Dislocations and stacking faults in ordered structures

4.6.5 Dislocations and stacking faults in ordered structures

When the alloy orders, a unit dislocation in a disor- dered alloy becomes a partial-dislocation in the super- lattice with its attached anti-phase boundary interface, as shown in Figure 4.52a. Thus, when this dislocation

Figure 4.51 Dissociated a/2 [1 1 1 ] dislocation in the bcc moves through the lattice it will completely destroy lattice (after Mitchell, Foxall and Hirsch, 1963; courtesy of

the order across its slip plane. However, in an ordered Taylor and Francis) .

alloy, any given atom prefers to have unlike atoms as

Figure 4.52 Dislocations in ordered structures .

114 Modern Physical Metallurgy and Materials Engineering its neighbours, and consequently such a process of slip

movement of coupled pairs of a/2[1 1 1]-type disloca- would require a very high stress. To move a dislocation

tions. The combined slip vector of the coupled pair of against the force exerted on it by the fault requires

dislocations, sometimes called a super-dislocation, is then equivalent to a[1 1 1], and, since this vector con-

tor; in ˇ-brass where is about 0.07 N/m this stress nects like atoms in the structure, long-range order will is 300 MN/m 2 . In practice the critical shear stress of

be maintained.

ˇ -brass is an order of magnitude less than this value, The separation of the super-partial dislocations may and thus one must conclude that slip occurs by an

be calculated, as for Shockley partials, by equating the easier process than the movement of unit dislocations.

repulsive force between the two like a/2h1 1 1i disloca- In consequence, by analogy with the slip process in

tions to the surface tension of the anti-phase boundary. fcc crystals, where the leading partial dislocation of

The values obtained for ˇ-brass and FeCo are about 70 an extended dislocation trails a stacking fault, it is

and 50 nm, respectively, and thus super-dislocations believed that the dislocations which cause slip in an

can be detected in the electron microscope using the ordered lattice are not single dislocations but coupled

weak beam technique (see Chapter 5). The separation pairs of dislocations, as shown in Figure 4.52b. The

is inversely proportional to the square of the ordering first dislocation of the pair, on moving across the slip

parameter and super-dislocation pairs ³12.5 nm width plane, destroys the order and the second half of the

have been observed more readily in partly ordered couple completely restores it again, the third disloca-

FeCo ⊲S D 0.59⊳. tion destroys it once more, and so on. In ˇ-brass 1 and In alloys with high ordering energies the antiphase boundaries associated with super-dislocations cannot similar weakly-ordered alloys such as AgMg and FeCo

be tolerated and dislocations with a Burgers vector the crystal structure is ordered bcc (or CsCl-type) and,

equal to the unit lattice vector ah1 0 0i operate to pro- consequently, deformation is believed to occur by the

duce slip in h1 0 0i directions. The extreme case of this is in ionic-bonded crystals such as CsBr, but strongly-

ordered intermetallic compounds such as NiAl are also When disordered, the slip vector is a/2[1 1 1], but this

1 Chapter 3, Figure 3.40, shows the CsCl or L 2 O structure.

observed to slip in the h1 0 0i direction with disloca- vector in the ordered structure moves an A atom to a B site.

tions having b D ah1 0 0i.

The slip vector to move an A atom to an A site in twice the Ordered A 3 B-type alloys also give rise to super- length and equal to a[1 1 1].

dislocations. Figure 4.53a illustrates three ⊲1 1 1⊳

Figure 4.53 (a) Stacking of ⊲1 1 1 ⊳ planes of the L1 2 structure, illustrating the apb and fault vectors, and (b) schematic representation of super-dislocation structure .

Defects in solids 115 layers of the Ll 2 structure, with different size atoms

together in pairs. However, because the distribution for each layer. The three vectors shown give rise

of neighbouring atoms is not random the passage to the formation of different planar faults; a/2[1 0 1]

of a dislocation will destroy the short-range order is a super-partial producing apb, a/6[2 1 1] produces

between the atoms, across the slip plane. As before, the familiar stacking fault, and a/3[1 1 2] produces a

the stress to do this will be large but in this case there super-lattice intrinsic stacking fault (SISF). A [1 0 1]

is no mechanism, such as coupling two dislocations super-dislocation can therefore be composed of either

together, to make the process easier. The fact that, for instance, a crystal of AuCu 3 in the quenched

[1 0 1] ! state (short-range order) has nearly double the yield [1 0 1] C apb on ⊲1 1 1⊳ C

2 2 strength of the annealed state (long-range order) may or

be explained on this basis. The maximum strength is exhibited by a partially-ordered alloy with a critical

[1 0 1] ! [1 1 2] C SISF on ⊲1 1 1⊳ C [2 1 1] domain size of about 6 nm. The transition from

3 3 deformation by unit dislocations in the disordered state to deformation by super-dislocations in the ordered

Each of the a/2[1 0 1] super-partials may also dis- condition gives rise to a peak in the flow stress with sociate, as for fcc, according to

change in degree of order (see Chapter 6).

a a a [1 0 1] ! [2 1 1] C [1 1 2].