wave scattering

Picture dropping a pebble into a still pond: circular ripples spread outward from the spot it hit. Now imagine the pond is full of little floating corks, and each cork, as a passing ripple lifts it, sends out its own fresh set of ripples. Wave scattering is exactly this. When a wave — a light wave, an X-ray, an electron wave — runs into an atom, the atom does not simply block it or let it pass; it grabs a little of the wave's energy and re-radiates a new wave of its own, spreading out in almost all directions. That re-radiated wave is the scattered wave, and the atom is a scatterer.

For X-rays the mechanism is concrete. An X-ray is an oscillating electric field; when it washes over an atom it makes the atom's electrons jiggle back and forth at the same frequency. An accelerating charge radiates, so each jiggling electron becomes a tiny antenna broadcasting a spherical wavelet of the same wavelength as the incoming X-ray. Because the wavelength is unchanged we call this elastic (or coherent) scattering — and it is only the coherent, same-wavelength part that can later interfere to build a diffraction pattern. A single free electron scattering this way is called Thomson scattering.

One atom scattering weakly in all directions is not yet diffraction, and on its own it would be almost too faint to notice. The magic appears only when a whole periodic army of atoms scatters together: their billions of feeble wavelets mostly cancel, but in a few sharp directions they line up crest-on-crest and reinforce into an intense beam. So wave scattering is the elementary event, the single brick; interference from the ordered array is the building. Keep them separate in your mind — scattering is what one atom does, diffraction is what the crowd does.