# Homework Help: Materials - unit cell question

1. Jan 17, 2009

### djroberts

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.

"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.

2. Jan 17, 2009

### Redbelly98

Staff Emeritus
Re: Materials -- unit cell question

Okay, yes, it's 4R from the atom at (0,0,0) to the atom at (1,1,1). But those are not adjacent atoms.

p.s. Welcome to PF

3. Jan 17, 2009

### djroberts

Re: Materials -- unit cell question

thanks for the welcome redbelly98! and I got it thanks :)