# Iron transforms from bcc to fcc.Ratio of nearest neighbour distance.

#### pranimaboity2050

1. The problem statement,*all*variables and given/known data
At about 1180K iron transforms into fcc structure from bcc structure which is also the structural form at room temperature.Assuming no change in density find the ratio of nearest*neighbour distance in fcc structure to that in bcc structure.*
2. Relevant equations
For fcc nearest neighbour distance is a/ 2^(1/2)
For bcc " """"""" """" [a × 3^(1/2)]/ 2
3. The attempt at a solution
I took the ratio of the above formula.I am getting 0.8 .But the given answer is 1.029.Clearly my method is wrong .Please help.

#### ChipB

PHF Helper
You are assuming that the dimension 'a' is the same for both structures. But since the body-centered cubic has 2 lattice points per cell, and the face-centered cubic has 4 lattice points per cell, if 'a' is the same for both then the density of the FCC would be twice that of the BCC structure. But you're told to assume that the density of both are the same - therefore the volume of the FCC cell must be twice as great as the volume of the BCC cell. Hence the dimension 'a' for FCC must be increased by a factor of 2^(1/3) compared to dimension 'a' for BCC. Multiply your answer by 2^(1/3) and see what you get!

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#### pranimaboity2050

Thank you for the reply.But say a question like this featured in my exam, how would you like me to write the answer?How should i express this answer of yours more mathematically and less qualitatively? Please help.