Open AccessThermal deformation of cryogenically cooled silicon crystals under intense X‐ray beams: measurement and finite‐element predictions of the surface shape
Author(s) -
Zhang Lin,
Sánchez del Río Manuel,
Monaco Giulio,
Detlefs Carsten,
Roth Thomas,
Chumakov Aleksandr I.,
Glatzel Pieter
Publication year - 2013
Publication title -
journal of synchrotron radiation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.172
H-Index - 99
ISSN - 1600-5775
DOI - 10.1107/s0909049513009436
Subject(s) - materials science , beam (structure) , optics , silicon , crystal (programming language) , finite element method , monochromator , monocrystalline silicon , synchrotron , thermal , physics , optoelectronics , thermodynamics , wavelength , computer science , programming language
X‐ray crystal monochromators exposed to white‐beam X‐rays in third‐generation synchrotron light sources are subject to thermal deformations that must be minimized using an adequate cooling system. A new approach was used to measure the crystal shape profile and slope of several cryogenically cooled (liquid nitrogen) silicon monochromators as a function of beam power in situ and under heat load. The method utilizes multiple angular scans across the Bragg peak (rocking curve) at various vertical positions of a narrow‐gap slit downstream from the monochromator. When increasing the beam power, the surface of the liquid‐nitrogen‐cooled silicon crystal deforms from a concave shape at low heat load to a convex shape at high heat load, passing through an approximately flat shape at intermediate heat load. Finite‐element analysis is used to calculate the crystal thermal deformations. The simulated crystal profiles and slopes are in excellent agreement with experiments. The parameters used in simulations, such as material properties, absorbed power distribution on the crystal and cooling boundary conditions, are described in detail as they are fundamental for obtaining accurate results.