تكملة 3  body-centered cubic (BCC):
Another common metallic crystal structure also has a cubic unit cell with atoms
located at all eight corners and a single atom at the cube center. This is called a
body-centered cubic (BCC) crystal structure. A collection of spheres depicting this
crystal structure is shown in Figure 3.2c, whereas Figures 3.2a and 3.2b are diagrams of BCC unit cells with the atoms represented by hard sphere and reduced-sphere models, respectively. Center and corner atoms touch one another along cube diagonals, and unit cell length a and atomic radius R are related through
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MSC. Baraa .h.hadi Notes Engineering Material 2016
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Chromium, iron, tungsten, as well as several other metals listed in Table 1.1 exhibit
a BCC structure.
Two atoms are associated with each BCC unit cell: the equivalent of one atom from the eight corners, each of which is shared among eight unit cells, and the single center atom, which is wholly contained within its cell. In addition, corner and center atom positions are equivalent. The coordination number for the BCC crystal structure is 8; each center atom has as nearest neighbors its eight corner atoms.
Since the coordination number is less for BCC than FCC, so also is the atomic packing factor for BCC lower—0.68 versus 0.74. The Hexagonal Close-Packed Crystal Structure:
(HCP); an assemblage of several HCP unit cells is presented in Figure 3b.1 The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center. Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes. The atoms in this mid plane have as nearest neighbors atoms in both of the adjacent two planes. The equivalent of six atoms is contained in each unit cell; one-sixth of each of the 12 top and bottom face corner atoms, one-half of each of the 2 center face atoms, and all 3 mid plane interior atoms. If a and c represent, respectively, the short and long unit cell dimensions of Figure 3.3a, the c_ a ratio should be 1.633; however, for some HCP metals this ratio deviates from the ideal value.
The coordination number and the atomic packing factor for the HCP crystal structure are the same as for FCC: 12 and 0.74, respectively .The HCP metals include cadmium, magnesium, titanium, and zinc; some of these are listed in Table1.1
MSC. Baraa .h.hadi Notes Engineering Material 2016
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