Question

Find the fill rate of the diamond structure, in which atoms covalently bond with each other.

Answer 1

Fill rate or packing density is defined as the ratio of volume filled by spheres to the total volume of cell.

So total volume of cubic cell is

a is dimension of unit cell.

So in diamond structure of lattice cell number of Lattice points are n=4

And number of atoms sitting on every lattice points is is N=2

So,

Total volume filled by spheres is

Now distance between centers of two joined sphere is can be calculated from the geometry

Which is

So radius r=d/2

So,

Volume filled by sphere is

So dividing this volume by total volume we get fraction of volume filled

So,

so in % fill factor is = 34%

For diamond structure.