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1. Each atom has six neighbours, and there are groups of three atoms in close contact. Using the two-dimensional close-packed structure as an example, we can identify a number of important components involved in the description of any crystal structure. First we consider how the atoms are packed into a periodically repeating arrangement. The periodicity is obvious from Fig. 1, and to formalize this may seem to be a distraction at this point, but it will quickly become apparent that the formalism will help to make the description of crystal structures much easier.

Since electromagnetic radiation is oscillatory, one might expect that if the frequency of the radiation matches a particular vibration frequency it will induce vibrational motions of the atoms as a resonance. The most promising candidate for linking absorption of electromagnetic radiation to atomic vibrations occurs for infrared (IR) radiation. Experiments of IR absorption point to the existence of vibrational frequencies of order 1012 –1014 Hz (1 THz is 1012 Hz), as shown in Fig. 10 (data on vibrational frequencies for a range of materials are given in Chapter 8).

However, this does not destroy the overall picture we have put together. 10 is that there is one vibration for each degree of freedom of each atom. We automatically accommodated the fact that the total number of vibrations is three times the number of atoms in the crystal, and the relatively few vibrations seen in a spectroscopy experiment have frequencies that are representative of the complete distribution of frequency values. So our task is to quantify the link between structure and dynamics, and also the links to the forces between atoms.

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