Question

8. (a) What factors control homogeneous nucleation? Please use graphs as part of your response. (b) What is the difference between the terms, ‘eutectic’, versus ‘eutectoid’? Use equations as part of your response.

Answer 1

a) Nucleation:-It is the formation of separate or distinct thermodynamic phase within the solution.It occures in the nucleation site on the surface but homogeneous nucleation is the nucleation that occures without preferential nucleation site and also occures randomly,spontaneously.

Factors that control homogeneous nucleation are Gibbs free energy,temperature and interfacial energy(produce kinetic barrier for phase transformation).

At any temperature below T_m there is driving force for solidification(T<T_m). T<T_m ;G^s_v < G^l_v solid is the equilibrium phase.T^*_m temperature of unstable equilibrium of a solid clusture of r^* with undercooled liquid.

i) nucleation from the free species(atoms or molecules) to form small particle(nucleus).G_r is increasing (+ve) means thermodynamically unfavourable( lots of particle dissolve back to liquid phase).

ii) When some particles passes r* (particle size) and pass G_r* barrier,then further growth will cause decrease G_r (-ve) means favourable for more solidification.

iii) and after passing r_o ,G_r will be more negative means formation of nucleus is highly favourable.For a nucleus with a radius r > r^* ,the gibbs free energy will decrease if the nucleous will grow. Beyond r^* ,G_r decreases with increasing r and at r₀,Gr is equal to zero.

As r increases, for small r, r² > r³ so G_r >0

                       for large r, r² < r³ so G_r <0

hence , G_r must go through a maximum.