Lab Help: Find Miller Indices from Diffraction Pattern?

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SUMMARY

The discussion revolves around an electron scattering experiment conducted in a modern physics lab, where the objective is to determine Miller indices from a diffraction pattern using a cathode ray tube. The participant measures the diameter of the ring diffraction pattern at three different accelerating potentials (8kV, 9kV, and 10kV) and attempts to plot sin[0.5*arctan(r/D)] against [π*h_bar/(a*√(2meV))]. The expected slope, representing the square root of the sum of squares of the Miller indices, is not achieved, leading to confusion regarding the calculation method and the value of D, the distance from the target foil to the screen.

PREREQUISITES
  • Understanding of electron scattering and diffraction patterns
  • Familiarity with Miller indices and their significance in crystallography
  • Knowledge of plotting mathematical functions and interpreting slopes
  • Basic principles of modern physics, particularly related to cathode ray tubes
NEXT STEPS
  • Review the calculation of the distance D in electron diffraction experiments
  • Investigate the relationship between accelerating potential and diffraction patterns in electron scattering
  • Learn about the significance of lattice constants in determining Miller indices
  • Explore common errors in data analysis for diffraction experiments and how to correct them
USEFUL FOR

Students in modern physics courses, particularly those involved in experimental physics and crystallography, as well as educators seeking to understand common pitfalls in electron diffraction experiments.

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I'm currently in a modern physics class and one of our labs was an electron scattering experiment that required the use of a cathode ray tube and a target foil. We aim the electron beam through one of four quadrants on the target foil and measure the diameter of the ring diffraction pattern produced. Only 4 rings were visible, so we measure all four, change the accelerating potential for the electron beam, and repeat the measurements.

In the data analysis, it's suggested that we plot sin[.5*arctan(r/D)] vs [pi*h_bar/(a*SQRT(2meV))]. This plot should result in a linear graph with a slope that is equal to SQRT(h^2 + k^2 + l^2 ).

My issue is that I create this plot for the first ring at 3 different accelerating potentials but my slope is nowhere near a reasonable value (.66, impossible for the square root of an integer). If someone sees an issue in my method I'd really appreciate the correction, because I don't see where I've gone wrong.

Here's the data:

for n=1

V = 8kV, 9kV, 10kV

r = 1.0167cm, 0.9583cm, 0.925cm

distance from target foil to screen is 17.3355cm

The quadrant used contained an aluminum polycrystalline target with a given lattice constant a = 4.04145 Angstroms.

That should be all anyone needs to check the data. Looking it up online I found that the first miller index of Aluminum polycrystalline should be [1,1,1] which means the slope of the line should be 1.732. My slope is 0.666...

My plot for the other rings is similarly incorrect, so I'm guessing if I can figure out what's wrong with the first plot it will fix the others.
 
Last edited:
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What is the distance between the crystal and the the foil? This is, what is D?
 

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