Question

atomic packing fraction of diamond cubic lattice is in percent​

Answer 1

Answer:

Packing fraction = (N atoms) x (V atom) / V unit cell

N atoms is the number of atoms in a unit cell. V atom is the volume of the atom, and V unit cell is the volume of a unit cell.

Substitute the number of atoms per unit cell into the equation. Diamond has eight atoms per unit cell, so the diamond packing fraction equation now becomes:

Packing fraction = 8 x (V atom) / V unit cell

Substitute the volume of the atom into the equation. Assuming atoms are spherical, the volume is: V = 4/3 × π × r3

The equation for packing fraction now becomes:

Packing fraction = 8 x 4/3 × π × r3/ V unit cell

Substitute the value for the unit cell volume. Since the unit cell is cubic, the volume is V unit cell = a3

The formula for packing fraction then becomes:

Packing fraction = 8 x 4/3 × π × r3/ a3

The radius of an atom r is equal to √3 x a/8

The equation is then simplified to : √3 x π/16 = 0.3401

نسخ ولصق