Epitaxial Growth and Surface Nucleation

The oriented overgrowth of a crystalline phase on the surface of a substrate that is also crystalline is called epitaxial growth [104]. Usually it is required that the lattices of the two crystalline phases match, and it can be a rather complicated process [105]. Some new applications enlist amorphous substrates or grow new phases on a surface with a rather poor lattice match. 

Calculate the value of the Zeldovich factor for water at 20°C if the vapor is 5% supersaturated. 

Because of the large surface tension of liquid mercury, extremely large supersaturation ratios are needed for nucleation to occur at a measurable rate. Calculate rc and ric at 400 K assuming that the critical supersaturation is x = 40,000. Take the surface tension of mercury to be 486.5 ergs/cm.  

Assuming that for water AGd is 7 kcal/mol, calculate the rate of nucleation for ice nuclei for several temperatures and locate the temperature of maximum rate. Discuss in terms of this result why glassy water might be difficult to obtain. 

Calculate what the critical supersaturation ratio should be for water if the frequency factor in Eq. IX-10 were indeed too low by a factor of 10 . Alternatively, taking the observed value of the critical supersaturation ratio as 4.2, what value for the surface tension of water would the corrected theory give  

---