Lab Help: Find Miller Indices from Diffraction Pattern?

In summary, the conversation discusses an electron scattering experiment in a modern physics class which involves using a cathode ray tube and a target foil. The experiment involves measuring the diameter of a ring diffraction pattern produced by an electron beam aimed at the foil. The data analysis suggests plotting sin[.5*arctan(r/D)] vs [pi*h_bar/(a*SQRT(2meV))], which should result in a linear graph with a slope equal to SQRT(h^2 + k^2 + l^2). However, when the experiment was conducted, the slope was found to be incorrect and far from the expected value. The data and relevant information for checking it is provided, and the issue is identified as the incorrect
  • #1
bGODLESS
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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.
 
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  • #2
What is the distance between the crystal and the the foil? This is, what is D?
 

1. What are Miller Indices?

Miller indices are a system used to describe the orientation of crystal planes in a material. They are represented by three numbers (hkl) and are used to label and identify specific planes within a crystal structure.

2. How do I find Miller Indices from a diffraction pattern?

To find Miller indices from a diffraction pattern, you will need to measure the distance between diffraction spots on the pattern and use this information to calculate the ratios of the h, k, and l values. These ratios can then be simplified to their lowest whole number values, giving you the Miller indices for the corresponding crystal planes.

3. What is the significance of Miller Indices in crystallography?

Miller indices are important in crystallography because they provide a standard way to describe and communicate the orientation of crystal planes in a material. This information is crucial for understanding the physical and chemical properties of a material and how it interacts with other materials.

4. Can Miller Indices be negative?

No, Miller indices cannot be negative. They are always expressed as positive whole numbers or zero. Negative values do not have any meaning in the context of crystal planes and would not accurately represent the orientation of the planes.

5. Are there any shortcuts or tricks for finding Miller Indices?

Yes, there are several shortcuts and tricks for finding Miller indices, such as using a diffraction ruler or using the concept of symmetry to simplify calculations. It is important to practice and familiarize yourself with these techniques to become more efficient at finding Miller indices from diffraction patterns.

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