Question

(a) What is the diameter of a spherical fcc cluster that has 10⁵ and 10⁸ atoms with effective atomic radius of 0.24 nm?

(b) Real clusters are not perfectly spherical. Why do you think that this the case? Would you expect them to become more spherical as the cluster size is increased?

Answer 1

(a) Diameter of spherical FCC cluster having 105 and 108 atoms with radius of 0.24 nm. In a cluster having 105 atoms, the net radius of this cluster will be 105 x 0.24 = 25.2 nm, therefore, the diameter will be

2(net radius) = 2 x 25.2 = 50.4 nm and for the cluster having 108 atoms, the diameter will be 2(108 x 0.24) = 2(25.92) = 51.84 nm.

(b) Real clusters are not perfectly spherical but in this case, the cluster is spherical because we are taking the net radius of the structure which will constitutes a spherical FCC. If the crystal size is increased, the cluster cannot be more spherical since it will suffer elongation from one side.