Chemistry
Solid State-II
Session Objectives Voids Packing fraction
Packing fraction for simple cubic unit cell Effective number of atoms = The fraction of total volume of a cube occupied by constituent particles.
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,
Packing fraction for bcc unit cell The number of effective atoms/anions/cations = 2 For bcc unit cell, By the definition of packing fraction,
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.
r h 2rc Packing fraction of hcp
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.
Interstitial sites in ccp
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
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.
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.
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
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.
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