Slip face-centred cubic

Let us assume that the particles pack as either an ordered hexagonal or face-centred cubic lattice. Both arrays yield identical results in the following analysis. There is definite evidence for the latter from light diffraction and small angle neutron scattering studies (Ottewill, 1980). The case of a hexagonally closed packed array is shown in Fig. 13.6. We will assume the complete absence of defects, which may well be very important in actual compression studies. We will calculate the pressure on one side of a hypothetical plane inserted into the lattice along a slip-plane. 

The preferred slip plane in ionic crystals with the halite (NaCl) structure, such as NaCl or LiF, is 110, and the slip direction used is (110). This slip system is sketched in Figure 10.17. For the more metallic halite structure solids such as titanium carbide (TiC), the slip system is similar to that in face-centred cubic metals, 1 1 1 (110). 

The face-centred cubic crystal is close-packed (see section 1.2.2). Planes of type 111 and directions of the type (110) are close-packed and thus form the slip systems (figure 6.14). If we consider planes as identical differing only... 

Fig. 6.14. Slip systems in face-centred cubic metals. The slip planes are the body diagonals the slip directions lie on the plane diagonals or on the edges of the octahedron in figure (c), respectively...

Table 6.1. Slip systems in face-centred cubic metals...

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). 

If we consider the Peierls force from section 6.2.9 as obstacle, it can also be overcome by thermal activation. This is especially relevant if the Peierls force is large i. e., when slip is along planes that are not close-packed, for example in body-centred cubic lattices. For this reason, the yield strength of body-centred cubic lattices is strongly dependent on the temperature, different from face-centred cubic metals (figure 6.29). The Peierls stress can reach values of up to several hundred megapascal. 

In a face-centred cubic metal h = a/VS and b = /V6 where a is the lattice parameter and so the theoretical shear strength is predicted to be (Tu—G/9. For chain direction slip on the (020) planes in the polyethylene crystal b = 2.54 A and h is equal to the separation of the (020) planes which is 2.47 A. The theoretical shear stress would be expected to be of the order of G/6. However, more sophisticated calculations of Equation (5.31) lead to lower estimates of which come out to be of the order of G/30 for most materials. Even so, this estimate of the stress required to shear the structure is very much higher than the values that are normally measured and the discrepancy is due to the presence of defects such as dislocations within the crystals. The high values are only realized for certain crystal whiskers and other perfect crystals. 

On the other hand, Cgo is a type of fullerene with a highly spherical molecular structure. The spherical molecules crystallise at room temperature in the form of a face-centred cubic (fee) structure with Cgo molecules at eight comers and six centres of a cube (Fig. 14.2). The Cgo crystal has unique mechanical properties owing to its highly symmetrical fee stmcture. Similar to common metals, the 111 <110> slip system allows the deformation of Cgo crystals. The elongation of a nanocrystalline Cgo specimen (approximately 50 nm in grain size) is larger... 

Fig. 3.7. Cubic model of a redox-linlced proton pump. OX and RED denote a redox centre in the oxidised and reduced state. The bar marked M or C next to OX and RED indicates an acidic group, the function of which is linked to the redox centre. M and C mean that the group is connected protonically either with the aqueous matrix or cytoplasmic phases, respectively. When the group is protonated the bar is supplemented with H. Left and right faces of the cube separate states in electronic and protonic contact with the input and output sides of the transducer, respectively. Allowed transitions between these are indicated by thick arrows. Dotted lines denote forbidden transitions. If the latter gain significant probability relative to allowed transitions proton transport becomes decoupled from electron transfer (so-called slipping ). (From Ref. 8.)...

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