How do I calculate the volume density of atoms in a diamond lattice?

[salman213]

1.Hey!

I don't get the solution to the following question so I am hoping someone can explain!

Ok so, the question is we have Silicon, which I have read has a DIAMOND LATTICE structure.
Which basically seems to mean two face centered cubes come together. Now I need to calculate the VOLUME DENSITY of ATOMS. I know the lattice constant ex. 5.4 x 10^-10 m

Now From my knowledge: fcc in 3d has 1/8th of an atom on each of the 8 corners of the cube. And has also has 1/2 of a atom on each of the 6 faces. That makes a total of

1/8*8 = 1
1/2*6 = 3
--------------
4 atoms in total

Now the solution says there are somehow 8 atoms. I am assuming there are 8 because it is a diamond lattice structure and so there are 2 cubes meaning 4 x 2 = 8 atoms..first is this assumption correct?



if that is correct then when they calculate the volume they use

(5.4 x 10^-10)^3 = I THOUGHT THIS WAS THE VOLUME OF ONLY ONE CUBE...:O..

answer somehow is

atom density = 8/ (5.4 x 10^-10)^3

HELP!

why did they use 8 atoms and why did they use that volume for only one cube if the 8 atoms come from fcc cubes!

please help!

 

[salman213]

ok i figured it out after some research ..