Thermal stress prediction in mirror and multilayer coatings

Multilayer optics for X-rays typically consist of hundreds of periods of two types of alternating sub-layers which are coated on a silicon substrate. The thickness of the coating is well below 1 µm (tens or hundreds of nanometers). The high aspect ratio (∼10⁷) between the size of the optics and the thickness of the multilayer can lead to a huge number of elements (∼10¹⁶) for the numerical simulation (by finite-element analysis using ANSYS code). In this work, the finite-element model for thermal-structural analysis of multilayer optics has been implemented using the ANSYS layer-functioned elements. The number of meshed elements is considerably reduced and the number of sub-layers feasible for the present computers is increased significantly. Based on this technique, single-layer coated mirrors and multilayer monochromators cooled by water or liquid nitrogen are studied with typical parameters of heat-load, cooling and geometry. The effects of cooling-down of the optics and heating of the X-ray beam are described. It is shown that the influences from the coating on temperature and deformation are negligible. However, large stresses are induced in the layers due to the different thermal expansion coefficients between the layer and the substrate materials, which is the critical issue for the survival of the optics. This is particularly true for the liquid-nitrogen cooling condition. The material properties of thin multilayer films are applied in the simulation to predict the layer thermal stresses with more precision.