On Strong Inorganic Bonds and Cation Cages

Strong inorganic bonds were mentioned in an earlier post. The term as used is descriptive and informal. I use the term to describe a bond formed in an irreversible reaction, one that runs to completion and where the bonds formed are permanent except under extreme conditions. If you have thoughts or suggestions on how to best describe or characterize such bonds, I would very much like to hear them.

The thing about strong inorganic bonds is that they are useful. To form coatings, you must start at some point where you only have a surface to be coated and then, through a series of generally irreversible processes, you must bring the elements of your coating together and form a lasting deposit on said surface. During processing, strong inorganic bonds are useful because they control the progression and direction of the processes. When you develop coatings, you develop more than the final composition of mater ultimately formed; you must also develop the processes for applying the coating. When the coating process is complete, there is generally some requirement for permanence or persistence of the coating. For the finished coating, strong inorganic bonds are useful because they impart durability and chemical resistance.

The purpose of this blog is to discuss coatings and coating development, not to give lessons in materials science unnecessarily. So, I’m going to try to cut to the chase and rather than go into the theory behind the nature of strong ionic bonds, I'm just going to jump ahead to the answer: strong inorganic bonding is due to a combination of ion size, cation oxidation number and the cation cage.

Let’s consider the example given in the earlier post. The example was that of sodium chloride, a highly ionic inorganic compound that readily dissolves in water, and aluminum oxide, a highly stable inorganic compound that is insoluble in water. In the following table, there are some quantities given. I’m not going to go into the theory behind these quantities or explain why I selected them except to say that these quantities illustrate some important differences between the two compounds and provide clues as to why the bonding in these two materials is so very different.

Figure 1. Comparison of selected properties of aluminum oxide and sodium chloride to provide clues for and to motivate an understanding of the origin of the differences in the bonding in these materials.

Figure 1 lists ionic radii for aluminum oxide and sodium chloride. The values include the anionic radii, r_a, for oxygen and chlorine and the cationic radii, r_c, for aluminum and sodium. The oxidation numbers, z_c, for aluminum and sodium are also given. Following that, there are various derived values including the ionic radius ratio (cation-to-anion ratio) and the Dietzel field strength for both compounds. Also, for reference, the melting point and single-bond strengths are given.

One of the first things that figure 1 brings home is that the sodium chloride ions are much larger than the aluminum oxide ions. Next, the oxidation numbers for the aluminum oxide ions are larger than for the sodium chloride ions. Therein lies much of the story: small ions with large oxidation numbers promote strong inorganic bonds. Those are clues, but they don't really explain anything as they suggest a difference in degree and not a difference in kind.

When we looked only at electronegativity earlier, sodium chloride and aluminum oxide seemed very similar: they both should be about 63% ionic in character but the behavior of the sodium chloride and aluminum oxide is such that it suggests that the bonding in these materials is of two different kinds. How can we account for the differences? A short answer would be that we can ascribe the difference to the shielding and tightness of the respective cation cages.

A cation cage is a structure found in most ionic and inorganic materials. The cage is not made of cations. Rather, it is made of anions. Anions are usually significantly larger than cations with the result that in most ionic and inorganic compounds, the anions are tightly packed and the cations take up positions in the small gaps between the anions. Think of pool balls tightly packed into a rack. The anions are like the pool balls: tightly packed and touching each of their neighbors at a single point. Like the pool balls in the rack, even though they are tightly packed, there are still small gaps or spaces: interstitial sites where a smaller object could be fit in. It is in these interstitial sites where the cation cages are formed. Not every interstitial site will act as a cation ion cage. Generally only a portion will be filled and the filled sites are generally distributed in a network of filled sites so as to preserve local electroneutrality. Each cation cage traps a single cation in the center of the cage. The anions that surround the cation shield it from the repulsive forces of nearby cations. The tighter the cage and the more effective the shielding, the stronger and more stable the bonding. We listed two properties in the table, melting point and single-bond strength, where the effects of the cation cage can be detected but the effect of the cation cage can be seen in many other properties as well such as hardness and density.

Cation cages are the building blocks of inorganic coatings. Being able to control the size, shape and distribution of the cages that are formed is an essential development tool. Cation cages come in a number of different shapes depending on the packing of the anions and the cation-to-anion radius ratio. The most common cages are tetragonal, octahedral, and square antiprism. Tetragonal is the simplest.

Figure 2. An aluminum(III) ion enclosed in a cation cage. The oxygen ions are the anions which form the cage and are centered on the cage's vertices (corners) shielding the cation from the charges of other nearby cations.

In figure 2, the first view is of the cation cage shown as a wire frame with an aluminum(III) ion disposed in the center of the cage. The next two views show how the oxygen ions are disposed at the vertices (corners) of the cage and how they act together to form the cage and to shield the trapped aluminum(III) ion. I find it helpful to think of the anions as pool balls in a rack except, instead of being packed in a two-dimensional arrangement, it is packed in various three dimensional arrangements that might comprise two or more layers. Then I like to remove a few pool balls at a time and look for the different interstitial spaces that different packing arrangements can provide.

The aluminum(III) ion, when surrounded by oxygen ions, does not normally reside in a tetragonal cage. It prefers an octahedral cage because the cation-to-anion radius ratio (0.536) is too large for a tetragonal cage. However, adding cations with high oxidation numbers, z_c > 4 such as phosphorous(V), promotes packing arrangements of the oxygen anions that can cause the aluminum(III)'s cages to adopt the tetragonal form.

The aluminum(III) ion in α-Al₂O₃ is enclosed in an octahedral cation cage.

Figure 3. An aluminum(III) ion enclosed in an octahedral cage. In the second and third views, the oxygen ions are added one level at a time to help visualize how the cation is disposed within the cage. In the bottom layer, the disposition of the anions is identical to the disposition of anions for the tetragonal cation cage shown in Figure 2. The shape of the octahedral cation cage could be described as a trigonal antiprism. It usually isn't.

Figure 3 shows the aluminum(III) ion in it's most usual configuration with oxygen ions. This configuration is very useful as it is possible to substitute other cations of about the same size for a portion of the aluminum(III) ions in a coating formula. This enables selective modification of properties, such as melting point, while retaining some of the chemical stability and transport properties of the unalloyed aluminum oxide. Examples of cations that could be substituted for a portion of the aluminum(III) ions would be the iron(III) and chromium(III) ions or any trivalent ion with a radius between about  52 and 81 pm. Thus yttrium(III) would be too large and boron(III) would be too small.

Sodium chloride is unable to take on the tetragonal or octahedral cation ion cage configurations. Because its cation to anion ratio is large (0.695), it must take on the larger and more complex square anti-prism form.

Figure 4. A sodium ion enclosed in a square antiprism cage. The shape of the cage is complex and comprises eight identical vertices and has two types of faces (two square and eight triangular).

Figure 4 shows a sodium ion in a square antiprism cage. The figures 2, 3 and 4 have been drawn to a common scale to help illustrate some of the features of the different kinds of bonding and to bring out some of the nature of the strong inorganic bonds. It can be seen that the ions in sodium chloride are significantly larger than those in aluminum oxide which leads to lower Dietzel field strengths in the sodium chloride. The sodium chloride cation cage also comprises more anions leading to lower single-bond strengths.

We can conclude from these illustrations that if we want to develop inorganic coatings with good durability and chemical resistance, we should be looking for cations with high oxidation numbers, small ionic radii and a small cation-to-anion radius ratio.

Cation cages are related to the topic of Coordination Number (CN). The coordination number for an anion is the number of cations that it touches. For oxygen, this is generally two. For a cation, the coordination number is the number of anions that it touches. For the cation cages that we looked at in this post, the coordination numbers would be 4, 6 and 8 for tetragonal, octahedral, and the square antiprism, respectively.

I think that that is enough talking about bonding for now. It's time to put some of what we have discussed to use and to see how it plays out in the real coating world. What we have discussed is going to be very useful and you can bet that the cation cages will play a significant role. Our upcoming discussion will cover many fields of application and, while what we have discussed so far will be useful, there are many big surprises to come. I am looking forward to it.

The next post will be about how to form coatings and will discuss the many ways that aluminum oxide coatings can be formed as they are very widely used in architecture, manufacturing and the power generating industries.