Section Four

Describing the Crystal Structure of Sodium Chloride

To practice applying the concepts described above, we’ll walk through describing the structure of the crystalline ionic solid that is probably the most familiar to you: table salt, or sodium chloride.

Model 25: Chime model of NaCl.

First, let’s determine the packing arrangements for each of the two kinds of ions in NaCl. Looking at the model, we’ll start with the green coloured spheres, the Cl^- anions. (Note: Since the NaCl stoichiometry is 1:1, both ions will have the same packing pattern, therefore we can arbitrarily assign a colour to each ion). Remember that in determining packing patterns and unit cell types, we only consider one type of ion at a time. Let’s look at the model from the top. First, we need to determine whether the packing is of the simple type (layers superimpose directly) or the closest type. The simple cubic packing is the easiest to find, because in it the ions in a given layer are arranged in an infinite array of squares. The ions in other layers are also arranged in squares that superimpose directly onto the first one.

In the case of NaCl, we do see squares, but a closer look shows that they are made of alternating kinds of ions. Looking only at the green coloured ions, we can see a square on the top layer if we rotate the model 45 degrees without tipping it, but there is no overlapping square in the next lower (middle) layer.

Model 26: Chime model of NaCl - squares highlighted.

Since the two layers do not superimpose, we do not have simple cubic packing for the green coloured ions. The remaining options are simple hexagonal packing and the two closest packing patterns: cubic closest packing, and hexagonal closest packing. No matter which of these three patterns NaCl will end up being, we need to search for a hexagonal packing layer made up of green ions. This part is a bit tricky and takes some practice to do quickly. The easiest thing to do in this case is to try to look at the model from all angles until you see a hexagonal layer. If the model "looks" square-like (as NaCl does when you first see it), you usually need to tip it up "on edge" to see the hexagon. A demonstration is given below; but here practice makes perfect. Allow your eyes to adjust and try to look "diagonally" through the structure.

Model 27: Chime model of NaCl - hexagon highlighted.

Now that you’ve identified the hexagon, we can determine whether the packing is simple hexagonal or one of the closest-packed patterns. In simple hexagonal packing, the hexagon that you see will stack up directly on top of another hexagon, and directly below yet another one. Every ion will have a partner of the same colour immediately above it and immediately below it. Again, there is a bit of a visual trick here because some of the models are not big enough to allow you to see three layers of hexagons. For example, the NaCl model will only show you a central hexagon and an equilateral triangle above it and below it. Nevertheless, this should be enough to verify that the green ions either stack up directly or don’t.

Model 28: Chime model of NaCl - layers highlighted.

In the case of NaCl, we can see that the equilateral triangles above and below the central hexagon do not directly overlap the ions in that central layer. Thus, we do not have simple packing for the green ions in this structure, and the two remaining options are cubic closest packing and hexagonal closest packing. With a bit of practice, these can be distinguished very easily. Let’s tip our model up on the edge again so that we see a hexagon of green ions in the middle, and two equilateral triangles, one of top and one below the central layer.

Do the triangles line up? If they do, the packing is hexagonal closest. Otherwise, our structure is cubic closest packed. In the case of the green ions in NaCl, the question is most easily answered if you look at the model, standing on a vertex, from the top, or else from the side. You can see that the triangles point in different directions! Thus, the green chloride anions in NaCl have a cubic closest packed arrangement.

Now, what about the blue counterions, those of the other colour? We can go through the above procedure to determine their packing patterns, but first let’s see if we can use the shortcut way described above. What is the stoichiometry of this crystal structure? The ionic formula, NaCl implies a 1:1 stoichiometry (although this property can be established in a number of other ways, such as comparing the number of atoms/holes in a unit cell, or comparing coordination numbers for anions and cations). Thus, because in NaCl the stoichiometry is 1:1, the blue sodium counterions are packed in the same way as the green chloride ions, in a cubic closest packed pattern.

Next, we consider the type of holes that this structure has. By twisting and turning the model, we can find tetrahedral holes and octahedral holes (see below for a demonstration). We can see that all of the tetrahedral holes are empty (convince yourself of this!), but that every octahedral hole is filled with a counterion. Thus, sodium chloride has a cubic closest packed array of anions with a cubic closest packed pattern of cations occupying every octahedral hole.

Model 25: Chime model of NaCl.

What are the coordination numbers of the cations and anions in this structure? By looking at the model sitting on a face, turned by 45 degrees (so that we see a vertical edge in the front), we can see that every green sphere has six closest neighbours of the opposite type. Likewise, by picking a sphere of the opposite colour in the middle of one of the faces of the model, and mentally extending the lattice sideways by one layer, we can see that every blue sphere also coordinates six counterions. Thus, the coordination number of every cation is 6; as is the coordination number of every anion. Note that we could also have inferred this finding from the fact that the structure has every octahedral hole filled.

Finally, let’s try to find the unit cell in our NaCl structure. To do so for a closest packed lattice, we need to look at the model at such an angle that the hexagons are not obvious (i.e. so that we see squares of some form). Twisting the model so that we’re looking at one of the faces does the trick, as shown in Model 25. We can see that the blue ions form a face-centered cubic unit cell. The model is not big enough to see the same pattern completely for the counterion, but mentally extending it by one layer allows us to infer that the counterions form an equally large, face-centered cubic unit cell. Since the unit cells are of the same size for each of the ions, either one repeated is sufficient to create the infinite lattice.

Again, remember that for structures that do not have cubic closest packing or simple cubic packing, you are not expected to locate the unit cell. While we’ve gone through a great deal of information, most of what you’ll be doing in this online lab is relatively straightforward as far as the chemistry goes. The hard part is learning to look at the models from different angles, but fortunately, with a bit of practice, this is a skill that should be quick to master.

Quick Guide to Types of Holes
 

Figure 12: Octahedral hole highlighted	Model 29: Chime Model with Octahedral Hole Included

Figure 13: Tetrahedral hole highlighted	Model 30: Chime Model with Tetrahedral Hole Included.

Figure 14: Cubic hole highlighted	Model 31: Chime Model with Cubic Hole Included

Experiment 7 Crystal Models

Chem 154: Using this tutorial and the flow chart on p. 109 of the lab manual, fill out the table on p. 108 and the blank sections of p. 110.

The lab report for experiment 7 must be submitted via WebCT as detailed in your lab manual.

Remember to always look for squares first when viewing a model. If you can not find any, regardless of how the model is rotated, then you should look for the hexagons / equilateral triangles. It is important to first eliminate the simple cubic packing pattern before looking for the patterns of simple hexagonal, cubic closest, or hexagonal closest.

Also, remember that you can change the display of the models from ‘Ball & Stick’ to ‘Spacefill’ by right-clicking on each model. Click a display that will make it easier for you to describe the model. For example, to emphasize one type of ion when looking for a packing pattern, right-click on Model 32 and click on Select -> Atom -> Cl. Right-click on the model again and then click on Display -> Spacefill. In this representation it is easier (though still takes practice) to see the hexagon of the green ions with the equilateral triangles above and below it. To return to the original display, right-click on the model, then click Display -> Ball & Stick.

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