SAED Patterns of Single Crystal, Polycrystalline and Amorphous Samples
a b c
r1 r2200
020
110
Electron Diffraction
Specimen foil
T D
e-
L 2
r
dhkl
[hkl] SAED pattern
L -camera lengthr -distance between T and D spots1/d -reciprocal of interplanar distance(Å-1)SAED –selected area electron diffraction
Geometry fore-diffraction
Bragg’s Law: = 2dsin
=0.037Å (at 100kV)=0.26o if d=4Å
= 2dr/L=sin2as 0r/L = 2
r/L = /d or
r = Lx1
d
hkl
Reciprocal lattice
Ewald’s Sphere
Ewaldcircle
0
incident beam
diffracted beam
2
C
ki Gg
130
H
Ewald’s sphere is built for interpreting diffraction
CG-C0=0G or kd-ki=g Laue equation
lkl=1/
kd
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.
Convergent Beam Electron Diffraction (CBED)
CBED uses a conver-gent beam of elec-trons to limit area of specimen which con-tributes to diffractionpattern.Each spot in SAED thenbecomes a disc withinwhich variations inintensity can be seen.CBED patterns containa wealth of informationabout symmetry andthickness of specimen.Big advantage of CBEDis that the informationis generated from smallregions beyond reachof other techniques.
SAED vs CBED
spots disks
lens
sample
Parallel beam Convergent beam
T D T D
Convergence angle
objective
SAED CBED
Spatial resolution >0.5m
Spatial resolutionbeam size
CBED-example 1
CBED-example 2
HOLZ
HOLZ - High Order Laue Zone
Applications of CBED
•Phase identification•Symmetry determination-point and
space group•Phase fingerprinting•Thickness measurement•Strain and lattice parameter measurement •Structure factor determination
Symmetry Deviations
Phase Identification in BaAl2Si2O8
200oC 400oC 800oC
<0001>
Hexagonal Orthorhombic Hexagonal
6mm 2mm 6mm
Phase Fingerprinting By CBED
[001] CBEDpatterns of anantiferroelectricPbZrO3 singlecrystal specimenat (a) 20oC, (b)280oC, (c)220oC.(d) [001] CBEDpattern of a rhombohedral ferroelectric Pb(ZrTi)O3 Specimen at 20oC.
Orthorhombic AFE Cubic PE
Rhombohedral FE Rhombohedral FE
Symmetry and Lattice Parameter Determination
BFEDS
[143]
[100]
[111]
CBED
CBED-HOLZ
Experimental simulated
Latticeparameters
SAED
010
001
0.2m
NbA
B
A
A
A
A
B
B
B
B