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.

Homework Answers

Answer #1

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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