Rate equations are proposed which describe the operation of a crystal as a resonant cavity for x rays. The formalism, which applies equally well to two-beam or multibeam diffraction cases, is not restricted to any particular mechanism of x-ray emission. It automatically takes into account dynamical diffraction effects on energy flow (group velocity) and absorption (the Borrmann effect) which are shown to be instrumental in increasing gain and lowering the lasing threshold. The resonant x-ray modes are those for which the group velocity vanishes (the resonant diffraction condition).

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The phase transition of NaNO2, is investigated by using X‐ray powder diffractometry. The temperature dependence of the lattice constants, peak intensities, and the order parameter of the ferroelectric phase, in the range of 27 to 200 °C, show the same results as obtained by using single‐crystal diffractometry. These experimental findings imply that the X‐ray powder method is suitable for the study of phase transition. The analysis of the powder diffraction profile would even improve the method.

The optical theory of Fabry-Perot interferometers (FPIs) for x rays using dynamically diffracting thin perfect crystals as reflectors is developed. Application to a device using high diffraction orders in silicon crystals of thickness of the order of 100 μm or more shows that energy resolutions of the order of a tenth of a meV are achievable. The effect that various features, such as gap and mirror thickness, lattice mismatches, etc., have on the FPI resonances is studied.