Halite 4: holes in the structure

We can think of the smaller sodium ions occupying holes in the face-centred cubic array of chloride ions. Inspection of the central sodium ion shows that its six chloride neighbours lie on the + and − x, y and z axes at an equal distance of half of the unit cell length away from the sodium ion. This is equivalent to the sodium being in the centre of a regular octahedron of chloride ions. This is shown in the image on the left, in which a black octahedral wireframe is drawn around the neighbouring chloride ions.

Ratio of holes to chloride ions:

As well as the centre of the cubic unit cell, the centres of the 12 edges are also octahedral holes since they also have six nearest neighbours along the + and − x, y and z axes. This is most apparent in the image in two pages' time by considering a sodium ion on one of the edges that is shared with the neighbouring cell, where five of the six nearest neighbour ions are visible. Since the cell occupancy of these hole positions (4) is equal to that of the chloride ions, there is a 1:1 ratio of octahedral holes to face-centred cubic ions.

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 octahedral hole lies in relation to the close-packed layers of chloride ions (they are not, strictly, close-packed as the chloride ions are not touching, but they occupy the lattice coordinates associated with close-packing). The close-packed chloride layers are horizontal when the cube is in this orientation. The hole can be seen to be nested between two equilateral triangles of chloride ions which point in opposite directions. This is a nice illustration of the three-fold symmetry found in octahedra.

Go to page 5 to focus on the octahedral hole between the close-packed layers.

Page 1 Page 2 Page 3 Page 5 Page 6 Page 7