Book contents
- Frontmatter
- Contents
- Preface
- 1 The nature of condensed matter
- 2 Order and disorder
- 3 Crystals, scattering, and correlations
- 4 Surfaces and crystal growth
- 5 Classical and quantum waves
- 6 The non-interacting electron model
- 7 Dynamics of non-interacting electrons
- 8 Dielectric and optical properties
- 9 Electron interactions
- 10 Superfluidity and superconductivity
- References
- Index
3 - Crystals, scattering, and correlations
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- 1 The nature of condensed matter
- 2 Order and disorder
- 3 Crystals, scattering, and correlations
- 4 Surfaces and crystal growth
- 5 Classical and quantum waves
- 6 The non-interacting electron model
- 7 Dynamics of non-interacting electrons
- 8 Dielectric and optical properties
- 9 Electron interactions
- 10 Superfluidity and superconductivity
- References
- Index
Summary
We have seen in the previous chapter that crystals are common in nature. In this chapter we will investigate in more detail how to think about such three-dimensional periodic structures. Then we will turn to the interaction of waves with such structures. This will lead us to a discussion of correlation functions in condensed matter.
Crystals
In the previous chapter we defined a crystal as a structure which repeats periodically in space. There is a mathematical framework for dealing with physical quantities in perfect crystals; it is the science of crystallography. We will review some of the elementary concepts from this subject.
Of course, any real material is an imperfect realization of a perfect crystal; real materials always have impurities and defects. Even if a crystalline solid is very close to being strictly periodic in bulk, all materials have a surface where the periodicity fails. However, consider a large chunk of matter, say a cube of edge L where the distance between the atoms is a. The number of atoms in the bulk is of the order of (L/a), but the number on the surface is of order (L/a). If L > > a the fraction on the surface is negligible.
Lattices
The first step to defining a crystal is to define a lattice. This is a set of points in d dimensions which are generated by taking linear combinations of d linearly independent vectors called generators: ak, k = 1, … d with integer coefficients.
- Type
- Chapter
- Information
- Advanced Condensed Matter Physics , pp. 25 - 52Publisher: Cambridge University PressPrint publication year: 2009