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