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):
Vd = Atm’, (4.9)
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.
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].
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4.2