Atom Density in Silicon (100), (110), and (111) Planes

[Lolsauce]

Homework Statement

For the (100), (110), and (111) planes of a Silicon crystal sketch the placement of atoms on the plane and determine the atom density (atoms/cm^2) on the plane.

Homework Equations

As of now I think the only relavent equation would be the atom density which is:

Atoms per unit cell / (area of the square = Atoms per unit cell/a^2

Where a is the lattice constant.

The Attempt at a Solution

I've already sketched the planes, but don't know how to find the atom density. I know that silicon has a diamond structured lattice meaning that it has 8 atoms in a square.

For the (100) plane it's just a square at located at the x, so this means the facing square contains 8 atoms, because silicon has a diamond lattice.

Does that mean the atom density is 8/a^2? Atleast for the (100)?

I'm not exactly sure how you find the (110) and the (111), the planes in the unit cell look odd to mean. How do I determine the number of atoms?

Any help would be appreciated! Thanks.

 

[anathema]

Hello there! Great job on sketching the planes and identifying the lattice structure of silicon. To determine the atom density on each plane, you are correct in using the equation "Atoms per unit cell / (area of the square) = Atoms per unit cell/a^2". However, the number of atoms per unit cell for a diamond lattice is not always 8. It depends on the type of lattice, which is determined by the Miller indices of the plane.

For the (100) plane, the Miller indices are [100], which corresponds to a simple cubic lattice. In this case, the number of atoms per unit cell is indeed 8, and the atom density would be 8/a^2.

For the (110) plane, the Miller indices are [110], which corresponds to a face-centered cubic lattice. In this case, the number of atoms per unit cell is 4, and the atom density would be 4/a^2.

For the (111) plane, the Miller indices are [111], which corresponds to a face-centered cubic lattice as well. In this case, the number of atoms per unit cell is also 4, and the atom density would be 4/a^2.

To determine the number of atoms per unit cell for different lattices, you can refer to a table or diagram that shows the different lattice types and their corresponding Miller indices. I hope this helps! Let me know if you have any other questions. Good luck with your calculations!