Assume that each atom is a sphere, and that the surface of each atom is in contact with its nearest neighbor. determine the percentage of unit cell volume that is occupied in (a) a face- centered cubic lattice, (b) a body-centered cubic lattice, and (c) a diamond lattice.

The percentage of unit cell volume that is occupied by atoms in a face- centered cubic lattice is 74.05% The percentage of unit cell volume that is occupied by atoms in a body-centered cubic lattice is 68.03%  The percentage of unit cell volume that is occupied by atoms in a diamond lattice is 34.01%

Explanation:

The percentage of unit cell volume = Volume of atoms/Volume of unit cell

Volume of sphere =

a) Percentage of unit cell volume occupied by atoms in face- centered cubic lattice:

let the side of each cube = a

Volume of unit cell = Volume of cube = a³

Radius of atoms =

Volume of each atom = =

Number of atoms/unit cell = 4

Total volume of the atoms =

The percentage of unit cell volume = = 0.7405

= 0.7405 X 100% = 74.05%

b) Percentage of unit cell volume occupied by atoms in a body-centered cubic lattice

Radius of atoms =

Volume of each atom = =

Number of atoms/unit cell = 2

Total volume of the atoms =

The percentage of unit cell volume = = 0.6803

= 0.6803 X 100% = 68.03%

c) Percentage of unit cell volume occupied by atoms in a diamond lattice

Radius of atoms =

Volume of each atom = =

Number of atoms/unit cell = 8

Total volume of the atoms =

The percentage of unit cell volume = = 0.3401

= 0.3401  X 100% = 34.01%

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