Physical Chemistry , 1st ed.

1 2(2.91 Å) sin 20.0°

1.99 Å

The (111) plane will diffract X rays having a wavelength of 1.99 Å at an an-

gle of 20.0°. Notice that this wavelength is smaller than the lattice parameter

itself. This is a consequence of the shorter dspacing that angled planes of

atoms in a crystal have.

The above example should make an important point: all planes of atoms or

ions in a crystal can serve to diffract X rays, not just the simple planes made

by the corners of the repeating unit cells. This suggests that the diffraction of

X rays by any real crystal can be very complex. It is. Figure 21.23 shows the

21.6 Miller Indices 747

W MgO CaO Al 2 O 3 NH 4 Cl

0 °

180 °

Figure 21.23 Examples of the diffraction of X rays by powdered crystals. Each strip is a piece

of photographic film, encircling the powdered sample, that is exposed only at the certain angles

that X rays are diffracted.