MT-0.6026 :Electron
Microscopy
Imaging
2015.11
Yanling Ge
Amplitude Contrast
What is contrast?
For eyes > 5-10%, 16 gray level
Amplitude Contrast – BF and DF Images
BF and DF 
interpretable
amplitude contrast
Objective Aperture: minimize lens
aberrations, enhance diffraction
contrast. Usage of it depends on
what features of specimen cause
scattering.
First, view
DP!
Mass-Thickness Contrast
Mass-thickness contrast arises from incoherent elastic
scattering (Rutherford scattering) of electrons, which is strong
function of atomic number Z (hence the mass or the density
) and the thickness, t, of he specimen.)
At low angles (< 5): massthickness contrast dominates but it
also competes with Bragg-diffraction
contrast;
At high angles (>5): where Bragg
scattering is usually negligible, the
low-intensity scattered beams
depends on atomic number (Z) only,
- so called Z-contrast.
Mass-thickness contrast is the
critical contrast mechanism for
biological materials.
Mass-Thickness contrast – TEM images
(A) TEM BF image of
latex particles on a
carbon support film
showing thickness
contrast only.
(B) Latex particles on a
carbon film shadowed
to reveal the shape of
the particles through the
addition of selective
mass contrast (the
edge of the shadow) to
the image.
(C) Reverse print of
(B) exhibits a 3D
appearance.
TEM variables: objective aperture size and the kV
Be careful when interpreting 2D images of 3D
specimens.
Mass-Thickness Contrast – STEM image
In a STEM you have more flexibility than in a TEM because by varying L,
you change the collection angle of your detector and create, in effect, a
variable objective aperture.
In summary, there are occasions when you might want to use STEM massthickness contrast images:
• The specimen is so thick that chromatic aberration limits the TEM
resolution.
• The specimen is beam-sensitive.
• The specimen has inherently low contrast in TEM and you can’t digitize
your TEM image or negative.
• Your specimen is ideally suited for HRTEM by Z-contrast imaging.
TEM BF
STEM BF Image processed TEM BF
Mass-Thickness
Contrast –
Specimens Showing
Mass-Thickness
Contrast
Carbon Replica –
Thickness contrast
Shadowed effect
– Thickness +
Mass contrast
Extraction replica – Mass
+ Thickness contrast
Mass-Thickness Contrast – Quantitative
Mass-Thickness Contrast
The probability that an electron scattered through greater than a given angle.
•
•
•
Higher-Z specimens scatter more.
Lowering E0 increase scattering.
Thicker specimen scattering more.
Variable for control mass-thickness contrast: Z, t, β, E0.
Z-Contrast – high-resolution (atomic),
mass-thickness, imaging technique
STEM ADF detector collecting low
angle elastically scattered
electrons of single heavy atoms on
low-Z substrate. Inelastic
scattering is removed by EELS, but
diffraction contrast is preserved in
the low angle EELS single.
Z-Contrast images are also termed as HAADF
images.
Bragg effects are avoided if the HAADF detector
only gathers electrons scattered through an angle
of > 50 mrad (3). Imaging away from strong
two-beam conditions and closer to zone-axis
orientations is wise. The image resolution is
determined by the probe size.
TEM Diffraction Contrast
- Coherent elastic scattering
Good strong diffraction contrast in
both BF and DF images need to be in
two-beam condition, in which only
one diffracted beam is strong. The
direct beam is the other strong spot in
the pattern.
For crystalline bulk specimen, to study
defects, BF and CDF must be done in
two-beam condition, which is a time
consuming and patient work!
•
•
•
•
Two-beam condition: good contrast, simple
interpretation.
Deviation parameter: s must small and positive for best
contrast from defects (The excess hkl Kikuchi line, just
outside the hkl spot).
Two-beam CDF, tilt weak –h-k-l to center.
Related DP to image, showing g vector in image.
Two-Beam Condition - CDF
BF
WBDF
CDF
STEM Diffraction Contrast
• The incident beam must be
coherent, i.e., the convergence
angle must be very small.
• The specimen must be tilted to a
tow-beam condition.
• Only the direct beam or the one
strong diffracted beam must be
collected by the objective aperture.
T = S
βT = βS
Or according principle of reciprocity:
 S = βT
T = βS
STEM images are rarely used to show diffraction-contrast
images of crystal defects. This is solely the domain of
TEM.
BF STEM
BF STEM βs smaller
BF TEM
Phase-Contrast Images
Introduction
Phase contrast arise due to the difference in the phase
of electron waves scattered through a thin specimen.
A phase-contrast image requires the selection of more
than one beam. In general, the more beams collected, the
higher the resolution of the image.
Phase-contrast is very sensitive to many factors: the
appearance of the image varies with small changes in the
thickness, orientation, or scattering factor of the
specimen, and variations in the focus or astigmatism of
the objective lens.
The Origin of Lattice Fringes
Two beam condition,
interference of
direction beam and
diffracted beam.
The intensity of phase contrast is a sinusoidal
oscillation normal to g’, with a periodicity that
depends on s and t.
This simple analysis shows that the location of a
fringe does not necessarily correspond to the
location of a lattice plane.
Some Practical Aspects of Lattice Fringes
If s = 0 s = 0,
hkl // optic s  0; hkl
edge on
axis
The fringe periodicity is the
same as the spacing of the
planes which give rise to g. this
result holds wherever s = 0 no
matter how 0 and g are located
relative to the optic axis, even if
the diffraction planes are not
parallel to the optic axis.
If s ≠ 0
If s is not zero, then the fringes will shift
by an amount which depends on both
the magnitude of s and the value of t,
but the periodicity will not change
noticeably.
We expect this s dependence to affect
the image when the foil bends slightly,
as is often the case for thin specimens.
We also expect to see thickness
variations in many-beam images, since
s may be non-zero for all of the beams;
s may also vary from beam to beam.
On-Axis Lattice-Fringe Imaging
In general, this
array of spots bears
no direct
relationship to the
position of atoms in
the crystal.
Fringes are not direct images of the structure,
but just give you information on lattice spacing
and orientation. There is cases that these
images can only be interpreted using
extensive computer simulation.
Moiré Patterns
General Moiré
Fringes
Rotational Moiré Fringes
Translational Moiré Fringes
Experimental Observations of Moiré Fringes
Translational Moiré Patterns
We know that the top of an
inclined island is not in contact
with the substrate yet it shows
fringes; so this reminds us that
moiré fringes do not tell us
about the interface structure!
Rotational Moiré Patterns
Dislocations and
Moiré Fringes
Fresnel Contrast
In any situation where the inner potential
changes abruptly, we can produce Fresnel
fringes if we image that region out of focus.
Magnetic-Domain Walls
Fresnel Contrast from Voids or Gas Bubbles
•
•
By orienting the region of interest so that s = 0; the cavity then reduces
the ‘thickness’ of material locally.
By using Fresnel contrast
Caution:
Small particles can give
similar contrast to small
voids, the Fresnel contrast
can easily be misinterpreted
as a core-shell structure!
In the Fresnel technique, the
image shows contrast
whenever the objective lens
is not focused on the bottom
surface of the specimen.
A dark fringe at under focus and
a bright fringe at overfocus.
Fresnel Contrast from Lattice Defects
When you use the Fresnel-fringe
technique to study grain boundaries or
analyze intergranular films, you must
orient the boundary in the edge-on
position so that you can probe the
potential at the boundary.
Using the Fresnel-fringe technique
to image end-on low angle grain
boundaries assume there is a
change in the mean inner potential
at the core of the dislocation.
Thickness and Bending
Effects
Thickness and Bending effects
- Diffraction contrast
•
All TEM specimens are thin but their thickness invariably
changes.
•
Because the specimens are so thin they also bend
elastically, i.e., the lattice planes physically rotate.
•
The planes also bend when lattice defects are introduced.
The Origin of Thickness Fringes and
Bend Contours
The diffracted intensity is periodic in the two independent quantities, t
and seff. If we imaging the situation where t remains constant but s (and
hence seff) varies locally, then we produce bend contours. Similarly, if s
remains constant while t varies, then thickness fringes will result.
Thickness Fringes
Intensity of both the 0 and g beams
oscillate as t varies. Furthermore, these
oscillations are complementary for the
DF and BF images.
As a rule of thumb,
when other diffracted
beams are present
the effective
extinction distance is
reduced. At greater
thicknesses,
absorption occurs
and the contrast is
reduced.
Thickness Fringes and DP
A general rule in TEM is that, whenever we see
a periodicity in real space (i.e., in the image),
there must be a corresponding array of spots in
reciprocal space; the converse is also true.
The minimum spot
spacing in the DP
corresponds to the
periodicity of the
thickness, which at:
s = 0 is given
directly by the
extinction distance
and the wedge
angle.
Bend Contours (Annoying
Artifact, Useful Tool,
Invaluable Insight)
ZAPs and Real-Space
Crystallography
Although the ZAP is distorted, the
symmetry of the zone axis is clear and
such patterns have been used as a tool
for real-space crystallographic analysis.
Each contour is uniquely related to a
particular set of diffraction panes, so
the ZAP does not automatically
introduce the twofold rotation axis that
we are used to in SAD patterns.
Also in this case, a small g in the DP
gives a small spacing in the image,
contrary to the usual inverse relationship between image and DP.
Absorption Effects
Summary:
• We can define a parameter
´g which is usually about
10 g and is really a fudge
factor which modifies the
Howie-Whelan equations
to fit the experimental
observations.
• The different Bloch waves
are scattered differently. If
they don’t contribute to the
image, we say that they
were absorbed. We thus
have anomalous
absorption which quite
normal!
• Usable thicknesses are
limited to about 5g, but
you can optimize this if you
channel the less-absorbed
Bloch wave.
Planar Defects
- Internal Interface
Translations and Rotations
Translation
Boundary, RB. R(r), 
is zero.
Grain boundary, GB.
Any values of R(r), n
and  are allowed.
Phase boundary, PB.
As for a GB, but the
chemistry and/or
structure of the regions
can differ.
Surface. A special
case of PB where one
phase is vacuum or
gas.
Why Do Translations Produce Contrast?
Planar defects are seen when  ≠ 0.
Stacking Faults in FCC Materials
Stacking faults bounds by 1/3
<111> Frank partial dislocations
Stacking faults bounds by 1/6
<112> Shockley partial
dislocations
Intrinsic fault: remove a layer
Extrinsic fault: insert a layer
For a FCC the translations are then directly related to the lattice
parameter: R is either 1/6 <112> or 1/3 <111>
Invisibility Criterion: g·R = 0
Some rules for interpreting the contrast
• In the image, as seen on the screen or on a print, the
fringe corresponding to the top surface (T) is white in BF
if g·R is > 0 and black if g·R <0.
• Using the same strong hkl reflection for BF and DF
imaging, the fringe from the bottom (B) of the fault
will be complementary whereas the fringe from the
top (T) will be the same in both the BF and DF.
• The central fringe fade away as the thickness increases.
• Displace aperture instead of CDF for using same hkl for
both BF and DF.
Other Translations: 
Fringes -  = 
Phase
Boundaries
Rotation Boundaries
Imaging Strain Fields
Why image Strain Field
•
The direction and
magnitude of the
Burgers vector, b,
which is normal to the
hkl diffraction planes.
• The line direction, u
(a vector), and
therefore, the
character of the
dislocations (edge,
screw, or mixed).
• The glide plane: the
plane that contains
both b and u.
Howie-Whelan Equations
Assumption: two-beam treatment, linear elasticity, column
approximation.
The contrast of the defects will depend on both s and g.
• g·R contrast is used when R has a single value,
• sR contrast is used when R is a continuously varying
function of z, which in turn is associated with g·dR/dz.
Contrast from a Single
Dislocation
The displacement field
in an isotropic solid for
the general, or mixed,
case can be written
as:
Contrast from a Single Dislocation
Screw dislocation:
be = 0 and b x u = 0.
g·R is proportional to g·b.
Pure edge dislocation: b = be.
g·R involves two terms g·b and g·b x u.
Contrast from a Single Dislocation
Experimental point:
you usually set s to be
greater than 0 for g
when imaging a
dislocation in twobeam conditions.
Then the dislocation
can appear dark
against a bright
background in a BF
image.
Identify two
reflections g1 and g2
for which g·b = 0, then
g1 x g2 is parallel to b.
Dislocation Nodes
and Networks
Dislocation Loops
Dislocation dipoles
Dipoles can be thought of
as loops which are so
elongated that they look
like a pair of single
dislocations of opposite
Burgers vector, lying on
parallel glide planes. As a
result, they are best
recognized by their
inside-outside contrast.
Dislocation Pairs, Arrays, and Tangles
Surface Effects
Dislocation strain fields are long range, but we often assign them a cut-off
radius of  50nm. However the specimen thickness might only be 50nm or
less. The surface can affect the strain field of the dislocation, and vice versa.
Dislocations and Interfaces
Misfit dislocations accommodate the
different in lattice parameter between
two well-aligned crystalline.
Transformation dislocations are the
dislocations that move to create a
change in orientation or phase.
Dislocations and Interfaces
Volume Defects and Particls
Weak-Beam Dark-Field
Microscopy
Intensity in WBDF Images
In a perfect crystal the intensity of the diffracted beam in
two beam condition:
In the WB technique we increase s to about 0.2
nm-1 so as to increase seff. If s >> g-2 then s  seff
and indenpendent of g except as a scaling factor
for t, this is known as the ‘kinematical
equation’, which cannot be applied for all s
unless the thickness, t is also very small.
How To Do WBDF
CDF with small
objective
aperture on
optimized
thickness
Thickness Fringes in Weak-Beam Images
Imaging Strain Field
Weak-Beam Images of Dissociated
Dislocations
In WB image with |g·bT| = 2, each of the partial dislocations will generally give
rise to a single peak in the image which is close to the dislocation core. You
can relate the separation of the peaks in the image to the separation  of the
partial dislocations.
High-Resolution TEM
The Role of An Optical
System
h(r) describes how a point
spreads into a disk, it is
known as the point-spread
function or smearing function,
and g(r) is called the
convolution of f(r) with h(r).
The Fourier transform
Here u is a reciprocal-lattice vector. This is to say g(r) is a combination of
the possible values of G(u), where G(u) is known as the Fourier transform of
g(r).
A(u): Aperture function; E(u): envelope function (attenuation of the wave); B(u):
aberration function; H(u): the contrast transfer function (CTF).
•
•
Each point in the specimen plane is
transformed into an extended region (or disk)
in the final image.
Each point in the final image has contributions
from many points in the specimen.
Contrast Transfer Theory - wikipedia
Contrast Transfer Theory provides a quantitative method to translate the exit
wavefunction to a final image. Part of the analysis is based on Fourier transforms
of the electron beam wavefunction. When an electron wavefunction passes
through a lens, the wavefunction goes through a Fourier transform. This is a
concept from Fourier optics.
Contrast Transfer Theory consists of four main operations:
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•
•
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Take the Fourier transform of the exit wave to obtain the wave amplitude in
back focal plane of objective lens
Modify the wavefunction in reciprocal space by a phase factor, also known
as the Phase Contrast Transfer Function, to account for aberrations
Inverse Fourier transform the modified wavefunction to obtain the
wavefunction in the image plane
Find the square modulus of the wavefunction in the image plane to find the
image intensity (this is the signal that is recorded on a detector, and creates
an image)
The Transfer function
If the specimen acts as a weak-phase object, then the transfer function
T(u) is sometimes called the CTF, because there is no amplitude
contribution, and the output of the transmission system is an
observable quantity (image contrast).
(u) is the phase-distortion function has the form of a phase shift
expressed as 2/ times the path difference traveled by those waves
affected by spherical aberration (Cs), defocus (z), and astigmatis (Ca).
The CTF shows maxima (meaning maximum transfer of contrast)
whenever the phase-distortion function assumes multiple odd values of
±/2. zero contrast occurs for (u) = multiple ±.
When T(u) is negative, positive phase contrast results, meaning that
atoms would appear dark against a bright background. When T(u) is
positive, negative phase contrast results, meaning that atoms would
appear bright against a dark background. When T(u) = 0, there is no
detail in the image for this value of u. (note that we assume here that Cs
> 0).
More on (u), sin(u), and cos(u)
• sin starts at 0 and
decreases. When
u is small, the f
term dominates.
• sin first crosses
the u-axis at u1
and then
repeatedly crosses
the u-axis as u
increases.
Scherzer Defocus
Scherzer found that the CTF could be optimized by balancing the effect of spherical
aberration against a particular negative value of f. this value has come to be known
as Scherzer defocus, fSch which occurs at
Scherzer resolution:
Simulation of sin
Experimental Considerations
Remarks:
•
Thinner specimen, ideal case single scattering event.
•
Coma-free alignment to align the beam with optic axis.
•
Specimen orientation is very critical for HRTEM.
The Future For HRTEM
Cs-corrected TEM: Cs is zero or as a variable like underfocus.
Resolution limit will be determined by Cc.
FEG TEMs and The Information Limit
The information limit is
determined by the envelope
function.
Ec(u): for chromatic aberration
Es(u): for the source dependence
due to the small spread of
angles from the probe.
Ed(u): for specimen drift.
Ev(u): for specimen vibration.
ED(u): for the detector.
•
•
•
•
http://www.maxsidorov.com/ctfexplorer/scie
nce/information_limit.htm
Information limit goes well beyond point resolution limit for FEG microscopes
(due to high spatial and temporal coherency).
For the microscope with thermionic electron sources, the info limit usually
coincides with the point resolution.
Phase contrast images are directly interpretable only up to the point resolution
(Scherzer resolution limit)
If the information limit is beyond the point resolution limit, one needs to use
image simulation software to interpret any detail beyond point resolution limit.
Some Difficulties In Using An FEG
•
•
•
•
A cold FEG has a small emitter area and Schotty emitter has a source
diameter 10 times greater, but with a decrease in spatial coherence
and a larger energy spread.
Correcting astigmatism is very tricky. Need on-line processing (live
FFT).
Focal series of image are a challenge with a large range of f values.
Image delocalization occurs when detail in the image is displaced
relative to its ‘true’ location in the specimen.
Selectively Imaging Sublattices
Interfaces And Surfaces
The fundamental requirement is that the interface plane must be parallel to the
electron beam.
Incommensurate
Structures
Quasicryatals
•
•
•
HRTEM excels when materials are ordered on a local scale.
For HRTEM, we need the atoms to align in columns because this is a
‘projection technique’, but the distribution along the column is not so
critical. And we can’t determine it without tilting to another projection in
the perfect crystal.
SAD and HRTEM should be used in a complementary fashion.
Single Atoms
Observation by Parsons et
al. with dedicated STEM:
uranium atoms in molecule
matrix.
homework
Question: T 24.13 P417, and select 2 other questions from the rest questions of
chapter 22 and 24.