1. Chemistry

2. Solid State-II

3. Session Objectives  Voids  Packing fraction

4. Packing fraction for simple cubic unit cell Effective number of atoms = The fraction of total volume of a cube occupied by constituent particles.

5. Packing fraction for fcc unit cell The number of effective atoms/anions/cations = 4 By the definition of packing fraction, Taking the value of ‘a’, we get For fcc unit cell,

6. Packing fraction for bcc unit cell The number of effective atoms/anions/cations = 2 For bcc unit cell, By the definition of packing fraction,

7. Packing fraction of hcp Volume of the unit cell=Base area x height Base area of regular hexagon =Area of six equilateral triangles each with side 2r and altitude 2rsin60 0 First we will calculate the distance between base atom surrounded by 6 other atoms and the centre of equilateral triangle formed by three atoms just above base atoms.

8. r h 2rc Packing fraction of hcp

10. Interstitial sites or Voids Surrounded by four spheres which lie at the vertices of a regular tetrahedron. The number of tetrahedral voids is 2 × number of octahedral voids. Surrounded by six spheres which lie at the vertices of a regular octahedron. The number of octahedral voids is the number of atoms present in close packed arrangement.

11. Interstitial sites in ccp

12. Interstitial sites in fcc 1 at the center 12 middle of the edge sites (each shared by 4 unit cells) Net 4 O h sites/unit cell Octahedral (O h ) sites Tetrahedral (T d ) sites Net 8 T d sites/unit cell

13. Locating Tetrahedral and Octahedral Voids: fcc Number of octahedral voids are equal to number of ions present in the unit cell. Number of tetrahedral voids are double of octahedral voids.

14. Locating Tetrahedral and Octahedral Voids : bcc Number of octahedral voids are equal to number of ions present in the unit cell. Number of tetrahedral voids are double of octahedral voids.

15. Interstitial sites in hcp 3 O h sites on top half of unit cell (by symmetry, 3 more on bottom half) Total 6 O h sites 6 T d sites on top half of unit cell (by symmetry, 6 more on bottom half) Total 12 T d sites

16. Locating Tetrahedral and Octahedral Voids : hcp Each body diagonal has two tetrahedral voids. Center of body and each edge center has octahedral void. Dividing cube into 8 minicubes, centre of each minicube has tetrahedral void.

17. Thank you