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In fcc arrangement of A and B atoms where A atom are at corner of the unit cell and B atoms are at face centre, one of the atoms are missing from the corner of the unit cell then find the percentage of void space in the unit cell?

Mandar Wani , 6 Years ago
Grade 12
anser 1 Answers
Arun

Last Activity: 6 Years ago

consider the lattice constant as a and radius of atom as r , picturing the face diagonal, it would be equal to
 
a * sqrt 2 = 4r
 
r = a / 2 *sqrt(2)
 

now usually an fcc structure has 4 atoms as follows,

1/ 8 * 8 = 1 atom contribution from 8 corners.
½ * 6 = 3 atoms from 6 faces.

But if 1 atom is missing from 1 corner than no of atom consideration should be,

 

3 + 1/8 * 7 = 31/8

 

hence volume of 31/8 atoms

4/3 * pi * r^3 = 0.7176 a^3

 

hence emplty space is around 28.24 %

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