Understanding Dot Product for Diffraction Peaks Calculation

In summary, the question involves finding the dot product of Ghkl2, a vector quantity, in order to solve a rearranged equation involving ln and a parameter. The student is unsure of how to convert this into a scalar value and is seeking clarification.
  • #1
Ryan P
3
0

Homework Statement



It is question number 1a here:

http://web.utk.edu/~tbarnes/website/cm/cm_hw/hw4/cm_hw4.pdf

The Attempt at a Solution



I'm not entirely sure how to go about this. I've rearranged this equation to get

-3ln(0.33)=Ghkl2<[tex]\delta^2[/tex]>The thing that confuses me is that Ghkl2 is a vector quantity, right? In this case, since we are talking about the (800) plane, would this be just the dot product of G with itself (64)? I'm just not sure how I'm supposed to turn this into a scalar. Any help would be greatly appreciated.
 
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  • #2
Please recheck your definition of the dot product.
 

What is the cause of fading diffraction peaks?

Fading diffraction peaks are caused by various factors such as beam damage, radiation damage, and sample instability. Beam damage occurs when the sample is exposed to intense beams of electrons or X-rays, leading to the degradation of the sample. Radiation damage occurs when the sample is exposed to high-energy radiation, causing structural changes in the sample. Sample instability can also contribute to fading diffraction peaks, as the sample may undergo phase transitions or structural changes during the measurement.

How can fading diffraction peaks be prevented?

To prevent fading diffraction peaks, it is important to minimize the exposure of the sample to intense beams of electrons or X-rays. This can be achieved by using lower beam currents or shorter exposure times. It is also important to handle the sample carefully and ensure that it is stable during the measurement. Additionally, using a cryo-stage or cryo-jet can help reduce the effects of radiation damage on the sample.

Can fading diffraction peaks be corrected?

In some cases, fading diffraction peaks can be corrected by adjusting the experimental conditions. For example, increasing the exposure time or using a lower beam current can help reduce the effects of beam damage. However, in cases where the sample has undergone irreversible structural changes, it may not be possible to correct the fading diffraction peaks.

What are the implications of fading diffraction peaks in data analysis?

Fading diffraction peaks can significantly affect the accuracy and reliability of data analysis. This is because the peak intensities may change over time, leading to incorrect measurements of peak positions and intensities. It is important to carefully evaluate and account for fading diffraction peaks in data analysis to ensure accurate and meaningful results.

Are there any techniques to minimize the effects of fading diffraction peaks?

Some techniques that can help minimize the effects of fading diffraction peaks include using a smaller beam size, using lower beam energies, and using a cryo-stage or cryo-jet. These techniques can help reduce the exposure of the sample to intense beams of electrons or X-rays, thereby minimizing the effects of beam damage and radiation damage.

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