Hexagonal crystals slip planes

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. 

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. 

Three independent slip systems are not sufficient for arbitrary deformations. For the hexagonal crystal, this is easily understood because shear deformation out of the common slip plane of the three systems is impossible. Therefore, other, more difficult, slip systems must be activated. Because real metals never show the ideal hexagonal structure, but possess either a stretched or a compressed unit cell (varying ratio <=/ ), it depends on the chemical element which other systems are activated. Table 6.3 gives a synopsis of the most important slip systems. The slip systems with the horizontal slip plane are called basal slip systems. If the slip planes are on the prism faces of the unit cell, they are called prismatic slip systems. The other slip systems are called pyramidal slip systems. 

Figure 3.26. Reciprocal mean effective resolved shear stress curves for Knoop indentation calculated for (a) 0001 (1120), (b) 1100 (U20>, (c) 3301 (1120), (d) U01 (1120), (e) 1210 <10l0) slip systems on (0001) planes of hexagonal crystals.

The structural representations shown in Fig. 3.2 are useful for visualizing the slip-planes that may exist in various metal crystal systems. For example, from the face-centered cubic (fee) lattice shown in Fig. 3.2a, it is easy to see how planes of atoms might slide rather easily over one another from the upper left to the lower right. This lattice also has several other such slip planes. While it is not readily apparent from the figure, a three-dimensional model of these crystal systems would show that the body-centered cubic (bcc) lattice offers the least number of slip planes of the three shown, and the hexagonal-close-packed (hep) system falls in between the fee and bcc systems. 

Since the number of slip systems is not usually a function of temperature, the ductility of face-centered cubic metals is relatively insensitive to a decrease in temperature. Metals of other crystal lattice types tend to become brittle at low temperatures. Crystal structure and ductility are related because the face-centered cubic lattice has more slip systems than the other crystal structures. In addition, the slip planes of body-centered cubic and hexagonal close-packed crystals tend to change at low temperature, which is not the case for face-centered cubic metals. Therefore, copper, nickel, all of the copper-nickel alloys, aluminum and its alloys, and the austenitic stainless steels that contain more than approximately 7% nickel, all face-centered cubic, remain ductile down to the low temperatures, if they are ductile at room temperature. Iron, carbon and low-alloy steels, molybdenum, and niobium, all body-centered cubic, become brittle at low temperatures. The hexagonal close-packed metals occupy an intermediate place between fee and bcc behavior. Zinc undergoes a transition to brittle behavior in tension, zirconium and pure titanium remain ductile. 

Slip in hexagonal metal crystals occurs mainly parallel to the basal plane of the unit cell, normal to the c axis. The slip systems can be described as 000 1 (1 1 20), of which there are three. Body-centred cubic metals have slip described by 1 1 0 (I 1 1), giving 12 combinations in aU. Other slip systems also occur in metals, but those described operate at lowest energies. 

As the name implies, the hexagonal close-packed crystal has the highest possible packing density. Its stacking sequence (cf. figure 1.9) differs from that of the face-centred cubic lattice. Only the 0001 -basal planes are close-packed. They contain the three (1120) close-packed directions, resulting in only three independent slip systems (figure 6.16). 

Figure 2.56. (a) The 111 <110> slip system for a face-centered cubic crystal. Note that there are 3 unique 111 planes, giving rise to 12 total slip systems fra-fee. (b) The (001 )<100> slip system fora hexagonal close-packed crystal. Shown is a 2 x 2 array of unit cells projected onto the (001) plane. Bold arrows indicate the three slip directions lying in each of the planes. 

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