Understanding Dot Product for Diffraction Peaks Calculation

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SUMMARY

The discussion focuses on calculating diffraction peaks using the dot product in the context of crystallography. The user seeks clarification on the equation -3ln(0.33)=Ghkl2<\delta^2> and the nature of Ghkl2 as a vector quantity. It is established that for the (800) plane, Ghkl2 is indeed the dot product of the vector G with itself, resulting in a scalar value of 64. Understanding this relationship is crucial for accurately determining diffraction peaks.

PREREQUISITES
  • Basic understanding of vector mathematics
  • Familiarity with crystallography concepts
  • Knowledge of diffraction theory
  • Experience with mathematical equations in physics
NEXT STEPS
  • Study the properties of dot products in vector mathematics
  • Explore the role of reciprocal lattice vectors in crystallography
  • Learn about the calculation of diffraction peaks using Bragg's Law
  • Investigate the significance of the (hkl) notation in crystallographic planes
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Students and professionals in physics, materials science, and crystallography who are involved in diffraction analysis and peak calculations.

Ryan P
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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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Please recheck your definition of the dot product.
 

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