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 ..

 

[Blueshift5]

Hi there,

To calculate the volume density of atoms in a diamond lattice, you need to consider the number of atoms within the unit cell and the volume of the unit cell. The unit cell in a diamond lattice is a face-centered cubic (fcc) unit cell, which contains 8 atoms. This is because in an fcc unit cell, there is 1/8th of an atom at each of the 8 corners and 1/2 of an atom on each of the 6 faces, resulting in a total of 8 atoms.

To calculate the volume of the unit cell, you need to consider the lattice constant, which is the distance between the centers of two adjacent atoms in the lattice. In this case, the lattice constant for silicon is given as 5.4 x 10^-10 m. The volume of the unit cell can be calculated as (5.4 x 10^-10)^3, which is the length, width, and height of the unit cell.

To calculate the volume density of atoms, you need to divide the number of atoms in the unit cell (8) by the volume of the unit cell [(5.4 x 10^-10)^3]. This will give you the number of atoms per unit volume, which is the volume density of atoms in the diamond lattice.

I hope this helps clarify the calculation for you. Let me know if you have any other questions.