MYSIMULATOR / STRUCTURE OF MATTER
BRAGG / C24
Order from interference.
One crystal. Many waves. A measurable pattern.
3D schematic · lattice spacing exaggerated
Up to 16 representative planes shown
Each segment is one plane.
The gold resultant gives
the total amplitude.
The experiment & model
2d sin θ = nλ. Waves reflected by successive planes accumulate a phase difference. At a Bragg angle they add constructively. A finite stack produces narrow peaks and side lobes.
We sum complex amplitudes from every plane: I = |Σ exp(i q zⱼ) / N|², with q = 4π sin θ / λ. Disorder adds fixed, seeded Gaussian displacements to plane positions. Wavelength and d use nanometres; intensity is normalized to the ideal coherent peak.
This is a monochromatic, one-dimensional, single-scattering teaching model. It omits atomic structure factors, absorption, instrument broadening and multiple scattering. It is not a powder diffractometer or a quantitative material identifier. Scientific reference ↗