1 Crystal structure

Picture with me an old cottage nestled in the woods. There is a small house built of clay bricks that were thoughtfully stacked and interlaced by a master bricklayer so as to produce a repeated interlocking pattern. The house has a thatched roof consisting of bundles of straw. The straws in each bundle are oriented in a common direction to direct rainwater off the roof, and are lashed together with twine. Around the house is a garden enclosed by a stone wall. Like the brick walls of the house, the stones in the wall are bonded together with mortar. But unlike the bricks, the stones lack any sense of a repeating pattern. In this part of the textbook, we examine the basic structures that are found in condensed matter as well as the forces (the mortar and twine) that maintain these structures over long time periods. For our purposes, structures are divided into two main categories: ordered (like the bricks and the straw of the house) and disordered (like the stones in the garden wall). We begin in Chapter 1 with an examination of the structure of crystals whose periodic arrangement of atoms is a prime example of ordered matter. Particle positions in the crystal are well-defined and the periodic structure is seen to extend for very long distances. As a result of this ordering, crystal structures are rather easy to describe mathematically and provide an excellent introduction to the concept of symmetry. All of this simplicity and symmetry is lost for amorphous materials and in Chapter 2 we examine alternative means for quantifying structures in which particle positions are aperiodic. In the third chapter, we pause to examine the inter-particle forces that provide the mortar necessary for condensed matter to form. There we survey the fundamental types of bonds and discuss how each can influence the resulting structure. In our final chapter on the topic of structures, we look at magnetic materials. Although the atoms that compose these materials may be arranged in an ordered manner, their magnetic moments can either be oriented randomly or, like the aligned straws of a thatched roof, assume an ordered configuration.