Crystal bending in triple-Laue X-ray interferometry. Part I. Theory

The measured value of the (220) lattice-plane spacing of silicon 28 using scanning X-ray interferometry is essential to realize the kilogram by counting Si-28 atoms. An assumption made is that the measured lattice spacing is the bulk value of an unstrained crystal forming the analyser of the interferometer. However, analytical and numerical studies of the X-ray propagation in bent crystals suggest that the measured lattice spacing might refer to the analyser surface. To confirm the result of these studies and to support experimental investigations of the matter by phase-contrast topography, a comprehensive analytical model is given of the operation of a triple-Laue interferometer having the splitting or recombining crystal bent.