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Packing of Particles in Crystal Lattice

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Estimated time: 5 minutes
Maharashtra State Board: Class 12

Key Points: Packing of Particles in Crystal Lattice

Close Packing of Spheres:

Packing Type Coordination Number
1D (linear) Spheres in a row 2
2D square (AAAA) Square close packed 4
2D hexagonal (ABAB) Hexagonal close packed 6
3D simple cubic (AAAA) e.g., Polonium 6
3D hcp (ABAB) e.g., Mg, Zn 12
3D ccp/fcc (ABCABC) e.g., Cu, Ag 12
 

Both hcp and ccp have the same coordination number (12) and same packing efficiency (74%).

Types of Voids:

Void Surrounded by Size (relative to r)
Trigonal / Triangular 3 spheres 0.15 r
Tetrahedral 4 spheres 0.225 r
Octahedral 6 spheres 0.414 r
 

Increasing order of void size: trigonal < tetrahedral < octahedral

Number of Voids (in hcp/ccp):

  • Tetrahedral voids = 2N
  • Octahedral voids = N (N = number of close-packed spheres)
  • Octahedral voids = half of tetrahedral voids
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