In this paper the authors present a general analysis of resonant elastic scattering of x rays. The approach exploits crystal symmetry, scattering geometry, and polarization. Extinction rules, their breaking, and the observation of forbidden reflections are discussed. As an application, a detailed description of the experiment performed by Finkelstein, Shen, and Shastri at the iron $K$ edge in $\alpha$ ${\mathrm{Fe}}_2$${\mathrm{O}}_3$ (hematite) is reported.

DOI:https://doi.org/10.1103/RevModPhys.66.1509