Theory and direct observation of dislocations in the Fe3Al superlattices

THEORY

AND DIRECT OBSERVATION OF DISLOCATIONS IN THE FesAl SUPERLATTICES* M. J. MARCINKOWSKIt

and

N. BROWNI

It has been found that in order for dislocations to travel through superlattices of the type DO,, L2, and B2 without creating any net disorder across the slip plane, they must move as superlattice dislocations. A theoretical analysis of the superlattice dislocations in the DO, and L2, type structures shows that they should consist of four &a,( 111) t,ype ordinary dislocations bound together by two different type antiphase boundaries. On the other hand, superlattice dislocations in the B2 structure consist of pairs of coupled dislocations. Calculations have been made of the separation between the superlattice dislocations for the specific case of the Fe,Al alloy exhibiting both DO, and B2 type ordered lattices. It has been found that for this specific alloy, the antiphase boundary energy associated with the superlattice dislocations is relatively low, resulting in a large extension of the individual dislocations constituting the superlattice dislocation. Because of this low energy, the possibility is suggested that dislocations might move through the Fe,Al lattice as ordinary &a,( 111) types. In order to determine experimentally whether or not dislocations travel through the lattice as superlattice dislocations or as ordinary dislocations, for the particular Fe,Al alloy possessing both DO, and B2 type structures, thin foils of the alloy were examined using transmission electron microscopy. It was indeed found that the dislocations in this alloy travel as ordinary dislocations, leaving behind on their In addition, a preponderance of screw dislocations were slip plane ribbons of antiphase boundaries. observed to be present, which in turn gives rise to wavy or noncrystallographic type slip behavior. THEORIE

ET

OBSERVATION DES

DIRECTE

SURSTRUCTURES

DE DISLOCATIONS DE

DANS

Fe,Al

11 a 6te trouve que des dislocations se deplaqant dans des surstructures du type DO,, L2, et B, doivent se mouvoir pour ne pas creer de desordre net le long des plans de glissements, comme des dislocations de surstructure. Une analyse theorique des dislocations de surstructures dans les reseaux du type DO, et L2, montre qu’elles devreient etre constituees de 4 dislocations ordinaires du type 1/2a, (111) reliees ensemble par deux limites antiphase de type different. D’un autre cot& les dislocations de surstructure dans le reseau B, sont constituees de paires de dislocations coup&es. La separation entre les dislocations do surstructure pour le cas, specifique de l’alliage Fe,Al presentant les deux types de reseau ordonne DO, et B2 a 6th calcule. 11 a Bte trouvi? que pour cet alliage specifique l’energie de la limite antiphase associee aux dislocations de surstructure, est relativement faible et conduisant ainsi a une estimation et importante des dislocations individuelles constituant les dislocations de surstructure. ,4 cause de cette basse energie, il est suggere que les dislocations pourraient se mouvoir au travers du reseau Fe,.41 comme des dislocations des types ordinaires 1/2n, (111). Afin de determiner experimentalement si les dislocations se deplacent ou non au travers du r&au particulier de l’alliage Fe,AI presentant des deux types DO et B, comme des dislocations de surstructure ou comme des dislocations ordinaires de pellicules minces de l’alliage ont Cti! examinees en utilisant le microscope Blectronique de transmission. 11 a et8 trouvi: en effet que les dislocations se deplacent dans cet alliage comme des dislocations ordinsires, en la&ant derriere sur leur plan de glissement les bandes de limite antiphase. En plus, on a observe en preponderance la presence des dislocations qui a leur tour donnent naissance a un comportement de glissement du type ondule ou non cristallographique. THEORIE

UND

DIREKTE IN

Fe,AI

BEOBACHTUNG

VON

VERSETZUNGEN

UBERSTRUKTUREN

Es wurde gefunden, dass sich Versetzungen durch die Uberstrukturen vom Typ DO,, L2, und B2 als Uberstrukturversetzungen bewagen mussen, wenn bei der Versetzungswanderung iiber die Gleitebene hinweg die Ordnung nicht zerstort werden ~011. Eine theoretische Analyse der Uberstrukturversetzungen in den DO, und L2, Strukturen zeigt, dass sie wohl aus 4 gewdhnlichen Versetzungen vom Typ l/2 cc,, (111) bestehen, die durch zwei verschiedene Arten von Antiphasengrenzen zusammengehalten werden. Andererseits bestehen Uberstrukturversetzungen in der B2 Struktur aus Paaren von Doppelversetzungen. Fur den speziellen Fall der Fe,Al-Legierung, die sowohl das geordnete Gitter DO, als such den B2 Typ aufweist, wurden Berechnungen fiir die Trennung zwischen den Uberstrukturversetzungen angestellt. Fur diese spezielle Legierung wurde gefunden, dass die Antiphasen-Grenzflachenenergie, die mit den Uberstrukturversetzungen verkniipft ist, verhaltnismassig niedrig ist. Dies fiihrt zu einer grossen Aufspaltung der Einzelversetzungen, aus denen die Vberstrukturversetzung aufgebaut ist. Wegen dieser niederen Energie wird die Moglichkeit erwogen, dass sich die Versetzungen wie gewiihnliche l/2 a,(1 11) Versetzungen durch das Fe,Al Gitter bewegen. *Received February 1, 1961. t Edgar C. Bain Laboratory for Fundamental Research, $ Department of Metallurgical Engineering, University ACTA

METALLURGICA,

VOL.

9,

AUGUST

1961

U.S. Steel Corporation, Monroeville, of Pennsylvania, Philadelphia. 764

Pennsylvania.

MARCINKOWSKI

AND

BROWN:

DISLOCATIONS

IN

Fe,Al

SUPERLATTICES

765

oder als Urn experimentell zu entscheiden, ob die Ve~etzun~en als ~erstrukturversetz~gen gewiihnliche Versetzungen durch das Gitter wandern, wurden im Fall der besonderen Fe,Al-Legierung mit sowohl DO, als such B2 Struktur diinne Folien dieser Legierung mit elektronenmikroskopischer Durchstrahlnng untersucht. Es wurdo tatsiichlich festgestellt, dass die Versetzungen in dieser Legierung als gewiihnlicheVersetzungen wandern und auf ihren Gleitobenen Bander von Antiphascn-Grenzflachen hinterlassen. Zusatzlich wurde boobaohtet, dass ein ifberschuss an Schraubenversetzungen vorhanden ist, der sainerseits Anlass gibt zu welligem oder nichtkristallographischem Gleitverhalten.

INTRODUCTION

Koehler and SeitG first proposed in 1947 that dislocations which are perfect in disordered alloys are not necessarily perfect in the ordered lattice, in that they might leave a strip of disordered lattice in their wake. As a result, dislocations in an ordered lattice should frequently consist of multiples of ordinary ~slo~tions. Brown and Hermant2) have carried out an analytical treatment for dislocations in the CuZn type superlattice. The somewhat more complicated dislocation configurations in the AuCu, and AuCu type superlattices were investigated theoretically by Marcinkowski et ,Z.m (to be referred to as MBF henceforth), and the results were confirmed by transmission electron microscopy techniques which revealed the superlattice dislocations directly in AuCu, for the first time. In particular, these superlattice dislocations were seen to consist of pairs of ordinary dislocations. However, to date, the dislocation configurations in another very important class of superlattice structures have neither been investigated theoretically nor ex~rimen~lly. These are the ordered alloys of the type D03* of which Fe&l and FesSi are classical examples, and the very closely related ternary alloys of the type L2i* or the so-called Heusler alloys. The first portion of this paper will concern itself with a theoretical analysis of the dislocation configurations in the above mentioned superlattice types. Finally, the second aspect of this investigation will be devoted to an experimental obse~ation of dislocations in thin-foils of a DOs type superlattice. The specific alloy chosen was FesAl, because it represents the classical DO, type superlattice with which most previous work has been done. DISCUSSION OF DO,, L2, AND TYPE SUPERLATTICES

IV while B atoms occupy the remaining type-1 sites. It may be noted that the B atoms have no first or second B atom nearest neighbors, and this immediately suggests that the interaction potential energy between second nearest neighbor B atoms is relatively large. Thus, unlike the CuZn and AuCu, superlattices, second nearest neighbor interactions are important in the DO, type superlattices and must be considered when calculating the energies involved in the formation of antiphase domain boundaries. Similar considerations should apply to Fe,Si although somewhat less work has been done with this alloy. Another type of alloy to be considered and one which is closely related to the DO, type superlattice is the L2, or Heusler type alloy, the classical example of which is CusMnAl. In this case, A atoms occupy III and IV sites, while B atoms occupy either I- or IItype sites, the remaining sites all being occupied by C atoms. Here again it will be noted that the B and C atoms are arranged so that they do not form like first or second nearest neighbors with one another.

B2

The most generalized description of all the superlattices to be considered here is shown by the unit cell in Fig. 1. This cell consists of four interpenetrating face-centered cubic lattices labeled I, II, III and IV. Specifically, for the DO, type superlattice, A atoms occupy sites of type II, III and * These structure classifications are those used by the ~t~~turbe~~t.(41

0 B o 0

- TYPE - TYPE - TYPE - TYPE

I II III Ip

SITES SITES SITES SITES

ON I SU8LATTlCE ON It SUBLATTICE ON IFI SUBLATTICE ON Ill SUELATTICE

FIG. 1. Generalized unit cell consisting of four interpen&rating face-centered cubic sublattices appropriate for a description of superlattices of the type DO,, L2, and 82.

‘766

ACTA

METALLURGICA,

Finally, the last type of superlattice to be considered is that of the B2 or beta brass type. In this structure, type III and IV sites are equivalent and contain all A atoms. Type I and II sites are also equivalent and, in the case of the true beta brass structure, contain all B atoms, The analysis ofthis particular superlattice type has been considered elsewhere(2) and will therefore not be treated in the present paper. On the other hand, it is of interest to consider here the imperfect BB-type order that occurs in some of the A& alloys, in particular FeaAl in which the type I and IL sites are occupied at random by equal numbers of A and B atoms. DISLOCATIONS IN THE TYPE SUPERLATTICES

DO,

The disordered DO, lattice is body-centered cubic, and it will be assumed that the slip direction frequently observed in body-centered cubic alloys, i.e. the close packed direction (111) will apply. For the present it will also be assumed that the slip plane is that of the close packed plane or (110). Thus a dislocation in the disordered lattice will have a Burgers vector ~aO(lll). It will also be assumed that no dissociation of the $zs,(lll) dislocations into partial disIocations takes place. Figure 2 shows the projection of the (110) glide

VOL.

9,

1961

plane onto the plane of the paper with a unit area of the shp plane 22/2a,s outlined, and which possesses the periodicity of the generalized DO,, L2, and B2 type superlattices. The various sublattices are labeled in accordance with Fig. 1. Now before slip occurs, the atom sites outlined by the unit area of plane a will be neighbors to certain sites in the plane immediately above or the 6 plane. Specifically, the a sites outlined by the unit area wil1 have eight first nearest neighbor sites with sites in the b plane shown by the solid lines. In addition, the a sites outlined by the unit area will have eight second nearest neighbor sites with sites in the b plane. After the passage of a dislocation of the type &,[ili], the nearest and next nearest neighbor sites do not remain the same but are altered in a manner shown by Table 1. In this table, A, and ANNrr TABLE 1. Change in bonding across (1 IO) slip plane associated with ordinary &,,l’ili] dislocations in the generalized DO,, L2, and B2 type superlattices -___-_.I__ ______-.-.._ -First $a.[ 11 l ] displacement

ANN = (I-I} + 2(1-II) + (II-II) + (III-III) + Z(III-IV) + (IV-IV) -- [2(1-III) + 2(I-IV) + ZIII-III) + 2(11-1vu ANKN = 2@11) + i(‘r-lir) + i&r-111) + 2(11-IV) -[4(1-II) + 4(111-IV)] Second &,[i17]

(110)

GLIDE

PLANE

displacement

NN = -[(I-I) + 2(1-II) i- (II-II) + (III-III) + Z(III-IV) + (IV-IV)] -t 2(1-III) + 2(1-IV) + 2(11-III) + 2(II--IV) AsaN = -[2(1-III) $ 2(1-IV) + 2(-I-111) + 2(11-IV)] + 2(1-I) + 2(II-II) + 2(TII-III) f 2(Iv-IV) _I_.. -~ -Third &,,[ 111 J displacement

-A

ANN = (I-I) + 2(1-II) + (II-II) + (III-III) + B(III-IV) + (IV-IV) - [2(1-III) f 2(1-IV) + 2(11-III) + 2(11-IV)] ANNN = 2(I-III) + 2(1-IV) f 2(X-111) + .2(11-Iv) -[2(1-I) + 2(II-II) i_ 2(111-III) + 2(IV-IV)] Fourth

#,~,~~,~~ - ATOM l~,~~~~,~~-~~~~,~~ES

SITES

IN IN

PLANE PLANE

OF ORAWING. IMMEDIATELY

displacement

A;?~‘N= -[(I-I) _t 2(1-X) -t (II-II) + (III-III) P(III-IV) + (IV-IV)] + 2(1-III) + 2(1-IV) 2(11-III) + 2(11-W) ANNN = -[2(1-III) + 2(1-W) + 2(II-111) + 2(11-IV)] + 4(1-II) + 4(111-IV) _____ .-.._ _.--..-_-._-^... ~______...._.._-_-~ ~-

$,,(D-----fb-----lo-----lf----I(J

“b-----~,D____=t~~,~6----Ipb‘

&[TlT]

___r

ABOVE

/

THAT

OF

=UNIT AREA OF SUPERLATTICE WITH RESPECT TO PLANE a. --BONDS CONNECTING NEAREST NEIGHBOR SITES ACROSS SLIP PLANE. -----BONDS CONNECTING NEXT NEAREST NEIGHBOR SITES ACROSS SLIP PLANE. SOLID DIAGONAL LINES ABOVE AND TO THE LEFT OF UNIT AREA INDICATE SITES THAT EVENTUALLY DAM NEIGHBORS WITH SITES OF UNIT AREA AFTER MULTIPLES DFA I ,a$11 TYPE DISPLACEMENT.

FIG. 2. Variation of bond types across a unit area of slip plane due to shear displacements of type .&a,,[11 11.

represent the net change in the first and second nearest neighbor sites with respect to the unit area 242 a(;” after the passage of a dislocation of type &,,[ili]over the (1X0) slip plane. As will be noted, there is a net change in both NN and NNN sites with the consequent formation of an antiphase boundary (APB). A second &JTIi]displacement re-orders the NN sites but results in a further change in the NNN sites. A third dislocation again disorders the NN sites and results in still another change in the number of NNN sites.

MARCINKOWSKI

AND

BROWN:

DISLOCATIONS

Finally, the fourth dislocation re-orders both the NN and NNN sites across the slip plane. The manner in -which each of the four &,[ 11l] ordinary ~sloc~tions alters the 6 sites with respect to a sites is also shown by the diagonal arrows in Fig. 2. It is therefore seen that a perfect dislocation in this generalized lattice will be a superlattice dislocation containing 4 ordinary -QaO[lll] type dislocations bound together by two distinct types of antiphase boundaries. The antiphase boundaries across the slip plane will be treated as discontinuous slip produced boundaries, in contrast to those that exist in equilibrium at higher temperatures as treated by Brawn(5). For the particular case of the DO, type superlattice, type II, III and IV sites are equivalent and will be labeled II. With this simplification, Table 1 transforms to Table 2. In this table, we see that dislocation TABLE 2. Change in bonding across (110) slip plane associated with ordinary *a&l 1 l] dislocations in the DO, type superlattioe

-

Number of ordinary +aJili] dislocations 1

-1

Net change in bonding AAxx = (I-I) + (II-II) - Z(I-II) NNN

0

2

3

ANN T= (I-I) + (II-II) - 2(1-II) ANNN = -[2(1-I) + 2(11-II) - $(I--II)]

4 a __.____~_

=

ANY = -[(I-I) _t (II-II) - 2(1-II)] ANNN = 2(1-I) + 2(11-II) - 4(1-11)

_____

ANN = -[(I-I) + (II-II) - 2(1-II)] NNN = 0 --._____ ~_

1 produces an antiphase boundary involving a net change in only nearest neighbor bonds (~APB). Dislocation 2, on the other hand, eliminates the NNAPB, however, it produn,es an antiphase boundary in which there is a net change in the number of next nearest neighbor bonds (NNNAPB). Similarreasoning holds for the third and fourth dislocation. The net result is the production of the superlattice dislocation shown schematically in Fig. 3. To find the energies associated with the NNAPB and the NNNAPB it is necessary to evaluate the energy associated with the various types of bonds. For the particular case of the DO, type superlattice, the ordering energy associated with the first nearest neighbor bonds can be written as

F=

v,,+

F,,-2F.4,

IN

Fe,AI

707

SUPERLATTICES

energy associated with the next nearest neighbor bonds is WI= w,+ WBB_2W/4, (lb) where W,, etc. are the interaction potentials between next nearest neighbor Fe atoms etc. Since in Table 2, A atoms occupy type II sites and B atoms type I sites, then from equation (la) the NNAPB energy per unit area is

V

ENN = -

.

Zy’Ba2

(24

Similarly with equation (lb), the NNNAPB

energy

per unit area is

E NNN

2w =

w-2

(2b)

*

Equations (2a) and (2b) have been derived for the particular case where the dislocations glide on the (110) plane and thus produce APB’s across this plane. This is expected to be true for a large number of DO, type alloys; however from the results obtained with many body-centered cubic metals and alloysc6) on which the DO8 type lattice is based, it is to be anticipated that there may be other planes on which slip will occur. Depending on the particular alloy, there may be one or more or any number of planes lying within (11 I> zone axes which may act as possible slip planes, an outstanding example of this being iron. It is therefore of interest to derive expressions for E NOTand J%NN which are valid for all of these possible choices of slip plane. A detailed derivation of the generalized expression for the APB energies in the .DOatype snperlattices will be considered in another paper(‘) dealing with those APB’s produced by diffusion in FesAl. For this reason, we will be content to merely indicate some of the results obtained therefrom, and apply them in detail to the case of slip produced APB’s. In the first NUMBER Z

OF DISLOCATION I

i

ha:iti

18 .-I

(la)

where V,, etc. are the interaction potentials between nearest neighbor A atoms, etc. Similarly, the ordering

FIG. 3. Za,[lll]

superlattioe dislocation in the 00% type superlattice.

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768

METALLURGICA,

VOL.

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1961

place, it will be noted from Fig. 1 that for the DO,

is first necessary

type

configuration

lattice,

a displacement

of one portion

of the

ordered crystal with respect to the other by &,(I 11)

a function

always results in a net change of only NN bonds, but

interaction dislocations

to write the total

energies and the

two

odd

theory for dislocations,

Thus,

dislocations

result in the formation

of NLNAPB’s assuming

the general dislocation On the other of

the

hand,

crystal

will always

with

produce

1 and 3 of Fig. 3

motion

is towards

a displacement respect

of the superlattice

qualitatively

the same result as aO(ll I). the

dislocations same

+ln

APB

shown

plane

{hid}

described

with NN and NNN

and characterized

for an arbitrary Burgers

-

1) +ln

(A,

-

l)](sin28

~-

(4)

+ HENNA, + ENNN (r - 2rl)

to be

in Fig.

3

first carried out by Flinncs), the

energy associated

dislocation

since this

are expected

as that

(t

Thus we see

regardless of what plane in the (111) zone on which they lie. Using a procedure

elastic

the total energy per unit length

by uO(l 11)

could also be written as ~(100)

that all superlattice

By using the isotropic

but not a NNAPB.

from Fig. 3 dislocations 1 and 2 combined form a NNNAPB. The displacement that characterizes the accomplishes

the four ~u,,(lll) associated with the

vector is

More generally, any nOa,,(111) displacement will accomplish this where n, is any odd integer. Thus,

NNNAPB

of APB.

between energies

of one portion

to another

a NNNAPB

that

the right.

types

of the that are

of r and rl. This energy will consist of the

not NNN bonds. In general, any total displacement of n,&+,(lll) will form a NNAPB where n, is any integer.

energy

using only those contributions

for any

by the displacements

above are found to be as fallows.(7)

where R is a term that has the dimensions

of the

crystal, y is Poisson’s ratio, G is the shear modulus, and b the Burgers vector of the ordinary dislocation. This calculation MBF

is somewhat

for the AuCu,

not be carried out in detail. r and r, are

(34

similar to that made by

superlattice

obtained

MILLER

INDICES

,

,

and will therefore

The equilibrium

by

minimizing

OF PLANES

values of

Etota, with

CORRESPONDING

TO 8

where h, k and 1 are the Miller indices of a particular plane, N = h2 + ii2 + 12 and h = k = 1. In order to see how ENNthklJ and ENNN(hkl) vary sider for convenience

with hkl, con-

those planes which have as their

zone axis the slip direction

[Iii].

For any plane in

this zone hkl must be all positive and may satisfy the requirement that h > k > 1. Furthermore, it is sufficient to consider only those planes which lie between (110) and (211) since they satisfactorily describe all of the planes which lie in the [Iii]

zone.

ENNthkz) is shown plotted in units of V/2a,,2 in Fig. 4 for all those planes between (110) and (211) which are 8 degrees from (110).

It is seen from the graph that

the APB energy is lowest across the (110) plane and highest across the (211) plane. However, this difference is only about 14 per cent. EN,N’hkL’ can a.lso be obtained in units of W/U,,~ from the same curve of Fig. 4 since h = k + 1. To find the equilibrium separation of the dislocations in the DO, type superlattice,

i.e. r and rl, in Fig. 3, it

& 52

4

0.70

-

!z

@,,,j 0

10

5 8UN

DEGREES)

FIG. 4. Variation

,

,

15 MEASURED

of antiphase

20 FROM

boundary

,

,

25 MO)

30 PLANE

energy with

hkl for those planes which have [I 1 l] as their zone axis.

MARCINKOWSKI

BROWN:

AND

respect to r and r, which leads to the following tions

:

DISLOCATIONS

equa--~ _____

~~~~~~~ -zzz () ar

IN

Fe,Al

TABLE 3. Change in bonding across (110) slip plane -associated with ordinary &,,[ 11 l] dislocations in the 52, (Heuster) type superlattice -

Numbor of ordinary &z,[H‘i] dislocations

i

and

expression

be solved

by graphical

ANN = -[(I-I) + (II-H) -t 4(X11-III) + 2(1-II)] + 4(1-1:11) + 4(II-III) ANNE = -[4(1-III) + 4(11-III) - 4(111-III)] + [2(1-I) + 2(11--II)]

for

r and rl from these two equations ; however they can

2

techniques. If E,,, were then an approximation similar

small compared to E,, to that made by MBF for the AuCu, type superlattice could be used to obtain rr. However,

closed expressions

as the following

ANN= (I-I) -+- (II-II)

+ 4(1H-III) + 2(1-H) -[P(T-III) + 4(11-HI)] ANNN = [4(1-III) + 4(11-III) - 4(111-III)] - [2(1-I) $- 2(11-II)]

for r and 3

sections will show, ENN

is about the same as that for E,,,,

at least in the case

of Fe,Al and FesSi.

ANB =

IN L2, TYPE

DISLOCATIONS

Consideration

SUPERLATTICES

of the type

Heusler

alloys,

L2,

commonly

of which the alloy

known

as the

Cu,MnAl

is best

known. In this case, A atoms are arranged on type III and IV sites and 3 and C atoms on type I and II Since both B and C atoms prefer

not to have like second nearest neighbors, that the second neighbor

interactions

it appears

will be impor-

tant, similar to the case of the DO, type superlattices. The net change in both NN and NNN resulting from the various

ordinary

slip plane is therefore

dislocations

gliding

shown in Table 3.

table, it is seen that the superlattice

over

the

Prom this

dislocations

in

this case will be very similar to those in the DO, type superlattice shown in Fig. 3. In particular, the superlattice dislocations. 4, however involves neighbor

dislocation will contain four ordinary Dislocations 1 and 2, as well as 3 and will be held together

by an APB

which

a net change in both first and second nearest atoms, whereas dislocations

2 and 3 will be

separated by an APB involving a net change in only second nearest neighbors. The expressions in Table 3 and therefore t#he corresponding for ANN and A,,,, energies of the APB are quite complicated.

Although

ordering in the Heusler type alloys has been considered by several authorscgJO) using the Bragg and Williams approximation, the results do not permit a determination of the interaction potentials between atom pairs in terms of those derived from Table 3 and which can

_~...~ --.-.

DISLOCATIONS TYPE

IN THE IMPERFECT SUPERLATTICES

Lastly, consideration

alloys possessing a B2 type

As previously

ordering

be

must

superlattice,

(B2)

will be given to the dislocation

in the As3

ordered lattice.

mentioned,

imperfect.

For

this

this kind of particular

type I and II sites are equivalent

will be labeled type I sites.

and

Type III and 1V sites are

also equivalent and will be labeled type II sites. With this notation, the change in bond sites across the slip plane for different

numbers

csn be readily constructed

of ordinary

dislocations

from Table 1 and are given

in Table 4. It will be noted that this table shows only those bond changes associated with first nearest neighbor

sites.

This follows

from the fact that the

type III and IV sites contain equal numbers of A and B atoms distributed

at random,

and since these are

the sites associated with the second nearest neighbor ordering energy, they are already disordered before slip and thus need not be considered in calculating APB energy.

the

Table 4 therefore shows that dislocation

TABLE 4. Change in bonding across (110) slip plane associated with ordinary $a,[ 1111 dislocations in the B2 type superlattice _____-. ___.~ _-.__-. __-. ~__ -. .._--Number of ordinary Net change in bonding &,[fli] dislocations i

be related to the critical ordering temperature. For this reason, we can at present give only the qualitative configuration of the superlattice dislocation in Heusler type alloys.

-.-

configurations

-[(I-I) + (II-II)

+ 4(IH’-III) + 2(1-II)] + (4(1-III) + 4(11-III)] Asxx = -[d(I-HI) + 4(II-III) - 4(III~III)] + 4(1-H) /_-.-._ -___--.-.

4

will next be given to ternary super-

lattices

sites, respectively.

Net change in bonding ANN = (I-I) + (II-II) + 4(111-III) + 2(1-H) -_14(1-III) + 4(11-III)] Axmq = [4(1-HI) + 4(11-III) - 4(111-III)] - 4(1-H)

1

(5b) It is not possible to obtain an analytic

760

SUPERLATTICES

1

2 __-.

!AXJN= 4(1-I) + 4(11-II) - 8(1-H)

ANNN= - 4(1-I) - 4(11-II) + 8(1-II)

‘A NN= -4(1-I)

- 4(11-II) + 8(1-II) ARNN= 4(1-I) + 4(11-II) - S(I-II) .-.-- -.

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770

METALLURGICA,

I gives rise to a net change in the NN and NNN atom sites across the (110) slip plane. Dislocation 2 on the other hand, completely re-orders the slip plane. The superlattice dislocation for this structure thus consists of a pair of ordinary dislocations held together by a NNAPB. Two such superlattice dislocations are shown schematically in Fig. 5. In order to calculate the energy associated with the APB between dislocation pairs, first consider the term 4(1-I) for ANN in Table 4. Both type I sites have equal probability of being occupied by either A or B atoms. The number of distinct atom pairs associated with 4(1-I) is thus simply (A-A)

+ (B-B)

+ Z(A-B).

(6)

Carrying out this procedure for both 4(11-II) and 8(1-II) in Table 4, we obtain for ANN A Nx = (A-A) + (B-B)

- 2(A-B).

(7)

VOL.

9,

1961 NUMBER

I

1 i

OF DISLOCATION

I [iii3

Ml

L FIG. 5. Pair of aJill] superlattice dislocations iu the imperfect B2 type superlattice. Note that there is no -coupling between a,[1 11) dislocations. Note: NNAPB in shaded area above should read APB only.

numbers of Fe and Al atoms distributed at random, while the type III and IV sites continue to be occupied by Fe atoms. It can therefore be inferred from this behavior that at about 56O*C, the thermal energy is v sufficient to overcome the second nearest neighbor A NN=w* ordering forces, but not those aosociated with the first nearest neighbors. For convenience, this structure Similarly ANNNis given by the negative of equation will be designated as Fe,Al-B2 since it is based on the (2b) since the order associated with NNN’s is restored B2-type superlattice. Finally, above about 8OO”C,the across the APB. The APB is also characterized alloy becomes compIetely disordered, there being no by a shear displa~enlent of the type ~u,,,(Ill>. In preference of any one type atom for any particular type addition, it can be shown(‘) that the general expression for the APB on any plane (hkl) in this imperfect B2 sublattice. It is now of interest to find the ordering energies type superlattice is given by equations (3a) and (3b). associated with the first and second nearest neighbor It is now a simple matter to calculate the equilibrium spacing of this superlattice dislocation. Since Etotal atom interactions in the Fe,AI alloy. This problem is now depends only on rr, then from equations (4) and obviously quite difficult to treat rigorously. On the other hand, Matsudat”) has used the Braggand Williams (5a), we obtain approxinlation in which both first and second nearest co&?e Gb2 sin2 6 + 1-y neighbor interactions are taken into co~ideration. rr = F9 It is not possible, even with this simple approximation, 27+&,--E,,,) to obtain an analytical solution for V and W; however, by assuming W = $V, Matsuda obtains rather good DISCUSSION OF THE PREVIOUS RESULTS qualitative agreement with the X-ray results of IN TERMS OF THE SPECIFIC Fe,Al AND Fe,Si SUPERLATTICES Bradley and JayoQ. Recently Rudman(15) has made The two classic alloys that undergo the DOs type a calculation of the relative ordering energies in the ordering transformation are Fe,Alt11+12)and FqSi.(i3) Fe-Al alloys very similar to that of ~atsuda, Since more work, both theoretical and experimental, apparently unaware of the previous work that had has been done with FesAl it will be treated in somewhat been done. Rudman, however, finds the ratio of more detail. second to first nearest neighbor ordering energies to Below about 56O”C, the Fe&l alloy possesses the be about one half. This is not significantly different DO, type superlattice in which iron atoms oocupy from that obtained by Matsuda and whose results we sites of type II, III and IV in Fig. 1, while the Al will therefore use in view of their good agreement with atoms occupy the remaining type-1 sites. Above experiment. An estimate of V is made by noting that 560°C this DO3 type superlattice disorders partially above 800°C the Fe&l-B2 type structure becomes in such a manner t,hat type I and II sites contain equal completely disordered; i.e. the f&t nearest neighbor In terms of equation (la), the energy per unit area associated with the NN interactions is

MARCINKOWSKI

order is destroyed. approximation

The simple Bragg and Williams

which involves

atom interactions

DISLOCATIONS

BROWN:

AND

only nearest neighbor

can thus be used and is given by(l@

IN

it may

perhaps

dislocations &,(l

Fe,Al

be not much

travel

through

11) type dislocations

type APB

771

SUPERLATTICES

more

difficult

the lattice leaving

on the slip plane.

if the

as ordinary

behind a &,(I 11)

The externally

applied

stress to do this is given by where k is Boltzmann’s

constant,

FAI and P,,

are the

ENN

q-z-

b

fractions of Al and Fe atoms in the crystal respectively, and Z is 8, the number Equation

of nearest neighbor

atoms.

(9) thus gives VcFe,blj = 10 x lo-l4 ergs, and

and leads to a value for r of 16.7 x lo8 dyn/cm2

therefore W(r+,) = 6.6 x lo-i4 ergs. Substituting these values into equations (2a) and (2b) and using

increments

a0 = 2.89 x lo-*

alloy possessing

cm,

we

obtain

&&+,)

= 42

ergs/cm2 and ENNNcFeaA,)= 56 ergs/cm2.

lattice.

The value of b is readily found to be 2.51 x

1O-s, Y is estimated to be the same as that for pure iron or 0.28 while C: is calculated from the work of Yamamoto

and Taniguchiu’)

of this order and larger occur in the FesAl

DO, type order.

Because of the lack of sufficient experimental

It is of interest now to find r and rl using equation (4) for superlattice dislocations in the FesAl super-

to be 5.86 x 10n dyn/

or

about 24,000 lb/in2 for the FesAl-DO, superlattice. The work of Kayseros) indicates that strengthening

no analysis

data,

of the ordering

energies associated with Reference has yet been made

the FesSi superlattice

to the Fe-Si system,us) however, indicates that the B2 type superlattice does not occur in this system. The

FesSi

alloy

appears

to possess

the

DO, type

cm2. The values of r and rl obtained from a graphical

structure up to its melting point of about 125O”C, which is nearly twice the critical temperature for the

solution

destruction

of equations

610 A and superlattice

(5a) and (5b) are found

represents the minimum superlattice extension

dislocation, results

are almost tion.

to be

260 A, respectively, for a pure screw dislocation i.e. 8 = 90” in Fig. 5, and

twice

extension. i.e.

in which that

The extensions

For a pure edge

f3 = O”, a the values

for the pure quoted

above

maximum

of r and rr

screw dislocarefer to super-

of

superlattice.

the

DO, type

order

It may be anticipated

in the

Fe,Al

therefore that the

APB energy between the individual dislocations constituting the superlattice

dislocation

shown in Fig. 3 for

the Fe,Si alloy is at least twice as great, as that in the Fe&l

alloy.

This in turn could reduce the extension

of the superlattice dislocations in Fe,Si to about half that of the Fe,Al alloy. In addition, as Barrett et c~Z.(~o)

lattice dislocations lying on the (110) plane. As has been previously shown, this is the plane on which the

have shown,

APB energy is the lowest, however,

give rise to straight slip lines on {llO]- planes. This inhibition of wavy slip with increasing silicon content,

is only

the APB energy

14 per cent higher than this on the highest

eliminate

silicon

the wavy

energy APB in the (111) zone, so that the superlattice

plus the relatively

dislocation extension is not expected to be significantly different from one plane to another in this zone. By

FesSi would

using equation dislocation

(8), rl can be found for the superlattice in the FesAl- B2 superlattice. In particular

for the screw type superlattice if Matsuda’s

dislocation

energy relationship

rl E 450 A

is used and infinite

if Rudman’s is used. We see then that the spacings between the ordinary dislocations constituting the superlattice dislocation in the FesAl and Fe,Al-B2 superlattices are quite large, and arise primarily from the relatively small

superlattice

experimental

of the APB’s

observing

the

work(‘) FesAl

on the

thermally

superlattice,

part of the investigation

with the observations

in

of

(Fig. 3).

previous in

by iron and

the probability

dislocations APB’s

greater than 4 wt. %

high energies

increase

In line with produced

additions

slip lines exhibited

of dislocations

EXPERIMENTAL

the

was concerned in Fe,Al.

PROCEDURE

The FesAl alloy was prepared by first melting 430 g of plastiron

under vacuum

in a zirconia crucible.

In

at

order to compensate for the loss of aluminum due to vaporization, 71.5 g of 99.99o/o aluminum were added

this point that these widely extended superlattice dislocations would be difficult to move as a unit over large distances through the crystal. This is particularly

to the iron after it had become molten. The molten alloy was then poured into a flat copper mold. Chemical analysis showed the resulting ingot to be

true in the case of the FesAl alloy where, as the following sections will show, cross-slip onto any of the planes lying in the (111) zone can occur with relative

homogeneous,

value of the APB energy.

ease.

It might be anticipated

Because of the relatively

low NNAPB

energy,

and to contain 25.5 at.yo aluminum.

The resulting ingot was sectioned into bars that were subsequently hot rolled at 1100°C into strips about 0.015 in. thick. These strips were in turn cold

ACTA

772

rolled to a final thickness reductions

of about 0.006 in.

led to severe cracking

order to obtain

METALLURGICA,

Further

of the strips.

a large grain size, portions

In

of these

VOL.

9, 1961

In both these micrographs, slip lines are extremely

it will be noted that the

wavy

and quite similar

those observed in iron.(22923) Furthermore,

to

there does

strips were sealed in evacuated Vycor capsules and annealed for 1 hr at 1050°C and finally air cooled to

not appear to be any significant difference between the slip markings in the Fe,AI-B2 and Fe,Al-DO,

room temperature. To ensure a high degree of the Fe&l-B2 type order, one half of the air cooled speci-

structures.

mens were annealed

however,

critical

1 hr at 6OO”C, i.e. just above the

temperature

for

the

DO, type

order

and

similarity

rate of 3.58”C/hr

essentially

a high

it is not possible to retain

state by quenching

the similarity

to those observed

the crystallographic

aspects

independent

in this alloy,

of the slip markings

types of ordered configurations

quenched. The remaining air cooled specimens were annealed 1 hr at 600°C and then slowly cooled at a to 250°C in order to develop

Unfortunately,

the fully disordered

in both

as well as their marked in iron, indicates

that

of the slip process

are

of the &ate of order and are

degree of the DO, type order which will be termed as

probably

the Fe,Al- DO, type henceforth.

can also be inferred from these results that aluminum

Square samples about 15 mm on an edge were then cut from the ordered polished that

specimens

and electrolytically

into thin foils using a procedure

employed

by Fisher

AuCu, alloys.

The electrolyte

acetic acid solution

similar to

and Marcinkowski(21)

for

was also the chrome-

used for AuCu, alloys.

In using

quite similar to that occurring

in iron.

It

additions, unlike silicon(20) have virtually no effect on the general features of the slip process occurring in iron. Although

a large number of grains in both types of

ordered alloys showed wavy slip lines, rather straight slip lines such as those at A in Fig. 6(a) could observed.

The most logical

explanation

be

to account

this solution to thin the Fe,Al samples, it was found that below a critical voltage ( z 30 V) the specimens

for these two types of slip patterns is as follows:

developed

straight slip lines are produced by the edge components

surface.

a brownish-yellow As the solution

became higher.

polishing

film on their

aged, this critical

voltage

The polishing times were rather long

and required on the average, about 3 hr. out of three specimens

About

one

was found suitable for trans-

mission electron microscopy. All

of

the

observations I operating diffracted

electron

microscopy

at 100 kV.

diffraction

In order to insure that no

rays contributed

a 20 ,u objective

to the bright field image,

aperture was used.

diffraction patterns were obtained mediate aperture of 20 ,IJ. EXPERIMENTAL

RESULTS

A few observations conventional

and

were made with the Siemens Elmiskop

AND

All selected area using

DISCUSSION

were first carried

light microscopy

an inter-

techniques

out

using

in order to

The

of dislocations which cannot cross slip nor climb at room temperature. On the other hand, screw dislocations are able to glide on any plane lying in the (111) zone, and can thus give rise to wavy slip lines.

This

latter process has often been termed “noncrystallographic” slip and will be so designated in this paper. In order to give a better insight into the configurations and movements slip patterns

of the dislocations

discussed

above,

giving rise to the

direct observations

of

these processes using the more powerful techniques of transmission electron microscopy will be discussed in the following sections.

Up to the present time most

such observations

have

been

packed structures,

with relatively

confined

to the close

little consideration

being given to the body-centered

cubic

metals and

alloys.

obtain some preliminary information concerning the general features of the slip markings produced on the

Figure 7 shows the dislocation configuration in an alloy that was ordered so as to form the Fe&l-DO,

surface of the Fe,Al specimens after deformation.

type superlattice. These dislocations are seen to originate at some region to the lower left hand corner

As

far as the authors are aware, there have not yet been any observations of this type reported for the Fe,Al alloy.

To accomplish

this, samples

of Fe,Al-B2

as

of the micrograph contour.

which is obscured

by an extinction

The general motion of these dislocations,

as

well as Fe,Al-DO, were first electropolished and then deformed plastically several per cent. Oblique illumination was then used to enhance the contrast

noted by the slip traces they leave behind, is to the upper right of the figure. Two very interesting observations can be obtained from Fig. 7. The first

arising from the slip lines on the surface of these samples. The results obtained therefrom for both types of order are shown in Figs. 6(a) and 6(b) and are

is that the dislocation lines all make an acute angle with the slip trace, and in addition they all lie in the same direction. From an analysis of this micrograph,

quite representative of the general features of the slip patterns observed throughout the entire specimen,

the direction of these dislocations was found to be [Ill], indicating that they all may be of pure screw

MARCINKOWSKI

AND

BROWN:

DISLOCATIONS

IN

FQ,AI

SUPERLATTICES

Fro. 6(a). Light micrograph taken with oblique illuminatio~l of slip line traces in Fe,AI-B2.

Fro. 6(b). Light micrograph taken with oblique illumination of slip line traces in Fe,Al-DO,.

character.*

The

observation

that

the

dislocations

below A and B of Fig. 7 have been able to move noncrystallographically leaving behind them sharply curved slip traces suggests that these dislocations are indeed of the pure screw type. A second important * It will be noted that in Fig. 7, as well as in subsequent micrographs, the vector indicating the (111) direction does not in general lie in the plane of the figure, but at some angle to it, and parallel to the dislocation line, and will therefore be drawn dotted.

feature of this micrograph

x 700

x 700

is that the genera1 direction

of the slip line traces vary in an almost continuous manner across a slip band. On the basis of the [liij slip direction found above, the possible range of slip planes in this zone, on which t2he dislocations have traveled, is shown in the upper left corner of Fig. 7. We see from this that the dislocations an almost continuous distribution included

between

(110) and (743),

have moved on of slip planes i.e. a spread

of

ACTA

METALLURGICA,

VOL.

9,

1961

FIG. 7. Band of screw dislocations in Fe,Al-DO, which have been nucleated in the region at the lower left hand corner of the micrograph. Normal to micrograph is [ 1111.

26”.

It is concluded

therefrom that screw dislocations

in Fe,Al can choose one of any of the possible planes which have (111) as their common zone axis. Not only are the screw dislocations alloy

able to travel

zone,

but

any

one

in the FesAl

on any slip plane in the (111) screw

dislocation

may

move

smoothly from one plane to another within this zone leaving behind wavy slip traces as shown in Fig. 8. In this figure a number of screw dislocations have moved from right to left. The rather sharp contrast produced by the slip traces is thought to be associated with an aluminum oxide film produced on the specimen

surface

interest

during

electrothinning.

to note at this point,

It is also

of

that the dislocations

observed

in the FesAI-DO,

far as can be determined,

ordered structure ordinary

are, as

dislocations

and

not superlattice dislocations of the type shown in Fig. 3. As was shown previously, this was expected on theoretical grounds for the Fe&l

alloy.

In Fig. 9(a), several bands of dislocations

which have

moved upward from the lower portion of the micrograph can be seen. Unlike the dislocations shown in Fig. 8, the dislocations here move on a single type of slip plane which was found to be (101). The reason why these dislocations are confined to move on given slip planes can be obtained by analysing the geometry of the dislocations themselves. In most cases they have a hooked appearance, and must therefore be of

MARCINKOWSKI

FIG.

8.

AND

BROWN:

DISLOCATIONS

IN

Fe,Al

SUPERLATTICES

775

Wavy slip traces created by the motion of screw dislocations in the Fe,Al-DO, structure.

varied character at different places along their length, i.e. either edge, screw or mixtures of the two.

since the angle that the dislocation line makes with DE approaches 90” as F is approached According

It is therefore the edge components

to the work of Chen and Pond(s*), edge dislocations

dislocations

to a given slip plane.

that confine the It is of int,erest to

are found to move much faster than screws because

examine the hooked appearance of these dislocations in somewhat greater detail. An enlargement of the region

jogs retard the screws. Gilman(25) have found

near A in Fig. 9(a) showing several of these dislocations is clearly shown in Fig. 9(b). We can give only the following tentative explanation for this behavior at the present time. Considering one of these dislocations

faster than screws. Similar behavior is expected to It therefore appears also be true for the Fe& alloy

DEF, screw

it is suggested that the segment DE is pure because it lies in the direction [ill]. In

traveling along the dislocation the edge component

line from point E to F,

must consequently

become larger

velocities,

In particular, Johnston and that over a large range of

edge dislocations

in LiF

logical to assume that the edge portion tion line near F can move much faster portion along DE with the consequent of the screw portion. The result of this fore is the hooked appearance

move

50 times

of the dislocathan the screw lagging behind behavior there-

of the dislocation

lines.

776

ACTA

METALLURGICA,

VOL.

9,

1961

FIG. 9(a). Dislocat,ions in the Fe,AI-DO, structure that vary between edge and screw character along their length and move on a single ( 101) plane. Normal to micrograph is [ Ill].

Another important feature of Fig. 9(a) is the elongated dislocation line BC. Both ends of this disloca-

appear to be arranged in pile-ups. However, closer examination of the slip traces on which the dislocations

tion line can be seen to terminate on the same surface.

lie shows that a relatively small number of dislocations are arranged on many closely spaced slip planes.

Furthermore, the only visible slip trace is that which connects the terminal points of the dislocation line,

Figure lO( a) illustrates the manner in which disloca-

area contained between itself and the slip line BC. We conclude therefrom that the dislocation line BC was nucleated at the surface of the foil and expanded

tions can be generated at a grain boundary. In particular, the dislocations are seen to originate from that portion of the grain boundary near the corner of the grain which forms a junction with two adjacent

into the configuration shown in Fig. 9(a). Several other similar loops can be seen at various other places in this micrograph. Finally, many of the dislocations,

grains. Junctions of this sort are expected to be particularly favorable for generating large stress concentrations. Furthermore, it was found here again

particularly

that the dislocations

indicating

that the dislocation

has swept out only that

those in the band to the left of Fig. 9(a),

are all alligned parallel to [ill]

MARCINKOWSKI

AND

BROWN:

DISLOCATIONS

IN

Fe,Al

SUPERLATTICES

711

FIG. 9(b). Enlarged view of area A in Fig. D(a) showing mixed character of dislocation lines.

and are therefore probably

of pure screw type.

The

rather sharp curvature of the slip traces near A in Fig. 10(a), as well as the divergence of the band of dislocations

from

its point

of origin

illustrates

large amount of freedom which these dislocations to move on any plane in the (Ill)

zone.

the have

The particular

dislocations.

These

dislocations

should

then

leave

behind them a strip of APB of the type &q-,(111). However, as Fisher and ~arci~owski(zl) have shown, APB’s

show contrast only when the foil is oriented so

that a strong superlattice the objective

aperture.

reflection is diffracting

into

Such is not the case in Fig.

plane within this zone that is chosen at any one point

10(a) so that no APB’s are seen; however it was found

in the crystal appears to be determined by the local stress conditions at that point although it will be noted that the slip band as a whole lies close to the (Oil) plane. Each individual screw dislocation will tend to travel on that plane within the (111) zone, on which

that by rotating the stereo holder of the Siemens Elmiskop I about one degree, it was possible to obtain strong diffraction from the ZOO-superlattice reflection. This was sufficient to resolve the APB’s produced by the dislocations seen in Fig. IO(a), and is shown in Fig. lO( b) . Because of the large number of dislocations

the resolved shear stress is a maximum.(2z) In addition, the dislocations in Fig. 10(a) appear to be of the ordinary

&,,(I 11) type as opposed to superlattice

giving rise to these boundaries, they are difficult to resolve in some areas, particularly near this poisrt of

778

ACTA

METALLURGICA,

VOL.

9,

1961

FIG. 10(a). Screw dislocations of the type [ill] originating from corner of grain in Fe,Al-DO,. Normal to micrograph is [013]. origin at the top of Fig. 10(b).

In addition to the APB’s

produced by slip, the large irregular thermally produced APB’s can also be observed. These boundaries are

associated

temperature

with

the

of

the

higher

B2 type order, and will be discussed

detail in another paper.(‘) thermally

formation

produced

APB’s

in

It can be shown that these are also described

shear of the type &z,(lll). We have mentioned above

that

APB

by a

contrast

arises only when the foil is oriented for strong superlattice reflection. The reason for this is that diffracted electrons undergo a change in phase angle tc as they travel through the APB given by

u=Zng.R

(11)

where g is the reciprocal lattice vector of the diffracted wave

hkl, and R is the shear displacement

describing

the APB

between the two portions

vector of the

crystal. This change in phase in turn produces a difference in intensity between that of electrons diffracted at the APB and those diffracted from its surroundings.

As described

previously,

R is simply &z,,(lll).

Now as Table 5 shows, cc = 0 for the fundamental reflections, while it is either &n/2 or &rr for the superlattice reflections depending on whether the indices of the superlattice reflection are all odd or all even. For convenience these have been designated as superlattice reflections of the first and second kind, respectively, in Table 5. Thus for the ZOO-reflection

MARCINKOWSKI

Ann

BROWN:

DISLOCATIONS

IN

Fe,Al

SUPERLATTICES

779

FIG. 10(b). Same area as that in Fig. 10(a) but tilted slightly to eliminate dislocation contrast and reveal both thermally produced antiphasa boundaries as well as those produced by the dislocations in Fig. IO(a). Antiphase boundary contrast afises from 200-su~rlattice reflection.

giving rise to the APB contrast in Fig. 10(b), a = V. It will be noted that in using equation (II), we have expressed R in terms of a0 which is only one half the unit cell dimensions of the FesAI- DO, structure. Thus g in this equation must be multiplied by a factor of one half, since hkl in Table 5 are given in terms of the actual unit cell dimensions of 2a,,. Another important feature of Figs. 10(a) and 10(b) is that the dislocation contrast exhibited in the former is not present in the latter. This is in general true since the conditions imposed which give rise to dislocation contrast are in general differ&t from those which produce APB contrast. A

6

TABLE 5. Phase angles TVassociated with first several hki reflections for APB produced by too{ 111) type slip in the Fe,AI-DO, superlattice _~ -- ..-__--____....-..__ hkE

I

Type of reflection

I

a

111

81

*;

200 220

811 P

rtrr 0

311

81

+;

z:

811 P

in 0 -/-.-..--.-- __..,_... .._.____ _-__._.L_ F refers to fundamenta1 reflections whereas SI and SII refer to superlattice reflections of the fhst and second kind, respectively.

780

ACTA

METALLURGICA,

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1961

FIG. 11. Formation of antiphase boundaries in Fe,AI-B2 by ordinary screw dislocations originating from region to the right of micrograph. Normal to micrograph is [IOO]. Antiphase boundary contrast arises from 100.superlattice reflection.

Finally,

it is instructive

to consider the interesting

but rather unlikely possibility

that the dislocations

in

Fig. IO(a) may actually be very closely spaced pairs. If such were the case, they would then leave behind them a NNNAPB

described

by a a,(lll)

or a,(lOO)

type shear. However, from equation (11) we see that under these conditions the 200-superlattice reflection could give no APB contrast since a would be 2rr. This rather unlikely possibility can therefore be eliminated.

ordered lattice described

as FesAl-B2.

a large burst of dislocations

Fig. 11 shows

originating

from

some

area, presumably

a region of high local stress concentration, to the right of the micrograph. Here again, it will be noted that the dislocations are of the ordinary screw type-i.e. &,,[I 1 l] since they are parallel to [I 1 II-exhibit noncrystallographic slip and leave A few large behind them APB’s of the type +z,[lll]. loops of the thermally produced APB’s can also be

Having considered the dislocation configurations and behavior of the FesAl-DO, superlattice, we now

seen. In addition, the foil is apparently bent so that a portion of Fig. 11 to the right is oriented for dislocation contrast but not APB contrast, whereas that

turn to those alloys which were annealed and quenched from above 6OO”C, and which therefore possess an

region to the left is oriented for APB contrast but not for dislocation contrast. The superlattice reflection

MARCINKOWSKI TABLE 6. Phase reflections _~_._

AND

-..

DISLOCATIONS

ngles a associated with first several hkl a &n,(111) type slip produced APB t,he Fe,AI-R2-s-uperl8.tt~ce _____

~~ _~._ hkl Type of reflection ----___ -I_~__.-____-_ 100 110 111 200 210 211 -. .~

BROWN:

s

F s P s P

.L

cf. +rr 0 J-a *or 0

= givir kg rise to contrast was found to be 100 and from equa ,tion (11) or Table 8, the phase angle associated with this reflection is hr.

IN

Fe,Al

781

SUPERLATTICES

At this point, it is of interest to notice that aside from the non~r~stallo~raphic one particular

dislocation

there is also an overall

type

beha.vior

of any

within the band of Fig. 11, tendency

for t,his band

of

dislocations to diverge away from its point of origin. This is a very common feature a.ssociated with all those dislocations

that appear

to originate

numbers from some particular source.

in large

Such behavior

has a,lready been seen in Figs. 7 and 10 ofthe FeaAl-DOa structure. Furthermore, the dislocations in ali c.ases have been of the pure screw type. We believe 1that the reason for this behavior is as follows.

FIG. l&(a). -Bright field micrograph of Fe,Al-B2 showing t,he formation of antiphase boundaries by moving dislocations of ordinary type. Normal to micrograph is [IOS]. Antiphase boundary contrast arises from IOO- superlattice reflection shown in selected area diffraction pattern of Fig. 12(b).

Each of ‘the

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9,

1961

PIG. 12(b). Selected area diffraation pattern obtained within area shown in Fig. 12(a).

screw

dislocations

has associated

with

it a radial

tions within the band,

and the smaller the applied

stress, the greater will be the divergence

stress field given by

OR = where r is the distance

and vice versa.

Gb

(12)

Fj-$

between

dislocations.

Since

sorew dislocations

together

with their easy mobility

on different slip planes also accounts for the observation that there is only rarely more than a single

all of these dislocations are of the same sign, they will exert repulsive forces on one another. The relative

dislocation

ease with which these screw dislocations

alloy are expected

can move

of the band

The mutual repulsive forces between

associated

with

follows also that dislocation

a given

slip trace.

It

pile-ups in this particular

to be virtually

eliminated,

which

from one slip plane to another within the (111) zone,

is also in agreement with the present observations.

coupled with these repulsive forces, will then cause the

Lastly, we wish to consider in some detail certain aspects of the APB contrast produced by the disloca-

indi~dual

dislocations

within

the band to separate

from one another until the repulsive forces are eventually balanced by the lattice friction forces. The rate of divergence of the dislocation flow from the source is quite likely influenced primarily by the density of dislocations within the band as well as the magnitude of the applied stress or stress concentrations. In particular, the higher the density of disloca-

tions in the FesAl-232 superlattice. No generahty will be lost in considering this particular structure since it is obvious at this point that the dislocation behavior as well as the APB’s produced therefrom are, as far as can be determined, identical in both the FesAl-BZ and FesAl-DO, superlattices. Fig. 12(a) show/s a bright field micrograph,

i.e. the contrast

was probuced

by

MARCINKOWSKI

AND

BROWN:

DISLOCATIONS

IN

Fe,41

783

SUPERLATTICES

Fro. 12(c). Dark field micrograph of approximately same area w. that shown in Fig. 12(a). Dark field antiphase boundary contrast arisesfrom 100~superlatticereflection of Fig. 12(b).

allowing only the direct electron beam to pass through

that the alternate light and dark contrast of the APB’s

the objective

in Fig. 12(a) is reversed in the dark field micro~aph

APB’s

aperture,

exhibiting

as well as the thermally

both slip-produced produced

FesAl-BZ

of Fig. 12(c).

In order to obtain more insight into the

domain boundaries. A selected area diffraction pattern obtained within this area is shown in Fig. 12(b). It is

details

obvious

areas labeled as A in Figs. 12(a) and (c) were enlarged by a factor of 2, and are shown in Figs. 12(d) and (e),

from this figure that the strongest

reflection

present is that of the lOO-superlattice reelection, and is responsible for the APB contrast shown in Fig. K?(a). In order to verify this, a dark field image of Fig. 12(a)

associated

with

generated by ordinary

the

formation

of

APB’s

$a,(11 1) type dislocations,

the

respectively. By very fortunate circumstances, the area obtained by bright field illumination in Fig. 12(d) was oriented so as to exhibit only dislocation contrast,

was formed by adjusting the objective aperture so as to allow only those electrons contributing to the loo-diffracted beam to pass through it. The resulting

This very same area, observed with dark field illumination, is shown in Fig. 12(e) and is oriented so as to show

micrograph which was found to be exceptionally sharp is shown in Fig. 12(c). As expected, it will also be noted

contrast only from the APB’s produced by the dislocations in Fig. 12(d). All of the dislocations in Fig. 12(d)

FIG. 12(d). Enlargrment of area A of Fig. 12(a) whichis oriented for dislocation contrast only.

FIG. 12(e). Enlargement of area A of Fig. 12(c) which is the same area. as that of Fig. 12(d), only oriented for contrast due to the antiphase boundaries produced by those &locations numbered in Fig. 1Z(d).

MARCINKOWSKI are numbered

AND BROWN:

and by referring to Fig. lZ{e), it will be

noted that all of the slip-produced thesameline

DISLOCATIONS

APB’s terminate in

(also numbered) corresponding

to the exact

IN Pe,Al

predominance

SUPERLATTICES

785

of pure screw dislocations.

there is as yet no satisfactory

theoretical

However, explanation

why the Peierls energy barrier should be appreciably larger in body-centered cubic structures than in close

places where the dislocations seen from Fig. 12(d) should lie. Here again the dislocations are found to be of the screw type, which in turn enables them to move

packed ones. On the other hand, several investigations of the large temperature dependence of the yield and

continuously

flow

from one slip plane to another.

very vividly APB’s

illustrated

left behind

This is

in Fig. 12(e) by following

by the moving

dislocations.

2, 6 and 7 is particularly

We have seen from the previous the majority

of dislocations

that

were of the pure

phenomenon. The first, and probably least likely, is that according to the isotropic elastic dislocation the strain

dislocation

energy

is about

associated

metal foils.

more favorable

of pure screw dislocations

However,

a screw

two thirds that for an edge.(ss)

Thus it may be energetically preponderance

with

cubic

that the Peierls mechanism

screw type, which in turn gave rise to complex slip behavior. There are several possible reasons for this

theory,

of body-centered

All

severe.

observations

observed

in a number

metals and alloys, and in particular iron,(28*2g)suggest

nine dislocations in these two figures give rise to wavy slip traces; however the change in direction associated with dislocations

stresses

the

Because with

may be predominant.

of the high degree of freedom

the

movement

of

dislocations

associated

in the

FesAl

superlattice, and also because these dislocations are of the ordinary type, the destruction of long range order by moderate This

cold work should be very great.

is in agreement

findings of Flinn(30). from that found

with

the preliminary

This behavior

in ordered

X-ray

is quite different

AuCu,

in which super-

lattice dislocations are present.@) In this alloy, cold work result,s in only a reduction of the antiphase domain size.

to have a SUMMARY

within the

if this were so, the same general

A tlleoretical

AND CONCLUSIONS

analysis has been made of the disloca-

results observed in this particular alloy should occur in many others, but such has not been found to be the

tion configurations

case.

dislocation in the DO, and L2, structures should consist of four ordinary dislocations of the type $a0

Another

and more likely possibility

for this behavior energy energy

is the relatively

fault

expected t.o exist in the FesAl alloy. This is apparently sufficiently great so as to

prohibit any dissociation into

to account

high stacking

partials.

of $a,,(1 11) type dislocat’ions

Therefore,

unlike

the

close

packed

structures, there is no favorable plane on which a dissociation of t,he whole dislocation into partials can take place, so as to lower its strain energy. Since there is no favorable plane on which the dislocation can

L2, and B2.

in superlattices

of the type

DO,,

It is found that a perfect or superlattice

(111) bound together by antiphase boundaries. The antiphase boundaries between these pairs are of two different type

types.

consists

In the DO, alloy in particular,

of only wrong

first nearest

whereas the second type consists of only wrong second nearest neighbors. dislocations

Consideration

in the imperfect

of the superlattice

B2

type

one that is based on the composition

AB,

lattice,

they should consist of pairs of ordinary dislocations

can lie, i.e. any plane in the (1 1 1> zone.

the type

&zo(lll) bound

boundary.

Expressions

before the dislocation

is able to glide from one plane

together

i.e.

shows that

glide, it. glides on any plane in which its Burgers vector However,

one

neighbors,

of

by an antiphase

for the spacings between the

to another in this zone, it must be of the pure screw type. It is concluded then that in order to move on

ordinary dislocations constituting dislocations as well as expressions

those planes on which the critical resolved sheer stress

boundaries between them have been derived. Application of the above results to the specific

due to stress concentrations greatest, the dislocations

and/or the applied stress is are forced into a parallel

alignment with the Burgers they are thus able to “seek”

vector.

In this manner,

those planes of highest

shear stress ; their movement through the crystal being determined by complexity of state of stress within the structure, Finally, there is a possibility that the Peierls energy barrier may be quite large in body-centered cubic metals and alloys, so that the dislocation lines possess minimum directions

energy when they lie along close packed in their slip plane.(27) This could lead to a

the superlattice for the antiphase

case of the FesAl alloy shows that when this alloy possesses the DO, type superlattice, of the superlattice 600 8.

dislocation

On the other hand,

the total extension

will be at least about

when the Fe&l

alloy is

in the B2 type ordered condition the extension of the superlattice dislocation may be infinite. These large extensions arise from the relatively low energies associated with the antiphase boundaries in FesA1, and because of this, it may be only slightly more difficult for the dislocations to travel as ordinary ~a,(lll) types instead of as superlattice dislocations.

786

ACTA

Brief

consideration

of the Fe,Si

METALLURGICA,

alloy,

which

also

possesses a DO, type superlattice, indicates that the antiphase boundary energies associated with the

VOL.

9,

than an edge, in that it is able to move on those slip planes in the (111) zone, on which the critical resolved shear stress is a maximum,

superlattice dislocations should be appreciably greater than those associated with the Fe,AI system, possibly more than double, so that the extension lattice dislocations small in this alloy.

is expected

to be comparatively

In order to check these theoretical dislocations

were observed

chemically

thinned

bulk material, type ordered

&z,,(lll)

and possessing

dislocations.

from the

As anticipated,

it was

in alloys of both ordered

through

dislocations

with electro-

obtained

both the DO, and B2

configurations.

travel type

by using trans-

techniques

foils of Fe,Al

found that the dislocations structures

considerations,

directly

mission electron microscopy

of the super-

the

lattice

instead

as ordinary

of as superlattice

In most cases, the dislocations

were found

to be of a pure screw type which were able to move on any slip plane within the (111) zone, thus giving rise to wavy slip traces.

By selecting the proper orientation

of the foil, it was possible contrast

conditions

to obtain

the necessary

needed to observe

the antiphase

boundaries left behind by the ordinary &z,,(lll) type dislocations. The absence of superlattice DO,

dislocations

in either the

or B2 structures in the Fe,AI alloy is attributed

two factors.

One that has already

to

been mentioned

is that the energy of the antiphase boundary generated by an ordinary &,(lll) dislocation is rather small so that a relatively

small applied

stress is necessary

move it against these ordering forces. ordinary

dislocations

Secondly,

to the

are highly mobile on any plane

within the (111) zone, making it difficult, for the superlattice dislocation to move as a unit through the lattice. On the other hand, the Fe,Si superlattice, because

of its relatively

large

energy as well as the possibility

antiphase

boundary

that it may possess

a single (110) slip plane, should make it a somewhat better

alloy than Fe,Al

in which to observe

super-

lattice dislocations of the type predicted. Finally, two possibilities have been suggested to account for the preponderance of screw dislocations in the Fe,Al

alloy.

may be associated

In the first place, this behavior with a significantly

smaller elastic

strain energy for a screw dislocation in the Fe&l alloy compared to that of an edge. In addition, a screw dislocation has a much greater degree of freedom

1961

ACKNOWLEDGMENT

The authors wish to express their gratitude to J-_C. R a1ey f or h’ISassistance in the experimental portion of this work. for

his

many

concerning

They also wish to thank D. S. Miller helpful

suggestions

and

criticisms

the present investigation. REFERENCES

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