Close-packed structures

Use Eq. Ill-15 and related equations to calculate and the energy of vaporization of argon. Take m to be eo of Problem 6, and assume argon to have a close-packed structure of spheres 3.4 A in diameter. 

The ultimate covalent ceramic is diamond, widely used where wear resistance or very great strength are needed the diamond stylus of a pick-up, or the diamond anvils of an ultra-high pressure press. Its structure, shown in Fig. 16.3(a), shows the 4 coordinated arrangement of the atoms within the cubic unit cell each atom is at the centre of a tetrahedron with its four bonds directed to the four corners of the tetrahedron. It is not a close-packed structure (atoms in close-packed structures have 12, not four, neighbours) so its density is low. 

Sharp melting point - the regular close-packed structure results in most of the secondary bonds being broken down at the same time. 

From the electron micrographs, assuming that PVAc particles in the latex are the same size, the formation model of the porous film from the latex film can be illustrated as in Fig. 3 [19]. When the latex forms a dried film over minimum film-forming temperature, it is concluded that PVA coexisted in the latex and is not excluded to the outside of the film during filming, but is kept in spaces produced by the close-packed structure of PVAc particles. 

Martensitic phase transformations are discussed for the last hundred years without loss of actuality. A concise definition of these structural phase transformations has been given by G.B. Olson stating that martensite is a diffusionless, lattice distortive, shear dominant transformation by nucleation and growth . In this work we present ab initio zero temperature calculations for two model systems, FeaNi and CuZn close in concentration to the martensitic region. Iron-nickel is a typical representative of the ferrous alloys with fee bet transition whereas the copper-zink alloy undergoes a transformation from the open to close packed structure. ... 

For this particular system, the phonon branches are not investigated as yet but, based on the accumulated knowledge on other B2 materials transforming to close packed structures, one would expect a low lying [110] TAi branch in the B2 range, possibly with a dip at 1/2... 

Beryllium is a light metal (s.g. 1 -85) with a hexagonal close-packed structure (axial ratio 1 568). The most notable of its mechanical properties is its low ductility at room temperature. Deformation at room temperature is restricted to slip on the basal plane, which takes place only to a very limited extent. Consequently, at room temperature beryllium is by normal standards a brittle metal, exhibiting only about 2 to 4% tensile elongation. Mechanical deformation increases this by the development of preferred orientation, but only in the direction of working and at the expense of ductility in other directions. Ductility also increases very markedly at temperatures above about 300°C with alternative slip on the 1010 prismatic planes. In consequence, all mechanical working of beryllium is carried out at elevated temperatures. It has not yet been resolved whether the brittleness of beryllium is fundamental or results from small amounts of impurities. Beryllium is a very poor solvent for other metals and, to date, it has not been possible to overcome the brittleness problem by alloying. 

McLT78 McLarnen, T. J. The combinatorics of cation-deficient close-packed structures. J. Solid State Chem. 26 (1978) 235-244. 

A freshly prepared flame-annealed Au(100) surface has been found to be reconstmcted188,487,534,538 and the surface atoms exhibit a hexagonal close-packed structure to yield the (hex)-stmcture. One-directional long-range corrugation of 1.45 nm periodicity and 0.05 nm height has been found on the Au( 100) surface.188,488 When the reconstruction is lifted due to specific adsorption of SO - anions at more positive , the surface changes to a (1 x 1) structure.538... 

The surface of a single crystal of nickel, showing the regularity of its cubic close-packed structure. 

FIGURE 5.24 A close-packed structure can be built up in stages. The first layer (A) is laid down with minimum waste of space, and the second layer (B) lies in the dips—the depressions—between the spheres of the first layer. Each sphere is touching six other spheres in its layer, as well as three in the layer below and three in the layer above. 

To see how to stack identical spheres together to give a close-packed structure, look at Fig. 5.24. In the first layer (A) each sphere lies at the center of a hexagon of other spheres. The spheres of the second (upper) layer (B) lie in the dips of the first layer. The third layer of spheres will lie in the dips of the second layer, with the pattern repeating over and over again. 

Even in a close-packed structure, hard spheres do not fill all the space in a crystal. The gaps the interstices—between the atoms are called holes. To determine just how much space is occupied, we need to calculate the fraction of the total volume occupied by the spheres. 

To calculate the fraction of occupied space in a close-packed structure, we considei a ccp structure, e can use the radius of the atoms to find the volume of the cube and ow muc o t at volume is taken up by atoms. First, we look at how the cube is built rom t e atoms. In Fig. 5.29, we see that the corners of the cubes are at the centers of etg t atoms, n y 1/8 of each corner atom projects into the cube, so the corner atoms collectively contribute 8xi/S=1 atom to the cube. There is half an atom on each of t e six aces, so the atoms on each face contribute 6 X 1/2 = 3 atoms, giving four... 

The holes in the close-packed structure of a metal can be filled with smaller atoms to form alloys (alloys are described in more detail in Section 5.15). If a dip between three atoms is directly covered by another atom, we obtain a tetrahedral hole, because it is formed by four atoms at the corners of a regular tetrahedron (Fig. 5.30a). There are two tetrahedral holes per atom in a close-packed lattice. When a dip in a layer coincides with a dip in the next layer, we obtain an octahedral hole, because it is formed by six atoms at the corners of a regular octahedron (Fig. 5.30b). There is one octahedral hole for each atom in the lattice. Note that, because holes are formed by two adjacent layers and because neighboring close-packed layers have identical arrangements in hep and ccp, the numbers of holes are the same for both close-packed structures. 

Which close-packed structure—if either—is adopted by a metal depends on which has the lower energy, and that in turn depends on details of its electronic... 

FIGURE 5.32 The body-centered cubic (bcc) structure. This structure is not packed as closely as the others that we have illustrated. It is less common among metals than the close-packed structures. Some ionic structures are based on this model. 

Many metals have close-packed structures, with the atoms stacked in either a hexagonal or a cubic arrangement close-packed atoms have a coordination number of 12. Close-packed structures have one octahedral and tivo tetrahedral holes per atom. 

The value is farther from 8.93 g-cm-3, the experimental value, than that for a close-packed structure, 8.90 g-cm-3, and so we conclude that copper has a close-packed structure. 

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. 

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