Derivation of the Relationship Between Radius r of the Octahedral Void and the Radius R of the Atoms in the Close Packing.
A sphere fitting into the octahedral void is shown by shaded circle. A sphere above and a sphere below this small (shaded) sphere have not been shown in the figure.
fig 2.13
Considering the triangle ABC
BC2 = AB2 + AC2
(2R)2 = (R+r)2 + (R+r)2
(2R)2 = 2 (R+r)2
r = 0.414 R
Radius ratio of the octahedral void = 0.414 R
