What Is the Distance Between Adjacent Atoms in BCC [111] Direction?

[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.


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.

 

[Redbelly98]

"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.

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.

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.

p.s. Welcome to PF

 

[djroberts]

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