Q 14 If the radius of the octahedral void is r and radius of the atoms in closepacking is R, derive relation between r and R.

Q 14 If the radius of the octahedral void is r and radius of the atoms in closepacking is R, derive relation between r and R.

 Let take r and R are the radii of the octahedral site and atoms respectively,

 then use Pythagoras theorem we get

(2R)² = (R+r)² +(R+r)²

4R²    = 2(R+r)²

Divide by 2 we get

2R²    = (R+r)²

Take root both side we get

R√2 =R+r

 R√2 – R = r

r  = R(√2–1)

value of √2= 1.414

r  = R(1.414–1)    

     r  = 0.414 R