Graef M. Introduction to conventional transmission electron microscopy

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258 Getting started

be several of those features with a nearly identical shape, or you may not see any

at all. When you change the orientation of the sample, you may see their number

change. When you approach the in-focus condition several of them will converge

to one location (at which you will generally see a dark version of the same feature),

and when they all merge, very little or no contrast will remain.

An example is shown in Fig. 4.10(a): the center image is an in-focus image of a

few grains near the edge of a Ti foil. When the image is defocused by ±2 and ±4

µm,

in-focus

- 2 µm +2 µm +4 µm- 4 µm

(a)

(b)

(c)

(d)

(e)

500 nm

Fig. 4.10. (a) Experimental illustration of in-focus and out-of-focus images of a Ti foil,

recorded with no apertures inserted in the column; (b) the selected area aperture is placed

at the dashed circle in the center image of (a), and the image inside the aperture is focused;

zone axis orientation); (d) the diffraction aperture is inserted around the central beam, and

(e) in image mode a high-contrast bright ﬁeld image is observed.

4.4 A typical microscope session 259

we obtain the images to the left and right of the center image (only the rectangular

region outlined in the center image is shown). There are clearly several bright

features visible inside the hole of the sample (negative defocus), and the distance

between those features and the sample edge increases with increasing defocus

(white arrows). When you approach the in-focus condition, all bright features merge

together with darker features that do not change position with defocus, and the

resulting image has very little contrast. Then you can insert the selected area aperture

into the column and position it at a region of interest, say the dashed circle in

the center image of Fig. 4.10(a); after you focus the image inside the aperture

(Fig. 4.10b) you switch to diffraction mode to obtain a selected area diffraction

pattern, similar to that shown in Fig. 4.10(c).

The origin of those “ghost images” is easy to understand. Consider the following

geometry: a sample, shown in Fig. 4.11, contains a rectangular particle which

strongly diffracts electrons into a number of diffracted beams. This means that,

generally speaking, the transmitted beam will have fewer electrons coming from

that particular location in the sample, whereas the diffracted beams will travel in

various directions predicted by the Bragg equation. Let us assume that every part of

this region scatters electrons equally strongly and that the surrounding matrix does

not scatter at all. If the imaging lenses are focused on the OL image plane, then on

the viewing screen all electrons that leave the particle will be recombined into a

magniﬁed image of that region (assuming that we have a reasonably good objective

lens). Since most electrons leaving the sample are recombined at the proper location

BFP

Image

plane

screen

OL in-focus OL over-focus

Fig. 4.11. Illustration of the origin of “ghost-images” when the objective lens is not properly

focused.

260 Getting started

in the image, we will not observe a lot of contrast. If, on the other hand, we focus the

imaging lenses onto a plane slightly above the OL image plane, then the resulting

image is quite different: instead of having one rectangular region where all electrons

merge into an image, we now have several of those regions in the image plane, each

corresponding to a different diffracted beam. On the viewing screen, each of those

regions will be separately imaged, and the spacing between the individual images

will vary with the amount of defocus. In principle, there should not be any contrast

in the in-focus image. In practice, spherical aberration will affect the trajectories

of the diffracted electrons, and the various images may not merge perfectly in the

in-focus image.

What we observe on the viewing screen when both selected area and diffraction

aperture are removed from the column is the result of all combined scattering

processes, both elastic and inelastic. By the time the electrons leave the sample in

various directions, nearly all of the relevant physics is over, and all we can do as

microscope operators is attempt to extract information from this complex pattern of

scattered electrons. Using the terminology introduced on page 106, what we observe

when we remove both post-specimen apertures from the microscope column is

essentially the function R



; when we change the focus of the objective lens we are

actually changing the point spread function T , and we observe “different versions”

of the modiﬁed signal R



. It is now your task, as a microscope operator, to cleverly

manipulate this function T (by twiddling knobs and moving apertures around), so

as to end up with a fairly accurate representation (image or diffraction pattern) of

the information that is present in the modiﬁed signal R



. The in-focus image just

happens to be the one that is easiest to interpret. The out-of-focus images contain

the same information, but the human brain is simply not capable of separating the

information content and the point spread function.

4.4.2.2 Working in diffraction mode

At the end of the routine discussed in the previous section, you should have a

diffraction pattern on the viewing screen. You can now change the magniﬁcation of

the diffraction pattern (i.e. the camera length L), and you can focus the pattern (i.e.

ensure that the back focal plane of the objective lens is conjugate to the viewing

screen). While in diffraction mode, you should also change the second condensor

lens current back and forth and observe what happens. Note that the diffraction

spots will change from spots to disks and back to spots as you change the C2

current. When C2 is under-focused (the knob turned counter-clockwise on most

microscopes), the electron beam will be more or less parallel when it enters the

sample. The OL will then focus this parallel beam into a point in the back focal

plane. When C2 is in-focus we observe the smallest possible beam diameter on

the sample, but now the beam is converged into a point and the OL will produce

4.4 A typical microscope session 261

a diffraction disk in the back focal plane. While this particular mode of sample

illumination is of importance for convergent beam electron diffraction (CBED)

observations, for now we will not use it; instead, you should always obtain regular

diffraction patterns with the C2 lens under-focused, i.e. with a reasonably parallel

incident beam.

As part of the alignment procedure, you used the projector lens controls to bring

the central beam (the transmitted beam) onto the center of the viewing screen. You

should periodically ensure that this is still the case. In particular, when you change

the camera length, the central beam may wander off the center of the screen, and

you can simply bring it back using the projector alignment. You should also ensure

that the diffraction pattern is properly focused; this can be done by inserting the

diffraction aperture and making sure that the edge of the aperture is as sharp as

possible. You can then remove the aperture again to observe the entire diffraction

pattern.

At this point you may also want to try changing the orientation of the sample

with respect to the incident beam. Since you have already made sure that the sample

is in the eucentric position, the sample region illuminated by the beam should not

move laterally while tilting the sample. Conversely, if you did not properly adjust

the eucentric position of the sample, then the area illuminated by the electron

beam will move back and forth as you change the sample orientation, and you

cannot be certain that the diffraction pattern you observe actually comes from the

sample region you selected while in image mode. This illustrates the importance

of a proper eucentric adjustment. On modern microscopes, the specimen attitude

(position and orientation) is controlled by a computer program that will attempt

to maintain the eucentric position at all times, so the operator should not have to

worry about this particular adjustment. The algorithms controlling the eucentric

specimen positioning are quite accurate, but you should be aware that small shifts

may still occur, in particular at higher magniﬁcations.

Continue to tilt the specimen around one or both of the tilt axes until you observe

many diffracted beams on the screen. Adjust the specimen tilts so that you obtain

a symmetric pattern with respect to the center of the screen (this is explained in

more detail in Section 4.6.2). We already know from the previous chapter that when

the crystal is oriented such that a zone axis is parallel to the incident beam, then

the planes belonging to that zone will all be close to the Bragg orientation. Their

reciprocal lattice vectors all lie in a plane which is tangent to the Ewald sphere.

Therefore, we expect to see a two-dimensional array of spots in the diffraction

pattern. Such a symmetric pattern is known as a zone axis diffraction pattern.

When the sample is tilted over a small angle, the intersection of the reciprocal

lattice plane and the Ewald sphere will become a circle (the Laue circle) along which

the reciprocal lattice vectors are close to Bragg orientation, and this is clearly visible

262 Getting started

in the diffraction pattern (see Fig. 4.20 on page 283). This is your ﬁrst experimental

proof that the Ewald sphere is indeed a valid tool for the description of electron

diffraction!

4.4.2.3 Obtaining a bright ﬁeld image

Once you have placed the sample in a suitable orientation (while working in diffrac-

tion mode), you may want to go back to image mode to see what things look like.

Here are a few steps to get back to the image (you may already have carried out a

few of them in the previous section).

Select a convenient camera length and, if necessary, bring the central beam to the center

of the viewing

screen using the projector alignment controls.

Partially converge the incident beam using the C2 lens (i.e. make sure you observe disks

rather than spots). If your sample is very sensitive to the incident electron beam you may

want to skip this step. It is not an essential step, it only makes it easier to center the

aperture in the next step.

Insert the diffraction aperture, select a suitable diameter (slightly larger than the diffraction

disk diameter), and center the

aperture on the optical axis around the central diffraction

disk.

Return to image mode.

At this point you will most likely not see very much contrast on the screen be-

cause the SA aperture is still inserted in the column. Remove the SA aperture

from the column and adjust the C2 lens to obtain an even illumination across the

entire viewing screen. Congratulations! You have just obtained your ﬁrst bright

ﬁeld image! The last two steps above are illustrated in Figs 4.10(d) and (e) on

page 258.

A bright ﬁeld image (or BF image) is deﬁned as an image obtained with electrons

from the transmitted beam only, i.e. electrons which left the sample in the same

direction they entered the sample. This does not mean that those electrons were not

scattered by the crystal. We will see in Chapter 5 that electrons can be scattered

many times on their way through the crystal foil, and some may end up traveling in

the original direction of the incident beam. Furthermore, many electrons will lose

energy as they are scattered; there are various inelastic scattering processes that

can give rise to such energy losses, and some of those electrons may also leave the

sample in the transmitted beam. The bright ﬁeld image is thus created by electrons

that leave the sample in the direction of the incident beam; these electrons may

have undergone multiple elastic and inelastic scattering processes.

As mentioned before, switching back and forth between image and diffraction

mode will become second nature to you, so that you no longer have to think about the

details of the procedure. At this point in time, however, you may be a bit confused

4.4 A typical microscope session 263

about apertures and various image, object, and focal planes. Do not worry, things

will get easier with time. The following brief summary might help.

In image mode, you will nearly always have an aperture inserted in the back focal plane

of the objective lens. This aperture selects which beam is used to create the image.

In diffraction mode, you will nearly always have the SA aperture inserted into the column,

so that the diffraction pattern arises from a “selected area” on the sample.

You will rarely use the microscope with both apertures taken out of the column. There is

very little contrast in such images (see Fig. 4.10a) at the lower end of the magniﬁcation

range, and the corresponding diffraction patterns are usually rather messy. At the highest

magniﬁcations you may use the microscope without apertures for high-resolution

obser-

vations, although typically a large-diameter diffraction aperture would be inserted in the

column. If you use a small spot size with a converged incident beam instead of a parallel

beam, then you can obtain so-called convergent beam electron diffraction patterns with

both diffraction and selected area apertures removed from the column.

You will never use the microscope with both apertures inserted in the column. There is

not much information to be gained from such a setup.

In other words, the one aperture (other than the condensor aperture) that should be

in the column is the one located in the plane that you are not looking at.

4.4.2.4 Obtaining a dark ﬁeld image

To obtain the BF image we inserted the diffraction aperture in the path of the

transmitted beam, centered along the optical axis. Nothing will keep you from

moving this aperture to another location in the back focal plane to select one of

the diffracted beams. The routine is exactly the same as for obtaining a BF image,

except that you should not use the projector lens alignment controls to bring the

diffracted beam to the center of the screen. This would be a rather inefﬁcient way

of doing things, and the projector controls may not even have a sufﬁciently wide

range to do this. There is another way to bring the relevant diffracted beam to the

center and we shall introduce it in a little while. First, you should take a look at the

image obtained when selecting an off-center diffracted beam with the diffraction

aperture.

Most likely you will observe a region on the sample that is very bright, while

the surroundings are dark. In particular, if you are looking close to the edge of the

thin foil you will ﬁnd that the hole in the sample is completely dark. The reason for

this is obvious: vacuum does not diffract electrons, and since you are only using

electrons scattered over an angle β the hole in the sample will not become bright.

This is known as a dark ﬁeld (DF) image. Any image created with a diffracted

beam is known as a dark ﬁeld image. Since there may be many diffracted beams,

you should always specify which diffracted beam you used to obtain the DF image,

264 Getting started

and we would typically speak of, for instance, a “two-oh-oh dark ﬁeld image” when

the operative reﬂection corresponds to the (200) lattice planes. We will see in a later

section how this information should be represented on an electron micrograph.

All of the diffracted beams in the pattern correspond to electrons traveling at an

angle β with respect to the optical axis, which means that those electrons will suffer

from spherical aberration (remember that spherical aberration goes with the cube

of the angle β). It would therefore be unwise to record images corresponding to

an off-center diffraction aperture. You can easily convince yourself that the image

quality deteriorates when you use diffracted beams at increasingly larger distances

from the optical axis. In addition, the electrons in a high-order diffracted beam

will come from a region on the sample that does not completely coincide with

the area selected by the SA aperture. This is again a consequence of spherical

aberration. Indeed, there will nearly always be a shift between a diffraction pattern

and the corresponding selected area. In Fig. 4.12(a) an object ab is centered on the

optical axis. Two sets of electrons leave the object: the transmitted beam (parallel

to the optical axis) and one diffracted beam (at an angle β = 2θ

). If an aperture

is introduced in the image plane, such that the image from the transmitted beam

exactly ﬁlls the aperture (between points A and B), then the image formed by the

diffracted beam will be shifted by an amount MC

, according to the deﬁnition

Apparent object for

diffracted beam

SA aperture

OL-BFP

(a)

(hkl)

(000)

Plane of focus

Defocus

(b)

α∆f

∆f

Fig. 4.12. (a) Illustration of the effect of spherical aberration on the image for two electron

beams. (b) Effect of overfocusing of the objective lens on the image for selected area

imaging.

4.4 A typical microscope session 265

of spherical aberration in Chapter 3. Assuming that the two images coincide, the

diffracted beam may be traced back (dotted lines) to the object plane, which results

in an object shift of C

; in other words, the diffracted electrons arise from a region

that is not completely identical to the region imaged by the transmitted electrons.

Since diffraction angles in electron diffraction are rather small (of the order of

milliradians), this shift effect is small, except for high magniﬁcations. There is a

much more important image shift effect: that caused by under- or over-focusing

of the objective lens. Figure 4.12(b) shows what happens when the image plane

of the objective lens does not coincide with the object plane of the imaging system.

The diffracted beam traveling at an angle β will arise from an area displaced by a

distance  fβ. The distance  f is known as the defocus. The total displacement in

the object plane caused by defocusing and spherical aberration is then given by

y = C

+  fβ. (4.1)

The out-of-focus images in Fig. 4.10(a) illustrate this image shift. For higher-

order reﬂections the image shift becomes increasingly more important. It is hence

important to correctly focus the image (so that  f ≈ 0) and to use only low-

order beams when obtaining DF images with an off-center diffraction aperture. We

recommend that you always use the centered dark ﬁeld method introduced in the

next section to minimize the effects of spherical aberration.

4.4.2.5 Centered dark ﬁeld images

Since the off-center dark ﬁeld image suffers from lens aberrations, we must ﬁnd a

way to bring the diffracted beam onto the optical axis, so that β = 0. Fortunately,

the microscope is equipped with pre-specimen beam deﬂection coils that allow us

to do just that. If your microscope has been aligned properly, you should be able to

focus the beam onto a small region (using C2), and then use the beam tilt controls

to change the orientation of the incident beam, without lateral motion of the beam.

You should try the following:

in image mode, focus the beam using C2 so that you obtain the smallest possible spot

size;

use the beam translation controls to bring the spot to the center of the viewing screen;

now change the beam tilt controls; you should not observe any beam shift on the screen

(although the contrast in your image will change);

if you do observe a beam shift, then that means that the beam deﬂection system is mis-

aligned, and you should refer to the standard procedures manual for the alignment pro-

cedure (this is essentially the iterative alignment procedure for the condensor lenses

discussed in Section 4.4.1).

266 Getting started

Once the beam tilt has been aligned properly, switch to diffraction mode, under-

focus the C2 lens, and change the beam tilt. You will ﬁnd that the diffraction

pattern shifts laterally. In other words, a tilt in direct space corresponds to a shift

in reciprocal space. This is not too difﬁcult to understand since the position of a

diffraction spot in the back focal plane is determined by the angle of the electron

trajectory with respect to the optical axis; if we tilt the entire beam, then all electron

trajectories will be changed by the same angle and thus the entire diffraction pattern

is translated in the direction opposite to the beam tilt direction.

We have seen before that we can also translate the diffraction pattern by means

of the projector lens controls. There is one important difference between those two

translations: shifting the pattern by means of the projector lens controls is a post-

specimen operation, and the intensity distribution in the diffraction pattern does

not change at all. Tilting the incident beam, on the other hand, is a pre-specimen

operation, and the intensity distribution in the back focal plane will change in

addition to the pattern shift.

Next, tilt your specimen while in diffraction mode to an orientation for which

one of the beams closest to the transmitted beam is very intense. It does not matter

whether other beams are intense as well. Switch the microscope to dark ﬁeld mode.

†

Then use the beam tilt to bring this intense reﬂection to the center of the screen. Do

not change the sample orientation. Insert an aperture around this beam and switch

to image mode. You will ﬁnd that the image has a rather low intensity. You may not

see anything at all! In fact, you may have noticed that the intensity of the diffracted

beam which you moved to the screen center decreased as you brought it closer to

the center.

To understand why this happens we need to take a close look at the Ewald

sphere construction for this situation. Consider the initial situation as shown in

Fig. 4.13(a): the reciprocal lattice point g is on the Ewald sphere and a high-

intensity diffraction spot is observed on the screen. The higher-order reﬂections 2g

and 3g are at increasingly larger excitation errors and will have correspondingly

lower intensities. The electrons in the beam g travel at an angle 2θ with respect to

the optical axis. The corresponding lattice planes are parallel to the perpendicular

bisector of the vector g, as indicated in the drawing. To bring the reﬂection g onto

the optical axis, we must tilt the incident beam towards the right by an angle 2θ,as

shown in Fig. 4.13(b). The crystal remains in the same orientation as before. Since

Bragg angles are quite small (of the order of a few milliradians) the electronic

beam tilt controls will be quite sufﬁcient to change the orientation of the incident

beam with respect to the optical axis. The angle between the incident beam and the

†

Most microscopes have multiple settings or memories for the beam tilt. It is a good idea to use the primary

setting or memory for the bright ﬁeld beam tilt condition, and other memory slots for various dark ﬁeld beam

tilts.

4.4 A typical microscope session 267

-g

θθ

(a)

2θ

θθ

2θ

(b)

-g

−2θ

θθ

(c)

-2g

Fig. 4.13. (a) Bright ﬁeld conﬁguration with g in Bragg orientation; (b) a beam tilt of 2θ

will bring g onto the optical axis but only 3g will be in Bragg orientation; (c) a beam tilt

of −2θ will bring −g to the optical axis and simultaneously in Bragg orientation. This is

known as the centered dark ﬁeld mode.

planes g is now 3θ, which is rather far away from the exact Bragg orientation. This

means that the reciprocal lattice point g has a large positive excitation error and

hence a weak diffraction spot. Since the incident angle is 3θ , the Bragg equation

will be satisﬁed for the reﬂection 3g, and the corresponding diffraction spot will

become bright. In other words, our attempt to bring the reﬂection g onto the optical

axis has changed the diffraction conditions to the extent that now the planes 3g are

strongly diffracting. We could now tilt the crystal over an angle 2θ to restore the

Bragg condition for the planes g. This would work ﬁne, but tilting a sample over

an angle of a few milliradians is not an easy task, especially when only mechanical

tilting controls are available. In addition, as is veriﬁed readily from a drawing of the

transmitted and diffracted beams, the bright ﬁeld image would then change from

what it was before the sample tilt.

There is a much easier way to obtain a dark ﬁeld image from the planes g, with the

operative reﬂection located on the optical axis of the microscope. You should now

try to bring the reﬂection −g onto the optical axis, using only the beam tilt controls.

Note that the intensity of the −g reﬂection increases and becomes maximal when

the beam is at the screen center. When you insert the diffraction aperture and switch

to image mode, a portion of your image will be rather bright, and you can easily

focus the image. This is known as a centered dark ﬁeld image (CDF image). To

understand why this works we need to go back to the Ewald sphere drawing in

Fig. 4.13. We have tilted the incident beam by an angle −2θ , to bring the reﬂection

−g onto the optical axis, as shown in Fig. 4.13(c). In other words, we have satisﬁed

the Bragg condition for the other side of the planes g, i.e. for −g. In Chapter 5