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Questions
Find the number of atoms in the fcc unit cell.
Calculate the number of particles per unit cell in a face-centred cubic system.
In a face centred arrangement of atoms of an element, what will be the number of atoms present in respective unit cells?
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Solution
A face-centred cubic (fcc) unit cell has particles at the eight corners plus particles at the centre of its six faces.
Each particle present at the corner of a given unit cell is shared with seven other neighbouring unit cells. As a result, its contribution to the given unit cell is only `1/8`.
Thus, the number of particles present at corners per unit cell
= 8 corner atoms × `1/8` atom per unit cell = 1
Each particle at the centre of the six faces is shared with one neighbouring cube. Thus, 1/2 of each face particle belongs to the given unit cell. Thus, the number of particles present at faces per unit cell
= 6 atoms at the faces × `1/2` atom per unit cell = 3
Therefore, fcc unit cell has one corner particle plus 3 face particles, making a total of 4 particles per unit cell.
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