Question

Show that a particle of radius less than 0.441 times the radius of the constituent particle can only be placed in an octahedral void without disturbing the crystal lattice.

Answer 1

In a close-packed structure, octahedral voids are formed by the arrangement of six surrounding spheres. Let the radius of the constituent particle be R and the radius of the octahedral void be r.

The radius ratio for a particle to fit into an octahedral void without disturbing the crystal lattice is given by `r/R` = 0.414

However, for the particle to fit comfortably and not distort the lattice, its radius should be slightly smaller than this limit.

The actual maximum ratio is

`r/R` < 0.441

This value (0.441) provides a safe threshold that allows some tolerance for atomic vibrations and imperfections while maintaining lattice stability.