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.