Face close-packed structure

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... 

FCC. Face-centered cubic the FCC structure is a close-packed structure. 

When the atomic size ratio is near 1.2 some dense (i.e., close-packed) structures become possible in which tetrahedral sub-groups of one kind of atom share their vertices, sides or faces to from a network. This network contains holes into which the other kind of atoms are put. These are known as Laves phases. They have three kinds of symmetry cubic (related to diamond), hexagonal (related to wurtzite), and orthorhombic (a mixture of the other two). The prototype compounds are MgCu2, MgZn2, and MgNi2, respectively. Only the simplest cubic one will be discussed further here. See Laves (1956) or Raynor (1949) for more details. 

Figure 3.11 Cubic close-packed structure of face-centered cubic crystals such as copper as a packing of atom layers (a) a single close-packed layer of copper atoms (b) two identical layers, layer B sits in dimples in layer A (c) three identical layers, layer C sits in dimples in layer B that are not over atoms in layer A. The direction normal to these layers is the cubic [111] direction.

The sequence ABCABC... having a cubic symmetry is shown in Fig. 3.21. It is the cubic (face-centred cubic) close-packed structure, also described as cF4-Cu type structure. 

Figure 3.21. The face-centred cubic close-packed structure (Cu type). On the left a block of eight cells is shown (one cell darkened). On the right a section of the structure is presented it corresponds to a plane perpendicular to the cube diagonal. Notice that the plane is the same presented on the left in Fig. 3.19. The sequence of the layers in this structure is shown in Fig. 3.20 in comparison with other close-packed elemental structures.

Any study of colloidal crystals requires the preparation of monodisperse colloidal particles that are uniform in size, shape, composition, and surface properties. Monodisperse spherical colloids of various sizes, composition, and surface properties have been prepared via numerous synthetic strategies [67]. However, the direct preparation of crystal phases from spherical particles usually leads to a rather limited set of close-packed structures (hexagonal close packed, face-centered cubic, or body-centered cubic structures). Relatively few studies exist on the preparation of monodisperse nonspherical colloids. In general, direct synthetic methods are restricted to particles with simple shapes such as rods, spheroids, or plates [68]. An alternative route for the preparation of uniform particles with a more complex structure might consist of the formation of discrete uniform aggregates of self-organized spherical particles. The use of colloidal clusters with a given number of particles, with controlled shape and dimension, could lead to colloidal crystals with unusual symmetries [69]. 

Physical properties of the element are anticipated or calculated. Sdvery metal having two aUotropic forms (i) alpha form that should have a double hexagonal closed-packed structure and (ii) a face-centered cubic type beta form density 14.78 g/cm (alpha form), and 13.25 g/cm (beta form) melting point 985°C soluble in dilute mineral acids. 

Keep in mind that for close-packed structures, the atoms touch each other in all directions, and all nearest neighbors are equivalent. Let us first examine the HCP structure. Figure 1.17 is a section of the HCP lattice, from which you should be able to see both hexagons formed at the top and bottom of what is called the unit cell. You should also be able to identify the ABA layered structure in the HCP unit cell of Figure 1.17 through comparison with Figure 1.16. Let us count the number of atoms in the HCP unit cell. The three atoms in the center of the cell are completely enclosed. The atoms on the faces, however, are shared with adjacent cells in the lattice, which extends to infinity. The center atoms on each face are shared with one other HCP unit cell, either above (for the top face) or below (for the bottom face), so they contribute only half of an atom each to the HCP unit cell under consideration. This leaves the six corner atoms on each face (12 total) unaccounted for. These comer atoms are at the intersection of a total of six HCP unit cells (you should convince yourself of this ), so each comer atom contributes only one-sixth of an atom to our isolated HCP unit cell. So, the total number of whole atoms in the HCP unit cell is... 

Figure 1.24(c) shows a unit cell of a face-centred cubic structure. If a single atom is placed at each lattice point then this becomes the unit cell of the ccp (cubic close-packed) structure. Find the 100, 110, and the 111 planes and calculate the density of atoms per unit area for each type of plane. (Hint Calculate the area of each plane assuming a cell length a. Decide the fractional contribution made by each atom to the plane.)... 

Here we have briefly considered the structures for various combinations of P, T, and O layers. All patterns for ccp structures are shown in Figure 3.12. The face-centered cube is the same as the cubic close-packed structure. The two names stress particular features. The unit cell of a ccp structure is fee. The packing direction, the direction of stacking the close-packed layers, is along the body diagonals of the cube. The packing direction is vertical in Figures 3.6, 3.7, and 3.8. 

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