XII. Electron diffraction in TEM
JEOLJEM-ARM200FTH
Spherical-aberration Corrected Field Emission Transmission Electron Microscope
Newest TEM in MSE
Other TEM in MSE
JEOL JEM-3000F
JEOL JEM-2100
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.
12-1. Electron radiation(i) ~ hundreds Kev
ph
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
ph
20
02
2
0 2122
cmKEKEm
cKEKEmp
220
22 )()( cmpcE
20
2 cmKEmcE 22
0222
0 )()()( cmpccmKE 22
022
02 )()()( cmcmKEpc
420
420
20
2 2 cmcmcKEmKE 2
02 2 cKEmKEpc
Massless particle: cKEp /
20
0 212
cmKEKEm
hph
voltageeKEh = 6.62606957×10-34 m2kg/sm0 = 9.1093829110-31 Kgc = 299792458 m/se = 1.60217657×10-19 coulombs
1eV = 1.60217656510-19 J (Kgm2/s2)
For 200 KV electrons)/smJ(Kg 10204.3keV 200 2214 KE
2831
14
20 )10998.2(10109.92
10204.312
1
cmKE
0934.11956.01
221431
234
0 s/mKg10204.3Kg10109.92Kg/sm10626.6
2
KEmh
m1074.2mKg/s10416.2
Kg/sm10626.6 1222
234
m 10506.2
21
12
12
20
0
cmKEKEm
h
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
2000012
1 620
cm
KE
J/eV1060217.1Kg10109.92Kg/sm10626.6
2 1931
234
0
mh
91022.1
For X-ray Wavelength = 1.542 Å
Ehc
pchc
ph
hcE
(m) 10542.1(m/s) 10998.2kg/s)(m 10626.6
10
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
(ii) electrons can be focusedc.f. x-ray is hard to focus
(iii) easily scatteredxe 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
12-2. Bragg angle is small sin2 hkld
for 100 KeV
A 037.0 Assume d = 2Å
037.0sin22 0925.0sin o53.01800925.00925.0
for 200Kev
A 025.0 o34.01800625.00625.0
12-3. d spacing determination is not good sin2 hkld sin2d (brevity)
For fixed
sin2d
2sin
cos2
d
)cot(sin
cossin2
dd
cot/ dd0 ;0cot ;90o d
we can get more accurate d at higher angle!o5.0In TEM
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.edu.tr/tem/TEMtext/TEMtext.html
(b) Dark filed image
http://labs.mete.metu.edu.tr/tem/TEMtext/TEMtext.html
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.