Question

Material Science question

Rank the following elements with regard to how rapidly they will diffuse into FCC Iron (fastest to slowest). Indicate the diffusion mechanism for each.

1) Mo

2) C

3) Cr

4) W

Answer 1

The steady state diffudion is governed by Fick's first law

Where

J= diffusion flux (mass diffused/(area x time), kg/m²/s

D=diffusivity, m²/s

C= concentration , kg/m³

We assume the same concentration gradient for all the allowing elements

Hence the diffusion flux depends of diffusivity D.

The diffusivity is given by

Where

D₀= Preexponential factor of diffusivity at infinite temperature (max diffusivity,), m²/s

Q= activation energy ,J/mol

R= Universal gas constant, J/mol

T= absolute temperature, K

It may be seen that diffusivity D is very sensitive to activation energy Q, and hence the rapidity of diffusion will depend primatily on Q, the concentration gradient and temperature remaining constant. Higher Q will result in lower D.

Hence the rapidity of diffusion for different alloying alloying elements in gamma iron in decreasing order is given below:

Comparative rapidity	Element	Q, J/mol
1	C	135,000
2	Mo	Higher than W
3	W	376,000
4	Cr	405,000

(Please note: Since temparature is not specified, the above table needs to be checked at actual temperature, which may result in readjustment of ranks)

As the size of C atom is small compared to gamma-Fe atom they can form interstitial solid solution, i.e thay can be located in between Fe atoms in lattice structure.

But the atoms of Mo, Cr and W are comparable in size to Fe atoms and hence they can not form interstitial solid solutions but they form substitutional solid solution where they occupy a place of vacant Fe atom in lattice structure.