Close-packed planes, directions

An analogy to sHp dislocation is the movement of a caterpillar where a hump started at one end moves toward the other end until the entire caterpillar moves forward. Another analogy is the displacement of a mg by forming a hump at one end and moving it toward the other end. Strain hardening occurs because the dislocation density increases from about 10 dislocations/cm to as high as 10 /cm. This makes dislocation motion more difficult because dislocations interact with each other and become entangled. SHp tends to occur on more closely packed planes in close-packed directions. 

Characteristically, glasses are brittle solids which in practice break only under tension. The ionic and directional nature of the bonds and the identification of electrons with particular pairs of atoms preclude bond exchange. This, coupled with the random nature of the atomic lattice, i.e. the absence of close-packed planes, makes gross slip or plastic flow impossible. 

Fig. 20.26 (a) Single close-packed sheet of atoms, with the close-packed directions arrowed and (b) stacking of three close-packed planes of atoms, showing aba and abc positions... 

The differing malleabilities of metals can be traced to their crystal structures. The crystal structure of a metal typically has slip planes, which are planes of atoms that under stress may slip or slide relative to one another. The slip planes of a ccp structure are the close-packed planes, and careful inspection of a unit cell shows that there are eight sets of slip planes in different directions. As a result, metals with cubic close-packed structures, such as copper, are malleable they can be easily bent, flattened, or pounded into shape. In contrast, a hexagonal close-packed structure has only one set of slip planes, and metals with hexagonal close packing, such as zinc or cadmium, tend to be relatively brittle. 

We have mentioned above the tendency of atoms to preserve their coordination in solid state processes. This suggests that the diffusionless transformation tries to preserve close-packed planes and close-packed directions in both the parent and the martensite structure. For the example of the Bain-transformation this then means that 111) -> 011). (J = martensite) and <111> -. Obviously, the main question in this context is how to conduct the transformation (= advancement of the p/P boundary) and ensure that on a macroscopic scale the growth (habit) plane is undistorted (invariant). In addition, once nucleation has occurred, the observed high transformation velocity (nearly sound velocity) has to be explained. Isothermal martensitic transformations may well need a long time before significant volume fractions of P are transformed into / . This does not contradict the high interface velocity, but merely stresses the sluggish nucleation kinetics. The interface velocity is essentially temperature-independent since no thermal activation is necessary. 

The mechanism for the transformation from 7-Fe203 to a-Fe203 has been proposed [29] to involve associated movements of the oxygen close packed planes in the (112) direction of the f.c.c. lattice and of Fe3+ ions so that the tetrahedral ions in 7-Fe203 move into vacant octahedral sites. 

Plasticity. Slip, the gliding motion of full planes of atoms or partial planes, called dislocation, allows for the deformation processing of polycrystalline metals (forging, extrusion, rolling, swaging, and drawing). Slip occurs much more readily across close-packed planes in close-packed directions. 

Slip occurs along specific crystal planes (slip planes) and in specific directions (slip directions) within a crystal structure. Slip planes are usually the closest-packed planes, and slip directions are the closest-packed directions. Both face-centered-cubic (FCC) and hexagonal-close packed (HCP) structure are close packed structures, and slip always occurs in a close packed direction on a closepacked plane. The body-centered-cubic (BCC) structure is not, however, close packed. In a BCC system, slip may occur on several nearly close packed planes or directions. Slip planes and directions, as well as the number of independent slip systems (the product of the numbers of independent planes and directions), for these three structures are listed in Table 7.2. 

Experimentally, it is observed that shp most readily occurs on close-packed planes in close-packed directions. The total strain of a dislocation is proportional to... 

Figure 10.7. The three close packed directions in the close-packed planes of the CCP lattice (a), and HCP lattice (b). The lightly shaded spheres, completing the hexagonal coordination around the sphere at the corner of the cubes, are in neighboring unit cells.

Body-centered cubic metals contain no close-packed planes, but do contain four close-packed directions, the four [111] body diagonals of the cube. The most nearly close-packed planes are those of the 1 10 set. In BCC crystals, slip has been observed in the [1 I 1] directions on the [1 10], [1 12], and 12 3 planes, but that, attributed to the latter two planes, may be considered the resultant of slip on several different (1 1 0) type planes (Weertman and Weertman, 1992). The von Mises criterion is satisfied, but higher shearing stresses than those of CCP metals are normally requited to cause slip in BCC metals. As a result, most BCC metals are classified as semibrittle. 

What is the most dense crystal packing that can be achieved To answer this question, constrnct a crystal by first pntting down a plane of atoms with the highest possible density, shown in Fignre 21.14a. Each sphere is in contact with six other spheres in the plane. Then pnt down a second close-packed plane on top of the first one (see Fig. 21.14b) in snch a way that each sphere in the second plane is in contact with three spheres in the plane below it that is, each sphere in the second plane forms a tetrahedron with three spheres beneath. When the third plane is laid down, there are two possibilities. In Fignre 21.14c, the atoms in the third plane lie on sites not directly over those in the first layer, whereas in Fignre 21.14d the third-plane atoms are directly over the first-plane atoms. 

Another apparent anomaly in the plastic behaviour of ice is the absence of any preferred glide direction in the basal plane. Metals glide preferentially in the most closely packed direction of the most closely packed plane and we might expect similar preference for glide in the directions in ice, since the necessary dislocations exist. Instead of his, the glide is nearly isotropic in the... 

The best fit (Fig. 1) of simulated pattern to the experimental XRD pattern was obtained when CdS nanoparticles were modeled as hexagonal prisms. Nanoparticles with a disordered structure and aspect ratio of 1.6 are optimal for this fit. The height of such nanoparticles is about 3 nm. The axis of the prism coincides with the direction of stacking of the close-packed planes. 

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