Question

what is Packing efficiency of FCC(Face centred cuboid).​

Answer 1

Answer:

In face-centred unit cell (FCC) contains atoms at all the corners of the crystal lattice and at the centre of all the faces of the cube. The atom present at the face-centre is shared between 2 adjacent unit cells and only 1/2 of each atom belongs to an individual cell. The packing efficiency of FCC lattice is 74%.

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Answer 2

Answer:

In face-centred unit cell (FCC) contains atoms at all the corners of the crystal lattice and at the centre of all the faces of the cube. The atom present at the face-centre is shared between 2 adjacent unit cells and only 1/2 of each atom belongs to an individual cell. The packing efficiency of FCC lattice is 74%.

Since a face centred cubic unit cell contains 4 atoms,

$volume \: occupied \: by \: atom \: \: = 4 \times \frac{4}{3} \pi {r}^{3} = \frac{16}{3} \pi {r}^{3}$

$\frac{volume \: occupied \: by \: atom}{volume \: of \: unit \: cell} \times 100$

$\frac{ \frac{8}{3}\pi {r}^{3} }{ 8 \sqrt{8 {r}^{3} } } \times 100 = 74.0\%$

The packing efficiency of the face centred cubic cell is 74 %. Thus 26 % volume is empty space (void space).