TABLE3.3.c/a ratios for some HCP metals
Cd 1.886
Zn 1.856
Mg 1.624
Zr 1.590
Ti 1.588
Be 1.586
pointing out that there are no close-packed planes in BCC ma-terials. Slip has to occur, therefore, in “near close-packed” slip systems, and there are 48 of them available. (More precisely, the slip directions are close-packed but the slip planes are not.) As a consequence, not only one, but several of these slip systems may be activated simultaneously when applying a force in a chosen direction. (Examples for those slip systems are {110} 具111典 or {112} 具111典 or {321} 具111典.) This results quickly in the mutual blocking of the dislocation movements and therefore in less duc-tility. By the same token, the mutual interaction of dislocation motions leads to a strengthening of the material. BCC metals are therefore strong but still somewhat ductile.
This explanation was revised in the 1970s as a result of the just-mentioned detailed investigations involving the temperature-dependence of the critical resolved shear stress of extremely pure, single crystalline, BCC metals. A strong sensitivity to interstitially dissolved impurity atoms, the existence of different strengthen-ing mechanisms at low and high temperatures, and an orienta-tion dependency of 0also have been found for BCC metals. Ad-ditionally, electron microscopy studies have been conducted which revealed that screw dislocations (see below), rather than edge dislocations (as in FCC and HCP metals), are predominantly involved when plastically deforming BCC metals. Even though this information has been available in the literature for about 20 years, it has not entered many general textbooks because of the complexity of the mechanisms involved. A few explanatory words may help to elucidate this issue.
Up to this point, we only discussed the edge dislocation which we described as a straight line perpendicular to its Burgers vec-tor. Generally, however, dislocation lines are curved [see Figure 3.24(b)]; that is, they may change their direction in the slip plane with respect to the Burgers vector. Thus, the case may occur where the dislocation line is parallel (or antiparallel) to its Burg-ers vector. The latter represents a screw dislocation [Figure 3.24(a)]. Specifically, a screw dislocation can be described by cutting a cylindrical crystal halfway along its length axis to its center. The opening is then displaced parallel to the axis by one atomic distance (i.e., by the Burgers vector) as depicted in Fig-ure 3.24(a). This results in a spiral plane which winds in a heli-cal form around an axis, that is, around the dislocation line. The screw dislocation was proposed in 1939 by J.M. Burgers. The in-volvement of screw dislocations is not restricted to BCC metals only.
Screw
Dislocation
In general, dislocations are thought to be composed of an edge part, and a screw part and are then called mixed dislocations.
If the edge part is larger, the dislocation is termed edge-like; in the other case, it is called screw-like.
As just mentioned, plastic deformation of BCC metals below the characteristic temperature Tc is predominantly governed by the movement of screw dislocations, involving the 1/2 具111典 Burg-ers vector. Screw dislocations have, however, no unique slip plane (as edge dislocations) since b and L are parallel to each other (Figure 3.24). As a result, a number of slip planes are possible.
For BCC metals, the mobility of a screw dislocation is small and decreases even further at lower temperatures. Moreover, the shape of the core of a screw dislocation possesses a threefold symmetry in the 具111典 direction of its Burgers vector. This three-dimensionality prevents the dislocations from moving easily.
However, when heat-induced thermal vibrations of the core atoms are involved, the dislocation movement is enhanced. In other words, the motion of screw dislocations in BCC metals is FIGURE3.24.Schematic representations of (a) a screw dislocation and (b) mixed dislocations for which the edge and the screw dislocations are extreme cases.
(a) (b) b
b
b
Dislocation line
Screw dislocation
Edge dislocation
⬜
Dislocation line
Dislocation core
Mixed
Dislocations
a thermally activated process that is similar to atomic diffusion (see Chapter 6). It should be added that screw dislocations may frequently change their glide planes during motion. This explains why a large number of slip systems are observed experimentally.
Some refinements to the above-stated general rules should be men-tioned at this point which are valid for all lattice types discussed so far. First, heating a solid may activate additional slip systems.
Second, additions of substitutional elements that have consid-erably larger or smaller atomic diameters than the host material distort the lattice. As a consequence, they may cause some ob-stacles for the movement of dislocations and thus some increase in yield stress (see Chapter 5).
Third, vacancies, interstitial atoms, other dislocations, bound-aries between individually oriented grains, stacking faults, and other lattice defects may influence, in various degrees, the move-ment of dislocations, thus exercising an influence on strength and ductility. As an example, a portion of a moving dislocation line
(a)
FIGURE3.25.(a) Schematic representa-tion of dislocarepresenta-tion multiplication by pin-ning of dislocations at lattice defects, as pro-posed by Frank and Read. (b) Electron mi-crograph of disloca-tion loops. (Si ion–implanted Si, an-nealed 800°C for 30 min.) Courtesy of Prof. K. Jones, Univer-sity of Florida.
Refinements
(b)
may be pinned at its ends in particular by intersecting disloca-tions. As a consequence, the center of the dislocation line bows out under continued stress until eventually a dislocation loop and a new pinned dislocation are formed, as depicted in Figure 3.25.
A dislocation line, thus, behaves like a flexible violin string which can be bent by an applied force. The bending changes the angle between the line direction L and the Burgers vector b.
A continuous dislocation multiplication mechanism as depicted in Figure 3.25(a) is called a Frank–Read source (after its in-ventors). The process may be repeated up to several hundred times until the source is blocked, i.e., until the loops cannot ex-tend any further. Dislocation sources such as the Frank–Read