Question

# Consider a simple cubic with a 6.0 Å lattice constant. The measurements of X-ray scattering from...

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  