Common Salt

How do Different Sized Atoms Pack ?

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Very often when we have two or more different atoms, the packing is determined by the larger atoms - the smaller atoms just have to make do with whatever space is left ! This is the case of some simple salts such as ¶lithium chloride (LiCl). Lithium is the smallest of all atoms with the exception of hydrogen, and the big chlorine atoms just pack together with the ¶CCP structure, leaving the small lithium atoms to squeeze into the octahedral holes.

Why are the holes called octahedral ? Because each hole occupied by a lithium atom is surrounded by six chorine atoms at the vertices of an ¶octahedron. Let's draw these atoms as small spheres to emphasise instead the "co-ordination polyhedrae". Such geometrical concepts are very popular with crystallographers since they help us understand the co-ordination of atoms (their nearest neighbours) in more complex structures, as we shall see.

Common salt or sodium chloride (NaCl) is actually a little more democratic than brother lithium chloride. The sodium atoms are bigger and can exert more influence than can the tiny lithiums. The structure of ¶sodium chloride should then be regarded as a cubic packing of almost equal spheres. But in practice these democratic considerations do not change the actual structure; sodium ends up in the same position as poor lithium !

As well as octahedral holes in the CCP structure, there are also tetrahedral holes. In structures such as that of the zinc sulphide (ZnS) mineral ¶zinc-blende the Zn atom prefers to occupy these tetrahedral holes, where it is surrounded by only four S-atoms. Note that only half of the tetrahedral holes are occupied in ZnS, where-as all of the octahedral holes are occupied in NaCl.

Again it is possible to draw the ¶co-ordination polyhedrae around zinc, but in this case it may be better to emphasise the actual bonds between the Zn and S atoms, using a so called ¶ball-and-stick model. As well as CCP cubic close packing ABCABC.. of the large anions as in zinc blende, we might alternatively expect to find HCP hexagonal close packing ABAB.. in some similar materials.

HCP packing of oxygen anions (red) produces the ¶ZnO wurtzite structure of zinc oxide. Notice that the co-ordination of Zn is still tetrahedral. Because there is little energy difference between the two types of structures, we can have more complex packing arrangements such as ABC.AB.ABC... which results in a whole series of polytype structures.

The anti-fluorite Li2S structure (not shown), like zinc-blende ZnS, consists of cubic close packed anions S, but now all of the tetrahedral holes are occupied - by small Li cations. When the cations are larger, such as those of calcium, the more common ¶CaF2 fluorite structure (shown opposite) is favoured, with the sites of the cations (blue) and anions (yellow) interchanged. The fluorite structure is favoured when the cations are so big that they need eight anions to cover them.

The ¶TiO2 rutile or cassiterite (SnO2) structure is adopted by quadri-valent metals or di-valent metal fluorides, such as MnF2. Here the blue Ti cations are in octahedral holes between the red oxygen anions, which is readily seen when we draw their co-ordination octahedrae.

Actually, the cation-anion distances are not all quite equal, two being a little longer than the other four. The ¶SnO2 cassiterite co-ordination octahedrae are then slightly stretched along one axis. Such elongated octahedrae are relatively common for di-valent and quadri-valent cations.

Returning to zinc-blende, we note that this tetrahedrally coordinated FCC structure takes a particularly simple form when there is only one kind of atom - it is the structure adopted by two of the most common elements, silicon and carbon, and is known as the ¶diamond structure (more later).

Many mineral structures are based on variations of the diamond or silicon structure. For example, if we replace the silicon atoms (Si) by silicon oxide units (SiO4) they pack together in a similar way to form the mineral ¶cristobalite SiO2. We see that the SiO4 units are tetrahedrae, and that these tetrahedrae are connected by all corners in cristobalite to form a relatively dense silica structure (more later).

But what happens when the second atoms are too small for the holes between the larger atoms ? And what happens when we have more than two kinds of atoms ? Let's look at one of the most common and most important mineral structures, that of perovskite.

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