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Question
A face centred cube (FCC) consists of how many atoms? Explain
Solution
Face-centred cubic lattice (fcc):
1) In face-centred cubic unit cell, eight constituent particles (spheres) are present at eight corners of unit cell. Six constituent particles (spheres) are present at centres of six faces
2) A constituent particle present at a corner is shared by eight neighbouring unit cells. Its contribution to a unit cell is only 1/8. Thus, the number of atoms present at corners per unit cell
= 8 corner atoms x 1/8 atom per unit cell = 1
3) A constituent particle present at the centre of a face is shared by two neighbouring unit cells. Its contribution to a unit cell is only 1/2.
The number of atoms present at faces per unit cell
= 6 atoms at the faces x 1/2 atom per unit cell = 3
4) The total number of atoms per unit cell = 1 + 3 = 4
Thus, a face-centred cubic unit cell has 4 atoms per unit cell.
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