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Chemistry

Chemistry. Solid State-II. Session Objectives. Voids Packing fraction. Effective number of atoms =. Packing fraction for simple cubic unit cell. The fraction of total volume of a cube occupied by constituent particles. For fcc unit cell,. Packing fraction for fcc unit cell.

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Chemistry

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  1. Chemistry

  2. Solid State-II

  3. Session Objectives • Voids • Packing fraction

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

  5. For fcc unit cell, 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

  6. For bcc unit cell, Packing fraction for bcc unit cell The number of effective atoms/anions/cations = 2 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 2rsin600 First we will calculate the distance between base atomsurrounded by 6 other atoms and the centre of equilateral triangle formed by three atoms just abovebase atoms.

  8. Packing fraction of hcp h r 2r c

  9. 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 Octahedral (Oh) sites Tetrahedral (Td) sites 12 middle of the edge sites (each shared by 4 unit cells) 1 at the center Net 8 Td sites/unit cell Net 4 Oh 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 Oh sites on top half of unit cell (by symmetry, 3 more on bottom half) 6 Td sites on top half of unit cell (by symmetry, 6 more on bottom half) Total 6 Oh sites Total 12 Td 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

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