Lesson_2 Behaviour of metals (4) - 3-3 Lattice Unit Cells...

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Packing Factor The packing factor is the fraction of space occupied by atoms, assuming that atoms are hard spheres sized so that they touch their closest neighbor. The general expression for the packing factor is: Packing factor ¼ ð number of atoms = cell Þð volume of each atom Þ volume of unit cell ð 3-4 Þ Example 3-3 illustrates how to calculate the packing factor for a FCC cell. EXAMPLE 3-3 Calculating the Packing Factor Calculate the packing factor for the FCC cell. SOLUTION In a FCC cell, there are four lattice points per cell; if there is one atom per lattice point, there are also four atoms per cell. The volume of one atom is 4 p r 3 = 3 and the volume of the unit cell is a 3 0 . Packing factor ¼ ð 4 atoms = cell Þ 4 3 p r 3 ± ² a 3 0 Since, for FCC unit cells, a 0 ¼ 4 r = ffiffi 2 p : Packing factor ¼ ð 4 Þ 4 3 p r 3 ± ² ð 4 r = ffiffi 2 p Þ 3 ¼ p ffiffiffiffiffi 18 p G 0 : 74 The packing factor of p = ffiffiffiffiffi 18 p G 0 : 74 in the FCC unit cell is the most e‰cient packing possible. BCC cells have a packing factor of 0.68 and SC cells have a packing factor of 0.52. Notice that the packing factor is independent of the radius of atoms, as long as we assume that all atoms have a fixed radius. The FCC arrangement represents a close-packed structure (CP) (i.e., the packing fraction is the highest possible with atoms of one size). The SC and BCC structures are relatively open. We will see in the next section that it is possible to have a hexagonal structure that has the same packing e‰ciency as the FCC structure. This structure is known as the hexagonal close-packed structure (HCP). Metals with only metallic bond- ing are packed as e‰ciently as possible. Metals with mixed bonding, such as iron, may have unit cells with less than the maximum packing factor. No commonly encountered
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  • Spring '14
  • Colombo
  • Physics, Material Science, Plastics, Manufacturing, Metals, Crystal system, Packing Factor

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