Solving Structure Factors for Cesium Chloride & X-Ray Diffraction

In summary, the ionic compound cesium chloride can have two values for its structure factor in x-ray diffraction due to the different orientations of the crystal. The -i*pi*(h+k+l) term in the structure factor equation accounts for the phase difference between the scattered waves from the cesium and chloride atoms. The intensities of the Bragg reflections in the x-ray patterns of cesium, cesium chloride, and cesium iodide would be highest for cesium iodide, followed by cesium chloride, and then cesium, due to the larger number of atoms and higher atomic number of iodine.
  • #1
captainjack2000
99
0

Homework Statement


I have the ionic compound cesium chloride and have been asked to use the equation

p(k) = (sum over j) exp(-iK.r)f(k)

to find the structure factor for x-ray diffraction from cesium and explain why it can take two values. It also asks how you would expect the intensities of the bragg reflections in the x-ray patterns of cesium, cesium chloride and cesium iodid to compare.


The Attempt at a Solution


I know that cesium chloride has a simple cubic structure with Cs at 0,0,0 and Cl at 1/2 , 1/2, 1,2
So I found the recipricol lattice vectors to be a*=(2*Pi/L)x b*=(2*Pi/L)y and c*=(2*Pi/L)z
The recipricol lattice vector is K=ha*+kb*+lc*

so
p(k) = f(Cs)exp(0) + f(Cl)exp(-iK.(L/2,L/2,L/2))
=f(Cs) + f(Cl)exp(-i*pi*(h+k+l))

which is =f(Cs) + f(Cl) if h+k+l is even or =f(Cs)-f(Cl) if h+k+l is odd.

I'm not sure where the -i*pi*(h+k+l) part came from? are h,k,l just 2,2,2??

for the second bit I know that the intensity is proportional to the structure factor squared...
not sure where to go from here.
 
Physics news on Phys.org
  • #2


Thank you for your question. The equation you have been asked to use is the structure factor equation, which relates the diffraction pattern of a crystal to its atomic structure. In this case, you are looking at the diffraction pattern of cesium chloride, which has a simple cubic structure as you correctly identified. The -i*pi*(h+k+l) term in the equation comes from the phase difference between the scattered waves from the cesium and chloride atoms.

As for the two possible values of the structure factor, this is due to the different orientations of the crystal in the diffraction experiment. When the crystal is rotated, the positions of the atoms within the unit cell also change, resulting in different values for h, k, and l. This leads to the two possible values for the structure factor, as you have correctly stated.

In terms of the intensities of the Bragg reflections, the structure factor equation tells us that the intensity is proportional to the square of the structure factor. Therefore, the reflection with the higher structure factor will have a higher intensity. In this case, cesium iodide would have the highest intensity, followed by cesium chloride, and then cesium. This is due to the larger number of atoms in the unit cell and the higher atomic number of iodine compared to chlorine.

I hope this helps to answer your questions. Keep up the good work in your studies!
 

1. What is the purpose of solving structure factors for cesium chloride in X-ray diffraction?

The purpose of solving structure factors for cesium chloride in X-ray diffraction is to determine the arrangement of atoms in the crystal structure of the compound. This information is crucial in understanding the physical and chemical properties of the compound.

2. How are structure factors calculated in X-ray diffraction?

Structure factors are calculated using the intensities of X-rays diffracted by the crystal lattice of the compound. The intensities are measured using a diffractometer and then converted into structure factors using mathematical equations.

3. What is the significance of the cesium chloride structure in X-ray diffraction?

The cesium chloride structure is commonly used as a benchmark for testing and calibrating X-ray diffraction equipment. Its simple cubic structure allows for easy calculations and analysis of diffraction patterns.

4. What factors affect the accuracy of structure factor calculations for cesium chloride in X-ray diffraction?

The accuracy of structure factor calculations can be affected by a number of factors, including the quality and resolution of the diffraction data, the crystal size and orientation, and the presence of impurities in the crystal lattice.

5. How is the solved structure factor for cesium chloride used in X-ray diffraction analysis?

The solved structure factor is used in conjunction with other data, such as the unit cell dimensions and atomic positions, to create a three-dimensional model of the crystal structure. This model can then be used to analyze the physical and chemical properties of the compound.

Similar threads

  • Advanced Physics Homework Help
Replies
1
Views
2K
Replies
3
Views
3K
  • Advanced Physics Homework Help
Replies
1
Views
918
  • Atomic and Condensed Matter
Replies
4
Views
1K
Replies
1
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
1K
  • Atomic and Condensed Matter
Replies
1
Views
2K
  • Advanced Physics Homework Help
Replies
17
Views
6K
  • Atomic and Condensed Matter
Replies
5
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
Back
Top