Messerschmidt U. Dislocation Dynamics During Plastic Deformation

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20 2 Experimental Methods

dislocations. An example is given in Fig. 2.6. In Fig. 2.6a, all dislocations in

the specimen area are visible. In Fig. 2.6b, the set marked A in Fig. 2.6a is

extinguished, in Fig. 2.6c it is set B. Finally, in Fig. 2.6d all dislocations except

some small loops are invisible. Considering the indexing of the g vectors in the

ﬁgure and the extinction rule (2.9), it may be concluded that the dislocations

marked A have Burgers vectors parallel to [010] and those marked B have such

parallel to [100]. For many TEM micrographs in this book, the g vectors are

indicated. If it is written, for example, g = (110) means that planes parallel

to the (110) plane are reﬂecting. In most cases, a reﬂection of higher order is

excited to obtain more narrow (sharper) images of the dislocations.

2.4 In Situ Straining Experiments in the Transmission

Electron Microscope

Performing complete plastic deformation experiments in situ in the specimen

chamber of a transmission electron microscope provides the unique opportu-

nity to observe the moving dislocations under stress at a resolution level that

allows conclusions to be drawn on many relevant mechanisms. Such experi-

ments were greatly facilitated by the commercial availability of high-voltage

electron microscopes (HVEM) with acceleration voltages of 1 MV, mainly in

Japan at the end of the 1960s. These microscopes allow the penetration of

specimens of thicknesses up to about 1–2 μm compared to some 100 nm in con-

ventional microscopes with an acceleration voltage of 200 kV. In addition, the

specimen chambers of most HVEMs oﬀer suﬃcient room to insert elaborate

in situ stages between the pole pieces of the objective lenses. As will be men-

tioned below, the high voltage leads to the formation of radiation damage in

most materials, which may impair the reliability of these experiments. There-

fore, in situ experiments are also performed in conventional microscopes where

this problem usually does not occur, for example, [27]. A number of strain-

ing stages had been designed by the pioneering work of the group of Imura

and others, for example, [28–32], using diﬀerent types of drive mechanisms.

The adjustment of proper imaging (diﬀraction) conditions requires the tilting

of the specimen. Most straining devices were designed for side entry specimen

stages and allow tilting only around a single axis. The present author designed

two straining stages for a 1 MV top entry HVEM with double tilting facilities,

one for room temperature [33] and another one for temperatures up to more

than 1,250

◦

C to be able to study also ceramic materials [34]. The stages will

be brieﬂy outlined in the following.

The room temperature stage shown in Fig. 2.7a consists essentially of a

single aluminium plate (1). It is supported by a screw at (2) and forms two

levers (3), which are connected with the support by thin parts acting as leaf

springs. The central bar (4) carries a heating coil. If the bar is heated, it pushes

the levers away from each other, resulting in a deformation of the specimen

(5), which is ﬁxed to the levers from below. The hatched areas of the levers

2.4 In Situ Straining Experiments in the Transmission Electron Microscope 21

(110)

[1–10]

(a)

(–103)

[010]

(b)

(0–13)

[531]

(c)

1µm

(002)

[010]

(d)

Fig. 2.6. Analysis of the direction of Burgers vectors using the g times b rule. MoSi

single crystal deformed along a 011 direction at 380

◦

C. The thick dark contrast

near the center is a precipitate that can be used as a marker to identify individual

dislocations. The directions of the respective g vectors are indicated by the indexed

bars in the upper corners, the poles that are close to the viewing directions are

marked by the indexed white dots in the lower edges of the images. From the work

in [15]

22 2 Experimental Methods

Fig. 2.7. Outline of in situ straining stages for a top entry HVEM. These stages

are placed on double-tilting goniometer stages. (a) Room temperature deformation

stage. (b) Hot zone of high-temperature deformation stage. From [33,34]. Copyright

Elsevier Science (1976, 1994)

are water cooled. The whole equipment is inclined with respect to the electron

beam so that the latter can transmit the specimen. Four semiconducting strain

gauges forming a full bridge are glued to the lower parts of the levers for

measuring the load. Another set of strain gauges is ﬁxed to a pair of leaf

springs (7) for measuring the specimen elongation. Thus, the stage allows the

recording of the load-elongation curve during the in situ experiment.

2.4 In Situ Straining Experiments in the Transmission Electron Microscope 23

Usually, high-temperature straining stages are heated by electrical resis-

tance heating. However, it is diﬃcult to generate the high heating power

necessary to reach very high temperatures by this method because of the high

radiation losses. A solution to the problem is heating by electron bombard-

ment, which was introduced in the design of electron microscopy stages in [35].

The environment of the specimen in the high-temperature stage is outlined

in Fig. 2.7b in perspective and in cross-section views. Two double T-shaped

bars carry the specimen grips (1) at their lower ends. They are made from a

W-27at% Re alloy having a high strength at high temperatures. The specimen

is mounted between these grips from below by two tungsten pins ﬁtting into

bores of the specimen. As seen in the cross-sectional view, the grips have a

U-shaped notch each. Tungsten ﬁlament coils (2) are situated in each notch.

They are attached to the thermal shields (3) via tungsten wires (4). As the

shields are at negative ﬁlament potential, they are electrically (and thermally)

insulated by small Al

spacers. For measuring the temperature, W-Re ther-

mocouple wires with 3 and 25% Re were welded individually to the top sides

of both grips. The T-shaped bars are connected to the drive mechanism. It

is made of copper and stainless steel and is similar to that of the room tem-

perature stage. For improving the heat transfer to the cooling water, heat

exchangers with copper lamellae are used. Outside, they carry the semicon-

ducting strain gauges for measuring the force acting on the specimen. The

whole system is digitally controlled by a personal computer equipped with

AD and DA converters. It provides the measurement of the temperatures of

both grips, of the electron beam current, and of the specimen load. The sys-

tem controls the electron beam current, the average temperature, the balance

between both grips, and the drive voltage.

The high-temperature straining stage allows a maximum specimen elon-

gation of 1 mm and a maximum load of 15 N. The thermal drive against water

cooling allows steady state behavior and ensures a very smooth and stable

operation. A number of experiments were performed at a grip temperature of

1,250

◦

C, corresponding to a specimen temperature of 1,150

◦

C, using a beam

current of about 60 mA at 700 V. The temperature is stable within about 3 K.

Duringtheinsituexperiments,theimages were recorded either as images

on photographic ﬁlm with a high resolution or by a video system mounted in

the base of the microscope with the usual TV resolution. Figure 2.8 shows the

HVEM equipped for performing straining experiments.

The specimens for in situ straining experiments have to meet the require-

ments of both transmission electron microscopy and of a tensile experiment.

In the case of these deformation stages, they are made from thin plates about

8 mm long, 1–2 mm wide, and 0.1 mm thick. For being ﬁxed to the stage by

pins, they have two bores 5 mm apart. The thickness at the center must be

small enough for electron transparency, that is, about 1 μm. Besides, the edges

of the central thin area have to be thin enough to cope with the maximum

load of the stage, that is, about 10 μm. Depending on the material, this shape

can be produced by grinding, dimpling, and ﬁnal ion milling, or by chemical

24 2 Experimental Methods

Fig. 2.8. View of the high-voltage electron microscope equipped for in situ straining

experiments. In the center, the microscope column and the control desk. At the top

right of the column, an extra turbo pump for improving the vacuum in the specimen

chamber. Left of the column, the video screen for the operator of the microscope.

In front, on the right side, the video recorder with another screen. On the left side,

the PC for controlling all functions of the straining stage

or electrolytical polishing. In the latter case, the thinning may be performed

in two steps using masks. In the ﬁrst step, a shallow dimple is thinned from

one side through a mask with a hole smaller than the sample width. In the

second step, the whole central area is thinned, including also the edges of the

sample. For brittle materials like ceramics, semiconductors, or quasicrystals,

it is advantageous if there is no hole in the center of the specimen. For opti-

cally transparent materials, the thickness can be estimated by watching the

occurrence of Newton fringes so that the thinning can be stopped before the

sample is perforated. Figure 2.9 presents an example of the central part of

aZrO

specimen without a hole after in situ straining. The bright contrasts

near the center show regions deformed by ferroelastic deformation. Metal spec-

imens usually have a hole in the center of the transparent area. Because of

the inhomogeneous cross section of in situ specimens, the stress distribution is

not uniform. According to calculations by the ﬁnite element method [37], the

stress state is complicated at the edges of the perforation lying in the tensile

direction. At the transverse edges, an almost uniaxial tensile stress occurs with

a stress concentration of three times the average stress in this cross section,

as results from technical elasticity calculations of a plate with a cylindrical

hole. Mainly these areas should be observed during in situ straining.

2.4 In Situ Straining Experiments in the Transmission Electron Microscope 25

Fig. 2.9. Micro-tensile sample of a ZrO

single crystal deformed during an in situ

straining experiment at 1,150

◦

C. The specimen was prepared by grinding, dimpling,

and ion milling. It does not have a perforation. The bright contrasts near the center

result from ferroelastic deformation. From the work in [36]

There are two problems limiting the reliability of in situ straining experi-

ments in an HVEM as discussed in [38,39]. The ﬁrst one regards surface eﬀects

due to the relatively low specimen thickness, even in the HVEM. The surfaces

close to the dislocations cause so-called image forces, which superimpose on

the forces from the applied stress. These forces are estimated in Sect. 3.2.3,

showing that the image forces are not of great importance in materials with

high ﬂow stresses like many contemporary materials, but they may produce

artifacts in pure f.c.c. metals, which have very low ﬂow stresses. Another

eﬀect may be called the interruption of the dislocation kinetics. During defor-

mation, new dislocations are generated in the interior of the specimen, which

may move out of the foil, but no dislocations move into the foil from outside.

This results in diﬀerences in the dislocation density between the interior of the

crystal and the regions near the surfaces. Therefore, in situ straining experi-

ments are well suited to study the dynamics of individual dislocations rather

than the development of complex dislocation structures.

The second problem is the occurrence of radiation damage. The imag-

ing electrons of high energy may displace atoms from their regular places

forming vacancies and interstitial atoms. The threshold voltage for this pro-

cess depends mainly on the atomic number of the material. As shown in

Fig. 2.10, the acceleration voltage of 1 MV exceeds the threshold voltage for

most materials. Even at 200 kV, displacement damage can occur in light mate-

rials. Whether the radiation damage disturbs the deformation experiment, or

not, depends on the temperature. At low temperatures, the generated pri-

mary defects are immobile. At intermediate temperatures, the defects diﬀuse,

at ﬁrst forming small clusters and later on dislocation loops. This process is

described for ZrO

single crystals in [40]. In this temperature range, straining

experiments cannot be performed. At high temperatures, the defects anneal

26 2 Experimental Methods

1500

1000

500

U (kV)

f.c.c.

b.c.c.

h.c.p.

20 40 60 800

Fig. 2.10. Dependence of the threshold voltage for displacement damage by electron

irradiation on the atomic number. Data from [38]

out at the near surfaces. How severe the radiation damage aﬀects the dislo-

cation motion in a particular experiment has to be checked individually. In

most experiments described in this book, the eﬀect is not strong so that the

results should be reliable.

As mentioned in the Introduction, video sequences of dislocation motion in

a number of materials can be downloaded from http://extras.springer.com/

2010/978-3-642-03176-2. These video clips will be described in some detail

in Part II in the chapters of the respective materials. Some videos showing

general features of dislocation motion will be referred to in the following chap-

ters. For a ﬁrst glance at dislocation motion and generation, please look at

Video 9.17. The video presents a rotating source which, at each revolution,

produces two dislocations afterwards moving in opposite directions. They are

mostly straight and aligned along crystallographic orientations. In addition to

qualitative information on the dislocation behavior, in situ straining experi-

ments yield a wealth of quantitative data, including the indexing of the planes

of motion, the preferred orientations of dislocations, the density and strength

of obstacles to the dislocation motion, or kinematic data like waiting times

and jump distances. The evaluation of such data is discussed in the respective

chapters.

2.5 Other Methods

The methods described in this section supplement the main techniques pre-

sented above to study dislocation dynamics and the processes controlling

it. They are mostly limited either to particular materials or to particular

2.5 Other Methods 27

processes. The contents of this section is better understood after reading Part

Iofthisbook.

2.5.1 X-Ray Topography In Situ Deformation Experiments

Using X-ray topography, dislocations can be imaged in a similar way as in the

electron microscopy diﬀraction contrast. A recent review of the topography

techniques is given in [41]. Accordingly, in situ straining experiments can also

be performed in an X-ray topography arrangement to directly observe the

processes controlling the dislocation motion. This requires dedicated strain-

ing stages to be positioned on the goniometer head of the X-ray topographic

device. However, there are two diﬀerences with respect to TEM. The high-

energy photons have a much higher penetration power compared to the

electrons of usual energies, and so crystals of bulk dimensions can be observed.

Besides, the width of the dislocation images is considerably greater than in

TEM diﬀraction contrast, resulting in a poor resolution power for disloca-

tions. This limits the application to the observation of single dislocations in

crystals of a very high perfection with zero or very low dislocation densities as

semiconductor single crystals, or to the observation of groups of dislocations,

so-called slip bands, in otherwise perfect crystals. To record the processes by

means of video systems, X-ray beams of a high intensity are necessary. This

can be achieved by conventional high intensity rotating anode X-ray sources

or, more recently, by synchrotron radiation.

In the ﬁrst type of experiments, mainly the multiplication of dislocations

in semiconductor crystals was studied [42, 43]. Microhardness indents were

placed on the surface to introduce nucleation sites. An example of a dislocation

source, which had emitted a number of hexagonal dislocation loops in an Si

single crystal, is presented in Fig. 2.11.

The ﬁrst occurrence and propagation of slip bands was studied in MgO sin-

gle crystals of thicknesses between about 60 and 320 μm[44]inanequipment

similar to that in [42]. First slip bands occur at about half the macroscopic

yield stress. During plastic instabilities causing decreases in the applied stress,

the bands propagate at high velocities of about 150 mm s

−1

. There exists a size

eﬀect of an increasing yield stress with decreasing specimen thickness. In this

respect, the X-ray topography experiments are a link between macroscopic

tests and in situ straining experiments in the TEM. In optically transparent

crystals, similar studies on the propagation of slip bands can be performed by

optical birefringence microscopy.

2.5.2 Surface Studies of Slip Lines

The occurrence and propagation of slip bands can also be observed on the

crystal surface by imaging the steps resulting from the motion of disloca-

tions with Burgers vectors pointing out of the surface. These experiments can

be performed on very diﬀerent levels of spatial and temporal resolution. In

28 2 Experimental Methods

1 mm

Fig. 2.11. Localized dislocation source in an Si single crystal observed during an

X-ray topography in situ straining experiment. The topography device included a

30 kW X-ray generator, the in situ straining stage, and a vidicon X-ray camera. From

the 1950s and 1960s, the surfaces of deformed crystals were imaged by opti-

cal microscopy or by surface replicas imaged in the TEM. These methods

do not resolve the steps produced by moving individual dislocations. Never-

theless, important information on the distribution and length of slip bands

formed by many dislocations has been obtained (e.g., the work by Seeger and

coworkers [45]).

To follow the temporal development of the slip bands, the optical micro-

scope was supplemented by a cine camera, ﬁrst applied by Schwink and

Neuh¨auser [46], and reviewed in [47]. Later on, the cine camera was replaced

by a video camera. Diﬀerent methods have been used to improve the time

resolution of speciﬁc processes, for example, a photo-diode was placed in the

intermediate plane of the microscope to record the intensity changes of an

imaged slip band (e.g., [48]). Recently, optical extensometers have been devel-

oped (e.g., [49]) where the gauge length of the specimen is coated with a

pattern of dark and bright stripes, which are scanned via a special line-scan

camera typically operating at a frequency of 250 Hz. The PC based evaluation

of the data allows the determination of the place and the time of a deformation

event. These data can be plotted in a correlation diagram.

The cinegraphic methods are mainly used to investigate the evolution of

slip bands at the heterogeneous deformation as it occurs at plastic instabilities

described in Sect. 5.3. The occurrence of slip bands can be correlated or un-

correlated. The heads of slip bands may move at velocities up to the m s

−1

range. In one study [48], a second video camera was placed on the opposite

side of the specimen to monitor the passage of slip bands through the crystal.

A method which is able to resolve slip steps of atomic height trailed

by moving individual dislocations is the so-called heavy metal decoration

2.5 Other Methods 29

technique [50,51]. It requires very smooth starting surfaces with a low density

of steps. Such surfaces can be obtained by cleaving ionic crystals in a very dry

atmosphere or in vacuum or by producing growth surfaces on metals. After

deforming the crystals and creating the slip steps in vacuum, a small amount

of gold or another heavy metal is evaporated on the surface. The gold forms

small nuclei distributed randomly on the atomically smooth surfaces. Along

monatomic steps, however, the nuclei are linearly arranged, thus decorating

the surface step. This method allows the paths of individual dislocations with

a Burgers vector component out of the surface to be imaged. The technique is

well suited to study cross slip as described in Sect. 4.3 and shown in Figs. 4.9

and 4.12.

In recent years, slip steps have also been imaged by atomic force

microscopy. Mostly, the resolution power is suﬃcient only to observe slip bands

(e.g., [52]). In some studies, also the steps of a few individual dislocations were

imaged showing cross slip events of superdislocations (e.g., [53]).

In general, the observations of slip bands on the crystal surfaces provide

a link between the behavior of individual dislocations and the macroscopic

plastic properties, in particular in the case of inhomogeneous deformation.

2.5.3 Internal Friction

If a material is deformed, the part W

of the total work W

expended is of

elastic nature, that is, it is re-gained after unloading. The rest is partly stored

in the material in the form of crystal defects produced by the deformation,

the so-called stored energy W

stor

, and partly transferred as friction W

into

heat

= W

+ W

stor

+ W

The stored energy is mostly only a small fraction (in the order of magnitude of

10%) of the nonelastic energy. Several methods have been designed to measure

the stored energy, mostly calorimetric ones. On principle, the nonelastic part

of the energy can be determined as the area enclosed in a stress–strain curve

of a specimen loaded and unloaded cyclically. Frequently, the driving stress is

harmonic

σ = σ

exp(iωt),

where σ

is the oscillation amplitude, ω the circular frequency, and t the time.

If the amplitudes are small so that no energy is stored, the behavior is anelastic

and the relative energy loss per cycle is called internal friction. An early

thorough review is given by DeBatist [54], and a later one in the proceedings

[55]. In most techniques, the specimens are excited in resonance modes. Two

types of measurement can be performed, either the oscillation amplitude is

maintained on a constant level and the necessary power is measured, or the

excitation is switched oﬀ and the decrease in the amplitude of the freely

vibrating specimen is recorded. One measure of the internal friction is the

ratio between the anelastic work ΔW and the total work W

during one cycle.