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djroberts

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**Materials -- unit cell question**

"In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the BCC crystal structure along the [111] direction."

I got the answer 4R but it is wrong. I came up with this by assuming that atoms touch each other in the [111] direction in a BCC structure. In this direction [111] there is one atom that goes through the (1/2,1/2,1/2) position and half an atom at the origin and half an atom at the (1,1,1) position summing to 4 half's of an atom in length. using the answer 4R I got the lattice parameter a=4R/sqrt(3) which is the true lattice parameter of BCC.

I also answered another question:

"In terms of the atomic radius, R, determine the distance between the centers of adjacent atoms for the FCC crystal structure along the [100] direction. "

and got the answer 2R*sqrt(2) which was right. This was derived by saying FCC has atoms that touch along the [101] direction, and then doing geometry to calculate the [100] direction.

any help on this would be great, thanks.