(a) Assume for the solidification of nickel (Problem 10.4) that nucleation is homogeneous...

(a) Assume for the solidification of nickel (Problem 10.4) that nucleation is homogeneous and that the number of stable nuclei is 106 nuclei per cubic meter. Calculate the critical radius and the number of stable nuclei that exist at the following degrees of supercooling: 200 and 300 K.

(b) What is significant about the magnitudes of these critical radii and the numbers of stable nuclei?

Problem 10.4

(a) For the solidification of nickel, calculate the critical radius r* and the activation free energy ΔG* if nucleation is homogeneous. Values for the latent heat of fusion and surface free energy are –2.53 × 109 J/m3 and 0.255 J/m2, respectively. Use the supercooling value found in Table 10.1.

(b) Now, calculate the number of atoms found in a nucleus of critical size. Assume a lattice parameter of 0.360 nm for solid nickel at its melting temperature.

Table 10.1 Degree of Supercooling (ΔT) Values (Homogeneous Nucleation) for Several Metals