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How to calculate packing efficiency of cubic unit cell of diamond ?

Diamond structure is ZnS type structure  in which carbon atoms forms  a face centred cubic (FCC/CCP) lattice as well as  four out of eight (50%) or alternate tetrahedral voids are occupied by carbon atoms. Every atom in this structure is surrounded tetrahedrally by four other. No discrete molecule can be discerned (identified) in diamond .the entire crystal is giant molecule a unit cell of which is shown as below.

Note : Only those atoms which form four covalent bond produce a repeated 3D structure using only covalent bonds.

Lattice of Diamond is ZnS type structure.

(1) C- form FCC/CCP (4-atoms)

(2) C- atoms present at the (50%) alternative tetrahedral voids (4-atoms)

(3) Total Number of one lattice unit is eight (8) hence molecular formula of diamond is (C8) (i.e. Z= 8)

(4) Number of C-C bond in lattice cell is = 4×4= 16

(5) Number of C-C bond per carbon atom is 16/8=2

(6) The distance between two Corbin atom is dC-C = a√3/4 and the radius of carbon atom = dc-c/2 = rc = a√3/2x4

(8) Packing efficiency (PE = π√3/10= 0.34 or 34%):

(9) Voids = 66 % 

Additional Information: 

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