Effects of Lattice Strain in Silicon Double Crystal Monochromators

Sammanfattning: Silicon double crystal monochromators are standard in modern synchrotron hard X-ray beamlines. Their role is reducing a polychromatic photon beam to a small range of wavelengths, typically within a bandwidth of 0.01-0.1%. These monochromators work through the principle of Bragg diffraction where the crystal lattice spacing, photon energy and incident angle determines the reflectivity of the crystal. One must consider that the first crystal in the system receives an enormous heat load as it absorbs the vast majority of the beam power, which is in the kilowatt regime. The heat creates thermoelastic stress that warps the crystal surface and alters its lattice spacing. This paper investigates the effects of this on the reflected beam through the help of simulations. Calculations using COMSOL for finite element analysis of heat transport, thermal expansion, elastic strain, and deformation and SHADOW3 for ray tracing of radiation transfer were coordinated by a framework called MASH. First, a numerical study of diffraction in Si 111 and Si 333 with a uniform strain gradient was performed. Then hard X-ray sources of varying energies were used to study reflectivity in Si 111 and Si 333 for the cases of strained and unstrained crystals with or without deformation. Monochromator performance, i.e. the attenuation and bandwidth of the beam after monochromation, was recorded. Significance of the results is discussed and further study proposed.