Perfect Crystals
In a crystal, the constitutive particles are arranged periodically, forming a lattice. In the following, we will consider that all particles are identical (so the above separation in factor and structure factors (3) holds). We also assume that all atoms have an identical environment (i.e. they form a Bravais lattice). The general case of lattice with a basis (see below) is not fundamentally different.
If the lattice is infinite and completely regular, the system is a perfect crystal. In addition, we will neglect all thermal motion, so that there is no need for averaging in (4). As in (2), we can write:
- .
The structure factor is simply the squared modulus of the Fourier transform of the lattice, and it is itself a periodic arrangement of points, known as the reciprocal lattice.
Read more about this topic: Structure Factor
Famous quotes containing the words perfect and/or crystals:
“On the earth the broken arcs; in the heaven a perfect round.”
—Robert Browning (1812–1889)
“It is clear that everybody interested in science must be interested in world 3 objects. A physical scientist, to start with, may be interested mainly in world 1 objects—say crystals and X-rays. But very soon he must realize how much depends on our interpretation of the facts, that is, on our theories, and so on world 3 objects. Similarly, a historian of science, or a philosopher interested in science must be largely a student of world 3 objects.”
—Karl Popper (1902–1994)