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A mineral having formula AB2 crystallises in ccp lattice with A atoms occupying the lattice points. The CN of A is 8 and of B is 4. What percentage of the tetrahedral sites is occupied by B atoms.

A mineral having formula AB2 crystallises in ccp lattice with A atoms occupying the lattice points. The CN of A is 8 and of B is 4. What percentage of the tetrahedral sites is occupied by B atoms.

Grade:12

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear sudhanshu,

Each host atom in a CCP lattice is surrounded by and touches 12 nearest neighbors, each at a distance of 2r: 

  • There are six atoms in the central A layer;
  • There are three atoms  in the B layer above the A layer; 
  • There are three atoms in the C layer below the A layer.

When spheres of equal size (radius r) are packed together as closely as possible by stacking layers of hexagonally closest packed planes, the spheres themselves occupy 74% of the available space. The cavities of empty space ("holes" or "interstices") are found between layers.

For example, consider any two successive planes in a closest packed lattice. One atom in the A layer nestles in the triangular groove formed by three adjacent atoms in the B layer, and the four atoms touch along the edges of a regular tetrahedron. The edges of the tetrahedron are of length 2r, and the center of the tetrahedron is a cavity called the Tetrahedral  hole (a common symbol for "tetrahedral" is Td). If a guest sphere in that cavity is in contact with all four host spheres, its radius is  about 0.22r

 

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