Page 129 - Geotechnical Engineering Soil and Foundation Principles and Practice

Soil Minerals
124 Geotechnical Engineering

6.2.4 Relating Diffraction Angles to Crystal Structure
The interpretation of X-ray diffraction would be relatively simple if each
crystalline material had only one set of reflecting planes, and as a matter of fact
analyses of clay minerals do emphasize only one set of planes. However, there
also are other planes having different interatomic spacings, much as parallel
lines drawn at various angles through figures in wallpaper have different
spacings (Fig. 6.2). Each mineral species therefore presents a combination of
diffraction angles and intensities that serves as a fingerprint to identify that
mineral.

Thousands of diffraction patterns have been collected, categorized, and published
for purposes of mineral or crystal identification by the American Society for
Testing and Materials. Because of its speed and accuracy, X-ray diffraction has
many uses including forensic investigations.

6.2.5 Bragg Made It Easy
The principles of X-ray diffraction were described by von Laue in the early
1900s, but a simplified model was needed before diffraction was easily under-
stood and utilized. The model was devised by father-and-son English
physicists William and Lawrence Bragg, who shared a Nobel Prize for their
contribution. The relationship describing diffraction of X-rays from crystals is
called Bragg’s Law, but a more accurate description is ‘‘Bragg’s reflection
analogy.’’

Figure 6.2
Atoms in a crystal
occur in a regular
pattern like
flowers in
wallpaper, so
distances
between identical
planes depend on
the orientation of
the planes
and the size and
arrangement of
the flowers and
caterpillars.

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