IUCr journals news
Nonlinear thermal-distortion predictions of a silicon monochromator using the finite element method
G. Tajiri, W.-K. Lee, P. Fernandez, D. Mills, L. Assoufid & F. Amirouche, J. Synchrotron Rad. (2001). 8, 1140–1148
Sometimes Nature provides us with perfect gifts. What would synchrotron radiation be without the perfect silicon crystals that are so valuable as monochromators, polarizers, and analysers in most beamlines? Nature offers the physical basis to grow perfect silicon crystals, engineers in the semiconductor industry have learnt to master the process of producing huge perfect monocrystalline ingots and the makers of synchrotron X-ray optics are capable of transforming the material into optical elements for X-ray beam conditioning. There is a further gift from Nature: at 125 K the thermal expansion of silicon is zero while the thermal conductivity increases threefold with respect to room temperature. This property is extremely valuable because it decreases the thermal deformation generated when cooling silicon crystal optics exposed to undulator or wiggler beams that have heat fluxes comparable to that at the sun’s surface. At room temperature the quality of the X-ray beams emerging from modern storage rings would be greatly deteriorated. Nowadays, most high heat load monochromators in beamlines at third-generation storage ring sources are cryocooled. The history of cryogenically cooled silicon monochromators has been described by Bilderback et al. (2000).
Because sources tend to become stronger and fourth-generation sources are under discussion, the question arises as to how far we can go with power loading before cryogenic cooling fails. Another important question is how accurately can the thermo-mechanical response and the diffraction properties of the cooled crystals be predicted? The modelling exercise starts with finite element analysis (FEA), in which the piece of material, heated on one side and cooled on the other, is subdivided into many small volumes (the 'mesh'). The computer calculates the temperature distribution and the overall shape of this piece by adding up the contributions of all the small, more or less expanding elements. FEA has been widely tested and gives very reliable results — if correctly applied. The latter sine qua non condition has been a challenge for some time. In most of the extensive work done over the past many years it was assumed that the radiation is absorbed at the surface or very close to it. The validity of the assumption depends on the spectral distribution of the incoming beam and on the Bragg angle.
If future machines such as the 'ultimate storage ring' (Ropert, 2001) generate still higher X-ray power, at least three avenues to solve the problem can be envisaged: spreading the beam on the surface of the cryocooled silicon crystal by asymmetric and inclined diffraction geometries, using isotopically pure silicon that has much enhanced thermal conductivity at even lower temperatures, or using single-crystal diamonds that have ultimate thermal performance and are already in use on several beamlines. All these developments will require further studies of the kind described by Tajiri and co-workers.
Bilderback, D.H., Freund, A.K., Knapp, G.S. & Mills, D.M.M. (2000).
J. Synchrotron Rad. 7, 53–60.
Ropert, A. (2001). Proc. SPIE, 4501, 3–16.
European Synchrotron Radiation Facility, Grenoble, France