*2.1.2 Interface free energy change*

Thermodynamically, when a new interface is generated due to the emergence of a solid from a liquid, there is a gain of free energy at the interface created. This free energy gained is gained is proportional to the surface area of the solid particle created. For the same sphere, as considered above, with a radius of ' ' *r* , the free energy gain can be given as:

∆*G* (interface) = <sup>2</sup> 4∏ *r* γ , where, all the terms have their usual meaning, ' ' γ being the interfacial free energy per unit area of a spherical surface.

The volume free energy change and the interfacial free energy change are both presented graphically in **Figure 2**. The **Figure 2** also depicts the overall free energy change as a consequence of the two components when the solid volume is created in the melt.

As seen in the **Figure 2**, for small values of ' ' *r* , the sum of free energy changes is positive. However, as ' ' *r* increases, this sum becomes negative. The peak positive value

**23**

*Solidification of Metals and Alloys*

**2.2 Heterogeneous nucleation**

a.impurities in the metal

b.the wall of the mould

**3. Growth processes**

*DOI: http://dx.doi.org/10.5772/intechopen.94393*

corresponds to the critical radius ' ' *cr* or the embryonic crystal. The radius of the embryonic crystal must be greater than' ' *cr* so that the free energy change ∆*G*

becomes negative, the embryonic crystal becomes stable and growth proceeds. On the other hand, till the ' ' *cr* is reached, the sum of free energy change remains positive and creates a barrier, obstructing nucleation and the consequent growth. An intent analysis reveals as the temperature falls ' ' *cr* goes on decreasing. This means, with the fall of temperature, more and more embryonic crystals tend to be stable and the probability of homogeneous nucleation is increased, permitting the growth process to proceed. From the above it follows, homogeneous nucleation conditions are not favourable at the beginning for the stability of the nuclei as considerable undercooling is necessary for homogeneous nucleation to be effective. In the practical case of casting in a foundry, however, the melt need not be supercooled to make the homogeneous, stable nuclei form to start the solidification process. This is because, in the practical melt in the foundry, solidification processes are initiated by heterogeneous nucleation.

For heterogeneous nucleation, the initial interface for growth is provided by a foreign particle [9]. This foreign particle can be provided from outside or formed in the melt itself. The impurities, foreign particles or even the mould wall (the subtstate) can provide for a part of the surface energy required for nucleation. It is a known fact that less activation energy (free energy barrier) is required for nucleation. Therfore, the presence of the substate as mentioned above reduced the free energy barrier and can be very helpful in creating more growth capable nuclei. This is known as heterogeneous nucleation which need less activation energy than homogeneous nucleation [10]. This second phase to act as a nucleus, however, must be capable of being wetted by the melt forming low contact angles and also it must have some structural affinity with the crystalline solid to be formed on it. This

c.deliberately added particles to encourage a particular mode of crystallisation

Once the heterogeneous nuclei meet the growth conditions, growth occurs on them. After a certain lapse of time, when the temperature of the melt is lowered, the homogeneous nuclei become stable, and more solid may get deposited on them. At the same time, fresh nucleation may occur generating further stable nuclei. These fresh nuclei may be of the same phase as the first nuclei or of a different phase.

The growth process is conceived as the sitting of further atoms on the stable nuclei which brings in the growth of individual crystal or a general growth in the mass of the solid as solidification proceeds *the latent heat of crystallisation* is liberated at the solid–liquid interface. *Zones of thermal supercooling* are generated in the liquid pool. Also, with the lowering of temperature the solubility of an alloying element in the liquid melt decreases. As a consequence, the solute is rejected at the solid–liquid interface. The equilibrium freezing temperature of the alloy is

second phase could be any one or any combination of the following:

**Figure 2.** *Change of free energy (volume and interface) as a consequence of the creation of solid phase.*

### *Solidification of Metals and Alloys DOI: http://dx.doi.org/10.5772/intechopen.94393*

*Casting Processes and Modelling of Metallic Materials*

*2.1.1 Volume free energy change*

due to the formation of the new volume.

*2.1.2 Interface free energy change*

energy gain can be given as: ∆*G* (interface) = <sup>2</sup> 4∏ *r*

liquid,

for the formation of the Nuclei and for the Nuclei to be stable and not to dry–out

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

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

Thermodynamically, when a new interface is generated due to the emergence of a solid from a liquid, there is a gain of free energy at the interface created. This free energy gained is gained is proportional to the surface area of the solid particle created. For the same sphere, as considered above, with a radius of ' ' *r* , the free

The volume free energy change and the interfacial free energy change are both presented graphically in **Figure 2**. The **Figure 2** also depicts the overall free energy change as a consequence of the two components when the solid volume is created in the melt. As seen in the **Figure 2**, for small values of ' ' *r* , the sum of free energy changes is positive. However, as ' ' *r* increases, this sum becomes negative. The peak positive value

, where, all the terms have their usual meaning, ' '

γ

' ' *r* - the radius of the freshly created spherical solid and ∆*Gv* - the bulk

prematurely, these thermodynamic conditions have to be met with.

free- energy change per unit volume of the spherical solid created.

being the interfacial free energy per unit area of a spherical surface.

*Change of free energy (volume and interface) as a consequence of the creation of solid phase.*

γ

**22**

**Figure 2.**

corresponds to the critical radius ' ' *cr* or the embryonic crystal. The radius of the embryonic crystal must be greater than' ' *cr* so that the free energy change ∆*G* becomes negative, the embryonic crystal becomes stable and growth proceeds. On the other hand, till the ' ' *cr* is reached, the sum of free energy change remains positive and creates a barrier, obstructing nucleation and the consequent growth. An intent analysis reveals as the temperature falls ' ' *cr* goes on decreasing. This means, with the fall of temperature, more and more embryonic crystals tend to be stable and the probability of homogeneous nucleation is increased, permitting the growth process to proceed.

From the above it follows, homogeneous nucleation conditions are not favourable at the beginning for the stability of the nuclei as considerable undercooling is necessary for homogeneous nucleation to be effective. In the practical case of casting in a foundry, however, the melt need not be supercooled to make the homogeneous, stable nuclei form to start the solidification process. This is because, in the practical melt in the foundry, solidification processes are initiated by heterogeneous nucleation.
