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So, you want to build a mineral structure? In the previous chapter, we learned all about the structure and bonding capabilities of atoms, but now we need some guidance on how best to arrange them in the three-dimensional, long-range ordered structures that make up minerals. This chapter is an introduction to the science of crystallography, which is a symbolic language for describing repeating patterns in 2-D, 3-D, or any dimension of space one wants. It just so happens that the crystal structures of minerals are repeating patterns in 3-D, and we can take advantage of all the work that has been done to study patterns to help us understand minerals. Much later on in this book, you will have a chance to learn the mathematical basis for everything we talk about, so don’t be fooled: what seems descriptive here is actually a very precise, mathematically-elegant way of describing space. In fact, it is really much easier to describe and understand symmetry based on mathematics than any other way.

The basis for the science of crystallography really began in 1669 with Nicolaus Steno, who noticed that quartz crystals, no matter where
they came from or what size they were, always had the same set of characteristic angles between their faces. This observation, which is called Steno’s Law, laid the foundation for subsequent studies of crystals in the 18th, 19th, and 20th centuries (Table 4.1). By the 1920s, the fundamental rules of crystallography, including its mathematical basis, had been worked out fairly well. Subsequent improvements in our ability to analyze crystals down to the atomic and subatomic levels have only confirmed what the early workers theorized—all on the basis of crystal morphology! However, they could only “theorize” structures based on morphology for fairly simple minerals like halite. This is just another example of how understanding a physical characteristic of a mineral (in this case, its shape), tells you something profound about the fine-scale details of its interior structure, because the internal structure really controls the shape.

All types of crystalline matter are based upon repetitions in space of identical structural units. These can be a single atom or a group of atoms, and are represented by the chemical formula of the material. This structural unit can be referred to as a motif or basis. In simple materials like the metals copper, silver, and gold, there is only one element in the crystal structure. In ice, the motif is the H₂O molecule, and in halite, Na¹⁺ and Cl^1– atoms. In silicates such as muscovite (KAl₂ (AlSi₃O₁₀) (OH)₂, a large number of atoms or groups of atoms makes up the structural unit. In proteins there may be 10⁴ atoms making up the motif!

We can describe the structure of crystals in terms of single periodic lattices that are repeated in three dimensions with our structural or chemical unit (motif or basis) repeated at or surrounding each lattice point (see Chapter 13). Crystal structures are therefore built up from various combinations of lattices (i.e., the repeating patterns) and structural units (i.e., the elements present).