In x-ray imaging and beam conditioning it is useful to magnify or demagnify the x-ray beam, or an image, approaching (sub)micrometre resolution or the (sub)micrometre illuminated region. Using an asymmetric diffractor it is possible to expand or compress the x-ray beam in one direction. Combining two such diffractors with mutually perpendicular planes of diffraction even two-dimensional beam expansion or compression can be obtained and, for suitable wavelengths, it is even possible to design and cut a single crystal in such a way that it works as a monolithic device expanding or compressing the x-ray beam in two directions. In this paper, a new magnifying monolithic optical device for a two-dimensional magnification of 25 at 10 keV, based on two noncoplanar asymmetrically inclined {311} diffractors, was designed and made from a single silicon crystal. A ray-tracing image has been simulated to check the functionality of the device. The experimental testing of this device was performed at Optics beamline BM5 at ESRF Grenoble. An undistorted image magnification of about 15 was achieved at a photon beam energy of 9.6 keV. When the photon energy was increased, a higher magnification and increased distortion were observed (horizontal magnification of 39, vertical magnification of 20) at an energy of 10.045 keV. The advantages and disadvantages of the device, as well as further steps to improve it are briefly discussed.

The diffractive–refractive optical device consisting of four crystals in (+, −, −, +) setting with longitudinal parabolic grooves has a geometrical aberration which influences the achievable focus size. This aberration is discussed analytically by using a new, more precise formula for the calculation of focusing distance, which respects the finite distance between optical elements. The calculation of the intensity distribution surrounding the focus is illustrated by a ray-tracing method based on the dynamical theory of diffraction. It demonstrates an achievable focus size. Finally we discuss that this aberration may be suppressed by the slight narrowing of the groove profile. In particular, the parameter a in the equation of parabola has to slightly grow with x. A practical application may require an ultra-precise fabrication of the grooves.

The classical theory of nucleation in solids is mathematically expressed by a system of differential equations for temporal development of cluster distribution (sizes and their concentration). Cluster sizes reach hundreds of nanometers during long annealing times, requiring us to deal with up to 107–108 differential equations. The full numerical simulation grows linearly with the number of equations, making the numerical solution extremely time-consuming. In this paper we develop a nodal-points approximation method with a logarithmic efficiency, which allows us to calculate the cluster distribution very quickly. The method is based on modified Becker–Döring equations solved precisely only within a given set of nodal points and approximated in between them. Availability of the method is shown by monitoring the kinetics of oxygen precipitation in Czochralski silicon for the case of a three-stage annealing for 8 h at 600 °C+4 h at 800 °C+8 h at 1000 °C, where the number of monomers in the clusters reaches more than 2 × 107. Examples are discussed, mainly about the development of a concentration gap and concentration wavelet of the cluster distribution and about interstitial oxygen concentration.

Using asymmetric diffraction in grazing incidence or in grazing emergence it is possible to expand or compress an x-ray beam in one dimension. Combining two asymmetric diffractions with non-coplanar planes of diffraction it is possible to obtain two-dimensional beam expansion or compression. This paper reports on a monolithic two-dimensional x-ray beam compressor consisting of two non-coplanar asymmetrically inclined {311} diffractors prepared in one silicon crystal block and tested at Optics beamline BM05 at ESRF, Grenoble. The design of the x-ray beam compressor, the results of beam tracing image simulation, the experimental arrangement used for testing and the properties of the x-ray microbeams formed are presented. For the beam energy of 9.5 keV 10- and 13-times beam compression in two directions was observed. Using a metal grid in the incident beam more than 400 microbeams smaller than 10 µm and separated by less than 5 µm were obtained in the outgoing beam. A gain of up to 100 times in intensity per unit area was obtained in comparison with the x-ray beam magnifier geometry, demonstrating a real two-dimensional beam compression.

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