Nonlinear thermal-distortion predictions of a silicon monochromator using the finite element method

Silicon crystal monochromators at cryogenic temperatures have been used with great success at third-generation synchrotron radiation sources. At the Advanced Photon Source the unique characteristics of silicon at liquid nitrogen temperatures (80 K) have been leveraged to significantly reduce the thermally induced distortions on beamline monochromators. Finite element simulations of the nonlinear (temperature-dependent material properties) thermal stress problem were performed and compared with the experimental measurements. Several critical finite element modeling considerations are discussed for their role in accurately predicting the highly coupled thermal and structural response of the optical component's surface distortion to the high thermal heat flux. Once an understanding of the effects of (i) local element mesh size, (ii) area/surface heat flux versus volumetric heat generation, and (iii) uniform volumetric absorbed power versus a depth-dependent absorbed power, a final series of simulations was performed. Depending on the estimated convection heat-transfer coefficient, the final refined finite element model's predictions correlated well with the experimental measurements. In general, the use of the finite element method in predicting the overall thermal and structural behavior of the surface of the optical components with a high heat flux was shown to be quite effective.