behavior. In fact, one major success of X-ray diffraction techniques was the
successful elucidation of the double-helix structure of DNA in the early 1950s
(see Figure 21.34).
Because of the regularity of atoms and molecules in a crystal, many of the
possible planes of atoms can diffract X rays. We use a system called Miller in-
dices to label which plane of atoms is diffracting X rays, and different Bravais
lattices have different planes, with characteristic Miller indices, that diffract. In
this way, we can differentiate unit cells by their characteristic X-ray diffraction
patterns. In the next chapter, we will find that Miller indices are also useful in
describing the orientation of the surface of the crystal.
Unit cells of compounds are not always arbitrary. For many simple ionic
compounds, the stoichiometry of the compound and the ion sizes contribute
to a favored unit cell. We therefore have some ability to predict the expected
unit cell of a compound. We can also calculate the bond energy of the ionic
compound. Of course, the term bond energy is not strictly correct, since ionic
crystals are held together by coulombic forces acting in three dimensions. The
phrase lattice energy is more appropriate, since the bond energy is actually the
energy released when oppositely charged ions attract each other to form a
three-dimensional lattice. In determining a lattice energy, we must consider
not just the attractions between oppositely charged ions, but the repulsions be-
tween like-charged ions as well.
Finally, we recognize that all crystals are not perfect. We can take advantage
of imperfect crystals, including using some of them as semiconductors. Being
able to take advantage of imperfect crystals depends, however, on an under-
standing of perfect crystals.21.10 Summary 761Figure 21.34 Diffraction patterns from crys-
talline DNA were interpreted as DNA having a
double-helix structure. The determination of
the structure of DNA was a major development
in biology.© Omikron/Photo Researchers, Inc.