X-Ray Diffraction with Calcite in Several Orders of Reflection

Theoretical and experimental values of the four properties of reflection (width of the ($n,-n$) rocking curve, percent reflection, coefficient of reflection and a factor determined by the shape of the ($n,-n$) curve) of calcite crystals have been compared throughout the wave-length ranges $0.71<\mathrm{}\lambda <5.83\mathrm{}\mathrm{A}$ in first order, $0.71<\mathrm{}\lambda <2.75\mathrm{}\mathrm{A}$ in second order, and with wave-lengths 0.71 and 1.54A in third order and 0.71A in fourth and fifth orders. The Darwin-Ewald-Prins theory was evaluated with an attempt to correct (1) for the effects of the thermal motions of the atoms in the crystal and (2) for the variation of the atomic structure factor of calcium in the wave-length region of anomalous dispersion. Excellent qualitative agreement is found but general quantitative agreement is not found. The concept of mosaic structure in the crystal lattice is not entirely sufficient to account for the discrepancies.