question_answer 38)

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. 

Answer:

                An octahedral site is created by the arrangement of four spheres (atoms) in one plane, one sphere (atom) on top and one sphere (atom) below this plane. The shaded portion in the figure represent an octahedral void. For clarity, the spheres present above and below the void are not shown. Let, length of each side of the square is 'a' and the radii of the void and the sphere (atom) are r and R respectively. Consider the right angled triangle ABC, As AC = 2r + 2R                                                                             ?.(i) Now AB = 2R or a = 2R Dividing Eqn. (i) by Eqn. (ii), we get Thus, for an octahedral void,  For octahedral void, the radius ratio = 0414