Packing Factor
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This document discusses packing factors for different crystal structures. It defines packing factor as the fraction of space occupied by atoms in a unit cell, assuming hard spheres. Simple cubic structure has a packing factor of 0.52 or 52%. Body centered cubic (BCC) has two atoms per unit cell, a packing factor of 0.68 or 68%. Face centered cubic (FCC) has four atoms per unit cell and the highest packing factor of 0.74 or 74%. Materials properties depend on their crystal structure and packing efficiency.
Packing Factor
- 2. Packing factor The packing factor or atomic packing fraction is the fraction of space occupied by atoms, assuming that the atoms are hard spheres. Expression to calculate packing factor is =(No. of atoms/unit cell)(volume of each atom) volume of a unit cell
- 3. Unit cell The unit cell is subdivision of a lattice that still retain the overall characteristics of the entire lattice. A lattice is a collection of point called lattice point which are arranged in a periodic pattern.
- 4. Number of atoms per unit cell A specific number of lattice points define each of the unit cell. For example the corner of the cell are easily identified as are the body centered and face centered position.
- 5. Packing factor of Simple cubic Unit cell of Simple cubic structure has eight corner atoms which are bonded to eight other atoms. All sides of cube are equal in length a=b=c Volume of a unit cell=a³=r³ Packing factor of simple cube=0.52 Packing density= 0.52× 100 = 52%
- 6. Body Centered cubic Body centered cubic structure has a unit cell having an atom at its center and eight atoms at corners. Each corner atom is bonded to 8 other atoms and 1 atom is present in the center. So no of atom in BCC unit cell=2 As (8×1/8)+1
- 7. Sodium an α-iron are example of BCC. The BCC structure has a coordination number of eight. Materials having BCC structure are soft and malleable.
- 8. General expression for packing factor is Packing factor= (No. of atoms/cell)(volume of each atom) volume of a unit cell Packing factor of BCC =0.68 Packing Density=packing factor ×100 =0.68 ×100 =68%
- 9. Face Centered Cubic A FCC has a unit cell having an atom at the center of each face of unit cell and 8 corner atoms. Each of 8 corner atom contribute 1/8 and each face atom contribute ½ in each unit cell. No. of atoms in FCC unit cell=4 As (8 ×1/8)+(1/2 × 6)=4
- 10. Copper and aluminium has FCC structure. The FCC structure has a coordination number of twelve. FCC structure are usually harder.
- 11. Packing factor of FCC As packing factor = (No. of atoms/cell)(volume of each atom) volume of a unit cell And volume of a unit cell= 4r ³ √2 Volume of an atom= 4πr³ 3 So The packing factor of FCC =0.74