PROPAGATION OF DISLOCATIONS IN LONG PERIOD ORDERED ALLOYS

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PROPAGATION OF DISLOCATIONS IN LONG PERIOD ORDERED ALLOYS

G. Vanderschaeve

To cite this version:

G. Vanderschaeve. PROPAGATION OF DISLOCATIONS IN LONG PERIOD ORDERED ALLOYS.

Journal de Physique Colloques, 1974, 35 (C7), pp.C7-47-C7-52. �10.1051/jphyscol:1974703�. �jpa-

00215859�

JOURNAL

DE

Colloque C7, suppliment au no 12, Tome 35, Dkcembre 1974, page C7-47

PROPAGATION OF DISLOCATIONS IN LONG PERIOD ORDERED ALLOYS

G. VANDERSCHAEVE

Physique des dCfauts de 1'Ctat solide (E. R. A. au C. N. R. S. no 374), UniversitC des Sciences et Techniques de Lille,

B. P. 36,59650 Villeneuve d'Ascq, France

ResumB.

A partir de considerations geometriques, on montre qu'il existe dans les alliages ordonnes a longue periode, des dislocations partielles limitant des fautes d'empilement sans faute d'ordre. En supposant l'energie de faute d'empilement suffisamment faible, on examine les conse- quences de cette situation sur le mode de deformation plastique et on montre qu'elle devrait se produire soit par maclage, soit par propagation de fautes d'empilement sur plusieurs domaines.

Un mecanisme de franchissement des parois de domaines est propose : un groupe de dislocations partielles doit glisser en m6me temps sur les couches atomiques successives : un arrangement atomique analogue a la nucleation d'un multipole est necessaire. Les consequences de ce modkle sont enoncees.

Abstract.

From geometrical considerations it is shown that in long period ordered alloys some partial dislocations exist, leaving behind only a stacking fault without destroying the chemical order. Providing that the stacking fault energy is low enough, theoretical implications of the defor- mation behaviour are examined. It is proposed that plastic deformation should take place either by twinning or propagation of widely extended stacking faults through several domains. A simple mechanism for crossing over domain boundaries is proposed : partial dislocations have to glide together on adjacent layers, in the sense that some convenient dislocation multipole has to be nucleated at the boundary. Some physical consequences are drawn from that model.

1. Introduction. -Long period ordered alloys (or periodic antiphase structures) can be thought as derived from a L1, structure by step shifts which occur at every M cube planes along a cube axis (Fig. 1).

Ordering in such alloys occurs with a change of the crystal structure type, from face-centred cubic to tetragonal. The long period (or superperiod) being parallel to any of the three original cubic axes, three types of domains may be formed within a disordered single crystal ; they are in fact limited by -order twin boundaries [I].

Because of the loss of symmetry, the < 110 > direc- tions of the disordered face-centred cubic lattice are no longer equivalent and with this crystallography, the major problem is to understand how a dislocation can propagate across neighbouring domains. Given a perfect dislocation in one domain, it is no more perfect when entering the neighbouring one, so that it has to trail behind an order fault making first neigh- bours wrong bonds between atoms of two adjacent layers.

In preceding studies [2, 31 on the deformation behaviour of long period ordered Ag,Mg (M

2), we have shown that the observed dissociation modes for some glide dislocations can be simply explained by geometrical considerations, assuming only the stacking fault energy to be low enough. A model for plastic

FIG. 1. - Unit cell of long period Ag3Mg

(M

deformation has been proposed. It happens that glide dislocations which are perfect in one domain can move through other domains without trailing an order fault behind, provided they dissociate and leave one certain partial at the first domain boundary. So that plastic deformation proceeds in extending numerous stacking fault ribbons resulting in a more and more profuse twinning throughout the crystal. Similar arguments account for the occurence of numerous stacking faults limited by domain boundaries as observed [4, 51 in deformed Cu,Pd (where M decreases from 7 to 4 as the palladium concentration increases).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974703

C7-48 G.

VANDERSCHAEVE In this paper, we study, from a geometrical point of

view, the propagation of dislocations in any long period ordered alloy whatever the value of M be. We show in the first part that there exists always in the structure some possible partial dislocations leading a geometrical stacking fuult which introduces only a modification in the . . . ABC . . . stacking sequence without any first neighbours wrong bonds. So that plastic deformation proceeds in extending such stacking fault ribbons instead of order fault ribbons.

In order to cut through some domains, partial dislo- cations have sometimes to be paired one above the other on successive fault layers provided that some atomic rearrangement occurs at the boundary.

2. Stacking faults and partial dislocations in long period ordered alloys. - We consider in the following only first neighbours atomic interactions. It is realized that this may be a poor approximation ; however it accounts qualitatively for the observed dissociation of dislocations in Ag,Mg and the plastic properties of some long period ordered alloys can also be under- stood from this model.

Let the composition of the alloy be A,B. The stacking sequence involves then 3 x 2 M (1 1 1)-planes and can be written as :

. . .AzM B 2 ~ CZM Al B1 C1 AZ BZ C2. . .

Note that the perfect stacking does not involve B-B atomic pairs.

A stacking fault without wrong bonds is made by shifting the B, plane into a C one without intro- ducing any wrong bonds with its neighbour A,. So B, must be shifted into a C,, position resulting in the following sequence.

Note that this intrinsic fault is formed by a thin lamella of two supplementary planes. It can also be regarded as being formed by two twinning opera- tions (at the crosses) separated by one atomic layer.

Let the superperiod be along [loo] : Following the generally used conventions, it is easy to show [3] that the Burgers vectors of possible leading partials in the (1 11) plane are of the type 2 6B + n.2 AC (n inte- ger 3 0) ; the shortest of them are 2 6B, 4 A6 and 4 C6. These partials lead a geometrical stacking fault in any long period ordered alloys. Other types of glissile partials may also be formed, but they do not deduce from 2 6B by lattice translations parallel to the diagonal shift vector and, therefore, depend on the M value.

Let us consider the Burgers vectors of such partials.

The shortest lattice translations not parallel to AC in the (111) plane can be easily determined by studying the arrangement of atoms in this plane. The effect of the diagonal shift is to transform triangles of B atoms into rectangles (Fig. 2). The positions of B atoms are

FIG. 2. - Atomic arrangement in the (111) close-packed plane of a long period ordered alloy A3B. The superperiod is along

[loo].

such that ( M

1) strips of triangles alternate with one strip bf rectangles. Lattice translations join the corner of a rectangle to the corresponding corner of another one. It may easily be found that the shortest lattice translations are :

- when M odd : M x 3 B6,

- when M even : ( M x 3 B6) f AC.

Therefore, the Burgers vectors of the possible partial dislocations in the (111) plane are respectively (3 M - 2) B6 or (3 M - 2) B6 f AC.

For example :

M = 1(D02, structure - Ni, V) b, = B6 M

2(DOz, structure - Ag,Mg) bp

4 B6fAC

M = 3 bp = 7 B6, etc.

The shortest perfect translations as well as the shortest Burgers vectors of those partial dislocations which bound a geometrical stacking fault on the right are listed in Table I for different values of M and for the three possible orientations of superperiod.

We study now how a superdislocation can dissociate.

We showed in [2] that eightfold dissociated super-

dislocations were present in long period ordered

Ag,Mg with the sixth unit split up into two Sho-

ckley partials, creating a wide geometrical stacking

fault in between. Some splitting could occur for the

other units dislocations also, but the fault formed

PROPAGATION O F DISLOCATIONS IN LONG PERIOD ORDERED ALLOYS

Direction of the long period

-

l O M = 1

Shortest perfect translations Shortest Burgers vectors of partials

2 0 M = 2

Shortest perfect translations Shortest Burgers vectors of partials

3 O M = 3

Shortest perfect translations Shortest Burgers vectors of partials

(d) plane [loo]

-

FIG. 3.

Eightfold dissociated superdislocation in Ag3Mg.

Note the large splitting of the sixth unit as compared with other partials. For detailed contrast experiments see [2].

there involves both order and stacking fault, with a higher energy and correspondingly with a much smaller dissociation width (Fig. 3). Tt can be shown that similar dissociation should always occur in any long period ordered alloys : the (2 M + 2)th unit should split up into two Shockley partials connected by a geometrical fault [3].

Till now, we have focused attention on the problem

of dislocation dissociation in one domain. We study now the propagation of dislocations accross neigh- bouring domains.

3. Propagation of dislocations in long period ordered alloys. - In long period ordered alloys, the major problem is to understand how a dislocation can move across neighbouring domains since the superperiod changes from one cubic axis to another one. We first develop a model for Ag,Mg(M

2), where plastic deformation occurs by propagation of 4 BS dislocations provided that stacking fault ribbons be paired in ,the sense that some convenient dipole has to be added to the leading superimposed partials [3]

for cutting through some domains. This mechanism is similar to the one proposed by Kear et al. [6] for shearing y' precipitates in nickel-base alloys ; it can be termed a synchro-shear or equivalently a viscous slip mechanism. This model is then extended to any long period ordered alloys : it turns out that a packet of M superimposed 4 B6-partial dislocations has now to glide together on M adjacent layers in order to propagate in the next domain without destroying the chemical order.

3.1 DEFORMATION

Ag3Mg.

-

We consider a 2 AC dislocation ; it is perfect in a

[loo] domain but it is no more perfect in domains

with another orientation (see Table I). So it cannot

C7-50 G. VANDERSCHAEVE

propagate in the next domain where it would have to trail behind a high energy order fault.

Let the superperiod in the second domain be along [OOI]. The dislocation would rather dissociate under the applied stress into two partials according to the reaction

As the 2 6C partial ente:s the new domain, a low energy stacking fault is left behind. In the contrary, the second partial is stopped at the domain boundary, for it would have to trail behind a high energy order fault. This dissociation scheme should hold in any long period ordered alloy with a low stacking fault energy and accounts for the occurence of numerous stacking faults limited at domain boundaries, as observed in Cu3Pd [4, 51 and in Ag3Mg (Fig. 4).

FIG.

4. - Stacking faults limited at domain boundaries in Ag3Mg.

Note that a 2 6C dislocation cannot enter a third domain either [loo] or [OlO], without creating an order fault. It happens in Ag3Mg, because of the value M

2, that an alternative model is possible, based on propagation of 4 BG dislocations in any domain. Experiments show that deformation occurs by profuse twinning, as evidenced by characteristic serrations on the stress-strain curve, and by Berg- Barett topographs of deformed single crystal (Fig. 5).

It can be seen from Table I that 4 B6 dislocation can propagate in two different domains ; in the third one, it has to be turned into 4 B6 + AC. Deformation may then proceed as follows : Let be a source emitting 4 B6 dislocations on adjacent (1 11) planes ; they can move through [OlO] and [OOl] domains, but are stopped at the boundary with [I001 domain. However, they can nucleate AC/CA dipoles, so propagating both

FIG. 5. - Berg Barett topograph of a Ag3Mg deformed single crystal showing a profuse twinning. This topograph has been performed using a [400]* reflection, i. e. a diffraction vector active only in the matrix and for which twin lamellae do not

diffract and exhibit therefore another shade.

4 B6 + AC and 4 B6

AC together on two succes- sive layers. Of course, they leave their dipole at the exit boundary with the next domain. Repeating this mechanism on a number of adjacent planes results in a twin lamella extending through several domains without any destruction of the long range chemical order.

The activation energy involved in such mechanisms are discussed in this conference in ESCAIG's lecture.

I t should be noted that forming a dipole is just like rearranging atoms within the wall formed by 4 B6 dislocations. Once nucleated the dipole should glide together with the leading partial without any further need of atomic diffusion.

4 BG-dislocations are easily nucleated either by pole mechanism, or by recombination of a 2 6A dislocation (trailing a stacking fault in a [010] domain) with a perfect one 2 BC [3].

Summarizing, propagation of 213 < 112 > partials throughout the crystal needs pairing the partials together on two adjacent layers ; atomic rearrange- ment equivalent to dipole nucleation is required at certain domain boundaries. We extend now this model to other values of parameter M.

3 . 2 PROPAGATION

ALLOYS.

A similar mechanism may be proposed for some alloys with the DO,, structure (M = 1) such as Ni,V, Pd3Nb, Pd3Ta, etc ...

The arrangement of B atoms in close-packed planes

is rectangular and, as can be seen from Table I,

4 A6, 4 B6 and 4 C6 are now possible Burgers vectors

of dislocations leading pure geometrical stacking

faults whatever be the orientation of the super-

period. These dislocations can therefore propagate

in the whole crystal without any chemical obstacle

requiring dipole nucleation as it was the case for

PROPAGATION OF DISLOCATIONS IN LONG PERIOD ORDERED ALLOYS C7-51 M

2. Thus as for as plastic deformation is control-

led by propagation of these dislocations, twinning should be made easier without any need of thermal activation, even at low temperature.

We study now larger values of M. First, we examine the case M

3 and then we extend our conclusions to any value of M. For M

3, the propagation of 4 BS dislocations across [loo] domains may proceed as follows. Let be a triplet of 4 BS dislocations moving on three adjacent (1 11) planes through [OlO] and [001]

domains. The dislocations are stopped at boundary with [loo] domain, where they would have to trail behind an order plus stacking fault. However, they can nucleate some multipole, with net Burgers vector equal to zero, propagating 7 BS, 2 dB, 7 BS dislocations on three adjacent layers, according to the reactions

7 BS and 2 6B are allowed Burgers vectors of dislo- cations for leading geometrical fault in [loo] domain.

A triplet of 4 BS dislocations can therefore propagate in the whole crystal without destroying chemical order, provided that a multipole is nucleated at the boundary with a [loo] domain. Of course, they leave the multi- pole at boundary with a next domain, either [OlO]

or [OOl].

The same model should apply for any long period ordered alloy. Here M 4 BS-dislocations propagate into the whole crystal on M successive (1 11) planes.

The atomic rearrangement needed at boundary with [loo] domain is :

(1) M, odd :

' 4 B S ; + ( 3 M - 6 ) B S - + ( 3 M - 2 ) B S

4BS ; + 6 6 B -+ 2 6B

-+

2 6B

. . .

M layers

; . . . . . .

(2) M, even :

M layers

All these partials lead geometrical faults in a [I001 domain. From this geometrical point of view, defor- mation in long period ordered alloys should proceed as follows : a packet of M 4 BS partial dislocations has to glide together on M adjacent layers, leading a low energy stacking fault in two types of domains. In the third one, some atomic rearrangement in the form of multipole nucleation is needed within the slip lamella in order to keep unperturbated chemical order.

As a result three main plastic consequences follow from this model :

(1) The glide direction shifts from < 110 > to

< 112 > directions ; this situation has been already observed in superalloys, where deformation mecha- nisms are quite similar [6].

(2) Propagating 213 < ¹¹² > partials on a certain

number of successive (1 11) layers is in fact forming

a sort of twin lamella extending through several

domains. Moreover, once a twin lamella has started, it

should thicken rather easily ; for no more fault energy

is added as leading partials sweep down more and more

adjacent planes, only the same interface energy between

C7-52 G. VANDERSCHAEVE twin and matrix being involved. So, twinning and

clustering of slip lamellae might be an easy mode of deformation in these alloys. Available observations show, at least for superalloys and Ag,Mg ( M

2), that such a pairing process does occur readily on two adjacent layers, giving some reality to slip packets even thicker.

(3) The deformation in long period ordered alloys is propagated by 213 < 112 > dislocations, while in the disordered face centred cubic alloy, it involves slip of 112 < 110 > dislocations. The situations looks like comparing the twinning versus slip flow stress in usual face centred cubic crystals [7] : 213 < 112 > ^disloca-

tions are mainly cutting through a dislocations forest, the friction of which should be proportionnal to the value of the slip vector 4 B6

_J3 4 b - ^{2.3 b as com-}

pared to the disordered flow stress, which is propor- tional to b. This gives a flow stress ratio of 2.3, which is in good agreement with experimental data on stoechiometric Ag,Mg [8]. For Cu,Pd however, the experimental yield stress ratio is 1.15 [5], but there is no evidence there for a propagation of dislocations through many domains : the published micrographs show only stacking faults limited at domain bounda- ries, which is consistent with a deformation controlled by 113 < 112 > partial dislocations only (see sec- tion 3.1) ; in such a case, the Burgers vectors ratio is expected to be 2 / 4 3

1.15, in good agreement with experiment. In this case (4 < M < 7) the nucleations

of multipoles might require either a higher stress or a higher temperature, making the propagation of 413 < 112 > dislocation possibly less easy.

Other mechanisms are on the other hand concei- vable, like requiring the production and migration of a vacancy along every atomic row in the slip plane [9].

A dislocation 2 6B trailing a stacking fault in a [I001 domain cannot enter a [OlO] domain, where the shear vector should be turned into 2 6A. This requires in the slip plane an additional atomic displacement of 2 BA obtained by convenient vacancy jumps along every atomic row. However, such a vacancy production and migration process, occuring on each layer of the slip lamella, seems rather hard to imagine working smoothly ; moreover it should lead to a stress inde- pendent activation energy rather similar to a diffusion energy, contrary to the previous model and contrary also to experiments 191.

Finally, it should be noted that the size of ordered domains influence the mode of deformation. If the domains are to small (a few hundred angstroms large), the observed dissociation of dislocations may be some- what different : 112 < 110 > dislocation pairs would rather spread through many domains [2]. It is believed that in this case the order fault energy could become lower than the geometrical stacking fault energy.

Acknowledgement.

The author wishes to thank Prof. B. Escaig for stimulating discussions.

References

[I] VANDERSCHAEVE, G., Phys. Stat. Sol. 36 (1969) 103. [5] BUYNOV, L. N., SYUTKINA, V. I., SHASHKOV, 0 . D., YAKOV- [2] VANDERSCHAEVE, G., COULON, G., ESCAIG, B., Phys. Stat. Sol. LEVA, E. S., Fiz. Met.

Metalloved.

(1972) 1195.

(a) 9 (1972) 541. [6] KEAR, B. H., LEVERANT, G. R., OBLAK, J. M., Trans. ASM62 [3] VANDERSCHAEVE, ^G., ESCAIG, B., Phys. Stat. Sol. (a) 20 (1973) (1969) 639.

309. [7] FONTAINE, G., J. Physique

(1966) 201.

[4] BUYNOV, L. N., SYUTKINA, V. I., SHASHKOV, 0 . D., YAKOV- [8] GANGULEE, A., BEVER, M. B., Trans. AZME 242 (1968) 278.

LEVA, E. S., Fiz. Met.

Metalloved.

[9] GUIMIER, A., Thesis. University of Nancy, 1972.