Electron Scattering
Lead
Carbon
10 nm
20 nm
θB
9%
91%
17%
83%
96%
0-100%
4%
100-0%
MSE 421/521 Structural Characterization
Image Contrast
Sample
Objective
Aperture
Electron Beam
Objective aperture removes
scattered off-axis beams
MSE 421/521 Structural Characterization
Objective aperture removes
diffracted beams
Mass-Thickness Contrast
Latex spheres on carbon
A
thickness contrast only
B
C
Carbon-on-carbon,
so only thickness
contrast
shadowed:
thickness + mass contrast
Evaporate Au or Au-Pd at
an angle to increase mass
contrast
reverse of B
MSE 421/521 Structural Characterization
Staining
Bacteria
Rat kidney cells
Negatively stained
(Phosphotungstic acid)
Bacillus bacterium.
Tumor Cell prepared by
ultramicrotomy
Negatively stained
Phage virus.
Microtubules in animal cells
MSE 421/521 Structural Characterization
 π
I g =  ξ



 g
2
sin2(πtseff)
(πseff)2
ξg = πVc cos θ
λFg
(s = 0)
seff = s 2 +1 ξ2g
Intensity of Diffracted Beam
Rocking Curve
t/ξg = 1.5
ξg/ξg' = 0.1
ξg/ξo' = 0.1
-0.04
-0.02
0
0.02
0.04
Deviation Parameter (nm-1)
Dark-Field bend
contours in
Pb3Nb2O8
Ig is periodic in t and seff.
If t is constant and seff is varied bend contours
MSE 421/521 Structural Characterization
Thickness Fringes
 π
I g = 
ξ
 g




2
sin2(πtseff)
(πseff)2
seff = s2 +1 ξ2g
Intensity of Diffracted Beam
If seff is constant and t is varied thickness fringes
ξg
ξg = 100 nm
ξg/ξg' = 0.1
ξg/ξo' = 0.1
w = 0 (s = 0)
Effective extinction distance
ξw
=
g
0
100
200
300
Thickness (nm)
400
ξ
g
1+ w 2
w = sξg
When other diffracted
beams are present, the
effective ξg is reduced.
ξg
MSE 421/521 Structural Characterization
Moiré Fringes
d1
d2
D
Beat Spacing
Parallel
Moiré Pattern
+
d1
Rotation
Moiré Pattern
=
Dp =
d1 d2
d1 − d2
d1
+
In general, D =
=
D
Beat Spacing
Dr =
d
2sin(½α)
d1 d2
d12 + d22 − 2d1 d2 cos α
MSE 421/521 Structural Characterization
Moiré Fringes
Mg0.05Ca0.95 CO3
The local increases in Mg content
slightly reduce the lattice constant,
thus d spacings of the planes, resulting
in the formation of Moiré patterns and
some strain contrast.
MSE 421/521 Structural Characterization
Graphene
Moiré fringes caused by [001]
rotational disorder in graphene layers
grown via CVD on C-terminated SiC
Howie-Whelan Equations
dφ o iπ
iπ
= φo +
φ g exp(2πisz )
ξo
ξg
dz
dφ g
dz
=
iπ
iπ
φ o exp(− 2πisz )+ φ g
ξo
ξo
 sin (πts ')

I g = 

ξ
s
'
g


2
 1
s ' = s + 
 ξg
2




2
MSE 421/521 Structural Characterization
Howie-Whelan Equations
dφ o iπ
iπ
= φo +
φ g exp(2πi( sz + g • R))
ξo
ξg
dz
dφ g
dz
=
iπ
iπ
φ o exp(− 2πi ( sz + g • R))+ φ g
ξo
ξo
 sin (πts ')

I g = 

ξ
s
'
g


2
MSE 421/521 Structural Characterization
 1
s ' = s + 
 ξg
2




2
Two-Beam Condition
g
Al-3wt% Li alloy
Zone Axis
BF
DF
Imaged with Al3Li
spot, only Al3Li
phase appears bright
Dark, strongly
diffracting Al3Li
precipitate phase
Complementary contrast
MSE 421/521 Structural Characterization
BF & DF Imaging
Io
Io
object
2θ
2θ
objective lens
g
T
objective aperture
T
g
It
Id=Io-It
Bright field
Dark field
MSE 421/521 Structural Characterization
Forming Images
Best contrast for s slightly positive
(bright Kikuchi line just outside g)
Extraneous
contrast
Narrower
(better
resolution)
but poorer
contrast
s=0
s>0
s >> 0
Never form BF/DF images with s < 0. Defects are more visible when s > 0.
MSE 421/521 Structural Characterization
Crystal Defects
1Å
Dislocations in Nickel
MSE 421/521 Structural Characterization
Twinning
001
010
[100]
100
16°
c*
-c*
[010]
100
200 nm
020
[001]
Dynamical DF image of twins/ferroelectric domains in m-Ca2Nb2O7
near the [011] zone, using the 711 reflection. The twin plane is (100).
MSE 421/521 Structural Characterization
High-Resolution TEM
Overlapping <101> SADPs of Sr2Ta2O7 showing (020) spacings (d = 13.599 Å)
of two twin variants sharing a common (151) habit plane.
MSE 421/521 Structural Characterization
Lattice Image
000
111
(Ca1.4Pb0.6)(Ta1.5Nb0.5)O7
MSE 421/521 Structural Characterization
High-Resolution TEM
Pb1.5Nb2O6.5
MSE 421/521 Structural Characterization
High-Resolution TEM
[111] [112]
[001]
[112]
[110]
50 Å
Pb1.6Nb2O6.6
MSE 421/521 Structural Characterization
End of Lecture
MSE 421/521 Structural Characterization