Question

derive a relationship between radius (r) of an octahedral void and radius (R) of an atom (sphere)
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Answer 1

Explanation:

Let the radius of the octahedral void be r and radius of the atoms in close-packing be R and the edge length be a.

In the right angle triangle ABC,

AB=BC=a

For the diagonal AC,

AC=

AB

2

+BC

2

=

a

2

+a

2

=

2

a

Also,

AB

AC

=

a

2

a

And, AB=2R

AC=R+2r+R=2R+2r

∴

2R

2R+2r

=

2

r=0.414R

Hence, the relation is r=0.414R