FCC has 8 and 4 octahedral and tertrahedral voids per unit cell respectively. whereas BCC has 12 and 6 respectively. octahedral in FCC is bigger than tertrahedral. C occupies octahedral with less distortion. Octahedral in BCC is smaller than tertrahedral. even in that case C occupies octahedral void due to lesser distortion (only top atom and bottom need to be distorted). No. of voids in BCC are more than FCC whereas size of voids in BCC are significantly smaller than FCC. For this reason austenite have higher solubility of C than ferrite.

Dear Prof. Ojha,

I think you wrote the answer by yourself: "The octahedron voids are more in austenite compared to that in ferrite."

I usually use following pictures to explain such a huge difference in carbon solubility in alfa and gamma Fe:

http://brykov.com/Ojha/

Hope this will help.

Best Regards,

Michael

Dear Dr. Michael,

Thanks for  providing very good illustrations. To know the quantitative value, one needs to know the exact ratio of two configuration in both ferrite and austenite.

Its good question, yes solubility of C in ferrite only 0.025% whereas in Austenite this is 2% even the atomic packing factor in austenite (fcc) (4 atom per unite cell) is higher than ferrite (bcc) (2 atoms per unit cell. The calculation of the amount of empty space in unfilled space in f.c.c is 25% and in b.c.c lattice is 32%, so it may seem strange that the solubility of C in austenite is much greater than in ferrite. The reason is

The largest hole in b.c.c ferrite is halfway between the center of the face and space between the two corner atoms. Two of the four possible positions for a Carbon atom on the front face of a body-centered cube. The largest interstitial sphere that would just fit has a radius of 0.36(10)-8 cm. The largest hole in f.c.c austenite is midway along the edge between two corner atoms. The largest interstitial sphere that would just fit has a radius of 0.52(10)-8 cm. therefore, austenite will have a greater solubility for carbon than ferrite.

FCC has 8 and 4 octahedral and tertrahedral voids per unit cell respectively. whereas BCC has 12 and 6 respectively. octahedral in FCC is bigger than tertrahedral. C occupies octahedral with less distortion. Octahedral in BCC is smaller than tertrahedral. even in that case C occupies octahedral void due to lesser distortion (only top atom and bottom need to be distorted). No. of voids in BCC are more than FCC whereas size of voids in BCC are significantly smaller than FCC. For this reason austenite have higher solubility of C than ferrite.

Carbon occupies interstitial sites of iron mainly the octahedral sites because in FCC(austenite) , these octahedral sites are larger than in BCC(ferrite) , irrespective of  the more number the octahedral sites in  bcc (ferrite)  than fcc (austenite), so mainly it zeros on the size of the octahaderal voids.

FCC interstitial radius(0.41R) is larger than BCC (0.291R). R is the radius of atom.so more carbon atoms are soluble in FCC then BCC.