If the radius of the octahedral void is r and radius of the atoms in close packing is R, derive relation between r and R.



In the given figure, let the sphere have the centre, O and is fitted in the octahedral void.


As given, radius of the sphere fitted in the octahedral void = r


And the radius of the atoms in close packing = R


Here, angle AOD = 900


In triangle AOD,


DA2 = OA2 + OD2


(R+R)2 = ( R + r )2+ (R+r)2


4R2 = 2(R+r)2


2R2 = (R+r)2


√2 R = (R+r)


R + r = R


r = R – R


r = R (1.414 - 1)


r = 0.414 R


This is the required relation between r and R.


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