Consider a simple cubic with a 6.0 Å lattice constant. The measurements of X-ray scattering from the powder sample are carried out with a 1.5 Å X-ray source.
(a) Using the diffraction condition relating G (a reciprocal lattice vector), k (the wave vector of the incident X-ray), and k' (the wave vector of the scattered X-ray) derive a relationship between |G|, |k|, and the scattering angle θ.
(b) Write a symbolic expression for |G|.
(c) Use the results of parts (a)-(c) to calculate the angular positions θ of the (100), (110), and (111) diffraction peaks.
a)
The Laue conditon for diffraction is given by
And the condition
And so, we get
So,
b)
And we know
So, we get from the relation of part (a),
where
So, for the plane (100),
So, if we consider only n = 1 peak, then
And similarly
for the plane (110),
So, if we consider only n = 1 peak, then
And for the plane (111),
So, if we consider only n = 1 peak, then
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