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Question

If for any fcc lattice, the tetrahedral void number is always 8 ? As the fcc's Zeff is 4 and remains constant, Justify


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Solution

FCC-Face centred cubic cell:

  • For a total of 8, a face-centred cubic unit cell contains net tetrahedral voids of 8. Tetrahedral voids are located between each corner and the base of the unit cell. Then there are 12 octahedral voids at the midpoints of the unit cell's sides and there are four net octahedral voids.

Tetrahedral voids:

  • The void observed in substances with tetrahedral crystal structures is known as a tetrahedral void. Voids are generally thought of as the empty areas that exist in crystal systems. These holes are mostly caused by the different atomic arrangements.

Tetrahedral voids in fcc:

  • If there are no atoms or ions in a close-packed structure, the number of octahedral voids and tetrahedral voids in a close-packed structure (ccporfcc) would be nn&2n2n respectively
  • Each unit cell in the fcc structure has 8 tetrahedral voids, where Zeff=4 which is nothing but the number of atoms in fcc. where the unit cell is partitioned into 8 small cubes.
  • If we divide the FCC unit cell into 8 small cubes then each small cube has one tetrahedral void located at its own body centre. Since the formula is 2n here, In other words, there are 2×Zeff=8 tetrahedral voids overall in a single cell.

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