Fee materials

Figure Bl.21.1 shows a number of other clean umeconstnicted low-Miller-index surfaces. Most surfaces studied in surface science have low Miller indices, like (111), (110) and (100). These planes correspond to relatively close-packed surfaces that are atomically rather smooth. With fee materials, the (111) surface is the densest and smoothest, followed by the (100) surface the (110) surface is somewhat more open , in the sense that an additional atom with the same or smaller diameter can bond directly to an atom in the second substrate layer. For the hexagonal close-packed (licp) materials, the (0001) surface is very similar to the fee (111) surface the difference only occurs deeper into the surface, namely in the fashion of stacking of the hexagonal close-packed monolayers onto each other (ABABAB.. . versus ABCABC.. ., in the convenient layerstacking notation). The hep (1010) surface resembles the fee (110) surface to some extent, in that it also...

The simple cubic crystal structure we discussed above is the simplest crystal structure to visualize, but it is of limited practical interest at least for elements in their bulk form because other than polonium no elements exist with this structure. A much more common crystal stmcture in the periodic table is the face-centered-cubic (fee) structure. We can form this structure by filling space with cubes of side length a that have atoms at the corners of each cube and also atoms in the center of each face of each cube. We can define a supercell for an fee material using the same cube of side length a that we used for the simple cubic material and placing atoms at (0,0,0), (0,g/2,g/2), (g/2,0,g/2), and (g/2,g/2,0). You should be able to check this statement for yourself by sketching the structure. 

This surface is therefore the (111) surface. This surface is an important one because it has the highest possible density of atoms in the surface layer of any possible Miller index surface of an fee material. Surfaces with the highest surface atom densities for a particular crystal structure are typically the most stable, and thus they play an important role in real crystals at equilibrium. This qualitative argument indicates that on a real polycrystal of Cu, the Cu(l 11) surface should represent a significant fraction of the crystal s surface total area. 

Figure 4.7 shows top-down views of the fee (001), (111), and (110) surfaces. These views highlight the different symmetry of each surface. The (001) surface has fourfold symmetry, the (111) surface has threefold symmetry, and the (110) has twofold symmetry. These three fee surfaces are all atomically flat in the sense that on each surface every atom on the surface has the same coordination and the same coordinate relative to the surface normal. Collectively, they are referred to as the low-index surfaces of fee materials. Other crystal structures also have low-index surfaces, but they can have different Miller indices than for the fee structure. For bcc materials, for example, the surface with the highest density of surface atoms is the (110) surface. 

In the example above, we placed atoms in our slab model in order to create a five-layer slab. The positions of the atoms were the ideal, bulk positions for the fee material. In a bulk fee metal, the distance between any two adjacent layers must be identical. But there is no reason that layers of the material near a surface must retain the same spacings. On the contrary, since the coordination of atoms in the surface is reduced compared with those in the bulk, it is natural to expect that the spacings between layers near the surface might be somewhat different from those in the bulk. This phenomenon is called surface relaxation, and a reasonable goal of our initial calculations with a surface is to characterize this relaxation. 

Faulting can be treated according to different approaches.Within the limit of small probabilities, twin (P) and deformation (a) faults in fee materials can be dealt with using a corrected version of Warren s theory,leading to the following expressions for the real and imaginary parts of the FT ... 

Silicon will serve as the paradigmatic example of slip in covalent materials. Recall that Si adopts the diamond cubic crystal structure, and like in the case of fee materials, the relevant slip system in Si is associated with 111 planes and 110> slip directions. However, because of the fact that the diamond cubic structure is an fee lattice with a basis (or it may be thought of as two interpenetrating fee lattices), the geometric character of such slip is more complex just as we found that, in the case of intermetallics, the presence of more than one atom per unit cell enriches the sequence of possible slip mechanisms. 

In this section, our aim is to compute the core geometry associated with a dissociated dislocation in an fee material. Our model will be founded upon a... 

Using the Johnson potential, determine the structure of the dislocation core in an fee material. Consider a conventional edge dislocation on the (111) plane with a [112] line direction. For a computational cell use a large cylinder in which the atoms in an annular region at the edge of the cell are frozen in correspondence with the Volterra solution. 

Energetics of Surfaces Using Pair Functionals Use the Johnson embedded-atom analysis to compute the energies of the (111) and (110) surfaces in fee materials. Carry out a ranking of the relative magnitudes of the (100), (110) and (111) surfaces using these potentials. 

Atomic-scale modeling of cross slip in fee materials... 

Rafii-Tabar, H., Shodja, H.M., Darabi, M. Dahi,A. Moleculardynamics simulation of crack propagation in fee materials containing clusters of impurities. Mech. Mater. 38 (2006), pp. 243-252. 

As stated, stretch blow molding is stretching fee parison or preform in both fee axial direction and fee hoop direction wife fee material in fee parisons or preforms temperature in fee orientation temperatures for the specific material to orient, and to blow it into a container shape at this temperature. 

Other hydrogen-dislocation interactions at the corrosion fatigue crack tip must be taken into account. One can show, for instance, that hydrogen promotes planar slip in fee materials. Cross-slip ability can be discussed for the peculiar situation of the dissociation of a perfect screw dislocation into two mixed partials separated by a stacking fault ribbon (Fig. 20). The cross-slip probability depends on the work necessary for recombination. 

A summary of the reported crystallographic data for californium metal is given in Table 11.3. Based on an extrapolation of data for trivalent americium, curium, and berkelium metals, californium metal would be expected to have a double hexagonal close-packed (dhcp) low-temperature phase, with parameters of approximately Oq = 0.34 and Cq = 1.10 nm, and a face-centered cubic (fee) high-temperature phase with an Oq 0.49 nm. Based on other extrapolations [75], a divalent form of californium metal would be expected to be cubic and have a larger lattice parameter than a trivalent cubic form. From the values in Table 11.3, the dhcp form with parameters Uq = 0.3384 and c = 1.1040 nm [71,72] is accepted to be the low-temperature form of trivalent californium metal. The fee material, with a = 0.494 nm [72], is very likely a high-temperature form of the trivalent metal, comparable to the fee forms of americium, curium, and berkelium metals. The second fee structure listed in Table 11.3, with Oo = 0.574 nm [70,72], has been observed by other workers using different preparative techniques. 

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