= X-ray scattering
{c}
\b[X-ray scattering] is the redirection of <X-rays> through interaction with matter. The angular distribution and <energy> of the outgoing radiation carry information about the material. In elastic scattering the <photon energy> is unchanged; in inelastic scattering energy is exchanged. <X-ray diffraction> concerns organized interference of scattered <waves>, rather than a separate kind of radiation.
The <scattering vector> $\mathbf q=\mathbf k_{\mathrm{out}}-\mathbf k_{\mathrm{in}}$ compares outgoing and incoming <wave vectors>. Consider two identical scatterers separated by $\mathbf d$, each with real elastic <scattering amplitude> $f$, and neglect multiple scattering. Their amplitude sum and intensity are
$$
F=f\left(1+e^{i\mathbf q\cdot\mathbf d}\right),\qquad I\propto |F|^2=2f^2\left[1+\cos(\mathbf q\cdot\mathbf d)\right].
$$
Two atoms can therefore scatter strongly in one direction and cancel in another. The measured pattern depends on arrangement, not merely on the number of atoms. For repeating <lattice planes> in a <crystal>, constructive interference gives <Bragg's law> $2d\sin\theta=n\lambda$.<Bragg's law>[IUCr dictionary, Definition and direct derivation]{ref}
The1913 experiment by <William Henry Bragg> and <William Lawrence Bragg> made the angular pattern measurable with a rotating <crystal> and an <ionization chamber> in place of a spectrometer telescope. Slits selected a narrow incoming beam; the detector current was measured as its angle changed. Peaks and repeated orders constrained <crystal structure> and <X-ray> <wavelengths>, linking an electrical measurement to atomic-scale geometry.<The Reflection of X-rays by Crystals by William Henry Bragg and William Lawrence Bragg>[pp.428–430 apparatus and angular scan; pp.435–438 reflection orders]{ref}
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