Question

Briefly explain why a critical size of nucleus is needed before the nucleus can grow during solidification of a liquid. Explain this using concepts of energy, associated with the nucleus, as a function of its size

Answer 1

Critical radius of nucleus:

When a second phase is formed in the system, it involves the gibbs free energy of the total system.

Gibbs free energy of the system is given by the equations:

The first term is the volume energy and the second term is the surface energy. As a new phase begins to form, the surface energy increases by r² while the volume energy decreases by r³. In the initial stages of the process, surface energy dominates and hence there is a increase in the gibbs free energy. But after a certain radius is reached, the volume effects tends to dominates and the energy falls down. This point of maximum energy of this transition is achieved at the critical radius and the nucleus is called as the critical nucleus.

The slope of Gibbs free energy curve is given by: