Performance of synchrotron X-ray monochromators under heat load Part 1: finite element modeling

In this paper we present the details of the finite element modeling (FEM) procedure used to calculate the thermal deformation generated by the X-ray power absorbed in silicon crystals. Different parameters were varied systematically such as the beam footprint on the crystal, the reflection order and the white beam slit settings. Moreover, the influence of various cooling parameters such as the cooling coefficient and the temperature of the coolant were studied. The finite element meshing was carefully optimized to generate a deformation output that could be easily read by a diffraction simulation code. Comparison with the experiments shows that the peak-to-valley slope error calculated by the FEM is an excellent approximation of the rocking curve width for a liquid nitrogen cooled silicon (3 3 3) crystal, and a quite good approximation for significantly deformed silicon (1 1 1) crystals.