# cubic lattice

#### navneetdh

I am confused about the different cubic lattice that are there.
I think its body centered, face centered. How do yo figure out how many atoms in each?

what else should we know about this?

#### alanan84

##### D1
10+ Year Member
5+ Year Member
Cubic Crystal System (unit cells):
• simple cubic  atom @ each point of the cube, each is shared by 8 other cells à (1/8)*8 corners = 1 atom per cell
• body-centered cubic  1 atom @ center of the cube + an atom @ each point of the cube (shared by 8 other cells) à[ (1/8)*8 corners]+1 body = 2 atoms per cell
• face-centered cubic  1 atom embedded @ the center of each cube face (shared with 1 other cell) + an atom @ each point of the cube (shared by 8 other cells) à (1/8) * 8 corners + (1/2) * 6 faces = 4 atoms per cell

#### jefff

5+ Year Member
Cubic Crystal System (unit cells):
• simple cubic &#8211; atom @ each point of the cube, each is shared by 8 other cells à (1/8)*8 corners = 1 atom per cell
• body-centered cubic &#8211; 1 atom @ center of the cube + an atom @ each point of the cube (shared by 8 other cells) à[ (1/8)*8 corners]+1 body = 2 atoms per cell
• face-centered cubic &#8211; 1 atom embedded @ the center of each cube face (shared with 1 other cell) + an atom @ each point of the cube (shared by 8 other cells) à (1/8) * 8 corners + (1/2) * 6 faces = 4 atoms per cell
hmm

#### nze82

Each corner atom is worth 1/8, each face atom is worth 1/2, and each center atom is worth 1.
For Face center cubic you have 8 corner atoms, and 6 face atoms:
8(1/8) + 6(1/2) = 1+3 = 4 atoms

For Body center cubic you have 8 corner atoms, and 1 center atom:
8(1/8) + 1 = 1+1 = 2 atoms

For simple cubic you have 8 corner atoms:
8(1/8) = 1 atom

OP
N

thank you

#### suhshi

10+ Year Member
7+ Year Member
how would you apply this knowledge to this question:

how many cl ions are in contact with any Na ion if sodium chloride crystallizes in a face centered cubic lattice of chloride ions, with the smaller sodium ions occupying holes between the chrloride ions

#### DaveyK

10+ Year Member
7+ Year Member
I was just about to post something on this same topic lol... strange.

thanks for the overview nze, I've been looking around the web for info on this and that is the best explanation I've seen

I do still have a question however... out of acs gchem:

"Copper crystalizes in a face centered lattice. If the edge of the unit cell is 362pm what is the radius of the copper atom?"

the answer is 128pm... I'm assuming there is some ratio to use, but since acs doesn't give explanations and I'm a little lost, if someone could explain how they got this number, I would appreciate it

#### nze82

I was just about to post something on this same topic lol... strange.

thanks for the overview nze, I've been looking around the web for info on this and that is the best explanation I've seen

I do still have a question however... out of acs gchem:

"Copper crystalizes in a face centered lattice. If the edge of the unit cell is 362pm what is the radius of the copper atom?"

the answer is 128pm... I'm assuming there is some ratio to use, but since acs doesn't give explanations and I'm a little lost, if someone could explain how they got this number, I would appreciate it
Look at my posts here:
http://forums.studentdoctor.net/showthread.php?t=628255&highlight=radius+of+copper+atom

Hopefully, they will answer your question.

#### DaveyK

10+ Year Member
7+ Year Member
hah.. should have used the search function. that's perect, thanks!