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Holes in Crystal Structures

Ionic Solids

You have seen that metals generally pack in a closest-packed structure (hcp or ccp). Metals are not always perfectly spherical, however, and orbital overlap between two metal atoms can lead to bonding that also influences the structure of the solid. Consequently some metals do not crystallize in a closest-packed structure.

What are the structures of ionic solids?

Regardless of the nature of a compound, a crystal can always be described as an array of unit cells. Any molecule, not just metals, will attempt to pack in the most compact structure; nature seeks the most efficient packing. Intermolecular interactions, however, may be more important than packing efficiency. Intermolecular hydrogen bonding, for example, is often quite important.

To simplify this topic, let's restrict our attention to ionic solids comprising monatomic ions (e.g., NaCl, KI, CaO, TiO2).

The crystal structures of ionic solids composed solely of monatomic ions is governed by two relatively simple factors.

  1. The most efficient packing of the ions is desired.
  2. Because like charges repel, it is necessary to prevent two anions or two cations from coming in contact with each other.

Just as covalent bonding and non-spherical atoms created exceptions to the closest-packing rule for metals, these same issues can be important in the packing of ionic solids. Consequently there are many exceptions to the simple rules discussed here.

Holes in Crystal Structures

In most ionic solids the cation and anion are different in size. The larger type of ion, which is typically the anion, packs to yield a particular structure, which is often a closest-packed structure. The smaller ion, typically the cation, then fits into the holes between the larger ion.

Holes come in a variety of geometries and sizes. Each atom in a crystal is surrounded by a certain number of ions of opposite charge. This number is called the coordination number for the ion. If an ionic solid has (6,3)-coordination, the cation has a coordination number of six (the first number) and the anion has a coordination number of three (second number).

Sizes of Holes

Subsequent exercises illustrate the geometries of the various hole sites. As you view the various hole sites, it will be obvious that the different geometries lead to holes of different sizes. Specifically, the ratio rhole/r is smallest for the trigonal hole and largest for the cubic hole.

The display below shows the relative sizes of the largest spheres that can fit into a hole of each geometry. The blue sphere on the far right shows the size of the surrounding atoms that form the hole. Follow the links for the different types of holes to examine the three-dimensional structure of hole site.

Trigonal Hole
coordination number = 3
Tetrahedral Hole
coordination number = 4
Octahedral Hole
coordination number = 6
Cubic Hole
coordination number = 8
Atom

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