> ## Documentation Index > Fetch the complete documentation index at: https://claude.com/docs/llms.txt > Use this file to discover all available pages before exploring further. # A first X-ray diffraction pattern: why silicon shows 6 peaks and salt 9 > Simulate the X-ray powder patterns of silicon and table salt and label every peak with Bragg's law.
Simulated X-ray diffraction patterns: silicon has 6 labeled peaks, with 200, 222, and 420 marked absent; rock salt has 9. Simulated X-ray diffraction patterns: silicon has 6 labeled peaks, with 200, 222, and 420 marked absent; rock salt has 9.
The numbers in your session might differ from this picture and from the summary in [Reference analysis](#reference-analysis). ## Prompt Copy the prompt and paste it into a new session in [Claude Science](/docs/claude-science/overview). By default, Claude asks with a [permission card](/docs/claude-science/core-concepts#permission-cards) before it runs code or installs packages. ```text Prompt wrap theme={null} X-ray diffraction is how we know where the atoms sit in a crystal. Simulate the powder diffraction patterns of silicon (diamond structure, a = 5.4311 Å) and rock salt (NaCl, a = 5.6402 Å) with pymatgen, for copper Kα₁ X-rays (wavelength="CuKa1", λ = 1.54056 Å) and angles 2θ up to 90°. Nothing needs downloading. Label every peak with its Miller indices hkl, and check each angle by hand with Bragg's law, λ = 2d sin θ, where d = a/√(h²+k²+l²). Both crystals share a face-centered cubic lattice, which allows 9 reflections in this range, yet silicon shows only 6: show that its 2-atom basis cancels 200, 222 and 420. In salt the all-odd peaks (111, 311, 331) are weak because Na and Cl scatter out of phase: show that too. Leave out other salts and what-ifs such as Na and Cl scattering equally, and round every number once, from its full-precision value. Put both patterns in 1 figure. Explain each step as you would to an undergraduate. ``` ## Reference analysis Simulates the X-ray powder patterns of silicon and table salt and labels every peak with Bragg's law. Both share a face-centered cubic lattice, yet below 2θ = 90° salt shows 9 peaks and silicon 6, because silicon's 2-atom basis cancels the 200, 222, and 420 reflections. ## Data This example doesn't download any data.