p17p35ujimn9ejc9cap81i1j7e4.pdf

Chapter 2
Basic Structural Concepts
A Introduction
Crystal structures have already been mentioned and a few simple diagrams
(Figs. 1.7a, 1.13, and 1.14c, for example) were presented in the last chapter. To
understand crystal structures in a systematic way, one must be familiar with the
formal methods of describing them. The objective of this chapter is to begin to
explain how crystal structures are described and classified. The most important
topics in this chapter are the definition of the lattice (both direct and reciprocal),
the description of techniques for quantifying lattice components (directions
and planes), and the idea that every structure can be described as a
combination of a lattice and a basis. This chapter also includes a description of
how crystal structures are visually represented and an introduction to polycrystallography.
B The Bravais lattice
The Bravais lattice is the periodic array in which the repeated units of the crystal
are arranged. Because there are only 14 distinct arrangements, the Bravais lattice
system provides a convenient mechanism for classifying the structural diversity
that occurs in nature. However, one must remember that the Bravais lattice
describes only the underlying configuration of the repeat units. It says nothing
about the arrangement of atoms within the repeat unit. In this case, specificity is
sacrificed for simplicity.
i. Definition
A good definition of a Bravais lattice is that it is an infinite array of discrete
points with an arrangement and orientation that appears exactly the same
regardless of the point from which the array is viewed. A more practical quantitative
definition is that a Bravais lattice consists of all points defined by position
vectors, R, of the form:
Ruavbwc (2.1)
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