in a ccp type structure ,if half of the face-centred atoms are removed,then % void in unit cell is approximately - Chemistry - The Solid State

Question

in a ccp type structure ,if half of the face-centred atoms are
removed,then % void in unit cell is approximately?

Tinku Jangra · Accepted Answer

For a CCP type structure, the atoms are present at the corners as well as in the face centre
So, the number of atoms present =18×8 + 12×6 = 4So, when the half of the face centred atoms are removed, the number of atoms present = 18×8 + 12×3 = 52Volume of the cube = a3 where is the edge length
The volume occupied by an atom = 43πr3  (r is the radius of atoms)For a FCC lattice, 4r=2aPacking efficiency = number of atoms present×volume occupied by one atomtotal volume of cube×100 = 52×43πr3a3×100=52×43πr3(22r)3×100=46
4%Hence the % of void = 100-46
4 = 53 6%

in a ccp type structure ,if half of the face-centred atoms are removed,then % void in unit cell is approximately?