X-ray Diffraction Homework: 2theta for (abc) and (def) Planes

In summary, the question is about deriving the angular position for (abc) and (def) planes of a crystal composed of two fractions with different cell parameters, using X-ray diffraction with both Ni k-beta and Zr b-beta radiation. The relevant equations are n\lambda=d\sin\theta and d_{hkl}=\frac{x}{\sqrt{h^2+k^2+y2}}. However, the question is unclear on whether to average over the two spacings and wavelengths or to consider the four specific cases. Further information or clarification may be needed to solve the problem.
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Homework Statement


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A crystal composed of two fractions, one having the a cell parameters of x and the other of y are subjected to X-ray diffraction using both a Ni k-beta and a Zr b-beta radiation. Derive the angular position (2theta) for (abc) and (def) planes

Homework Equations


[itex]n\lambda=d\sin\theta[/itex]
[itex]d_{hkl}=\frac{x}{\sqrt{h^2+k^2+y2}}[/itex]

The Attempt at a Solution



First of all I am not sure what composed of two fractions means.

With the relevant equations it is pretty easy to solve this for a crystal composed of one "fraction" with one incident wavelength of xray. With two fractions and two incident wavelengths I am not sure if I should average over the the two spacings and the two wavelengths(The wording of the question implies there is one angular position for each plane) or if I do it for the 4 specific cases.
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

FAQ: X-ray Diffraction Homework: 2theta for (abc) and (def) Planes

Question 1: What is X-ray diffraction?

X-ray diffraction is a technique used to analyze the structure of a material by bombarding it with X-rays and observing the diffraction pattern produced.

Question 2: What is the significance of 2theta in X-ray diffraction?

2theta (2θ) is the angle between the incident X-ray beam and the diffracted X-ray beam. It is an important parameter in X-ray diffraction as it helps determine the position of diffraction peaks and provides information about the crystal structure of a material.

Question 3: How is the 2theta value calculated for (abc) and (def) planes?

The 2theta value for (abc) and (def) planes can be calculated using the Bragg's law: nλ = 2dsinθ, where n is the order of diffraction, λ is the wavelength of the incident X-rays, d is the distance between the crystal lattice planes, and θ is the angle of diffraction.

Question 4: How does the 2theta value for (abc) and (def) planes help in identifying the crystal structure?

The 2theta values for (abc) and (def) planes can be compared to the known values for different crystal structures to help identify the crystal structure of a material. This is because the spacing between crystal lattice planes is unique for each crystal structure, resulting in different 2theta values.

Question 5: Are there any limitations to using 2theta for (abc) and (def) planes in X-ray diffraction analysis?

While the 2theta value for (abc) and (def) planes can provide valuable information about the crystal structure of a material, it is not the only parameter that needs to be considered. Other factors such as the intensity and shape of diffraction peaks also play a role in identifying the crystal structure. Additionally, 2theta values may be affected by experimental errors and sample preparation methods, so they should be interpreted carefully.

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