The driving force for phase transformation arises if the free energy of parent phase becomes higher than that of product phase through a change in temperature or pressure. Below melting point, liquid can spantaneously transform to the solid. but the transformation can’t take place all at once.
The transformation can be divided into two steps that occur sequentially.
Nuclaetion: The formation of tiny particles (nuclei) that are stable to further fluctuations and will not dissolve.
Growth: The increase in the size of thse stable nuclei particles.
Nuclaetion: The formation of tiny particles (nuclei) that are stable to further fluctuations and will not dissolve.
Growth: The increase in the size of thse stable nuclei particles.
The difference in the volume free energy helps to create the interface between tiny solid and the liquid. But a very small particle has a large surface area to volume ratio. i.e. the volume free energy available is lesser than required to create the surface area and thus is unstable. Hence during nucleation stage surface energy is the dominant factor or inhibiting factor for phase change to occur.
Homogenous nucleation
The probability of nucleation remains constant throughout the volume of the parent phase. i.e. solid begins to nucleate throughout the bulk of the liquid without preference of any point.
A grater amount of supercooling is needed for homogenous nucleation to occur. Homogeneous nucleation is a difficult process and almost never occurs in industry. In practice, nucleation occurs at preferred sites. Heterogeneous nucleation is a much easier process.
Heterogenous nucleation
The probability of nucleation occuring at certain preferred sites in the liquid is much more than that at other sites i.e. solid nucleates preferentially at certain sites in the liquid phase. The preferred sites are the walls of container (in the case of liquid), inclusions, grain boundaries, stacking faults and dislocations (incase of solids).
The key to reduction of the nucleation berrier is a small value of θ.
Note: critical radius remains same in both homogeneous and heterogeneous (independent of contact angle).
The rate of heterogenous nucleation is much higher than the homogenous nucleation (because Δf*het < Δf*hom).
Nucleation rate (I) and growth rate (U): both are highly dependent on thermal fluctuations. I and U are zero at melting temperature as well as at 0 K. they passes through a maximum at some intermediate temperature. growth maximum turns out to be higher than that for the nucleation maximum.
Overall transformation rate: This is a function of both nucleation rate and growth rate. It has the same temperature dependence as nucleation and growth i.e. zero at Tm, increases with decreasing temperature (or increasing super cooling), reaches a maximum and then decreases to zero at 0 K.
T-T-T diagram: The data on transformation rate are usually plotted in the form of a T-T-T (temperature – time – transformation) diagram. The time for a fixed fraction of transformation is plotted as a function temperature. This has a C-shape where the nose of the C-curve corresponds to the minimum time (or maximum in rate). The transformation is delayed at high temperatures due to low driving force, and delay at lower temperatures due to low diffusion.
Importance of I and U: The grain size of the product phase depends on the relative rates of nucleation and growth. The combination of high nucleation and a low growth rate yields a fine grain structure. A low nucleation rate combined with a high growth rate yields a coarse grain size. If the cooling rate is very high then results in combination of low nucleation rate and slow or no growth yields a meta stable structures.