Electron microscopy of a low stacking fault energy alloy

ELECTRON

MICROSCOPY H.

P.

OF A LOW

KARNTHALER,?

P.

M.

STACKING

FAULT

ENERGY

ALLOY*

and M. S. SPRING9

HAZZLEDINE:

The images of dissociated dislocations, simulated by a oomput>er controlled cathode ray display The comparison system are comprared with experiment.&ll~ observed images in Cir-10 at. oAAl crystals. allows the dislocations to be identified unambiguously and the details of the dislocation-disIoc~tion interactions to be deduced. It, is concluded thet in cry&& deformed into stage II of the work-hardening curve primary and secondary disiooations interact to form short lengths of Lamer-Cottrell dislocation as assumed in the forest theory of the flow stress. ETUDE

AU MICROSCOPE

ELECTROKIQUE D’UN ALLIAGE FAUTE D’EMPILFMENT

A FAIBLE

ENERGIE

DE

Les images des dislocations dissociiies, simulees par un systeme Q rayons c~thodiques control6 par un ordinrttenr, sont comparees sux images observees e~p~rimentalement drms des cristaux &-IO %a&. Al. LB eomprtraison permet d’identifier les dislocations sans ambiguit6 et den deduire les details des inter&&ions dislocations-dislocations. Los auteurs concluent que dans les cristaux deform& jusqu’au stade II de la courbe de consolidation, les dislocations prim&es et second&es agissent de faeon B former de courtes longueurs de dislocations de Lomer-Cottrell, comme le suppose la theorie des for& pour la. contrainte plastique. EL~KTRO~E~~~IKROSKOPISCH~

U~TERSUCHU~G ST~P~LFEHLERE~ERGIE

EIXER

LEGIERUXG

MIT KLEINER

Die auf einem computer-kontrollierten Kathodenstrahlsystem simulierten Bilder aufgespaltener Versetzungen wurden mit experimentell beobachteten Kontrastbildern van Versetzungen in Cu-10 Anhand dieses Vergleiches ist es miiglich, Versetzungen eindeutig zu At. ‘A Al-Kristallen verglichen. identifizieren und Einzelheiten der Wechselwirkung zwischen Versetzungen abzuleiten. Es zeigt sich, daB in den bis in den Bereich II der Verfestigungskurve verformten Kristallen durch Wechselwirkung zwischen Prim&r- und Sekundiirversetzungen kurze Lomer-Cottrell-Versetzungen entstehen, wie dies in der Theorie der ~~~~dvcrsetzun~n sngenommen wurde.

1. INTRODUCTION In transmission electron microscope studies of the deformation of low stacking fault energy alloy~‘~-~) the full inte~retation of the micrographs is often prevented by the fact that the contrast from the dissociated dislocations is not known. The dissociation of the dislocations creates difficulties in the interpretation only when the separation of the partial dislocations r is of the order of the extinction distance .&,_ When r < Is, the dislocations may be treated as undissociated and when r > 5, the partial dislocations may be considered separately. In both these cases the expected contrast is well known.@) In the intermediate range, r rti 0.5[,, the theoretical contrast should, in principle, be computed explicitly for each alloy. The object of the calculations and experiments in this paper is to determine to what extent it is possible, without recourse to elaborate computation (e.g. using many-beam theory or elastic anisotropy) to determine the Burgers vectors and the three dimensional arrangement of the dislocations in a deformed alloy. The alloy chosen is Cu-IO at.% Al in which r varies between O.l3E,,, and 0.67E,,, for the different * Received July 7, 1971. t II Physikalisches Institut, University of Vienna, Vienna, A-1090 Austria. $ Department of 3%etallurgy, University of Oxford, Oxford, England. Q Department of Architecture, University of Edinburgh, Edinburgh, Scotland. ACTA

METALLURGICA,

VOL.

20, MARCH

1972

dislocations considered. Particular attention is paid to glissile dislocations and to the composite dislocations which lie parallel to the intersection of two slip planes. The method is complementary to the weak-beam methodu’) in that the experiments may be performed more rapidly and hence larger areas of the specimen may be studied. 2.

CALCULATION AND DISPLAY

The following dislocations in Cu-10 at. y0 Al are considered : edge and screw glissile dislocations, 120’ (Lomer-Cottrell) locks and 90” (Hirth) locks.(le*lJi) The separation between partial dislocations (stacking fault ribbon width) was calculated using the stacking fault energy value of Howie and Swannos) and Brown,(13) taking the shear modulus C to be 4020 kg mrnm2 (from the measurements of Neighbours and Smith),(iQ and assuming that Poisson’s ratio = +. The stacking fault ribbon widths in screw and edge dislocations are 50 and 120 A, respectively. The width of each stacking fault in the 120” lock(i5) is 35 A and in the 90” lock it is 170 B (for the arrangement of the partials see Fig. 1). The contrast calculations have been made specifically for primary dislocatioIls (b = ~~~iOl~(lll)) and for composit,e dislocations formed from the primaries and dislocations on (lli) by the following 459

ACTA

460 ii1

IIT lir ili

ill

Iii 052

METALLtJRGl(‘A,

025

520

220

I02

205

_.1'2 y & ii0

ii2

002

VOL.

“0,

1972

For a dislocation at a particular depth in the foil the transmitted electron intensity was computed (using the displa~ement~sgiven above) at a number of points in the form of an image profile. Profiles were calculated for a number of dislocation depths and by interpolation between the profiles a tno dimensional array of intensity values was generated which, when displayed, simulat,es the image from an inclined dislocation.(lg*2*) Scar the ends of t,he dislocation the profile was assumed to remain the same from the foil surface to the closest comput’ed profile (a distance of 0.2[, in each case except, for 90” locks for which the distance was 0.5$,). For the purpose of display the dislocations were assumed to lie at an angle 0 of tan-l 4 to the foil surface but the pictnres may be demagnefied laterally (c.g. by viewing through a cylindrical lens) t’o represcut’ a dislocation at an angle 0 < tan-l 1.

ii2

y__________* : : -I'll2

FIG. 1. Computed micrographs of edge, screw, LomerCottrell and H&h dislocations for 12 different reflections. At the foot is the grey scale used for thr disptay.

reactions --i-

(fi2+2ll)+(iiZ+l2i)-ii2+iiO+ll~ (ii2+2ll)+(ll2+2il)+ii-2+002+112

(1207

(90”)

For each dislocation images have been calculated corresponding to those twelve (111) and (SZO} g vectors obtainable by tilting a foil specimen with [ill] normal through <20°, namely: ill, iii, lil, 220,202,OZZ and their negatives. The set of computed images may, however, be compared with micrographs of dislocations belonging to any glide system. 2.2 Image calculation The dislocation images were computed using the two-beam column approximation in the dynamical theory of electron diffraction.(16) The constants used were {in the notation of Wowie and ~~helal~) 1111= 250 11, &,, = 450 A, &l&’ = &/‘&,’ = 0.1, w = 0.3, t = 7%, and the following further approximations were made: isotropic elasticity theory was used, no allowance was made for surface relaxationcl’) and g mb x u wits approximat,ed by g * b, tan y. Thus the displacement R at a point r, + from each partial dislocation is R = & {b+ + b,[$ sin 24 + tan y x (4 log T -

g cos2&]~

A precision cathode-ray system in conjunction with a PDP7 computer was used to generate the displayed images from the computed intensities. The method is similar to that previously described for displaying bend contour cnlculations(21) and affords better area resolution and more intensit.y st,eps than earlier line-printer methods. In t,his ease, 21 approximately equally spaced steps of intensity were used and balanced by microdensiometry to give similar contrast on the recording film to that obtained in the microscope. The recording camera was defocussed by a standard amount to provide a smooth half-tone image. 2.4 Computer results The computed images are shown in Fig. 1. Of the 48 images in Fig. 1 only 24 were calculat,ed independently. For the edge dislocations the images in the ill, iii, 022, 022, 202 reflections are mirror images (mirror parallel to the long side of the picture} of the images in the 111, iii, 220, 220, 202 reflections, respectively. For the screw dislocation the same relationships hold but the images in the 022,022, 220 and 220 were not calculated; instead t#hey were assumed to be the same as the images in the Tii, 111, 111, lli reflections, respectively. This assumption was made because by comparing the computed profiles of the screw dislocation with those of undissociated screws(*) it is apparent that the slight dissociation of the screw dislocation has almost no effect on the image. The form of the image is controlled by the value of g - b for the total dislocation. For the Lomer-Cottrell and Hirth locks the dislocation images in the ill, iii, 022, 022 reflections are the same as those in lil, i11, 202, 202, respectively. In the

KARNTHALER

ELECTRON

et al.:

iWICROSCOPY (ii) sections

OF .A F.C.C. ALLOY

461

cut in such a way that specific

dis-

locations would both lie at an angle of 30” (Y tan-’ to the foil surface and be the shortest locations their

possible

4) dis-

in the foil (so that they could not change

character

by

shortening

their

length).

The

normals to the required sections are shown in Fig. 2 for edge (lll)[lOl] (lll)[iOl] locations to [liO]

dislocations

dislocations on primary

For

and conjugate

the vectors

dislocations

(E, E’) and for screw

(S, 8’).

composite

dis-

planes (parallel

are LC, LC’ and for composite

parallel to [Oli] the vectors are LC”, LC”‘.

Composite

dislocations

cannot

length but the “shortest

glide to shorten their

dislocation”

criterion is still

useful for identification. For each type of dislocation : edge, screw and com200 FIG. 2. Foil normals composite dislocations

for edge E, E’, screw S, S’ and LC, LC’ and LO’, LO. A circle

For edge dislocations

should be completely

foils which are 7.05, thick

(two physically

foils for g = (111) and g = (220)) the deviation

dislocations

from the Bragg position,

48 rectangles (8 x 6) of equal intensity. which is a fraction

different

w = 0.3.

0.02 to 0.49 in steps of 0.01 (48 steps). rectangles

includes several intensity steps.

to be obtained.

LC” was taken as the foil nor-

mal instead of E or E’ to increase the number flections

and in this case the dislocations

shows as an example the orientation of screw dislocations.

of re-

are at 25”

cates the possible

foil normals

in the grey scale

All intensities greater

and the available

re-

space

between the 70 and 110” small circles centred on S.

A

list of Iow order available reflectlions is given in Table 1. TABLE

from

simulation

used in the case

A circle of 20” around S indi-

flections therefore lie in the region of reciprocal

increases

Since only 21

of grey were used in the image

each of the 21 visible

into

The intensity,

of the incident intensity

from the top right to the top left boustrophedon shades

in

and in each case

The grey scale at the foot of Fig. 1 is divided

(20”), permit the

and their slip plane at 30” to the foil surface. Figure 2

invisible. All the images in Fig. 1 represent

which with

best selection of low order reflections

g * b and g . b, are zero for

each partial and the dislocation

and those

chosen (LC”, S, LC) are the foil normals the available tilt in the microscope

of 20” around S indicates the possible beam directions in the case of screw dislocations and the available reflections lie in the region of reciprocal space shown hatched. 220 and 220 reflections,

posite there are two possible foil normals

Dislocation

Line direction

Edge s xew Composite

1

Foil normal

[ii01

Reflections *t20, h220, 1022,

m

&202, 5022, ~202,

ilil, *iii, &iii,

*ill

*iii *iii

than 0.49 appear white and those below 0.02 appear black.

It should

3. EXPERIMENTS 3.1 Experimental

method

deviation

Single crystals of Cu-10 at. y. Al were grown by the Bridgman strained

in

technique, in an Instron

vacua

and

stage

shear

The

crystals

stress).

(
t’ensile tester

(1 .l kg mm-2)

II

be mentioned

that experimentally

very difficult to set the specimen

x

1O-5 torr),

into

stage

I

(2.3 kg mm-2

resolved

were sectioned

with

a

it is

at a predetermined

(w = 0.3) from the Bragg angle, especially

for higher order reflections. the diffraction

patterns

But an examination

showed

90 per cent of al1 the micrographs 3.2 Experimental

of

the result that for 0.2 < w < 0.4.

results and discussion

spark cutter and discs of diameter 2.3 mm were trepanned from the 1 mm thick sections, chemically

(a) Irzlined dislocations. The micrographs obtained from foils of type (ii) are directly comparable

thinned

with the computed images. In Figs. 3 and 4 the outlined computed dislocations have been given the

and

jet-electro-polished

niques and examined scope. The crystallographic

by standard

in a Siemens Elmiskop

techmicro-

length appropriate orientations

of the specimens

were of two types: (i) sections parallel to the primary slip plane (111) ;

to a foil thickness

of 75, and are

mounted on the micrographs in the correct orientation. In Fig. 3 the images of a set of dislocations close to edge orientation

((lll)[iOl])

may be compared

with

ACTA

462

FIG . 3. Computed

and observed

VOL.

20,

1972

(outlined) and el;perimental images for edge dislocations (lll)[lOl] showing in 8 different reflections. Foil normal of the micrographs is LC”.

the con tputed images. culated

METALLURGICA,

The general form of the calimages (e.g. “chain”

image for

strong double

image when g = ill

very slight doubling

t,he same area but in Fig. 3(g)

of the image may be seen.

The

g = 22c ), double image for g = 202, spotty image for g = lil and intense image for g = iii) is sufficiently

slight asymmetry from top to bottom of a dislocation whichismostnoticeableinthe weakimages (g = f lil)

close in each case that the Burgers vector of the dis-

and which does not appear in the computed images is due to the approximation used (see Section 2.2)

location s may

definitely

be

identified

as

@[iOl].

Althoug ;h the general forms match well and the width of the irnages agree, even with all the approximations

for g . b x u.@~) Figure 4 shows two sets of screw dislocations

used in the calculations, perfect.

with

match

is not

b = &&[iOl]

(the left and right sets in each picture

One feature which is never observed

is the

are of opposite

sign) in which the agreement between

the detailed

KARNTHALEK

FIQ. 4.

theory and experiment to

MICROSCOPY

their with

The screw dislocations

is close.

invisible

The dissociation partials

ELECTRON

when

very

g = jlil

slight

dissociation

of the screw dislocation some

edge

character

sufficient to give an asymmetry Figure

5(a)

shows

a typical

in stage II.

is,

(0.2E1,,). into

two

however.

Fig.

The

5(a)

reactions

in detail

and

the same Bmea

showi]

with the symmetry

Whelan.(16)

This

obviously

be true for glide dislocations,

true

Lomer-Cottrell

for

result

must

but it is also

dislocations

(which

are

on two planes) even though it is not true

that the Lomer-Cottrell

image is the same at the top

in Figs.

Figure 6 shows as an example b

are

at A

in

5(b-m).

foil thickness contrast.

the influence

of the

and the value of w on the dislocation

In Fig. 6(a) the deviation

from the Bragg position

w = 0.25 + 0.05

and the images of the dis-

sign

locations are in good agreement with the computed images where the foil is an even number of half extinc-

dislocations

of the same

tion distances thick (bright regions of the micrograph)

There are therefore two attractive

(C) and two

Two primary interact sign.

by dark field microscopy)

are analysed

of Howie

163

ALLOY

of a foil as at the bottom.

area of dislocation

Lomer-Cottrell

rules

dissociated

from top to bottom

The top t and the bottom

of the foil (determined indicated.

A F.C.C.

Figs. 5(h) and (k), in accordance

(g * b = 0)

of the foil through the g * b x u term. reactions

OF

images for screw dislocations (lll)[iOl] ComFlute d (outlined) and experimental in 8 different reflections. Foil normal of t,he micrographs is S.

are virtually owing

et al.:

(lll)[iOl]

dislocations

with two (Til)(OTi]

repulsive

(R)

type is visible.

junctions,

of opposite

and one junction

and the images are still readily identifiable where the foil has other

thicknesses.

in regions

In Fig.

6(b)

are indexed

in Fig.

w = 0.9 + 0.1 and the images show much less detail

5(l) and Fig. 5(m) is a view of the interactions

normal

and differ greatly from the computed images (Fig. 1, screw or edge, g = +202). For identification, there-

to (iii).

The dislocations

of each

In Figs. 5(j) and (k) the foil has been turned

upside down in the microscope so that dislocation ends which, in Figs. 5(h) and (i) are at the top of the foil are at the bottom

of the foil in Figs. 5(j) and (k).

It may be seen that the images at the ends of all the dislocations

are the same in Figs. 5(i) and (j) and in

fore, it is necessary

that the computed

and experi-

mental values of w should match closely but it is less important that the foil thicknesses should agree. (b) identify

Parallel

dislocations.

dislocations

in foils

It

is more

parallel

to

difficult

to

an active

5. (l), (m). ~~SIuc~t~on~eaet~o~~ at-d. (1) 8chemat~c of network in Figs. 5(b)-(i) with Burgers vectors of the various dislocations indicated. (m) View of t’he interact,ions normal to (ii 1) showing the attractive (C) and repulsive (R) junctions. FIG.

slip plane than in inclined foils because dislocations one character depths

in the foil.

However,

using the computed

images of Fig. 2. the conservation and the line directions network,

of

may appear quite different at different of b at a, junction,

of the dislocations,

a stage II

such as the one in Fig. 7, may be indexed

with very little ambign~ty Fig. *I(k). The dislocation structure consists of intersecting FIG. .5. (a) Region

of

inclined

dislocation

Top t and bottom b indiented.

reactions.

three slip planes (ill), diGcations

(lil)

slip lines parallel to

and (iii).

formed at attractive

The composite

junctions

are rarely

longer than 0.5y but are fre~~~e~~l~ placed end to end to give the impression of greater length. Cottrell dislocations never observed even

FIG. 5. (b)-(i)

Area. A of (ef in 8 reflections. Foil normal is LC. (j), (k) Area A but with foil inverted.

lower

Many Lomer-

are visible in Fig. 7, but we have

a Hirth lock ; their density

than

in

Cu. fz3j

The

must be

arra~~geme~~t of

FTC. 6, (a) Variation of image with foil thickness, 20 = 0.25 & 0.05. (b) Variation of image with foil thickness, W = 0.9 & 0.1.

FIG. ?(a).

FIG. 7 (c)I

FIG. 7(b).

FIG. 7(d).

ACTA

166

Fra. 7(e).

Fm. 7(f).

METALLURGICA,

VOL.

20,

1972

FIG. 7(g).

FIQ. 7(h).

KARNTHALER

et al.:

ELECTRON

MICROHCOPY

OF

A F.C.C.

467

ALLO\-

FIG. 7(i)

\

i

i FIG. 7(k).

FIG. 7. (a)-(j). Dislocation reactions. 10 different reflections showing the same area. [ill] foil normal. (k) Schematic of network with Burgers vectors of the dislocations.

The

only

dislocations

which

are the Lomer-Cottrell

completely

dislocations,

to their length (g = f%O),

disappear

when g is parallel

which is in accord with

the theory. 4. CONCLUSIONS

1. In an alloy such as Cu-10 at.% paratively Burgers

low anisotropy vectors

generally mental

approximation diffraction. dislocation reflections

FIG. 7(j)

compute

of the dissociated

be identified

images

Al with a com-

constant by

with those

(A = 3.66) dislocations

comparing calculated

of the dynamical

the

the may

experi-

in the lowest

theory

of electron

For a definite identification the same must be imaged using several different but for this purpose it is not necessary

to

the contrast for each micrograph.

2. The

images

of

dissociated

dislocations

differ

interacting primary and secondary dislocations in Fig. 7 is typical of that assumed in the forest model of

markedly from those of perfect dislocations separation of the partials >0.3E,.

work-hardening.(24-26)

3. In Cu-10 at. o/o Al many Lomer-Cottrell reactions are observed but Hirth locks have not been encoun-

Nearly all of the dislocations vectors sociation

which lie in (lil) many

are visible

in Fig. 7 have Burgers

but, because

of their dis-

when g = +lil

(e.g. at

B the [iOl] dislocation almost disappears in (g) and (h) where it is screw and is visible where it is edge).

when the

tered. 4. The arrangement slip planes

is precisely

of dislocations that

theory of strain hardening.

assumed

in intersecting in the forest

ACTA

465

METALLURCICA,

ACKNOWLEDGEMENTS

P. K. wishes to acknowledge financial support from the Royal Society European Exchange Programme and from the Oesterreichische Akademie der M. S. S. is grateful to the S.R.C. for a Wissenschaften. K.

grant.

would like to thank Drs. A. Howie, J. Goringe, MI.J. Whelan, D. Blaher and R. Perrin for many helpful discussions and Professor P. B. Hirsch F.R.S. for the provision of laboratory facilities. We

M.

REFERENCES I. M. J. WHELAN, Proc. R. Sot. A249, 114 (1958). 2. A. HOWIE, Direct O~eer~at~on of ~~perfect~o~~ in Crystals. Interscience (1961). 3. S. MADER and H-M.

Conference

for

THIERINGER, Fifth ~nt~r~at~onuZ Electron Microscopy. “Academic Press

(1962). 4. A. SEEOER,N.P.L.Symposium 15,~. 1. H.M.S.O. (1963). 5. J. W. STEEDS and P. M. HAZZLEDINE. Discuss. Paradav Sot. 38,103 (1964). 6. T. C. TISONE, J. 0. BRITTAIX and M. MESHII, Phil. Msg. 16,651 (1967). 7. P. B. HIRSCH and F. J. HUXPHREYS, Physics of Strength and PEastieity. M.I.T. Press (1969).

VOL.

20,

1972

8. P. B. HIRSCH, A. HOWIE, R. B. Krcaomow, D. W. PASHLEY and M. J. WHELAN, Electron &ficroseopy oj Thin Crystal. Butterworths (1965). 9. D. J. H. COCKAYNE, I. L. F. RAY and M. J. WHELAN. PhiE.Mug. 20, 1265 (1969). 10. J. FRIEDEL, PhiE. Mug. 46, 1169 (1955). 11. T. Jsssa~c, J. P. HIRTH md C. S. HARTLEY, J. Apple. Phys. 36, 2400 (1965). 12. A. HOWIE and P. R. S’CVAKN,Phil. Afag. 6, 1215 (1961). 13. L. M. BROWN, Phil. Hag. 10, 441 (1964). 14. J. R. NEIGHBOURS and C. S. SMITH, acfa Met. 2, 591 il9.541 i-“--I15. 4. S. STROH, Proc. Ph?/B.Sot. 6?B, 427 (1954). 16. A. HOWIE and M. J. WHELAN, Proc. R. Sot. A263, 215 (1961). 17. W. J. TUNSTALL, I’. 13.HIRSCH and J. W. STEEDS, Phil. Xag. 9, 99 (1964). 18. A. HOWIE and M. J. WHEL~~N, Proc R. Sot. A267, 206

(1962). 19. A. K. HEAD, AU&. J. Php. 20, 557 (1967). 20. P. !&!I\TBLE,AZ&. J. P&s. 21, 325 (1968). 21. M. S. SPRING and J. W. STEEDS, Phys. Status Solidi 37, 303 (1970). 22. J. SILCOCKand W. J. TIJNSTALL, Phil. Nag. 10,361 (1964). 23. H. STRUNK. Phil. Maa. 21. 857 (19701. 24. 2. S. BAS&KI, Phil. kigf6y:4, 39‘3 (19bS). 25. P. B. HIRSCH, Internal Stresses and Fatiglce in Metals. Elsevier (1959). 26. G. &ADA, A&z Met. 8, 541 (1960).