In typical solid-state system, ΔgB = −2000 J/mol and γ = 100 mJ/m2 . Calculate the critical size Rc and free energy barrier ΔGc for homogeneous nucleation under these conditions. Assuming that the material is f. c.c. and has a lattice constant of 0.38 nm, how many atoms are there in the critical nucleus? Compare ΔGc to 76kT, assuming a nucleation temperature of 800 K. Is homogeneous nucleation likely under these conditions? (Hint: Read section 19.1.7 of textbook to understand the significance of ΔGc ≈ 76kT for observable nucleation rate)