Page 115 - Materials Science and Engineering An Introduction

3.16 X-Ray Diffraction: Determination of Crystal Structures • 87

3.16 X-RAY DIFFRACTION: DETERMINATION
OF CRYSTAL STRUCTURES
Historically, much of our understanding regarding the atomic and molecular arrange-
ments in solids has resulted from x-ray diffraction investigations; furthermore, x-rays are
still very important in developing new materials. We now give a brief overview of the
diffraction phenomenon and how, using x-rays, atomic interplanar distances and crystal
structures are deduced.

The Diffraction Phenomenon
Diffraction occurs when a wave encounters a series of regularly spaced obstacles that
(1) are capable of scattering the wave, and (2) have spacings that are comparable in
magnitude to the wavelength. Furthermore, diffraction is a consequence of specific
phase relationships established between two or more waves that have been scattered
by the obstacles.
Consider waves 1 and 2 in Figure 3.21a, which have the same wavelength (l)
and are in phase at point O–O . Now let us suppose that both waves are scattered

O Scattering
Wave 1 Wave 1'
event

A A

Amplitude + 2A

A A

Wave 2 Wave 2'
O'
Position
(a)

P
Wave 3 Scattering Wave 3'
event

A A
Amplitude +

A A

Wave 4
P' Wave 4'
Position
(b)

Figure 3.21 (a) Demonstration of how two waves (labeled 1 and 2) that have the same wavelength l and remain
in phase after a scattering event (waves 1 and 2 ) constructively interfere with one another. The amplitudes of the
scattered waves add together in the resultant wave. (b) Demonstration of how two waves (labeled 3 and 4) that have
the same wavelength and become out of phase after a scattering event (waves 3 and 4 ) destructively interfere with
one another. The amplitudes of the two scattered waves cancel one another.