Messerschmidt U. Dislocation Dynamics During Plastic Deformation

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412 10 Quasicrystals

Fig. 10.13. Dislocations inside a band in i-Al–Pd–Mn from the same specimen as

Fig. 10.12. Image taken near twofold pole. From [707]. Copyright Elsevier (2004)

Fig. 10.14. Dislocation structure after deformation at 532

◦

C in the range of high

work-hardening. From [707]. Copyright Elsevier (2004)

dislocations, contrast fringes are imaged parallel to the extension of the bands

(arrows), particularly to the left of the image at the upper edges of the bands.

These fringes are visible only under strong excitation conditions. They can be

imaged over most parts of the dislocation bands. Two types of pronounced

fringes were observed in one experiment at 610

◦

C, as illustrated in Fig. 10.16.

Strong fringes marked A extend between two dislocations whereas weak fringes

B “decorate” the whole path of the dislocations. The fringes belong to planar

faults. In the HVEM studies, it had not been possible to characterize these

10.3 Microscopic Observations of Dislocations 413

Fig. 10.15. Dislocation structure after deformation at the lowest temperatures in

the range of high work-hardening. (a) 482

◦

C, ﬁvefold compression axis. (b) 487

◦

twofold compression axis. Images taken near the poles of the compression axes. From

[707] and [709]. Copyright Elsevier (2004) and Wiley-VCH (2003)

414 10 Quasicrystals

Fig. 10.16. Microstructure in i-Al–Pd–Mn after deformation at 610

◦

C. From [709].

fringes in more detail. In post-mortem TEM of deformed specimens, they have

never been observed above 610

◦

Deformationatevenlowertemperatures can be achieved by applying con-

ﬁning hydrostatic pressure as described for ZrO

in Sect. 7.3. Such experiments

have been performed in a multianvil apparatus at 300

◦

C, a pressure of 7.5 GPa

and compression along a ﬁvefold axis [702]. Pairs of superpartial dislocations

with Burgers vectors parallel to the compression axis extended on planes per-

pendicular to the compression axis and had dragged phason faults on these

planes. Other dislocations with Burgers vectors in twofold directions were

extended on planes perpendicular to their Burgers vectors. It is assumed that

these dislocations had moved on the mentioned planes, i.e., they had moved

by (mostly pure) climb. Part of the dislocations experience a high climb stress

and another part climbs under zero mechanical stress. The dislocations drag

phason faults and are all curved. Similar experiments [710], also including

room temperature, showed dislocations concentrated in narrow bands. From

the directions of the Burgers vectors and the planes which the dislocations

were extending on, it was concluded that climb and glide contributed to the

deformation.

Split dislocations have also been observed by HVEM in specimens deformed

at lower temperatures. One example is presented in Fig. 10.17.

In the high-temperature range, the dependence of the dislocation density

on the strain and temperature was studied in detail in [338]. The dislocation

10.3 Microscopic Observations of Dislocations 415

200 nm

Fig. 10.17. Split dislocation in an i-Al–Pd–Mn single quasicrystal deformed at

487

◦

C along a twofold direction. From [708]

density increases strongly during initial loading, reaching a maximum at about

5% plastic strain before it decreases. The temperature dependence in the

steady state range of the ﬂow stress was presented in Fig. 5.29b together

with a few data measured from HVEM micrographs of deformed samples.

The ﬁgure also includes values from the deformation associated with strong

work-hardening at lower temperatures. During annealing at a deformation

temperature of 730

◦

C, about 60% of the dislocation density anneals out within

one hour with a half-time of 10 min. The dislocation density data will be

discussed in Sect. 10.5.7.

In summary, at high temperatures dislocations of diﬀerent Burgers vec-

tors in bands form a three-dimensional network. At low temperatures, the

dislocations are concentrated in narrow bands. They show straight oriented

segments particularly at high temperatures, whereas many dislocations are

curved at low ones. Some segments strongly bow out between pinning agents

near 550

◦

C. At 482

◦

C, also curved dislocation loops are formed, which do not

show pinning agents. At 610

◦

C and below, dislocations may trail fringe con-

trasts. There are sets of dislocations with either parallel components of their

Burgers vectors parallel to the deformation axis, which should experience only

a climb force from the external stress, or with Burgers vectors perpendicu-

lar to the loading axis, which experience no mechanical force at all. In the

following, these sets are termed A and B.

In situ Straining Experiments in an High-Voltage Electron

Microscope

In situ straining experiments on i-Al–Pd–Mn were successful only in a rel-

atively narrow temperature window between 625 and 765

◦

C, i.e., in the

high-temperature range, where steady state deformation is possible at usual

416 10 Quasicrystals

strain rates. Details of the experiments performed at the Halle HVEM facility

are described in [711].

During in situ straining, the ﬁrst dislocation bands are frequently formed at

inhomogeneities, mostly near the perforation of the specimen, like the primary

band PB in Fig. 10.18. Dislocations are emitted from the primary band into

secondary bands SB. The dislocations imaged in dark contrast trail traces,

which mark the planes of their motion. The latter were identiﬁed by simulating

the respective geometry. The planes observed are listed in [711]. They are

perpendicular to twofold, threefold, ﬁvefold, and pseudo-twofold orientations.

Often, the primary bands are almost edge-on with a trace perpendicular to the

tensile direction as in Fig. 10.18. These bands have only a small orientation

factor for glide but a maximum one for climb, therefore belonging to set

A. Many dislocations consist of straight segments in preferred orientations

like those in the conventional HVEM micrographs from the high-temperature

range described earlier. Well identiﬁed are the three twofold directions on

planes perpendicular to the threefold directions as of the segments marked by

the small arrow. Twofold orientations are generally the dominating directions

of the dislocation lines in macroscopic tests as well as in in situ experiments

[704].

Fig. 10.18. Dislocation structure during in situ deformation of i-Al–Pd–Mn at

750

◦

C in an HVEM. Threefold image plane. Twofold tensile direction (TD). From

[709]. Copyright Wiley-VCH (2003)

10.3 Microscopic Observations of Dislocations 417

The dynamic dislocation behavior is illustrated in the following video

sequences.

Video 10.1. Dislocation motion in i-Al–Pd–Mn single quasicrystals at 750, 720

and 685

◦

C: Two of the three of these videos are from the series of in situ straining

experiments performed in Halle which, for the ﬁrst time, yielded direct evidence that

plastic deformation in quasicrystals occurs by the motion of dislocations [647]. The

most important observation is that the dislocations move in a smooth viscous way

on diﬀerent crystallographic planes. As described above, many dislocations move on

planes perpendicular to the tensile direction (TD) indicated at the beginning of the

video, i.e., they move under a high climb force (set A). In the second sequence at C,

the dislocation moving upwards interacts with a dislocation on another plane. As a

consequence, the dislocation changes its plane of motion to a more steeply inclined

one without changing its direction of motion. Such a change is not possible by slip

and cross slip alone and also not by climb alone. The other dislocation continues

moving without any changes. In the third sequence, a dislocation moves on a plane

parallel to the tensile axis. On this plane, there neither acts a glide nor a climb force,

except residual forces originating from the inhomogeneous stress ﬁeld in the in situ

specimen. This dislocation belongs to set B.

These observations conﬁrm the conclusion from the post-mortem TEM anal-

ysis that dislocations move under the action of pure climb forces or even

without a force component from the applied stress. In the following video

clip, the shapes of moving dislocations can well be observed.

Video 10.2. Dislocation motion in an i-Al–Pd–Mn single quasicrystal at 710

◦

The dislocations exhibit almost straight crystallographically oriented segments, as

illustrated in the secondary band SB in Fig. 10.18. In the ﬁrst sequence, relatively

long dislocations assume three preferred orientations. In the second one, long dislo-

cations move on a steeply inclined plane. The dislocations keep their oriented shape

during the motion.

Both the oriented shape and the fact that the dislocations do not take the

shortest length in the thin foil indicate the action of a high lattice resistance.

The next video sequences are recorded at the relatively high temperature of

750

◦

Video 10.3. Dislocation motion in an i-Al–Pd–Mn single quasicrystal at 750

◦

The video clip consists of ﬁve sequences. They all show dislocation motion on dif-

ferent planes. Many of the planes are oriented so that they do not correspond to

very high orientation factors for climb. Also at this high temperature, many dis-

locations are straight and oriented along crystallographic directions. Dislocations

with an angular shape with quite an acute angle are visible in the third sequence.

Some dislocations change the width of their traces of motion without changing the

orientation, especially in the ﬁrst (marked by C) and ﬁfth sequences. The example

of the ﬁrst sequence is displayed also in Fig. 10.19. In the fourth sequence at R,

two dislocations moving on diﬀerent planes react with each other, the result is not

entirely clear. Figure 10.18 belongs to this sequence.

All the videos demonstrate the crystallographic character of the dislocation

motion in i-Al–Pd–Mn at high temperatures. The orientations of the planes of

418 10 Quasicrystals

0.5 µm

Fig. 10.19. Section of a frame of the ﬁrst sequence of Video 10.3 showing a slip

trace changing its width without changing its orientation (arrow). From the work in

[647]

motion indicate partly high climb forces without glide forces from the external

stress, and partly no mechanical force at all. The mode of motion, i.e., glide

or climb, could not be decided from the videos shown here since the Burgers

vectors had not been determined. This decision was made by the work of Cail-

lard and coworkers by their combined analysis of the Burgers vectors and the

planes of motion during in situ straining [701,704]. In the cases analyzed, the

dislocations always moved by pure climb. During in situ straining, sometimes

dislocations of opposite sign moving across each other annihilate. In [705], two

edge dislocations are shown approaching each other on slightly displaced ﬁve-

fold planes forming a dipole which can annihilate only by glide on a twofold

plane. At the high temperature of 740

◦

C, this dipole is stable over more than

30 min indicating that, under these conditions, glide is, by more than three

orders of magnitude, slower than climb. In conclusion, at high temperatures

straight dislocations in icosahedral Al–Pd–Mn oriented mainly along twofold

directions primarily move by climb along high-symmetry planes.

The velocities of dislocations moving on certain traces were analyzed by

plotting the position of the dislocations versus time followed by diﬀerentiation

of these curves. Histograms of the velocities indicate that in some traces dis-

locations move at two well-deﬁned diﬀerent velocities. In a special experiment

at 625

◦

C, the velocity v

of a single dislocation was followed under decreasing

external load F , exerted by the in situ stage. The slope of a plot of ln v

ver-

sus ln F in Fig. 10.20 yields the eﬀective stress exponent of the motion of an

individual dislocation (4.12) m



=dlnv

/dlnτ =dlnv

/dlnF. The result is



≈ 6 [711]. This value can be compared with the macroscopic one discussed

in Sect. 10.4.

10.3 Microscopic Observations of Dislocations 419

In [F(N)]

In [v

(μm s

–1

)]

1.6 1.8 2.0 2.2

–5

–4

–3

–2

m = 6

Fig. 10.20. Dependence of the velocity of a single dislocation on the force acting

on the specimen during an in situ straining experiment on an i-Al–Pd–Mn single

quasicrystal at 625

◦

C. Data from [711]

Video 10.4 presents two sequences of dislocations with particular contrasts.

Video 10.4. Special contrasts at the motion of dislocations in i-Al–Pd–Mn single

quasicrystals: The two sequences were taken at 675 and 685

◦

C. The ﬁrst sequence

was recorded at a twofold specimen normal and a twofold tensile axis. The dislocation

clearly shows a double contrast. Thus, these dislocations move in the split conﬁgu-

ration. The dislocation in the second sequence trails a fringe contrast which should

result from the phason fault dragged behind. The contrast becomes weak about two

or three micrometers behind the dislocation.

Split dislocations were observed earlier in macroscopic specimens (Fig. 10.17).

Special core conﬁgurations may control the dislocation mobility. Dislocations

D trailing phason walls are also illustrated in Fig. 10.21.

Almost all dislocations shown in the videos above did not drag phason

defects in their wake. Since the parallel part of the displacement vector of

the phason faults ought to equal the parallel part of the Burgers vector, the

faults should have been visible under the same imaging conditions as the

dislocations themselves. Since this is not the case, the dislocations should be

perfect dislocations above about 700

◦

C, i.e., in the high-temperature range of

deformation. In the border region as in the above video, the faults evaporate

after a short time so that they are absent a short distance behind the disloca-

tions. Similar observations are described in [704]. Phason faults generated by

the movement of grown-in dislocations anneal out at high temperatures. Dur-

ing in situ heating, the fringe contrasts between the dislocations in the upper

part of Fig. 10.22 anneal out between 610 and 690

◦

C and have completely

disappeared at 700

◦

C (lower part of the ﬁgure). According to [712], phason

walls at grown-in dislocations disappear at 560

◦

C within hours, whereas those

behind moving dislocations vanish at 750

◦

C within seconds. An Arrhenius plot

of the reciprocal time to disappearance yields an activation energy of 4.3 eV.

This value is unreasonably high with respect to the atomic diﬀusion energies

(2.32 eV for Pd [670], 1.99 eV for Mn [713] and an even lower value for Al [714])

420 10 Quasicrystals

1 µm

Fig. 10.21. Dislocations D trailing phason walls in i-Al–Pd–Mn during in situ

deformation in an HVEM at 695

◦

C. From the work in [647]

Fig. 10.22. In situ annealing of grown-in phason faults in an i-Al–Pd–Mn single

quasicrystal

10.3 Microscopic Observations of Dislocations 421

and to the results on phason relaxation studied by X-ray scattering mentioned

in Sect. 10.2.2. Owing to longer times available for annealing in macroscopic

deformation experiments, fringe contrasts of phason walls have never been

observed there above 610

◦

C. On the other hand, plastic deformation in the

high-temperature range (760

◦

C) causes linear phason strains which can be

observed by a shift of the diﬀraction spots at selected area electron diﬀraction

in regions between the dislocations [715]. The spots are displaced out of their

systematic rows with the shift increasing with increasing absolute value of the

component of the reciprocal vector g

⊥

in perpendicular space. The orienta-

tion of the respective phason stress ﬁeld varies spatially. It is argued that the

phason strain is not attributed to the dislocations but to the material itself.

An important question is the origin of the dislocations created dur-

ing plastic deformation. In crystals, dislocations frequently multiply by the

double-cross slip mechanism (Sect. 5.1.1). In situ experiments often show this

process with a characteristic intermediate stage similar to the letter α as high-

lighted in Fig. 5.5c. Such conﬁgurations are also observed during the in situ

deformation of Al–Pd–Mn quasicrystals, as marked by arrows in Fig. 10.23.

In contrast to crystals, dislocations in quasicrystals move on well-deﬁned

planes, mostly by climb. After a change from the primary plane of motion

PP onto a secondary one SP, the dislocations usually do not return onto a

plane parallel to the primary one but spread on the secondary plane as out-

lined in Fig. 10.24. If only part of the dislocation changes onto another plane

as in position 2, the point connecting the two segments can move only along

the intersection line between the planes. Thus, it acts as an obstacle to the

forward motion so that dislocation segments bow out on both planes (stage 3).

Accordingly, the two ends of the α-like conﬁgurations in Fig. 10.23 extend on

Fig. 10.23. α-shape conﬁgurations during multiplication of a dislocation in an

i-Al–Pd–Mn single quasicrystal. From the work in [711]