Question

A beam of X-rays impinges on a three-dimensional rectangular array whose periods are a, b, and c. The direction of the incident beam coincides with the direction along which the array ** is equal to a. Find the directions to the diffraction maxima and the wavelengths at which these maxima will be observed.

Answer 1

Suppose α, β, and γ are the angles between the direction to the diffraction maximum and the directions of the array along the periods a, b and c respectively ( call them x, y, & z axes). Then the value of these angles can be found from the following familiar conditions

(These formulas are, in effect, Laue equations, see any text book on modem physics).

Squaring and adding we get on using

Knowing a, b, c and the integer k1, k2, k3 we can find α,β, γ as well as λ.