GC question from destroyer'13

This forum made possible through the generous support of SDN members, donors, and sponsors. Thank you.

hope_to_match

Full Member
10+ Year Member
Joined
Feb 7, 2011
Messages
1,145
Reaction score
220
in the solution to Q111 he mentions ' a body centered cubic unit cell has 2 atoms, while a face-centered unit cell has 4 atoms'

can someone please explain what in the world he means by this..thanks :luck:

Members don't see this ad.
 
He is talking about crystal lattice and the way the cubes are arranged. There are multiple ways it can be arranged. From very basic to advanced. I think there is like 6-7 different arrangements or something. I seen a question about that in Achiever.
 
Members don't see this ad :)
I'll give it a stab.

This is what I think of when I was first asked that question.

BODY CENTERED:



Picture a cube (or look at the one in the picture). You have one CENTER atom. At each corner, you have 1/8 of another atom (because remember, this is a cube, and there are multiple ones of the same thing around it. Here though, we are just looking at one single cube). So, we have 1 in the center and 8(1/8) for a total of 2 atoms.

FACE CENTERED:



So, again, it's a cube. This time though, there is no atom in the center of the lattice. Using our PAT skills, we know that we are only being shown three of the sides here so we can assume that the other three sides mirror these since it's a cube. There is half of an atom on each face of the cube. Since the cube has six sides, and each side has a half, there is two total atoms just on the sides 6(1/2). Now, look at the corners. Like the body centered cube, there is 1/8 of an atom at each corner. So, now, it's also 8(1/8) which gives us 1 on just the corners.
 
Last edited:
  • Like
Reactions: 1 users
I believe you have the face centered one wrong. Face centered still has 8 corner atoms that are 1/8 atom. The face centers are 1/2 an atom and we have 6 of them.

So we have (1/8)(8) + (1/2)(6) which gives you 4. Same number you arrived to.
 
Top