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Derive the atomic packing fractions for the diamond structure and for the monatomic fcc lattice. For...

Derive the atomic packing fractions for the diamond structure and for the monatomic fcc lattice. For the fcc lattice, determine which real-space planes have the highest density of atoms.

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Answer #1
  • It is formed by carbon atoms.
  • Every carbon atom is surrounded by four other carbon atoms

    situated at the corners of regular tetrahedral by the covalent

    linkages.

  • The diamond cubic structure is a combination of two

     interpenetrating FCC sub lattices displaced along the body

    diagonal of the cubic cell by 1/4th length of that diagonal.

  • Thus the origins of two FCC sub lattices lie at (0, 0, 0) and

    (1/4, 1/4,1/4)

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