Answer:
a) 4
b) 2
c) 8
Explanation:
In a cubic lattice, each atom of the vertex is shared among other 8 unit cells, so the atoms on the vertex contribute to 1/8 to a given unit cell.
a) Ina face-centered cubic we have 8 atoms on the vertex and one in each face, which is shared with another unit cell, so it contribute to 1/2
Therefore, the total atoms are:
8*(1/8) + 6*(1/2) = 4
b) In the body centered cubic structure, the centered atom is not shared with another cell, therefore it contribute to 1 to the given cell:
The number of atoms per unit cel is:
8*(1/8) + 1 = 2
c) The diamond lattice is similar to the face-centered cubic lattice but it contains two identical atoms per lattice point.
Therefore it must contain twice atoms than the face-centered cubic lattice:
that is, it has 8 atoms per unit cell
