[Sona]

A solution of carbon in face centered cubic
iron has a density of 8-105 g cm-3 and a unit
cell edge of 3-589 A. Are the carbon atoms
interstitial or do they substitute for iron atoms
in the lattice ? Calculate the weight % of
carbon.

Can anyone help me to solve it?

How I was thinking is that I can calculate the vol of cube and the volume occupied by Fe, hence from there the free volume, now if C atoms present possesed a volume which is beyond this value that means it is substituting Fe. But they havenot given the value of C's radius. If this is the right approch then how to proceed after calculating the vacant volume and if not then how to solve it?

please help

[Enthalpy]

You might first compute a density for pure iron with that cell edge and compare with 8105kg/m³ to make deductions.

Then, as the cell edge is known, no atomic radius is needed.

[Sona]

I calculated the density. It is 8.044 g/cm³.
the difference is 0.061 g/cm³.
If it is interstitial then this is the density of C, and number of C present per unit cell an be calculated.
But from here how can I comment on whether it is interstitial or substitutional?

[Enthalpy]

C atoms are lighter than Fe atoms, so what happens to the density in case of a replacement?
And if insterstitial, how does the density evolve? You can deduce how much C there is.

I'm not quite sure that the figures here are realistic.