**2. Concept of nucleation**

Any phase change has to get initiated by the emergence of the new phase at some instant of time. Likewise, when a solid phase emerges out of the liquid metal/alloy, it begins with the appearance of Nuclei. These are the cluster of atoms which come together during their course of random motion in the melt and can be termed as the embryonic crystals. These embryonic crystals permit further sitting at atoms on their surfaces which causes the growth of the solid phase. However, many of the nuclei again disappear in the melt, the clustered atoms again moving randomly in the melt. Only those nuclei which are stable and meet the thermo-dynamic requirements, allow growth to take place on their surfaces.

**Nucleation can take place in two ways.**

## **2.1 Homogeneous nucleation**

The coming together of the randomly moving atoms, from within the melt to form the embryonic crystals, the Nuclei, is known as Homogeneous Nucleation. These are smaller zones of higher density, formed by the ordered cluster of atoms [6]. Mahata et al. have conducted experiments to understand homogeneous nucleation in solidification of aluminium by molecular dynamics simulation [7]. They are of the opinion that there are many methods like X-ray scattering [8] etc., to monitor solid to liquid transformation. However, these methods are limited by several factors that make it difficult to study Homogeneous Nucleation in pure metals.

The precipitation of the group of atoms as the embryonic fresh phase in the melt, is subjected to a change in the free energy. The total free energy change comprises of two components, VOLUME FREE ENERGY CHANGE and INTERFACE FREE ENERGY CHANGE. Thus, a thermodynamic set of conditions is set up

for the formation of the Nuclei and for the Nuclei to be stable and not to dry–out prematurely, these thermodynamic conditions have to be met with.

### *2.1.1 Volume free energy change*

Thermodynamically, when a solid comes out as a liquid, there is a negative free energy change in the system. This change of free energy is directly proportional to the new volume(solid) transformed. Thus, for a spherical solid particle formed in a liquid,

( ) <sup>4</sup> <sup>3</sup> , ∆ =− ∏ ∆ *G Volume r G* <sup>3</sup> *<sup>v</sup>* where ∆*G Volume* ( ) - the change in free energy

due to the formation of the new volume.

' ' *r* - the radius of the freshly created spherical solid and ∆*Gv* - the bulk free- energy change per unit volume of the spherical solid created.
