Dislocation Velocity

Dislocation velocity depends on the purity of the crystal, applied shear stress, tem­perature, and dislocation type. Johnston and Gillman (1959) developed an expres­sion for the dislocation velocity in freshly grown lithium fluoride crystals. It was found that the edge dislocations travel about 50 times faster than screw disloca­tions. Studies on the close-packed FCC and HCP metals have revealed that the dis­location velocity approaches ~1 ms-1 at the critical resolved shear stress of the specific crystal. Dislocation velocities have been found to be a very strong function of applied shear stress as shown in Eq. (4.9):

Подпись: Figure 4.6 Dislocation velocity as a function applied stress in 3.25% Si containing iron from D.F. Stein and J.M. Low [28].

Vd = Atm’, (4.9)

Подпись: Observing Dislocations As mentioned previously, the concept of dislocations was first introduced by Taylor, Polanyi, and Orowan in 1930s. Following the discovery of dislocation, several theories were proposed supported by the indirect observation of dislocations. However, later with the advent of more sophisticated characterization techniques, the dislocations were directly observed and likewise related theories were rapidly developed. Almost all techniques used to visualize the dislocations utilize the strain field around the dislocations. Some methods are discussed very briefly. Etch Pit Technique This is one of the simplest chemical technique methods to observe dislocations indirectly. Dislocations intersecting the surface etch at a different rate than the surrounding matrix and the region appears as pits. An example of etch pits in a lithium fluoride crystal is shown in Figure 4.7. The relative position of the etch pits represents the location and number of dislocations. However, the etch pit method has serious limitation when the etch pits tend to overlap. That is why the etch pit technique is applicable only for a low dislocation density (106 cm-2).

where m’ is a material constant with values ranging from 1.5 to 40 for various types of materials and A is a constant. However, for pure crystals, m’ generally remains ~1 at 300 K and 4-12 at 77 K. At lower temperatures, dislocation velocity is higher compared to that at higher temperatures because phonons (lattice vibra­tions) are more at higher temperatures obstructing the dislocation velocity. The the­oretical maximum velocity of dislocation in a crystalline solid is the velocity of the transverse shear wave propagation. However, damping forces (related to phonons) are enhanced as the dislocation velocity reaches 1/1000 of the theoretical limit. Figure 4.6 illustrates the variation of dislocation velocity as a function of applied stress in an iron alloy containing 3.5% Si.

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Figure 4.7 An optical micrograph of etch pits produced on a lithium fluoride crystal [4].

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Decoration Technique

This is another type of chemical technique in which dopants are added to the crystal. By suitable heat treatment, these foreign atoms precipitate near the dis­location core and decorate the dislocations. Dislocations in KCl are revealed by adding AgCl to the melt prior to the crystal growth. An optical micrograph in Figure 4.8 shows silver particles decorating dislocations in KCl. This technique has been mainly used in ionic crystals.

Transmission Electron Microscopy

Transmission electron microscopy is the most powerful technique for direct visualization of dislocations. Transmission electron microscopes (TEM) use an electron beam in a high-vacuum environment to pass through the electron — transparent region (~100nm or so) of a thin foil specimen. Very high resolu­tions on the order of few angstroms can be easily achieved in advanced TEMs. Generally, a semester-long, stand-alone graduate course on TEM is offered in most research universities. The topic in itself is complex enough to be covered in a single paragraph. TEM is a versatile tool that can be used to detect not only the dislocations but also a host of other defects ranging from stacking faults, twins, voids, and so forth. The key to imaging dislocations with TEM is the way the electrons interact with the dislocation strain field, as illustrated inFigure 4.9b. Bragg’s law is the guiding principle behind the electron diffraction responsible for the dislocation contrast and specialized technique such as weak beam imaging is used to image dislocations with better clarity. A TEM micro­graph of the titanium alloy samples with a number of dislocations is shown in Figure 4.9a. There are several limitations of the TEM technique, including the limited sample volume that can be examined.

 

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Figure 4.8 An optical micrograph of a KCl crystal with dislocations decorated by silver due to the addition of AgCl [5].

 

Подпись: Figure 4.9 (a) Morphology of a dislocation pileup [6]. (b) The electron diffraction occurs differently near the plane of the edge dislocation compared to the dislocation-free crystal portion [3].
Подпись: X-Ray Diffraction Topography This is another technique of direct dislocation observation, albeit with much lower resolution. Figure 4.10 shows an X-ray diffraction topograph in a single crystal of silicon. Dislocation widths imaged are quite coarse (on the order of 1 pm). Hence, it is not possible to image dislocations of samples with dislocation density higher than 106cm~2. X-rays generally got higher penetration compared to the electrons. Thus, the specimen used is large single crystal oriented in such a way that strong reflections are obtained. The difference in the intensities of the diffracted X-rays when recorded as photomicrographs shows the dislocation structures, as depicted in Figure 4.10. Nowadays, this technique is not much used for characterizing dislocations.

4.2