (bright field, dark field)
(a) Bright field image
http://labs.mete.metu.edu.tr/tem/TEMtext/TEMtext.html
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(b) Dark filed image
http://labs.mete.metu.edu.tr/tem/TEMtext/TEMtext.html
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http://www.microscopy.ethz.ch/BFDF-TEM.htmExample: microcrystalline ZrO2
Diffractionpattern
Bright-FieldImage
Dark-FieldImage
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.