Ewald sphere

Predicting which diffraction spots will show up can feel like guesswork. The Ewald sphere turns it into a clean piece of geometry — like laying a transparent globe over a field of dots and reading off exactly which dots the globe's surface touches. It is a drawing trick that tells you, for a given beam and crystal orientation, precisely which reflections will flash on.

Here is the construction. Draw the reciprocal lattice as a grid of dots. Pick the spot where the incoming beam enters and draw a sphere whose radius is set by the wavelength (one over the wavelength), positioned so its surface passes through the lattice's origin. The rule is simple and exact: a diffraction spot appears for every reciprocal lattice dot that happens to lie on the surface of that sphere. Each such dot satisfies the Laue condition automatically, because the geometry was built to encode it.

This matters because it makes a daunting 3D condition visual and predictive: rotate the crystal and you rotate the dots, sweeping different ones onto the sphere, which is exactly why crystallographers spin their samples to collect a full set of reflections. The honest caveat is that the Ewald sphere is a bookkeeping picture in reciprocal space, not a physical ball inside the crystal — and for short-wavelength electrons the sphere is so large it is nearly flat, which is why electron patterns show many spots at once.