Interactive visualization of Bragg's Law: X-ray diffraction by crystal lattices, demonstrating constructive interference when 2d sinθ = nλ across cubic crystal systems
When X-rays strike a crystal, they scatter off the periodic arrangement of atoms. Constructive interference occurs when the path difference between waves reflected from adjacent crystal planes equals an integer multiple of the wavelength: 2d sinθ = nλ, where d is the interplanar spacing, θ is the angle between the incident beam and the crystal plane (not the normal), λ is the X-ray wavelength, and n is the diffraction order. When the extra distance 2d sinθ equals exactly nλ, the scattered waves add coherently, producing a bright diffraction spot.
Simple Cubic (SC): atoms at cube corners only. BCC: extra atom at center, requires h+k+l = even. FCC: atoms on cube faces, requires h,k,l all odd or all even. These selection rules arise from destructive interference within the unit cell. The structure factor F(hkl) determines which reflections appear.
Protein crystallography determines 3D structures (180,000+ in PDB). Materials science: phase identification, lattice measurement. Drug design: structure-based optimization. Nanotechnology: nanoparticle sizing via Scherrer equation. Forensics: powder diffraction identification. Rosalind Franklin's Photo 51 was key evidence for DNA's double helix.
The upper canvas shows crystal planes with X-ray beams reflecting off them. When 2d sinθ = nλ exactly, the status panel shows the diffraction order and maximum intensity. The lower canvas plots intensity vs angle with sharp peaks at Bragg angles. Use the angle slider to scan θ. Switch between SC, BCC, FCC to see systematic absences. Custom mode lets you adjust d and λ freely.