Unit – IV A

Number of Particles in Unit Cell and coordination Number

Simple Cubic Structure (scc):

  • From structure we can see that there are 8 particles at 8 corners of the unit cell. Each corner particle is shared by 8 neighbouring unit cells. Hence each unit cell contains 1/8 th of the particle at its corner.
    Number of corners = 8, Hence number of particles in unit cell  
  • Each particle in this structure is directly in contact with four other particles in its plane and one particle each in layer above and the layer below. Hence the coordination number for simple cubic structure is 4+ 1+ 1 = 6

Body Centered Cubic Structure (bcc):

  • From structure we can see that there are 8 particles at 8 corners of the unit cell. Each corner particle is shared by 8 neighbouring unit cells. Hence each unit cell contains 1/8 th of the particle at its corner.
    Number of corners = 8, hence number of particles in unit cell at corners

  • At the same time there is an atom at the centre of the cell, hence number of particles in unit cell 1 + 1 = 2
  • Each particle in this structure is directly in contact with four other particles in the layer above and four particles in the layer below. Hence the coordination number for body centred cubic structure is 4 + 4 = 8

Face Centered Cubic Structure (fcc):



  • From structure we can see that there are 8 particles at 8 corners of the unit cell. Each corner particle is shared by 8 other neighbouring unit cells. Hence each unit cell contains 1/8 th of the particle at its corner.
    Number of corners = 8. Hence number of particles in unit cell at corners

  • There are 6 particles at 6 faces of the unit cell. Each face particle is shared by 2 neighbouring unit cells. Hence each unit cell contains 1/2 of the particle at its face.
    Number of faces = 6. Hence the number of particles on face
  • Hence number of particles in unit cell 1 + 3 = 4
  • Each particle in this structure is directly in contact with 4 other particles in its layer and with 4 particles in the layer above and 4 particles in the layer below. Hence the coordination number for face centred cubic structure is 4 + 4 + 4 = 12

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