Q.How many lattice points are there in one unit cell of each of the following lattice?

$(i)$ fcc: $8\times\tfrac18 + 6\times\tfrac12 = 1 + 3 = 4$.

$(ii)$ face-centred tetragonal: same corner+face count $= 4$. …

Contribution rules.

1. Face-centred cubic.

   $8\ \text{corners}\times\tfrac18 + 6\ \text{faces}\times\tfrac12 = 1 + 3 = 4$

2. Face-centred tetragonal. Same lattice-point positions as fcc (only the axial lengths differ):

   $8\times\tfrac18 + 6\times\tfrac12 = 1 + 3 = 4$

3. Body-centred. …

Apply the sharing fractions to corner, face, edge and body positions and sum. Face-centred cells (cubic or tetr …

• Using $\tfrac12$ for corner atoms instead of $\tfrac18$.
• Thinking a tetragonal face-centred cell has a different count than fc …