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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. |
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Answer» Solution :The relation between R and R for OCTAHEDRAL void is derived as under : A sphere fitting into an octahedral void is shown in the Fig. For CLARITY, the spheres above and below have been REMOVED. ABC is a right angled triangle. `therefore""BC^(2)=AB^(2)+AC^(2)` `"or"(2R)^(2)=(R+r)^(2)+(R+r)^(2)=2(R+r)^(2)` `"or"((2R)^(2))/(2)=(R+r)^(2)` `"or"(2sqrt2R)^(2)=(R+r)^(2)` `"or"R+r=sqrt2R` `"or"r=sqrt2R-R` `"or"r=R(sqrt2-1)` `"or"r=0.414R` 
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