Factors affecting the dissociation width of dissociated dislocations in FCC metals and alloys

Abstract

Dislocations in FCC structure are dissociated into two partial dislocations. The dissociation width of a dissociated dislocation controls the mechanical behavior of the alloy. Experimental work using transmission electron microscopy on factors determining the dissociation width is reviewed with special reference to the Suzuki segregation.

Appendix practice of weak-beam dark-field (WBDF) technique

In the normal bright-field (BF) or dark-field (DF) imaging, dislocation images have widths of typically >10.0 nm [41]. Under the WBDF technique, the detail observable is five to ten times finer than in normal two-beam conditions.

The practical procedures are as follows (Fig. 32a) [42].

Fig. 32

Schematic diagram illustrating the change in the diffraction conditions for BF (a) and for WBDF [42] (b)

• 1. First, in the BF mode, tilt a specimen so as to satisfy the Bragg condition for the reflection vector g. Kikuchi lines for g (the broad full lines) pass through the direct spot (0) and the spot of g.

• 2. Next, switch to the DF mode and deflect the direct beam to the position of −g in the previous BF mode. At this stage, because the crystal is not tilted, the Kikuchi lines do not move, but the diffraction spots move and now 3g is excited instead of g (Fig. 32b).

This mode is called (g/3g) condition. Figure 33a, b shows examples of diffraction patterns in the BF and WBDF conditions, respectively.

Fig. 33

Diffraction patterns in BF (a) and in WBDF in (g/3g) mode (b). Crosses show the optical axes. Objective aperture is to be inserted at the cross [42]

In this condition, the deviation parameter s _g is given by

$$ \left| {{\mathbf{s}}_{g} } \right| = \frac{{(n - 1)\left| {{\mathbf{g}}*} \right|^{2} }}{{2\left| {\mathbf{k}} \right|}} , $$

(8)

where |k| = 1/λ, n = 3 (because 3g is excited).

The actual separation of partial dislocations (Δ) is given from the experimental separation Δ_obs according to the equation proposed by Cockayne et al. [43].

$$ \Delta_{\text{obs}} = \left[ {\Delta^{2} + \frac{{\left( {a + b} \right)^{2} }}{{a^{2} b^{2} }} + \frac{{2\left( {a + b} \right)\Delta }}{ab} - \frac{4\Delta }{a}} \right]^{1/2}, $$

(9)

where

$$ a = - s_{g} /\left[ {\frac{{\mathbf{g}}}{2\pi }\left( {{\mathbf{b}}_{1}^{p} + \frac{{{\mathbf{b}}_{1e}^{p} }}{{2\left( {1 - \nu } \right)}}} \right)} \right] $$

and

$$ b = - s_{g} /\left[ {\frac{{\mathbf{g}}}{2\pi }\left( {{\mathbf{b}}2^{p} + \frac{{{\mathbf{b}}_{2e}^{p} }}{{2\left( {1 - \nu } \right)}}} \right)} \right] $$

${\mathbf{b}}_{\text{ie}}^{\text{p}}$ being the edge component of the ith partial and ν Poisson’s ratio.

It is noted that the Shockley partials are not always visible. Suppose that dissociated dislocation of b = 1/2[1$\bar{1}$0] is imaged in g = 2$\overline{2}$0. In this case, both partials 1 and 2 are visible because g. b = 1 for each partial (Fig. 34a). But in g = 0$\bar{2}$2 only partial 1 is visible (Fig. 34b) and in g = $\bar{2}$02 only partial 2 is visible (Fig. 34c).

Fig. 34

Typical WBDF micrographs of a dissociated dislocation. In a both partials, 1 and 2 are visible. In b, only partial 1 is visible and in c only partial 2 is visible [42]. Reproduced from [42]

Another important point is that caution must be paid to discriminate from a dipole. In a dissociated dislocation, one of the Shockley partials appears stronger than the other. In Fig. 35a, the upper partial is stronger than the lower partial. If imaged in −g (Fig. 35b) the reverse is true. On the other hand, in the case of a dipole, both of the two dislocations comprising the dipole are either strong or weak. In Fig. 36a, A and C appear weak, while B appears strong. On the other hand, in Fig. 36b, the reverse is true. Also, the separation of A is larger in Fig. 36a than in Fig. 36b.

Fig. 35

WBDF micrographs of a dissociated dislocation imaged in +g (a) and in –g (b). Note the asymmetry in the contrast of the partials on the reversal of the sign of g [42]. Reproduced from [42]

Fig. 36

WBDF micrographs of closely spaced dislocation dipoles A, B, and C imaged in +g (a) and in –g (b). Note the change in the contrast of the dipoles and the individual component separation on the reversal of the sign of g [42]. Reproduced from [42]

This difference is explained using Fig. 37 [4, 42], which shows schematically the bending of lattices around individual Shockley partials of a dissociated dislocation (a, b) and the individual components of an edge dislocation dipole (c, d). The Burgers vectors b of the dislocation are defined according to FS/RH (perfect) convention, with the positive dislocation line direction (ζ) into the paper. Therefore, it is recommended to image the same dislocation in both +g and −g, to distinguish between a dissociated dislocation and a closely spaced dislocation dipole.

Fig. 37

Schematic diagrams illustrating contrasts of Shockley partials of a dissociated dislocation on the reversal of the sign of g (a, b) and that of a closely spaced dislocation dipole (c, d) [3, 42]. Reproduced from [42] and [3]