Compute the percentage void space per unit volume of unit cell in zinc-fluride structure. In zinc fluoride, anions occupy
fcc positions and half of the tetrahedral holes are occupied by cations.
25%
Since anions occupy fcc positions and half of the tetrahedral holes are occupied by cations. Since there are four anions and 8 tetrahedral holes per
unit cell, the fraction of volume occupied by spheres/unit volume of the unit cell is
=4×(43πr3a)+12×8×(43πr3c)16√2r3a = π3√2{1+(rcra)3}
∗∗ for tetrahedral holes,
=rcra=0.225
=π3√2{1+(0.225)3}=0.7496
∴Void volume = 1-0.7496 = 0.2504/unit volume of unit cell % void space = 25.04%