Question

Average number of atoms per unit cell for all crystal structures

Answer 1

Hello friend...

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)

plus

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

which equals to 4

Hope this helps you...