Locating Tetrahedral and Octahedral Voids

LOCATING TETRAHEDRAL AND OCTAHEDRAL VOIDS The close packed structures have both octahedral and tetrahedral voids. In a ccp structure, there is 1 octahedral void in the centre of the body and 12 octahedral void on the edges. Each one of which is common to four other unit cells. Thus, in cubic close packed structure. Octahedral voids in the centre of the cube =1 Effective number of octahedral voids located at the 12 edge of = 12 × 1/4 = 3 ∴ Total number of octahedral voids = 4 In ccp structure, there are 8 tetrahedral voids. In close packed structure, there are eight spheres in the corners of the unit cell and each sphere is in contact with three groups giving rise to eight tetrahedral voids

Circles labelled T represent the centers of the tetrahedral interstices in the ccp arrangement of anions. The unit cell "owns" 8 tetrahedral sites.
Circles labelled O represent centers of the octahedral interstices in the ccp arrangement of anions (fcc unit cell). The cell "owns" 4 octahedral sites. Illustration 16. In a solid, oxide ions are arranged in ccp. Cations A occupy one – sixth of the tetrahedral voids and cations B occupy one third of the octahedral voids. What is the formula of the compound? Solution: In ccp with each oxide there would be 2 tetrahedral voids and one octahedral voids 1/3rd octahedral voids is occupied by B and 1/6th tetrahedral void by A. Therefore the compound can be Illustration 17. In a crystalline solid, having formula AB2O4, oxide ions are arranged in cubic close packed lattice while cations A are present in tetrahedral voids and cations B are present in octahedral voids (i) What percentage of the tetrahedral voids is occupied by A? (ii) What percentage of the octahedral voids is occupied by B? Solution: In a cubic close packed lattice of oxide ions there would be two