Zinc blende 5: holes in the structure

We can think of the zinc ions occupying holes in the face-centred cubic array of sulfide ions. Inspection of any of the zinc ions in the unit cell shows that its four sulfide neighbours lie on the corners of a tetrahedron with the zinc ion at its centre. This is shown in the image to the left, in which a green tetrahedral wireframe is drawn around the neighbouring sulfide ions around the top left zinc ion.

Holes and stoichiometry:

In the fluorite lattice we saw that there is a 2:1 ratio of tetrahedral holes to cubic close-packed ions, and that there is a tetrahedral hole in the middle of the eight octants of the unit cell cube. (Cubes can be divided into eight smaller cubes, called octants, four in the top half and four in the bottom half of the larger cube.) In zinc blende only half of the octants are occupied by a zinc ion. An example of an empty tetrahedral hole is outlined using a violet wireframe. You should be able to see the four empty and four occupied tetrahedral holes in the eight octants. This is all consistent with the 1:1 stoichiometry of zinc and sulfur in the compound. Note that the zinc ions occupy alternate octants such that the four zinc ions in the unit cell themselves form a tetrahedron. At the centre of this tetrahedron is an empty tetrahedral hole; to see a tetrahedron of zinc ions around an occupied tetrahedral hole look at the centre of the large cube on the previous page.

Holes in the close-packed layers:

If you rotate the image so that the cube is standing on a corner with the body diagonal running vertically you can see how the tetrahedral holes lie in relation to the close-packed layers of calcium ions (they are not, strictly, close-packed as the calcium ions are not in contact). The close-packed sulfide layers (also not strictly close-packed) are horizontal when the cube is in this orientation. The holes can be seen to be nested above the centre of an equilateral triangle of sulfide ions and beneath another sulfide ion. This is a nice illustration of the three-fold symmetry found in tetrahedra.

Go to page 6 to focus on the tetrahedral hole between the close-packed layers.

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