Example of Solid Solution:

Given that the size of FCC unit cell of iron = 3.60Å, calculate the radius of an atom for which you would expect a high probability to form an interstitial solid solution alloy. Calculate the range in radius for an atom in which you would expect extensive substitutional solid solution. Comment on the nature of solid solution of Carbon in Iron.

Answer:
For the initial unit cell, a₀ = 3.60Å, since the atoms contact along face diagonal for the FCC so 4r = √2 a₀; r =1.27Å.

Void diameter = 3.60 – (2)(1.27) = 1.05Å; r_void = 0.53Å

Therefore the atom will have a high probability of interstitial solid solutions for atoms with r = 0.53Å

For extensive substitutional solid solution, the diameter range is
[(r_solute – 1.27)/1.27]100 = -15 ; r_solute = 1.08Å

[(r_solute – 1.27)/1.27]100 = +15 ; r_solute = 1.46Å

Therefore for extensive solid solution the range of radius is from 1.08Å to 1.46Å

The radius of C = 0.71Å. However, the interstitial size is only 0.53Å.

Hence, when carbon goes into solution with Fe, it will severely distort the unit cell making the other interstitial sites smaller. This will make more solid solution of carbon difficult.