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