1.

Calculate the packing effeciency of a fcc crystal in which all the tetrahedral and octahedral voids are occupied by the largest spheres without disturibing the lattice.

Answer» Fcc has 4 atoms per unit cell
No. of tetrahedral voids = 8
No. of octadedral voilds = 4
If R is the radius of the atoms in the packing
Radius of tetahedral void = 0.225 R
Radius of octahedral void = 0.414 R
for fcc, ` a = 2 sqrt2 r = 2sqrtR`
packing efficiency ` = (" Volume occupied by all spheres")/("Volume of the unit cell") `
` = (4 xx 4/3 pi R^(3) + 8 xx 4/3 pi ( 0.225 R)^(3) + 4 xx 4/3 pi ( 0.414 R)^(3))/((2sqrt2R)^(3))` = 0.81


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