Part 1

Crystals

Lesley Smart

1 INTRODUCTION

You will be aware how atoms sometimes bond together to make individual molecules, as in carbon dioxide, chlorine and iodine for instance, but how in other cases, like diamond, silica, and sodium chloride, it is not possible to distinguish individual molecules (Figures 1.1a-d). You should also remember that bonding, and thus the arrangement of electrons, influences the shape of a molecule such as ammonia (Figure 1.1e). Many chemicals are solids at normal temperatures, and in the first part of this Book we are going to investigate the variety of structures adopted by elements and compounds in the crystalline solid state. The second part of the Book will concentrate only on the structure and shape of individual molecules.

To begin with, we are going to look at the structure of metals and of ionic solids. Such materials are very different from those containing individual molecules, in that they comprise extended arrays of atoms or ions in which discrete molecules are not identifiable. For instance, as well as diamond (Figure 1.1c) we can consider another familiar example, sodium chloride (common salt, Figure 1.2a), which has the empirical formula NaCl. Although the formula gives us the highly important information that there is one sodium atom present for every chlorine atom, it disguises the fact that crystalline sodium chloride does not comprise discrete NaCl molecules.

* What is the structure of sodium chloride?

* It is an aggregate of Na+ ions and Cl- ions arranged together in a regular, repeating three-dimensional pattern, with six ions of one type octahedrally surrounding an ion of the other type (Figure 1.2b).

The structure adopted by NaCl is also adopted by many other compounds, but it is not the only type of crystal structure. Ionic solids adopt a variety of patterns in the arrangements of their constituent ions. We shall show you a few of the ones that are more commonly found, and discuss the reasons for the variations.

We shall then move from ionic solids to look at a variety of structures adopted by solids where covalent rather than ionic bonding is predominant. For instance, silica (quartz), with empirical formula SiO2 (Figure 1.3), is covalently bonded: in its crystals we find an extended structure of covalently linked silicon and oxygen atoms, but no distinguishable individual molecules of SiO2.

In the final kind of solid state structure that we consider — molecular structures — small individual, covalently bound molecules such as iodine form crystals in which the molecules are held together by weak bonding (Figure 1.4).

Not everyone finds it an easy matter to visualize things in three dimensions, and so we have devised several ways of demonstrating the structures; you will have to find out which method helps you most. First and foremost is the use of WebLab Viewer Lite™ to look at the structures. Most of the diagrams of crystal structures in this Book can be viewed using WebLab ViewerLite. You will find the files on one of the CD-ROMs associated with this Book; you can access them via the CD-ROM Guide (p. 240) under 'Figures'. WebLab ViewerLite allows you to view a structure in any orientation: the instructions for using it can be found on one of the CD-ROMs, and if you haven't used it before, you should practise now with the four structures in this introduction. In addition to WebLab ViewerLite on one of the CD-ROMs, there is a program Virtual Crystals to work through, model-building exercises to view, and a program entitled Crystals, which contains some computer animations. If at all possible, try to study this Book near your computer, so that you can more easily use some or all of these aids.

Many ionic crystal structures can be regarded as based on a few very simple ways of packing spheres together in three dimensions. The simple sphere-packing schemes are best illustrated by the structures of metals, and so it is with these that we begin in the next Section.

2

STRUCTURES OF METALS

2.1 Close-packing in two dimensions

Before moving on to three-dimensional structures, it's convenient first to take a look at the efficiency of close-packing in two dimensions, by looking at two different ways in which circles may be arranged. Figure 2.la shows a close-packed arrangement, whereas Figure 2.1 b contains a square arrangement. The first apparent difference is that each circle touches six others in Figure 2.la, but only four others in Figure 2.1b. How do the two arrangements compare for efficient use of space? The bounded areas highlighted on the two diagrams both enclose a total of four complete circles. If we overlay these two areas (Figure 2.lc), we can see clearly that the four circles (comprising two whole circles, two half circles, and four quarter circles) in Figure 2.la occupy less total area than the four circles in Figure 2.lb (comprising one whole circle, four half circles, and four quarter circles) — about 15% less in fact. Now let's move on to the three-dimensional case.

COMPUTER ACTIVITY 2.1 Using computer animation and models to study close-packing

The close-packing of spheres is demonstrated by building models in Model Building on one of the CD-ROMs associated with this Book.

There is a computer animation of close-packing in the first part of...