packing factor of diamond cubic crystal structure of

Hello aspirant,

Hope you are doing well,

The diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as they solidify. While the first known example was diamond, other elements in group 14 also adopt this structure, including α- tin, the semiconductors silicon and germanium, and silicon/germanium alloys in any proportion.

The atomic packing factor of the diamond cubic structure (the proportion of space that would be filled by spheres that are centered on the vertices of the structure and are as large as possible without overlapping) is π√3/16 ≈ 0.34, significantly smaller (indicating a less dense structure) than the packing factors for the face-centred and body - centred cubic lattices. Zincblende structures have higher packing factors than 0.34 depending on the relative sizes of their two component atoms.

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Hello student

Packing factor of diamond cubic structure is 0.34.

The equation for finding the packing fraction is No of atoms in unit cell ×Volume of atom/Volume of unit cell.

Diamond has eight atoms per unit cell.

The ratio of volume of atoms in a cell compared to total volume of cell is the packing factor or packing fraction.

Hope this helped you.

Dear student,

Diamond structure forms a Face Centered Cubic unit cell. And the packing fraction means, the proportion of space that would be filled by spheres that are centered on the vertices of the structure and are as large as possible without overlapping. Now we have to calculate the packing fraction of diamond.

So for diamond PF = 8 * Volume of atom/ Volume of unit cell

By substituting the values of volumes we get

PF = π√316 ≈ 0.34.

Hope this helps.