Structure & Reactivity in Chemistry

IC. Ionic Compounds

IC5.  Structures of Ionic Solids

 The structure of ionic solids is determined by how the cations and anions can pack together. Generally, one of the ions adopts a standard packing structure, like the metal atoms in a metallic solid.  The counterions then fit into the holes or interstitial spaces among these ions.  It is pretty common for the anions to form a close-packed structure, and for cations to find room in the resulting holes, but sometimes it is the other way around.


Problem IC5.1

Match each isoelectronic ion with the correct picture of its radius.

Five spheres decreasing in size from left to right.

 

Problem IC5.2.

Why might anions more commonly pack into a close-packed structure, rather than the cations?

The holes between the atoms have particular coordination numbers and geometries.  There are many possible holes of different shapes where a counterion can find room.  However, some of these geometries are very common.

For example, in the center of a simple cube, there is room for an additional atom.  This atom is described as sitting in a cubic hole.

A small blue sphere with a square of four larger spheres in front and four larger spheres behind. Dashed lines conect the small sphere with the other spheres.

Figure IC5.1.  An ion in a cubic hole.

 

  The above drawing emphasizes the relationship between the central atom and the atoms that form the corners of the cube.  The central atom is in a cubic coordination geometry.  Alternatively, we could describe the coordination number of the central atom.  Instead of describing the shape formed by the surrounding atoms, we simply count the number of near neighbours.  In this case, the coordination number of the central atom is 8.  We can think of the central atom as sharing ionic bonding with its eight near neighbours.

An atom in a cubic hole might be viewed more easily if we draw lines between the various atoms at the corners of the cube, however.  In that way,we can see more clearly the cubic shape of the cage in which the central atom is sitting.

A cube with large spheres at the corners and a small sphere at the centre.

Figure IC5.2.  An alternative view of an  ion in a cubic hole.

 

   Another common interstitial space in ionic solids is an octahedral hole.  An octahedral hole forms in between two close-packed layers.  Because the atoms in the layers are packed more tightly than in a simple cube, this octahedral hole is generally a little smaller than a cubic hole. 

A triangle of spheres viewed from one edge. Below it is another triangle of spheres facing the other direction and also viewed from the edge.

Figure IC5.3.  An octahedral hole.

 

  An octahedral hole is a space in between six atoms. The six atoms are spread as far apart from each other as possible.

Edge view of a triangle of spheres. Below it is another triangle of spheres facing the other direction. There is a smaller sphere in between these six spheres.

Figure IC5.4.  An atom in an octahedral hole.

 

   A third, common type of interstitial space is a tetrahedral hole.  Tetrahedral holes, like octahedral holes, are found between two close-packed layers.

A triangle of spheres viewed from one edge. Above them is a fourth sphere.

Figure IC5.5.  A tetrahedral hole.

 

  A tetrahedral hole is a space in between four atoms. The four atoms are spread as far apart from each other as possible.

A triangle of spheres viewed from one edge. Above them is a fourth sphere. There is a smaller sphere between these four spheres.

Figure IC5.6.  An atom in a tetrahedral hole.

 

Problem IC5.3.

In the following structures, the anions are represented in red and the cations are represented in blue.  For each structure,

a)  identify the type of unit cell that is visible

b)  identify the type of hole occupied by the counter ion

c)  identify the fraction of those holes that are occupied

d)  identify the number of anions and cations in the unit cell

e)  state the empirical formula (the lowest possible ratio of atoms in the material)

i.  The ions are formed from cesium and chlorine.

A cube with red spheres at each corner, in the middle of each face, and in the middle of each edge. There is a blue sphere in each octant of the cube.

 

ii.  The ions are formed from sodium and chlorine.

A cube with red spheres at each corner. There is a blue sphere in the center of the cube. There is a blue sphere midway along each edge of the cube.

 

iii.  The cations are formed from calcium and the anions are formed from fluorine.

A cube with blue spheres at each corner and in the middle of each face. There is a red sphere in each octant of the cube.

 

iv.  The cations are formed from zinc and the anions are formed from sulfur.

A cube with blue spheres at each corner and in the middle of each face. There is a red sphere in alternating octants of the cube.

 

v.  The cations are formed from zinc and the anions are formed from sulfur.

A rhombic prism with a red sphere in each corner and one displaced to the right of centre, with a blue sphere a third of the way down each edge and just below the red one in the middle.

 

 

 

Additional Information on solid structures:

Liverpool Solid State

      Visualization of solid state structures: unit cells, etc.

 

This site was written by Chris P. Schaller, Ph.D., College of Saint Benedict / Saint John's University (retired) with contributions from other authors as noted.  It is freely available for educational use.

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Structure & Reactivity in Organic, Biological and Inorganic Chemistry by Chris Schaller is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License. 

Send corrections to cschaller@csbsju.edu

 

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