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.