The Solid State

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Number of Atoms in a Unit Cell

Body-Centred Unit Cells: A unit cell contains one constituent particle (atom, molecule or ion) at its body-centre and eight particles are at its corners.
Number of atoms present in the unit cell =open parentheses 8 space straight x 1 over 8 close parentheses space plus space 1 space equals space 2
Thus, Number of lattice points: 9, coordinate number:er : 8 and  number of atom per unit cell (Z): 2

Body Centred Cubic Unit Cell

Body-Centred Unit Cells: A unit cell contains one constituent particle (atom, molecule or ion) at its body-centre and eight particles are at its corners.
Number of atoms present in the unit cell =open parentheses 8 space straight x 1 over 8 close parentheses space plus space 1 space equals space 2
Thus, Number of lattice points: 9, coordinate number:er : 8 and  number of atom per unit cell (Z): 2

End Centred Cubic Unit Cell

End-Centred Unit Cells:Unit cell contains one constituent particle present at the centre of any two opposite faces along with eight particles at its corners.

Number of atoms present in this unit cell = open parentheses 8 space straight x space 1 over 8 close parentheses space plus space open parentheses 2 space straight x space 1 half close parentheses space equals space 1 space plus space 1 space equals space 2
Thus, Number of lattice points:10

Face Centred Cubic Unit Cell

Face-Centred Unit Cells: A unit cell contains one constituent particle present at the centre of each face, along with eight particles at its corners.

Number of atoms present in this unit cell = open parentheses 8 space straight x space 1 over 8 close parentheses space plus space open parentheses 6 space straight x 1 half close parentheses space equals space 1 space plus space 3 space equals space 4
Thus, number of lattice points: 14, coordination number: 12 and  number of atom per unit cell (Z): 4

Primitive Cubic Unit Cell

Primitive Unit Cells: When constituent particles are present only on the corner position of a unit cell.

No of atoms present in this unit cell = 8 space straight x 1 over 8 space equals space 1 (Each Corner atom contributes1/8th portion to the unit cell Thus,
Number of lattice points: 8, Coordination Number: 6 and number of atom per unit cell (Z): 1

Centred unit cells: Constituent particles present at a position other than corners in addition to those at corners, it is called a centred unit cell.

Centred unit cells are of three types:

  1. Body-Centred Unit Cells
  2. Face-Centred Unit Cells
  3. End-Centred Unit Cells