Graef M. Introduction to conventional transmission electron microscopy

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238 Getting started

Table 4.1. Material parameters for Cu-15 at% Al

(taken from [Vil97]); [copper–aluminum Bronze;

Pearson Symbol cF4; Strukturbericht Notation A1].

Space group Fm

Lattice parameters a = 0.365 26 nm # 225

Asymmetric unit Cu,Al at 4a (0, 0, 0)

There are many crystallographic resources available, both in electronic and paper

form. The following list provides some of the most important reference works and

journals for crystal structure data:

Pearson’s Handbook (Desk Edition) [Vil97]; contains 27 686 different compounds.

Atlas of Crystal Structure Types [DVvV91]; contains complete geometric descriptions of

all structure types referenced in Pearson’s Handbook.

Crystal Structures [Wyc63]; a six-volume detailed description of many structure

prototypes.

Chemical Abstracts, published by the American Chemical Society, contains a large

amount of crystallographic information on both organic and inorganic compounds.

Structure Reports (ﬁrst started as Strukturbericht), published by the International Union

of Crystallography.

Acta Crystallographica also published by the International

Union of Crystallography.

Powder Diffraction File; a large collection of (x-ray) powder diffraction patterns, available

from the International Center for Diffraction Data.

†

Collaborative Computational Project Number 14 for Single Crystal and Powder Diffrac-

tion; a large collection of crystallography related links.

‡

You should be able to ﬁnd crystallographic information for nearly all known com-

pounds in at least one of the above sources.

4.3 The study materials

4.3.1 Material I: Cu-15 at% Al

4.3.1.1 Crystallography

Cu–Al alloys are commonly known as bronzes, and are solid solutions of up to

18.8 at% Al (at room temperature) in a face-centered cubic matrix of Cu atoms.

Space group and lattice parameter information can be found in Table 4.1, and

†

www.icdd.com (Since the web is a dynamic medium and links can change, the reader is referred to the

website for a reasonably up-to-date listing of crystallography related links.)

‡

www.ccp14.ac.uk

4.3 The study materials 239

(a) (b)

Fig. 4.1. (a) Parallel projection of the close-packed cubic structure; (b) [110] projection

illustrating the ABC stacking sequence of the fcc lattice.

structure drawings are shown in Fig. 4.1. There are several reasons for selecting

this material as one of the four study materials: ﬁrst of all, the crystal structure is

cubic, which is one of the easier structures to deal with for the beginning micro-

scopist. Secondly, Cu–Al bronzes have a relatively low stacking fault energy, so

the probability of ﬁnding a stacking fault is reasonably high. Lastly, after a proper

heat treatment, the Al atoms are no longer randomly substituted on the Cu lattice,

but instead will form a short-range ordered state.

It is easy to obtain a Cu–Al bronze:

†

simply melting pure Cu and Al together in

a sealed quartz tube will do the trick. The melting temperature of a Cu-15 at% Al

alloy is around 1050

◦

C [Com73, page 259]. Alternatively, Cu–Al bronzes can be

obtained easily from metals supplies companies.

Any Cu–Al bronze will do, but if you are going to make your own material the Al

content should be between 10 and 15 at%, so that the short-range ordering effect can

be made more pronounced. Higher Al contents should be avoided, unless you want

to deal with hexagonal and monoclinic martensitic phases! If you cannot obtain a

Cu–Al bronze, then the next best thing would be pure copper; with the exception

of SRO, you will be able to reproduce most of the Cu–Al-based ﬁgures in this text.

We have also prepared pure copper foils with a small grain size (around 2

µm) and

will use them for some of the observations in this chapter.

4.3.1.2 Thin-foil preparation

If you made your own alloy and slowly cooled it from the melt, then you should

have a reasonably coarse-grained microstructure. If you purchased a rod of Cu–Al

bronze it might be a good idea to subject it to a solutioning heat treatment before you

begin to prepare a TEM foil; quite often the microstructure of extruded or swaged

†

In some countries bronze coins are still in use. You could simply take one of these coins, check its composition,

and use it to prepare your samples!

240 Getting started

Liquid nitrogen

+--

Insulated container

Glass container

Pump

Sample

Electrolyte

Detector

Light

source

Mechanical

punch

Mechanical

grinding

100−200 µm

3 mm

(a) (b)

Fig. 4.2. (a) Mechanical grinding and mechanical punching are used to obtain a 100–200 µm

thick 3 mm diameter

thin foil; (b) schematic illustration of the double-jet electro-polishing

process.

rods will have a very high defect density, something we wish to avoid in this case.

A heat treatment of1hat700

◦

C will drastically reduce the defect density.

Use a diamond saw or wire electro-discharge machining (EDM) to cut a thin slice

of material, about 300–500

µm thick. Using coarse sandpaper, reduce the thickness

of the slice to around 100–200

µm, by removing material from both sides (Fig. 4.2a).

Then use ﬁne sandpaper to get a smooth surface. Use a mechanical punch to punch

out 3 mm diameter disks from the thin sheet. If you want to introduce a signiﬁcant

dislocation density in your samples, then you can bend the sheet a bit (making sure

you deform the material plastically) and bend it back to a ﬂat sheet before you

punch out the disks.

For many metals and alloys the best thin foils are obtained using double-jet

electro-polishing. The basic electrolyte used for many different copper alloys con-

sists of 70 vol% methanol and 30 vol% nitric acid (HNO

†

Other mixtures are

also used and often a mixture used for a material similar to the one you intend to

study can be used as a starting point.

The basic electro-polisher is shown schematically in Fig. 4.2(b): a glass container

with the electrolyte is placed on supports in a cooling vessel. Typically this vessel

contains a small amount of liquid nitrogen at the bottom; evaporation of the nitrogen

then cools down the glass container and its contents. The sample is mounted in

between two teﬂon support plates and positioned in between two nozzles. A rotary

†

A word of caution: chemicals can be dangerous to your health in many different ways. Always read the safety

instructions that come with the chemical, usually in the form of a Material Safety Data Sheet or MSDS. Those

sheets can be obtained from the manufacturer. Since every microscopy laboratory will have its own safety rules

and guidelines, we urge the reader to familiarize himself/herself with all applicable rules and to follow them at

all times.

4.3 The study materials 241

Table 4.2. Material parameters for Ti (taken

from [Vil97]); [titanium; Pearson Symbol

hP2; Strukturbericht Notation A3].

/mmc

Space group a = 0.2950 nm

Lattice parameters c = 0.4681 nm # 194

Asymmetric unit Ti at 2c





pump is used to produce two ﬁne jets that are directed at the center of the disk.

Typically, the jets are about 0.5 mm in diameter and the pump velocity should be

controlled to give straight jets at the sample location. A voltage is then applied

between the sample (positive) and the two nozzles (negative). As the voltage is

increased, material is removed from the sample and a current will begin to ﬂow

between the sample and the nozzles. At the lowest voltages, only a small amount

of material is removed and the sample is “etched”. At a slightly higher voltage, the

sample is “polished”, and at the highest voltage “pitting” (i.e. a rapid, uncontrolled

removal of material) occurs. It takes some experience to ﬁnd this polishing plateau in

the current–voltage curve; the type of electrolyte, the applied voltage, the electrolyte

temperature, and a host of others parameters (including jet alignment, age and purity

of the electrolyte, and “good fortune”) will determine the quality of the thin foil.

It may take a bit of experimenting to ﬁnd the right conditions for your material.

For the Cu-15 at% Al foils we used the following conditions: electrolyte methanol –

20 vol% HNO

, T =−30

◦

C, voltage V = 5–8 V. Polishing took 30–60 s per foil,

for an initial foil thickness of 100

µm. The applied voltage will depend on the age

of the electrolyte; the more Cu-ions are present in the electrolyte, the larger the

voltage must be to obtain well-polished foils.

4.3.2 Material II: Ti

4.3.2.1 Crystallography

Pure Ti has a hexagonal crystal structure with lattice parameters a = 0.2950 nm and

c = 0.4679 nm. The space group information and atom positions for the asymmet-

ric unit are given in Table 4.2. There are two atoms per unit cell, and the structure

can be described as a two-layer stacking of close-packed planes, usually repre-

sented by the stacking symbol AB, the Ramsdell symbol 2H, or in triangle notation

(∇)

[HB84]. The stacking symbol indicates that the close-packed planes al-

ternate between two different positions. Each close-packed plane has two kinds of

triangular dimples in between groups of three atoms. Those dimples are represented

242 Getting started

(a)

(c)

(b)

Fig. 4.3. (a)

Parallel projection of the T

i unit cell; (b) single close-packed layer showing

two sets of triangular dimples; (c) projection along the [2

1.0] direction showing the ABAB

stacking sequence.

by the symbols  and ∇, as shown in Fig. 4.3(b). If we represent the ﬁrst plane

by the letter A, then the next plane can be located on the  dimples, producing a

B plane, or on the ∇ dimples, producing a C plane. If we alternate the stacking of

close-packed planes such that dimples of opposite orientation are ﬁlled, then we

obtain the hexagonal close-packed structure. If we always ﬁll only one kind of dim-

ple, say (∇)

, then we obtain the face-centered cubic structure shown in Fig. 4.1(b),

with a stacking sequence of ABCABC or 3R (R stands for rhombohedral, which

is the primitive unit cell corresponding to the fcc cell). Several defects, such as

stacking faults and twins, can be described in terms of such stacking symbols.

The reasons for including titanium as a study material are twofold: ﬁrst of all,

titanium has a hexagonal structure, which will permit us to illustrate the use of

the 4-index system along with the conventional 3-index system for the other three

study materials. Secondly, it is rather straightforward to produce inclusions in ti-

tanium; as described in more detail in the next section, if we use an electrolyte

containing hydrogen ions (and many commonly used electrolytes do) then we can

cause precipitation of TiH

hydride particles in the thin foil. This is an artifact of

specimen preparation, but we will use it to our advantage to study image formation

and diffraction for a material containing precipitates.

Pure titanium can be obtained from many different sources. We ordered a 15 ×

15 cm

thin sheet (0.9 mm thick) of grade 2 titanium from McMaster-Carr Supply

Company for about U.S. $80. Other sources are obviously also acceptable. Ti

manufacturing is technologically demanding because of the high reactivity of Ti in

an oxygen atmosphere; this makes it unlikely that you will have easy access to Ti

manufacturing equipment.

4.3 The study materials 243

4.3.2.2 Thin-foil preparation

Thin-foil preparation for titanium proceeds along the same lines as for the ﬁrst study

material. We used the following conditions: electrolyte 95 vol% methanol, 5 vol%

sulfuric acid (H

), T =−35

◦

C, voltage V = 35–40 V. Polishing took 4–6 min

per foil, for an initial foil thickness of 190

µm. At lower temperatures, polishing was

signiﬁcantly slower and upon perforation resulted in foils with rapidly increasing

thickness away from the hole. At higher temperature a signiﬁcant number of hydride

particles were produced in the foil. This is something you will need to avoid if you

are preparing Ti-based thin foils. It is possible to use electrolytes that do not contain

hydrogen ions, such as a solution of 40 g of CaCl in 500 ml of methanol at −45

◦

and 35 V [Pie95]. For the purposes of this text we will actually make use of the

hydride particles so do not worry too much about them as you prepare the thin

foils. You could also use the dimple grinding and ion milling method, described in

the next section, if you want to avoid completely the introduction of hydrides in

your foil.

4.3.3 Material III: GaAs

4.3.3.1 Crystallography

We have selected GaAs as the third study material because it is easy to obtain

in single-crystal form, and because it has a non-centrosymmetric space group.

As we will describe in detail in the next chapter, there are a few subtle differ-

ences both in image formation and diffraction between centrosymmetric and non-

centrosymmetric crystals. GaAs will be used to illustrate those differences. The

crystal structure of GaAs, shown in Fig. 4.4, is that of zinc-blende (also known as

sphalerite); it is a face-centered cubic structure with two atoms in the asymmetric

unit, and four formula units per unit cell. GaAs can be regarded as the prototype

of an important class of materials, the binary semi-conductors. A signiﬁcant part

Fig. 4.4. Parallel projection of a single unit cell of the GaAs structure.

244 Getting started

Table 4.3. Material parameters for GaAs

(taken from [Vil97]); [zinc-blende or

sphalerite; Pearson Symbol cF8;

Strukturbericht Notation B3].

Space group F

43m

Lattice parameters a = 0.5652 nm # 216

Asymmetric unit As at 4a (0, 0, 0)

Ga at 4c





of all TEM-based research worldwide is centered on materials with this particular

crystal structure, or on ternary structures derived from it.

As an illustration of the use of the

xtalinfo.f90 program we list a portion of the

output of this program for the GaAs structure in Fig. 4.5 on the following pages.

The output has been reduced in size to ﬁt within the margins of this book. The ﬁrst

portion of this ﬁgure shows standard crystallographic output, along with various

matrices useful for crystallographic computations. The second part lists information

for all independent families of planes with Miller indices less than 5. Some of the

entries in this table will be deﬁned in Chapter 5. The third portion of Fig. 4.5

shows a number of representative zone axis diffraction patterns. These patterns

can be drawn to the correct scale for a given microscope camera length. Crosses

indicate systematic absences. The multiplicity mentioned alongside each pattern

is actually a useful piece of information because it indicates how easy it will be

to ﬁnd that particular zone axis. A small multiplicity means that it will be more

difﬁcult to obtain this zone axis orientation, whereas a multiplicity of 48 indicates

that you will not have to look for very long to ﬁnd it. The probability of ﬁnding a

particular zone axis orientation will be modiﬁed if the (polycrystalline) sample has

a preferential texture.

4.3.3.2 Thin-foil preparation

GaAs is typically manufactured as a [001]-oriented wafer (Fig. 4.6a). The {110}

planes in the [001] zone are good cleavage planes. We prepared two different

samples: a [001]-oriented foil and a [110]-oriented foil. The [001]-oriented foil

is rather easy to prepare. Cleave the wafer until you have a square sample of

approximately 2 × 2mm

. GaAs can be cleaved in the same way that you would

cut glass: use a sharp razor blade and a ruler to score one surface along a [110]

direction. Then support the wafer and use the ruler to press down on the part that

you wish to cleave (see Fig. 4.6b). You should have no trouble obtaining perfectly

straight cleavage planes.

4.3 The study materials 245

gaas.xtal

Distances [nm], angles [degrees]

Direct Space

a :

b :

c :

0.5653

α :

β :

γ :

90.0000

Space Group : F -4 3 m [#216]

Bravais Lattice : cF

Volume V [nm^ 3] : 0.1806

Reciprocal Space

a* :

b* :

c* :

1.7690

α∗ :

β∗ :

γ∗ :

90.0000

Volume V* [nm^

-3] : 5.5356

Important Matrices

g =

0.31956

0.00000

0.31956

0.00000

0.31956

g*=

3.12926

0.00000

3.12926

0.00000

3.12926

a =

0.56530

0.00000

0.56530

0.00000

0.56530

b =

1.76897

0.00000

1.76897

0.00000

1.76897

Asymmetric Unit

atom x y z occ. B

Ga [31] 0.0000 0.0000 0.0000 1.0000 0.0058

As [33] 0.2500 0.2500 0.2500 1.0000 0.0063

Fig. 4.5. Partial output of the xtalinfo.f90 program for the GaAs structure.

246 Getting started

Structure Factor Information

Distances [nm], angles [mrad], potential [V,rad]

h k l p d g 2θ |V| Vphase |V’|

V’phase

ξ'

0 0 0 1 0.00000 0.00000 0.0000 21.08094 0.00000 1.11911 0.00000 0.00 535.93

1 1 -1 4 0.32638 3.06395 7.6839 9.71481 0.84450 0.47377 0.84165 61.74 1265.94

1 1 1 4 0.32638 3.06395 7.6839 9.71481 -0.84450 0.47377 -0.84165 61.74 1265.94

2 0 0 6 0.28265 3.53794 8.8726 0.76727 -3.14159 0.03662 -3.14159 781.70 16375.89

2 2 0 12 0.19986 5.00341 12.5478 8.89642 0.00000 0.56329 0.00000 67.42 1064.74

3 1 -1 12 0.17044 5.86702 14.7136 5.30499 -0.82069 0.37275 -0.84480 113.06 1609.02

3 1 1 12 0.17044 5.86702 14.7136 5.30499 0.82069 0.37275 0.84480 113.06 1609.02

2 2 -2 4 0.16319 6.12790 15.3678 0.22302 -3.14159 0.03069 -3.14159 2689.36 19541.95

2 2 2 4 0.16319 6.12790 15.3678 0.22302 -3.14159 0.03069 -3.14159 2689.36 19541.22

4 0 0 6 0.14132 7.07589

17.7453 6.05159 0.00000 0.48008

0.00000 99.11 1249.30

3 3 -1 12 0.12969 7.71077 19.3376 3.85773 0.79954 0.32425 0.84446 155.47 1849.69

3 3 1 12 0.12969 7.71077 19.3376 3.85773 -0.79954 0.32425 -0.84446 155.47 1849.68

4 2 0 24 0.12640 7.91109 19.8399 0.06867 -3.14159 0.02662 -3.14159 8734.28 22531.40

4 2 2 12 0.11539 8.66616 21.7336 4.70112 0.00000 0.42597 0.00000 127.58 1407.99

4 2 -2 12 0.11539 8.66616 21.7336 4.70112 0.00000 0.42597 0.00000 127.58 1407.99

3 3 3 4 0.10879 9.19185 23.0521 3.07112 0.79504 0.28985 0.84346 195.29 2069.21

3 3 -3 4 0.10879 9.19185 23.0521 3.07112 -0.79504 0.28985 -0.84345 195.29 2069.20

4 4 0 12 0.09993 10.00682 25.0960 3.85023 0.00000 0.38411 0.00000 155.78 1561.45

4 4 -2 12 0.09422 10.61383 26.6184 0.03757 -3.14159 0.02074 -3.14159 15965.04 28921.36

4 4 2 12 0.09422 10.61383 26.6184 0.03757 -3.14159 0.02074 -3.14159 15965.04 28921.36

4 4 -4 4 0.08159 12.25580 30.7366 2.78370 0.00000 0.31926 0.00000 215.46 1878.59

4 4 4 4 0.08159 12.25580 30.7366 2.78370 0.00000 0.31926 0.00000 215.46 1878.59

Fig. 4.5 (cont.).

Measure the thickness of the sample using a micrometer. In our case we measured

630

µm. Mount the small sample on a dimple grinder support stub (Fig. 4.6c) using

a small amount of low melting point mounting wax. Let the wax cool down and

center the stub on the dimpler. Gently lower the dimpler arm with a wheel in place

onto the sample, and set the amount of material that you wish to remove.

†

Then

place a small amount of 6

µm diamond polishing compound and a drop of a water-

soluble lubricating oil on the sample. Lower the wheel onto the sample and remove

a preset amount of material.

We used a 20 mm diameter dimpling wheel on a Gatan Model 656 Dimple Grinder

to obtain a shallow dimple, and set the dimple weight at 15–20 g. The wheel speed

was kept rather low, around 2–3 rev s

−1

. Remove 80–90% of the thickness using

µm diamond compound (550 µm in our case, with three steps of 150 µm each,

followed by one step of 100

µm). In between steps, gently wash away the diamond

compound using a methanol squirt bottle and check the surface with an optical

microscope. The nominal thickness of the sample at the center of the dimple should

†

There are several models of dimple grinders or “dimplers” available and we refer the reader to the instructions

that come with each machine for more details.

4.3 The study materials 247

Kinematical Zone Axis Patterns

scale bar in reciprocal nm

Camera Constant [nm mm] 3.0094

Structure File : gaas.xtal

Powder Pattern

Zone axis [ 1 0 0]

Multiplicity 6

Zone axis [ 1 1 0]

Multiplicity 12

Zone axis [ 1 1 1]

Multiplicity 4

Zone axis [ 2 1 0]

Multiplicity 24

Zone axis [ 2 1 1]

Multiplicity 12

Fig. 4.5 (cont.).