(ii) For a constructive interference between the rays scattered from any two
consecutive crystal planes, the path difference must be an integral multiple
of the wavelength (Fig. 7.5).
The resulting Bragg’s equation is
2dsinh = nk
ð7:2Þ
where d is the interplanar spacing and n = 0, 1, 2 ….., represents the order
of reflection. The highest possible order can be determined by the
condition
sin h
ð
Þ max ¼ 1; so that
nk
2d
1
This indicates that k must not be greater than twice the interplanar
spacing, otherwise, no diffraction will occur.
(b) The vector form of the Bragg’s law is given by
G
2 + 2k.G = 0
Fig. 7.5 Bragg’s reflection of
X-rays from the atomic planes
Fig. 7.6 Ewald construction
7.2 X-Ray Diffraction by Crystals
273