Graef M. Introduction to conventional transmission electron microscopy

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268 Getting started

we will see that the dark ﬁeld images for g and −g are identical. Summarizing,

to obtain a centered dark ﬁeld image for the reﬂection g we bring −g onto the

optical axis using the beam tilt controls. After insertion of the diffraction aperture,

we can simply switch from BF to the CDF image by pressing a single button on

the microscope console. When you switch back and forth in diffraction mode you

will see the diffraction pattern jump between the two positions; when you switch

back and forth in image mode the image will switch from BF to DF and back.

Both images should be simultaneously in focus, provided all alignments have been

carried out properly.

We will see later on in this book that the ﬁrst method of bringing g to the optical

axis is very useful, and is the basis of the so-called weak beam imaging method,

also known as g–3g imaging. This is a very powerful method for observing crystal

defects with a high spatial resolution. The dark ﬁeld images thus obtained do not

suffer from spherical aberration since the electrons travel along the optical axis, as

they do in the CDF technique. As you have discovered, such weak beam images

have a very low overall intensity and require long exposure times.

4.4.2.6 Astigmatism and BF/DF images

Astigmatism is a parasitic lens aberration, which means that it is caused by imper-

fections in the lens surfaces, inhomogeneities in the lens coils, or possibly by small

magnetic ﬁelds caused by the sample itself. Astigmatism correction is perhaps the

most difﬁcult aspect of electron microscopy; it takes practice and a skilled micro-

scopist can correct astigmatism about as well as a computerized system, which uses

discrete Fourier transforms of digital images.

The easiest procedure for astigmatism correction relies on the use of Fresnel

fringes; these fringes arise wherever the specimen has an edge or any other discon-

tinuity. Electrons scattered from the edge (in a spherically scattered wave) interfere

with the transmitted electron beam and form an interference pattern. The number of

fringes in this pattern is a direct measure of the beam coherence. For conventional

TEM one can usually distinguish only one fringe; for a ﬁeld emission machine as

many as 100 fringes have been observed. As shown in the through-focus series

of gold particles on a holey carbon support ﬁlm in Figs 4.14(a)–(c), this fringe is

bright in under-focus and dark in over-focus. By changing the current through the

objective lens we can switch from one to the other. The fringe must have the same

distance to the sample edge all around the hole; if this distance is not constant,

or if part of the fringe is bright and part dark, then astigmatism is present in the

image, as ilustrated in Figs 4.14(d) and (e). Correction of the astigmatism either

involves obtaining a circular Fresnel fringe around the entire hole, or, alternatively,

no preferential direction in the image. The images in Figs 4.14(d) and (e) clearly

4.4 A typical microscope session 269

in-focus

-2

µm +2 µm

-2

µm

(a)

(b)

(c)

(d) (e)

100 nm

bright

fringe

dark

fringe

Fig. 4.14. Illustration of the effect of astigmatism on Fresnel fringes around a circular hole

in a holey carbon ﬁlm with gold particles. Parts (a)–(c) are a through-focus series with

prefectly corrected astigmatism. Parts (d) and (e) show the clear presence of astigmatism,

indicated by the absence of a Fresnel fringe around the entire hole, and the presence of a

preferential direction (arrowed) in the image. (JEOL 2000EX operated at 200 kV.)

show a preferential direction (arrowed). Astigmatism can be corrected by removing

this preferential direction from the images for all focus values. Astigmatism cor-

rection is easiest when there are small holes in the sample. If there are no holes,

then you may have to move to the edge of the sample, speciﬁcally where the edge

is not perfectly straight.

†

At the highest magniﬁcations one can often observe a

narrow amorphous area at the edge of a sample (even a crystalline sample) and

this amorphous area can be used to correct the astigmatism (see Chapter 10 for

examples).

4.4.2.7 Taking good pictures

Now you are ready to take a picture of what you see on the viewing screen. This is

a crucial step and you should learn how to properly expose an electron micrograph,

either the standard photographic negative or the electronic (digital) version. The

exposure time τ should be such that the relevant information will be recorded in

the nearly linear part of the characteristic curve (see page 229). If τ is too short,

†

You cannot use a straight Fresnel fringe to correct astigmatism. Why not?

270 Getting started

portions of your image may be invisible (intensity below the fog level of the ﬁlm

or the background level of the CCD camera); if τ is too long, the ﬁlm will be

overexposed and saturated.

We know from Chapter 3 that the density of a developed negative is related to

the number of electrons per unit area that hit the emulsion. We have estimated this

number using the concept of beam brightness on page 186. Typical current densities

are in the range of tenths to hundreds of pA cm

−2

, which translates into exposure

times in the range of 0.1 to several tens of seconds, considerable longer than the

times needed for most conventional light photography.

Every TEM is equipped with a sensitive exposure meter, which measures the

current density at the screen. It is important to realize that this is an average num-

ber, and that local current densities can be several orders of magnitude larger or

smaller than the average, in particular for electron diffraction patterns. The ex-

posure meter signal is automatically converted into an exposure time τ , and the

microscope operator can choose to use this value as the exposure time (automatic

exposure mode) or to set a different value (manual exposure mode). The au-

tomatic exposure mode has one adjustable parameter known as ﬁlm sensitivity

(related to the electron speed of the ﬁlm). This parameter is set once and for

all after a series of calibration exposures, and should be changed only if the ex-

posure meter is replaced or if the user switches to a different brand or type of

negatives.

The automatic exposure mode can be used for bright ﬁeld images that do not

have signiﬁcant contrast variations (i.e. rapid intensity changes from bright to dark

regions). Depending on the microscope magniﬁcation you may have exposure times

in the range 0.1–2 s. It is usually not a good idea to focus the incident beam using

the C2 lens so that maximum intensity is observed on the screen. A converged

incident beam has a lower beam coherence than a parallel beam and you may want

to record image details (such as Fresnel fringes) that are only visible for a reasonably

coherent beam. So, even if you have more electrons available to reduce the exposure

time, sometimes you will need to use a longer exposure time. For many dark ﬁeld

images the image contrast will vary strongly from one location to the next, and

the automatic exposure meter will typically underestimate the exposure time (large

portions of your dark ﬁeld image may be dark). You will have to manually increase

the exposure time by a few clicks but only experience will tell you the correct

number of clicks.

For all other images we recommend that you use the manual exposure mode.

Estimating the exposure time requires some experience, so until you have acquired

this expertise you should always record more than one micrograph at different

exposure times, and make a note (both mental and written) of the exposure times

that work best for a given type of image. For instance, for a zone axis diffraction

4.4 A typical microscope session 271

pattern on which you plan to perform measurements (indexing of the pattern) you

could use the following procedure:

place the sample in the proper orientation for the pattern that you wish to record;

under-focus the C2 lens (in diffraction mode) to obtain a more parallel incident beam and

therefore smaller diffraction spots;

reduce the C2 lens current until you can barely see the weakest diffraction spots on the

screen (make sure the room is completely dark, so that you have good night vision);

focus the diffraction spots (you may have to use the binocular to see the spots);

use the projector lens alignment to bring the transmitted beam to the center of the screen;

set the manual exposure time to somewhere in the range 22–45 s;

place the viewing screen cover over the screen and take a picture.

Most of the zone axis patterns shown in this book were recorded using this pro-

cedure. If diffuse features are present in the diffraction pattern (thermal diffuse

scattering, short-range order scattering, etc.), then you will probably have to use

either a longer exposure time, or increase the C2 current a bit. Again, it might be a

good idea to record multiple images with different C2 settings.

If you are about to record a convergent beam electron diffraction pattern, then

you can obviously not change the C2 current, since this would destroy the CBED

pattern (see Section 4.6.4). You will then have to record multiple images with

different exposure times to record all the image details present in the pattern. Weak

beam dark ﬁeld images require very long exposure times, in the range of 22–90 s,

and again you will need to take multiple recordings.

Digitally acquired images have one signiﬁcant advantage over conventional pho-

tographic images in that they are immediately available for inspection. If an image

is over-exposed, you can simply discard it, adjust the exposure time, and record

another one before saving it to disk. The best digital images are those that use the

entire available dynamic range of intensities (e.g., 0 to 2

− 1, with N = 12, 14,

or 16 for modern CCD cameras).

Photographic negatives must be developed and printed or digitized if they are to

be used for analysis or publication. The standard procedure for developing electron

micrographs is as follows (all steps to be carried out in a darkroom with only red-

ﬁltered safelight present; latex or lint-free gloves should be worn whenever the

negatives or negative holders are manipulated):

remove the exposed negatives from the negative holders and place them in a metal or

plexiglass carrier;

place the carrier in the developer tank; develop for 3–5 min, depending on the type and

strength of the developer;

agitate the developer either manually or by means of nitrogen bursts once every 10 s or so;

remove the carrier from the developer and rinse in room-temperature running water for

90 s;

272 Getting started

place the carrier in the ﬁxing bath and ﬁx for 8–10 min, again depending on the type and

age of the ﬁxing solution; use frequent agitation;

rinse in room-temperature running water for 20–30 min, apply a soapy solution to mini-

mize drying marks (optional), and dry in a warm and dust-free place.

The details of this procedure may vary depending on the type of chemicals and

negatives used. For nearly all micrographs reproduced in this book we used Kodak

Electron Image Film SO-163 with 2:1 diluted D19 developer.

If you plan to digitize your negative, you should use a good ﬂatbed scanner with

a transparency adaptor, and scan the negative at a resolution of 1200 or 2400 dpi.

The grain size in the photographic emulsion is then about equal to the pixel size of

the digitized image. There is little point in using a higher resolution, unless you use

special ﬁlm with a smaller grain size. Once you have a digital version of the image,

you can use the full power of image analysis programs to enhance the contrast,

scale the brightness linearly or non-linearly, select portions of the image, place a

micron bar on the image, and so on. If you alter the image in any non-standard way

(i.e. adding or removing information, enhancing features, etc.), then you should

explicitly state this in the ﬁgure caption (assuming that you are going to use the

ﬁgure in a report or paper).

4.5 Microscope calibration

As with any other scientiﬁc instrument, a transmission electron microscope must

be calibrated. The image magniﬁcation and diffraction camera length are perhaps

the most important calibrations for conventional TEM observations. In addition,

the relative orientation of the image and the corresponding diffraction pattern must

be calibrated. The following two subsections will describe brieﬂy how these cali-

brations can be performed. It is likely that calibrations will have already been

carried out for the microscope(s) you are using, so it may not be necessary to repeat

them yourself. However, you should make sure that you understand the imaging

conditions used for the calibrations, so that you can reproduce them in case you

wish to make accurate measurements.

Calibrations must be carried out not only for conventional micrographs, but also

for digital and analog cameras. In all cases it is important to know the absolute

orientation of the camera/negative with respect to the column. For a negative it is

rather easy to ﬁnd out how it is oriented inside the column (the emulsion side faces

the electron beam, and there is usually a ﬁducial marker along the side of the negative

which indicates its orientation in the camera). Calibration measurements should

always be carried out with the negative placed in the same orientation as it was

inside the microscope. Note that it is not sufﬁcient to calibrate magniﬁcations for

electron micrographs alone; if your microscope is equipped with a digital camera,

4.5 Microscope calibration 273

a magniﬁcation calibration must be carried out since the image plane of the camera

does not in general coincide with the image plane of the negative. There are several

other microscope parameters that may need to be calibrated. We will expand on the

topic of calibration in Chapter 10.

4.5.1 Magniﬁcation and camera length calibration

The diffraction camera length can be calibrated using a polycrystalline sample

of a known material; commonly used calibration samples consist of evaporated

aluminum or gold on a holey carbon grid. Figure 4.15 shows a diffraction pattern

for polycrystalline aluminum, obtained with the nominal camera lengths of 60, 80,

and 100 cm on a JEOL 2000EX microscope (the nominal camera length is what is

indicated on the microscope console). The ﬁrst six ring diameters were measured

in two different ways: by hand using a ruler, and numerically, by ﬁrst digitizing the

negatives at a resolution of 1200 dots per inch and then ﬁtting a circle to each ring.

Example results from the second method are shown in Table 4.5. The measured

average values for L are close to the nominal values. The standard deviations are

simply based on the number of measured values. A more realistic standard deviation

would take into account the accuracy of the digital measurement, which is estimated

to be slightly better than 1%.

The orientation of the diffraction pattern with respect to the corresponding image

must also be calibrated. The most straightforward method involves the use of α-

MoO

, an orthorhombic oxide with lattice parameters a = 0.3963, b = 1.3856, and

111

200

220

311

222

400

λL = 100 cm

λL = 80 cmλL = 60 cm

Fig. 4.15. Calibration of the camera length of a 200 kV JEOL 2000EX microscope using

an evaporated aluminum ﬁlm. The diffraction rings used for the calibration are indicated;

the (400) ring is just barely visible. The bottom quarters represent λL = 60 and 80 cm, and

the top corresponds to 100 cm.

274 Getting started

Table 4.5. Camera length calibration results for a

JEOL 2000EX microscope operated at 200 kV, using an

evaporated aluminum ﬁlm. λ is measured in nm; L

is computed by dividing by the electron wavelength

λ = 0.002 508 nm.

(hkl) d

hkl

[nm] λL

λL

100

111 0.234 1.537 2.004 2.493

200 0.202 1.531 1.989 2.484

220 0.143 1.529 1.994 2.487

311 0.122 1.524 1.994 2.487

222 0.117 1.528 1.995 2.494

400 0.101 1.528 1.983 2.491

λL 1.529 1.993 2.489

Standard deviation 0.004 0.007 0.004

L 60.96 79.46 99.24

c = 0.3697 nm, space group Pbnm.

†

This oxide grows in elongated platelet form,

with the normal to the platelet along the [010] direction, and the platelet length axis

along [001]. The [010] zone axis pattern is therefore rectangular, with the longest

axis along [001]. Figure 4.16(a) shows a double exposure of a single platelet along

with its diffraction pattern. The 100 and 001 reﬂections are labeled. The longest

axis in reciprocal space corresponds to the length axis of the platelet, and the angle

between the two directions is measured to be nearly 6

◦

Since the diffraction pattern in Fig. 4.16(a) is symmetric, the angle between the

image and the diffraction pattern is either 6

◦

or 186

◦

. We can determine which of

the two angles is the correct one by defocusing the diffraction pattern (decrease the

current through the diffraction lens, so that its focal length increases). The resulting

image is shown in Fig. 4.16(b); a dark ﬁeld image of the platelet is visible in each

diffraction spot. The orientation of the platelet is clearly rotated by 180

◦

, as can

be seen by comparing the circled regions in Figs 4.16(a) and (b). The diffraction

pattern can be brought into the proper orientation with respect to the image by a

counterclockwise rotation of 186

◦

When the camera length is changed the diffraction pattern may also rotate around

the origin. To determine whether or not this rotation is present we can simply

obtain a multiple exposure of the diffraction pattern at different camera lengths, as

shown in Fig. 4.16(c). Between exposures the diffraction pattern was re-centered

using the projector lens shift controls. It is clear that there is no rotation between

†

This is not a standard space group setting. The International Tables give the setting Pnma, which can be obtained

from Pbnm by cyclic permutation of the unit cell axes.

4.5 Microscope calibration 275

200nm

(a) (b)

5.8

[100]

100

001

[001]

100

20 lines = 4.57 cm = 9.26 µm

Fig. 4.16. (a) Double-exposure micrograph of an α-MoO

platelet and its diffraction pattern;

(b) defocused diffraction pattern showing a dark ﬁeld image of the platelet in each reﬂection;

reveals no rotation between

different camera lengths; (d) image at 5000× (indicated on the microscope console) of

a 2160 lines per millimeter calibration grating. All images obtained on a JEOL 2000EX

microscope.

different camera lengths for this particular microscope (JEOL 2000EX). For other

microscopes there may be a signiﬁcant rotation, which can simply be measured

from the multiple exposure diffraction pattern.

Calibration gratings for magniﬁcation calibration (image mode) are available

from many of the microscopy supply companies (listed on the

website). Typically

a calibration grid with around 2000 lines per millimeter should be sufﬁcient to

calibrate all but the highest magniﬁcations. It is important that the sample should

be at the eucentric position throughout all calibration steps. For all microscope

magniﬁcations record a bright ﬁeld image of the calibration grid. After developing

276 Getting started

the micrographs, use a ruler to measure the distance between two grid lines on

opposite sides of the micrograph and divide by the number of lines in between

them. You should perform this measurement a couple of times for each micrograph

and take the average of all measurements. Figure 4.16(d) shows a typical image

for the magniﬁcation 5000× for a JEOL 2000EX microscope, operated at 200 kV.

The calibration grid has 2160 lines per mm, so that the spacing per grid line is

equal to d = 463 nm. Twenty lines correspond to a measured distance of 45.7mm

(Fig. 4.16d), which should also be equal to 20d = 9260 nm. The magniﬁcation is

therefore equal to 45.7 × 10

/9260 = 4935, close to the 5000× indicated on the

microscope console. If you make multiple measurements for each micrograph then

you can compute error bars for the measured magniﬁcations.

For the highest magniﬁcations, only a single grid line will be visible on the

micrograph. Measure the distance between two easily recognizable features, and

compare it with the same distance at the largest magniﬁcation for which two grid

lines are present. The ratio between those two distances can then be used as a

multiplicative factor to compute the actual magniﬁcation. Typically, magniﬁcations

above about 60k× are obtained in that way. For the highest magniﬁcations (about

200k× and above) it is customary to use lattice fringes with a known spacing.

If you are going to publish micrographs, then you will need to convert the cal-

ibrated magniﬁcations to “micron bars”. If your images are conventional micro-

graphs on photographic negatives, you will need to know how many millimeters

in the image correspond to a typical distance on the object (1

µm, 10 µm, etc.). If

you digitized your micrograph, or the image was digitally acquired, then a more

convenient parameter may be the number of pixels per unit image length. We leave

it to the reader to derive the appropriate conversion relations.

4.5.2 Image rotation

In many older microscopes, the image rotates around the optical axis as the magni-

ﬁcation is changed. This is due to the Lorentz force on the electrons, which causes

a helical path around the optical axis, as described in Chapter 3. Modern micro-

scopes may have an additional lens in the magniﬁcation stage, so that this image

rotation is minimized or, ideally, eliminated. For such machines, the image does

not rotate when the magniﬁcation is changed, and the diffraction pattern is in the

correct relative orientation with respect to the image.

If the image does rotate, then we must calibrate the rotation angles as a function

of magniﬁcation. First of all, we must determine the relation between the physical

orientation of the primary tilt axis and the projected orientation of this axis. This

can be done in the following way: lower the sample using the z-control so that the

sample holder is near its lowest point. Adjust the image focus and bring a feature

4.6 Basic CTEM observations 277

to the center of the screen. Then tilt the sample along the primary tilt axis by a

positive rotation angle until this feature is a few centimeters away from the center.

Record a double-exposure micrograph of these two images (i.e. with the feature at

the center and tilted away). The line connecting the two images of this feature on the

micrograph is normal to the primary tilt axis. Since the tilt angle was positive, the

direction of the image shift also indicates the absolute orientation of the primary

tilt axis with respect to the negative.

This procedure is illustrated in Fig. 4.17: the ﬁrst image on the top left shows a

double exposure of the calibration line grid at a nominal magniﬁcation of 8200×.

The image was acquired using a Gatan DualView camera on a Philips EM420

microscope operated at 120 kV. The arrowed feature moved from right to left for a

positive (counterclockwise) rotation around the primary tilt axis. The tilt axis is then

oriented at right angles to the line connecting two identical features in the double-

exposure image. The image rotation at other magniﬁcations (two representative

ones are shown in Fig. 4.17) can then be measured with respect to the tilt axis.

At the highest magniﬁcations only a single grid line may be visible in the image,

making it difﬁcult to obtain an accurate measure of the image rotation.

It is convenient to represent rotation data in graphical form. The drawing in the

lower half of Fig. 4.17 represents the orientations of the bottom edge of the image

with respect to the primary tilt axis. The orientation of three diffraction patterns

(different camera lengths) are also added to the ﬁgure. They were measured using

the double-exposure technique shown in Fig. 4.16(a). We will use this graphical

calibration chart later on, when we describe how to determine the orientation of

a crystal with respect to the microscope column. Regardless of the type of mi-

croscope you use, it is important to understand the relative orientation of tilt axes

and images/diffraction patterns. We encourage the reader to perform a series of

calibration measurements similar to that described in this chapter.

4.6 Basic CTEM observations

Now we are ﬁnally ready to start some basic TEM observations. In the following

sections we will describe typical image and diffraction features that are easily

observed in the four study materials. We will emphasize those features that are

common to all four, and which therefore appear to be relatively independent of the

particular details of the crystal structure. We will discuss basic imaging techniques,

and illustrate how information from a zone axis electron diffraction pattern can be

transposed onto a stereographic projection.

The images shown in the following sections are easy to obtain, and we encourage

the reader to spend time on the microscope with one or more of the study materials.

You should feel free to experiment with the microscope (within reasonable limits