1. SAED Patterns of Single Crystal, Polycrystalline and Amorphous Samplesb c
020
110
200 r1 r2

2. Electron Diffraction
Geometry for
e-diffraction  e-
Bragg’s Law: l = 2dsin
l=0.037Å (at 100kV)
=0.26o if d=4Å
dhkl
Specimen
foil
l = 2d
L 2
r/L=sin2
as   0
r/L = 2
r/L = l/d or
r = lLx r
T D
Reciprocal
lattice
Due to short wavelength, diffraction angle in TEM is very small. Diffraction angle in diagram is exaggerated. Value of dhkl can be obtained by measuring rhkl. 1 d
L -camera length
r -distance between T and D spots
1/d -reciprocal of interplanar distance(Å-1)
SAED –selected area electron diffraction
hkl
[hkl] SAED pattern

3. Ewald’s Sphere Ewald’s sphere is built for interpreting diffraction
lkl=1/
Ewald
circle C
incident
beam
diffracted
beam 2 kd H ki g G
130
- Compare XRD (long wavelength) with SAED (short wavelength)
To build the Ewald sphere
1. k has a magnitude of 1/ and points in the direction of the electron wave,
2. Construct a circle with radius 1/, i.e., lkl, which passes through 0,
3. The Ewald circle intersects the lattice point at G.
CG-C0=0G or kd-ki=g Laue equation
Wherever a reciprocal lattice point touches the circle, e.g., at G, Bragg's Law is obeyed and a diffracted beam will occur. At H, no diffraction.

4. Convergent Beam Electron Diffraction (CBED)
CBED uses a conver-
gent beam of elec-
trons to limit area of
specimen which con-
tributes to diffraction
pattern.
Each spot in SAED then
becomes a disc within
which variations in
intensity can be seen.
CBED patterns contain
a wealth of information
about symmetry and
thickness of specimen.
Big advantage of CBED
is that the information
is generated from small
regions beyond reach
of other techniques.

5. SAED vs CBED SAED CBED Parallel beam Convergent beam sample objective
Spatial
resolution
>0.5m
Spatial
resolution
beam size
Convergence angle
sample
objective
lens
spots
disks
T D
T D
SAED CBED

6. CBED-example 1

7. CBED-example 2
HOLZ
HOLZ - High Order Laue Zone

8. Applications of CBED Phase identification
Symmetry determination-point and
space group
Phase fingerprinting
Thickness measurement
Strain and lattice parameter measurement
Structure factor determination

9. Symmetry Deviations

10. Phase Identification in BaAl2Si2O8
Hexagonal Orthorhombic Hexagonal
6mm
6mm
2mm
800oC
200oC
400oC
<0001>

11. Phase Fingerprinting By CBED
Orthorhombic AFE Cubic PE
[001] CBED
patterns of an
antiferroelectric
PbZrO3 single
crystal specimen
at (a) 20oC, (b)
280oC, (c)220oC.
(d) [001] CBED
pattern of a
rhombohedral
ferroelectric
Pb(ZrTi)O3
Specimen at
20oC.
Rhombohedral FE Rhombohedral FE

12. Symmetry and Lattice Parameter Determination
EDS
CBED A BF A B
010 Nb A B
001 B
[100]
SAED
0.2m A B A
[111]
EDS can identify difference in chemical composition between the core and shell regions.
Using CBED HOLZ line pattern accuracy of lattice parameter measurement is ~0.1%.
[143]
CBED-HOLZ B
Lattice
parameters
Experimental
simulated