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Question
If the radius of the octachedral void is r and radius of the atoms in close packing is R, derive relation between r and R.
Solution
A sphere with centre O, is fitted into the octahedral void as shown in the above figure. It can be observed from the figure that ΔPOQ is right-angled
∠POQ = 900
Now, applying Pythagoras theorem, we can write:
`PQ^2 = PO^2 + OQ^2`
`=>(2R)^2 = (R+r)^2 + (R+r)^2`
`=>(2R)^2 = 2(R+r)^2`
`=rR^2 = (R+r)^2`
`=>sqrt2R = R +r`
`=>r =sqrt2R -R`
`=> r = (sqrt2-1)R`
`=>r = 0.414R`
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