I don't understand the concept of unit cell and the number of atoms per unit cell in a cubic lattice also the calculations for the number of atoms. For example in the $\ce{fcc}$ lattice, number of atoms per unit cell is:

$$8\cdot\frac{1}{8} + 6\cdot\frac{1}{2}=4$$

  • what does the 2 and 8 in the denominator stand for?
  • also 4?

1 Answer 1


The denominator signifies the number of cubes that are needed to completely encompass the whole point. For example, a corner point can be thought of as a center of 8 whole cubes, while a face centre is enclosed by 2 cubes and an edge center by 4. Hence, only 1/8 of a corner atom is in a specific unit cell and so on and so forth.

Consequently, the total number of atoms in a unit cell (say a FCC) would be equal to -

(no of corners)(fraction of corner in the unit cell) = 8(1/8)


(no of face centers)(fraction of face center in the unit cell) = 6(1/2)

which equals to 4

  • 1
    $\begingroup$ It should be noted that this answer (and the question!) only make sense for a unit cell which contains an atom in the corner and one on each symmetry-equivalent face. You might then translate the unit cell (or the atoms) to show how one can arrive at the end result of four in a different way. $\endgroup$
    – Jan
    Oct 8, 2017 at 15:59

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.