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

[sudipmaity]

Homework Statement

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.

Homework Equations

For fcc nearest neighbour distance is a/ 2^(1/2)
For bcc " """"""" """" a(3^1/2) / 2[/B]

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.[/B]

 

[stevendaryl]

Homework Statement

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.

Homework Equations

For fcc nearest neighbour distance is a/ 2^(1/2)
For bcc " """"""" """" a(3^1/2) / 2[/B]

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.[/B]

This is possibly relevant: The problem statement doesn't say that the constant $a$ (presumably, that's the length of one of the edges of the cube?) stays the same. It says that the density stays the same. So you need to compute the density as a function of $a$ for fcc an bcc. Then you need to figure how $a$ changes if the density stays constant.

That's just a guess as to what the problem might be.