A Calculate the radius of the critically sized nucleus for p

A) Calculate the radius of the critically sized nucleus for pure copper when homogeneous nucleation takes place. Assume the freezing point of 1356 K and 236 deg C undercooling.

Answer: 1.39e-7 .

B) Calculate the number of atoms in a critically sized nucleus for the homogeneous nucleation of pure nickel. Assume 20%Tm under-cooling.

Answer: ??

Solve just Part B .

Solution

A) Calculate the radius of the critically sized nucleus for pure copper when homogeneous nucleation takes place. Assume the freezing point of 1356 K and 236 deg C undercooling.

Answer: 1.39e-7 .

T = undercooling = 236^oC

Tm= Freezing point = 1356^oK

Heat of Fusion = Hf = 1628 j/cm³ (from Text book)

_sf = Solid –Liquid interfacial energy = 177 x10^-7 (j/cm²)

Critical radius r* = 2 _sf Tm/ (T Hf) = 1.249x 10^-7cm

B) Calculate the number of atoms in a critically sized nucleus for the homogeneous nucleation of pure nickel. Assume 20%Tm under-cooling.

For Ni

Tm= Freezing point = 1453+273=^oK

T = undercooling = 20% of Tm = 345^oC

Heat of Fusion = Hf = 2756 j/cm³ (from Text book)

_sf = Solid –Liquid interfacial energy = 255 x10^-7 (j/cm²)

Critical radius r* = 2 _sf Tm/ (T Hf) = 9.25x 10^-8cm

Lattice constant ao= 0.3524 nm= 3.524x10^-8cm

Volume= a0³= 3.524^3 x10-24= 43.76 x10^-24cm

Vr=4/3r*³= 4/3* (9.25x 10^-8)³=3315*10^-24 cm

Number unit cells in critical nuclei = 3315*10^-24 cm/43.76 x10^-24cm=75 unit cells

There are 4 atoms each of the FCC metals. Hence number of atooms in critical nuclei = 75*4=300 per nucleus