A crystal acts as a grating fine enough for X-rays
Laue’s proposal tested two open ideas at once: that X-rays are waves, and that a crystal holds a regular three-dimensional arrangement. Friedrich and Knipping did the experiments in 1912. Distinct spots appeared around the transmitted beam, and their symmetry followed the crystal’s orientation, so both ideas faced one quantitative test.
Each spot marks a direction where some wavelength in the broad incident spectrum meets the interference condition; the pattern is not a magnified picture of atoms. Different spots can come from different wavelengths, so giving them all one wavelength misreads the experiment.
Sources: [1]
Angle scans with selected radiation give the plane spacing
W. L. Bragg described the diffraction condition in terms of families of crystal planes. W. H. Bragg’s spectrometer made it practical to measure intensity against angle with selected characteristic radiation. With the source, crystal and detector geometry known, the peak angles give the plane spacing.
In the equation below, the Bragg angle is measured from the reflecting planes, not from their normal, so the diffracted beam turns through twice that angle from the incident direction. The order is a positive integer. The equation says where a reflection can appear; it says nothing about how strong the reflection is.
Sources: [2]
Reflection strengths carry the structural clues
Salts with similar geometry could give very different relative intensities. The Braggs compared these differences with arrangements in which each repeating unit holds unlike atoms. In sodium chloride, two sublattices interpenetrate; treating every lattice point as identical throws away the scattering difference between the two kinds of ion.
In a single-scattering approximation, the structure factor below adds the complex amplitudes from each atom at its fractional coordinates. Each atom’s scattering factor depends on the probe and on the scattering vector, so an electron scattering factor cannot be reused in an X-ray calculation. Measured intensities also need corrections for absorption, geometry and thermal motion.
Sources: [2]
Measured intensities lose the phases
A detector generally records intensity and loses the phase of each structure factor. Solving a structure therefore also draws on indexed peaks, chemical composition, symmetry and other constraints. An arrangement that reproduces one pattern is weaker evidence than a model checked against independent reflections and against alternative models.
Laue’s 1914 prize and the Braggs’ 1915 prize reward related but distinct work. The lectures read here came later: Laue spoke in 1915 and W. L. Bragg in 1922. The experiments, the prizes and the lectures looking back on them each have their own date.
Read positions before intensities
Start by comparing the first spot photographs with the spectrometer scans, then follow the salt examples in Bragg’s lecture. Keep two questions apart: which reflections the geometry allows, and how strong the structure makes them. The linked models let you change each one separately.