Question

4. (a) Compute the critical radius and the activation free energy for the solidification of a metal if nucleation is homogeneous. It is given that the latent heat of fusion and surface free energy are -3.53*10^9 J/ m^3 and 0.255 J/m^2, respectively. The melting temperature of this metal is 1455 degrees Celsius and the supercooling value 329K.

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

Answer 1

Answer :

156 atoms / critical nucleus .

J Ima .4) giveni DHE = -3.5 x 10 data. r = 0.255 J / m² In = 1455°C +273 = 1728 K Too- T = 329 K we know equation; 22 Tm H To-T I 7= DHE -(2) (0.255 71 m2) (1728 K) -3.33x100 Ilom? 7.588 x 1000 m 0.75 88 nm 329k 3 3 d giren : lattice parameter = d= 0.360 nm we know for mulai 483 unit cells parotick tice = (1) 0) (0.7588 nm) (0.360 hm) whit cello 39.20 = 39 unit cells. 3 3 particle . 4 atoms are associated with each FCC. unit cell, the total ho. of atoms per critical nucleus is just. 139 unit cells atoms Critical nucleus = 156 unit cell nucleus. Inatoms critical