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Fuel loss and environmental contamination by tritium permeation through structural materials are critical issues for the establishment of a fusion DEMO reactor. In this study, the effectivity of a chromium oxide layer formed on reduced activation ferritic/martensitic steel F82H as a tritium permeation barrier and its stability under simulated solid/liquid breeder blanket conditions have been investigated. A uniform 100-nm-thick chromium oxide layer was formed by heat treatment at 710 °C for 5 min in 50% argon-50% hydrogen mixed gas with the flow rate of 200 standard cubic centimeter per minute. After exposure to simulated solid breeder blanket conditions, an iron oxide layer and a spinel-type iron-chromium oxide layer formed. In the case of a liquid breeder blanket condition, the chromium oxide layer partly lost at 500 °C for 100 h. The chromium oxide-formed sample decreased deuterium permeation flux by a factor of up to 150. The permeation reduction efficiency deteriorated after exposure to a solid breeder blanket condition due to a change of the chromium oxide layer. However, the chromium oxide formation would play a role to reduce hydrogen isotope permeation even after reduction of the oxide layers.

Non-coplanar 18-beam X-ray pinhole topographs for a silicon crystal were computer simulated by fast Fourier transforming the X-ray rocking amplitudes that were obtained by solving the n-beam (n = 18) Ewald–Laue dynamical theory (E-L&FFT method). They were in good agreement with the experimentally obtained images captured using synchrotron X-rays. From this result and further consideration based on it, it has been clarified that the X-ray diffraction intensities when n X-ray waves are simultaneously strong in the crystal can be computed for any n by using the E-L&FFT method.

X-ray rocking curves are reported which have been obtained by fast-Fourier-transforming X-ray amplitudes in three-beam pinhole topographs. The topographs were computer-simulated based on the Takagi-Taupin equation with the condition of spherical-wave X-ray incidence. This is another strategy for calculating three-beam rocking curves, which are usually calculated based on the Ewald-Laue dynamical theory.

X-ray six-beam pinhole topograph images were obtained for a silicon crystal with incident synchrotron X-rays. The polarization state of X-rays incident on the sample crystal was controlled by using a four-quadrant phase-retarder system [Okitsu et al. (2002). Acta Cryst. A58, 146-154] that can be rotated around the transmitted beam axis to generate arbitrarily polarized X-rays. Quantitative agreement was found between the experimental and computer-simulated topograph images based on the n-beam Takagi-Taupin dynamical theory under the assumption that the polarization state of the incident X-rays was identical with the experiment. This result confirmed the validity of the computer algorithm to solve the n-beam dynamical theory and the proper operation of the rotating four-quadrant phase-retarder system simultaneously.

A `six-beam X-ray section topograph' experiment was performed whose images are in excellent agreement with the images computer-simulated using the theory derived by one of the authors [Okitsu (2003). Acta Cryst. A59, 235–244] based on the Takagi–Taupin dynamical theory. X-rays whose wavefront was limited to 0.1 \times 0.1 mm were incident on a [1 \bar1 1]-oriented floating-zone silicon crystal with thickness of 9.911 mm so that a six-beam condition was satisfied. The six reflection indices were 000 (forward diffraction), 440, 484, 088, \bar448 and \bar404. The plane of incidence of the 088 reflection was adjusted so as to be perpendicular to the direction of the incident horizontal linear polarization of the synchrotron radiation, which was monochromated into 18.5 keV (0.670 A wavelength). While the simulations were performed under the assumptions that the incident X-rays were linearly polarized both horizontally and vertically, they were evidently different and only the simulated images under the assumption of horizontally polarized incident X-rays were in excellent agreement with the images obtained by the experiment.

A new X-ray dynamical diffraction theory that can deal with n-beam cases comprehensively (n in [3, 4, 6, 8, 12]) has been derived based on the Takagi-Taupin dynamical theory. The new theory takes into account correctly the effects of arbitrarily polarized incident X-rays and the polarization states of X-ray wavefields in a crystal. Furthermore, an arbitrary lattice displacement in the crystal can be dealt with. The new theory has a high symmetry and therefore can be written with one equation supposing that suffixes are taken in 2n ways, where the suffixes indicate ordinal numbers of waves and polarization states. This simplicity of the theory enables a computer program to solve the equations to be coded easily. A method to solve the theory numerically is also described. 'Six-beam X-ray section topographs' computer simulated based on the new theory are also presented.

An X-ray transmission-type double phase-retarder system that can compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident X-rays) has been developed and its advantage over a conventional single transmission-type X-ray phase retarder was demonstrated. However, it was noticed that the transmission-type X-ray phase retarder suffers from not only off-axis aberration but also chromatic aberration (phase-shift inhomogeneity due to energy spread of incident X-rays). In this paper, a transmission-type X-ray four-quadrant phase-retarder system is proposed that can compensate for both off-axis and chromatic aberrations. The X-ray four-quadrant phase-retarder system is composed of four transmission-type X-ray phase retarders. The scattering planes of four phase-retarder diamond crystals are set to be inclined by 45^{\circ}, 135^{\circ} \,(= 45^{\circ} + 90^{\circ}), 225^{\circ}\,(= 45^{\circ} + 180^{\circ}) and 315^{\circ}\, (= 45^{\circ} + 270^{\circ}), respectively, with respect to the plane of incident polarization. Under the conditions of 7709 eV photon energy, 1.5 eV energy spread and 45′′ angular divergence (FWHM) of incident X-rays, the X-ray four-quadrant phase-retarder system created 0.98 degree of vertical-linear polarization from horizontal-linear polarization. This value was favorably compared to 0.89 and 0.96, which were obtained by the single and double phase-retarder systems, respectively. The principle of the X-ray four-quadrant phase-retarder system will be described together with its advantage over the single and double phase-retarder systems.

An X-ray double phase retarder system composed of two transmission-type phase retarders is proposed and developed in order to compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident X-rays). The scattering planes of the two phase retarders are set to be inclined by 45 degrees with respect to the plane of incident polarization, but the two phase retarders give Bragg reflections in opposite directions. By using this X-ray optical system, vertically polarized X-rays with a 0.99 degree of linear polarization were obtained from horizontally polarized synchrotron radiation with a horizontal beam divergence of 20 arcsec (0.1 mrad). This value is favorably compared with the value of 0.87 which was obtained using a conventional single phase retarder of identical total thickness, 627 microns. The comparison was made at the nickel K-absorption edge (8333 eV) with the condition that 47% of incident X-rays were transmitted through the two phase retarder crystals. The crystals were (100)-oriented diamond plates giving asymmetric 111 Laue reflections.

X-ray polarization-contrast images resulting from x-ray magnetic circular dichroism (XMCD) in hard x-ray region have been successfully recorded for the first time. The apparatus used consisted of an x-ray polarizer, double x-ray phase retarders, and a high-spatial-resolution x-ray charge-coupled device (CCD) detector. The sample used was a hexagonal close packed (h.c.p.) cobalt poly-crystal foil of thickness about 4 μm. The x-ray polarization-contrast image resulting from XMCD was observed at a photon energy 10 eV above the cobalt K-absorption edge (7709 eV). The observed contrast in the images was reversed by inversion of a magnetic field. Furthermore, the contrast was reversed again at a photon energy 32 eV above the cobalt K-absorption edge.

A new type of energy-tunable X-ray polarimeter has been developed by introducing a Hirano-Ishikawa-Kikuta's transmission-type X-ray phase retarder into an X-ray polarimeter consisting of Hart-Rodrigues' polarizer and analyzer. By using the new type of polarimeter, simultaneous detections of X-ray linear birefringence and dichroism, and simultaneous detections of X-ray linear triple refraction and trichroism, have been made for the first time. The Kramers-Kronig relation has been confirmed in the absolute scale of dielectric constant between linear birefringence and dichroism (and between linear triple refraction and trichroism), which correspond to the real and imaginary parts of dielectric anisotropy, respectively. Phase shift due to the birefringence (or the triple refraction) has been measured with a precision of 2π 110, 000, which is limited mainly by photon-counting statistics.

In the field of X-ray crystal structure analysis, while the absolute values of structure factors are directly observed, phase information is lost in general. However, this problem (phase problem) has been overcome mainly by the direct method developed by Hauptmann and Karle except for protein crystals. In the case of protein crystal structure analysis, the isomorphous replacement method and/or anomalous dispersion method are mainly used to solve the phase problem. Phasing the structure factors is sometimes the most difficult process in protein crystallography.

X-ray three-beam pinhole topograph images for spherical silicon crystals were computer-simulated based on the n-beam Takagi-Taupin (T-T) equation. They were compared with those for parallel-plate crystals. The procedure to integrate the n-beam T-T equation for a crystal with an arbitrary shape has been validated in a separate paper [Okitsu et al. (2011), Acta Cryst. A67, 550-556] from comparison between experimentally obtained and computer-simulated six-beam pinhole topographs for a channel-cut silicon crystal.

A method of calculating the polarization state of X-rays transmitted through a rotating four-quadrant X-ray phase retarder system is described using Jones calculus. This method was applied to correcting the polarization states of X-rays incident on a channel-cut silicon crystal. Details and results of this experiment are given in a separate paper [Okitsu et al. (2011), Acta Cryst. A67, 550-556].

It was pointed out in a previous paper [Okitsu et al. (2006), Acta Cryst. A62, 237-244] that an n-beam Takagi-Taupin (T-T) equation can be solved for a crystal of arbitrary shape. The procedure to integrate the n-beam T-T equation is to let all the Fourier coefficients of the electric susceptibility be zero at positions inside the Borrmann pyramid but outside the crystal. The efficiency of this simple procedure is verified in the present paper by showing qualitative and quantitative agreements between experimentally obtained and computer-simulated X-ray six-beam pinhole topographs for a channel-cut silicon crystal.

A new type of X-ray diffraction interferometry is described, in which σ- and π-polarized X-rays diffracted by a sample crystal interfere with each other. A reversal of image contrast in `polarization interference topograph' due to contrary sign of a spherical strain field in a crystal is demonstrated in terms of numerical simulations by Takagi-Taupin's dynamical theory. Further, a feasibility of `polarization holography' of X-ray diffraction is pointed out.

X-ray linear birefringence and linear dichroism spectra have been measured simultaneously and quantitatively for the first time. The sample was a hexagonal cobalt single-crystal foil. The apparatus used was an energy-tunable X-ray polarimeter, consisting of a polarizer, a phase retarder and an analyser. The X-ray energy was scanned over a range of 350 eV near the K-absorption edge. The Kramers–Kronig relation between the refraction and absorption anisotropy has been confirmed on an absolute scale. The phase-difference sensitivity of the polarimeter as a polarization inferometer is as small as 2π/10000, which is about 100 times smaller than that of the Bonse–Hart inferometer.

Even though conventional X-ray polarizers with multiple-reflection channel-cut structures perform well, they suffer from the disadvantage that the polarized beam is non-stationary as the energy is scanned. In this paper the possibility of using a thin Bragg reflector as a polarizing filter is investigated, so that the transmitted beam (rather than the Bragg-reflected beam) is used. Consequently, the position and direction of the transmitted beam are unchanged as the energy is changed, or even when the polarization direction to be filtered out is changed. Theoretical considerations as well as experimental results on the performance characteristics of the proposed transmission-type X-ray linear polarizer are presented. A polarization ratio, defined as I H /I V , higher than 105 was obtained.

X-ray triple refraction and triple absorption have been quantitatively measured for the first time. The samples were (100)-, (010)- and (001)-oriented plates of a cobalt-complex monoclinic crystal. The apparatus used was an energy-tunable X-ray polarimeter with a phase retarder. The X-ray energy was scanned over a range of 150 eV near the cobalt K-absorption edge. Both the spectra of ellipticity and rotation of polarization were completely different for each crystal plate, which revealed that the biaxial crystal had three refractive indices and three absorption coefficients in the X-ray region. The Kramers–Kronig relation between the real and imaginary parts of the dielectric anisotropy has been quantitatively confirmed for all three different orientations.

X-ray phase-retarder systems to compensate for aberrations which arise from angular divergence and energy spread of x rays, have been developed. The two-quadrant x-ray phase-retarder system consists of two diamond crystals of almost identical thickness. It can compensate for off-axis aberration (phase-shift inhomogeneity due to angular divergence of incident x rays). The four-quadrant x-ray phase-retarder system consists of four diamond crystals of almost identical thickness. The scattering planes of four phase retarders were set to be inclined by 45 deg, 135 deg (= 45 deg + 90 deg), 225 deg (= 45 deg + 180 deg) and 315 deg (= 45 deg + 270 deg), respectively, with respect to the direction of incident polarization. It can compensate for not only the off-axis aberration but also chromatic aberration (phase-shift inhomogeneity due to energy spread of incident x rays). The principles and applications of the two-quadrant and four-quadrant phase-retarder systems will be described.

We report on the x-ray magnetic linear dichroism (XMLD) spectra and x-ray polarization-contrast images arising from XMLD in the hard x-ray spectral range. The sample used was an iron-rich metal-particulate magnetic recording medium with a $3.6\ensuremath{-}\ensuremath{\mu}\mathrm{m}$ thickness of a magnetic layer. The magnitude of the XMLD signal was about 0.06% at the maximum near the iron K-absorption edge (7111 eV). The contrast between $90\ifmmode^\circ\else\textdegree\fi{}$ magnetic domains, which were made artificially on the sample, was clearly observed at a photon energy of 1 eV about the iron K-absorption edge. The contrast in the image was reversed at a photon energy of 6 eV above the iron K-absorption edge.

X-ray polarization-contrast images resulting from X-ray magnetic circular dichroism (XMCD) in the hard X-ray region have been successfully recorded for the first time. The apparatus used consisted of an X-ray polarizer, double X-ray phase retarders, and a high-spatial-resolution X-ray charge-coupled-device detector. The sample used was a hexagonal-close-packed cobalt polycrystal foil having a thickness of about 4 microns. The X-ray polarization-contrast image resulting from XMCD was observed at a photon energy of 10 eV above the cobalt K-absorption edge (7709 eV). The observed contrast in the image was reversed by inversion of the magnetic field. Furthermore, the contrast was reversed again at a photon energy of 32 eV above the cobalt K-absorption edge.

X-ray polarization-contrast images resulting from X-ray linear dichroism (XLD) in the hard X-ray region have been successfully recorded for the first time. The apparatus used consisted of an X-ray polarizer, double X-ray phase retarders and a high-spatial-resolution X-ray charge-coupled device (CCD) detector. The sample used was a hexagonal close packed (h.c.p.) cobalt single-crystal foil of thickness about 12 microm. The experiment was performed at X-ray energies of 23 and 29 eV above the cobalt K edge (7709 eV), at which the maximum linear dichroisms (approximately 3%) were observed, with their signs reversed, in the XLD spectrum measured with quadruple X-ray phase retarders. The contrasts in the images at the two X-ray energies were reversed as a result of the XLD in the sample. Furthermore, the values of the contrast in the images arising from the linear dichroism (approximately 3%) were in good agreement with those yielded by the XLD spectrum.

The possibility of a transmission-type X-ray linear polarizer is investigated using a thin Bragg reflector as a polarizing filter. In this device, the transmitted beam (rather than the Bragg-reflected beam) is the useful output of the device. Consequently, the position and the direction of the transmitted beam are unchanged as the energy is changed, or even when the polarization direction to be filtered out is changed. Theoretical considerations as well as preliminary transmissivity measurements are presented. The use of perfect crystals of silicon and diamond is examined. A polarization ratio, defined as I_H/I_V, higher than 105 was observed in experiments to measure the performance characteristics of the proposed X-ray polarizing reflector. The transmission-type X-ray linear polarizer is well suited for spectroscopic measurements with polarized X-rays.

We have measured the Faraday effect of cobalt polycrystalline foil near cobalt K-absorption edge with the energy-tunable x-ray polarimeter. The Kramers-Kronig (K-K) relation between spectrum of the Faraday rotation and magnetic circular dichroism measured by using the ellipticity polarized synchrotron x-radiation has been confirmed. Furthermore, we have constructed, a new type of x-ray polarimeter with a diamond phase retarder and measured x-ray linear dichroism (LD) and linear birefringence (LB) simultaneously using an hcp cobalt single crystal foil. The K-K relation between LD and LB has also been confirmed clearly.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

X-ray polarization-contrast images arising from x-ray magnetic linear dichroism (XMLD) in hard xray spectral range have been recorded in an iron-rich metal-particulate (MP) magnetic recording medium for the first time employing an interesting optical system: polarization switching optics. The contrast of 0.06/0 between 90-degree magnetic domains, which were made artificially on the sample, was clearly observed at photon energy of 1 eV above the iron K-absorption edge.

The dislocation loops grown as vacancy source after up-quenching in 99.9999 % aluminum single crystals with a low dislocation density were examined by synchrotron topography in order to determine the Burgers vector and the nature directly. The specimen crystal was heated to 295°C and hold for 15min. at the temperature, then cooled down to room temperature to freeze the loops in the specimen. Topographs were taken on the high-speed X-ray topographic station (BL-15B) at the Photon Factory (KEK-PF). White beam topographs were taken using four of symmetrically equivalent 111 and 220 reflections for the determination of the Burgers vector. Monochromatic section topographs were also taken with 111, 222, 333 and 444 reflections at a wavelength of 0.62Å. The image of the loops was simulated by numerical solution of the Takagi-Taupin equations. Burgers vector of the frozen loops was determined to be a/2. And comparison between the observed loop image and the simulated one showed that the dislocation loop grown as a vacancy source was interstitial-type and the size ranged from 3 µ m to 10 µ m in radius.

Grown-in microdefects of a Czochralski (CZ) silicon crystal grown at a slow growth rate were studied by section topography using high energy synchrotron radiation. Images of the microdefects in the section topographs were analyzed quantitatively using computer simulation based on the Takagi-Taupin type dynamical diffraction theory of X-rays, and reproduced successfully by the simulation when the microdefects were assumed to be spherical strain centers. Sizes and positions of the microdefects were able to be determined by detailed comparison between the experiments and the computer simulations. The validity of the computer simulation in an analysis of the section topographs is discussed.

Microdefects in as-grown Czochralski silicon crystals have been investigated by means of X-ray topography using 60 keV radiation from a synchrotron radiation source. In crystals grown at the pulling rate of 0.4 mm/min, very fine defects were observed and their density was about 1×103/cm3, which was in agreement with the result obtained by the flow pattern technique using Secco preferential etching. The strain field of the defects was analyzed from the topographic image height of defects using the kinematical diffraction theory. The values of the defect strength that gave a measure of the size of the defects were from 2 to 40×10-20m3.

An undoped floating zone (FZ) silicon crystal has been investigated by synchrotron X-radiation section topography with high-order reflections up to 14 14 0. Numerically simulated topographs based on the Takagi-Taupin equations were in good agreement with experimental distorted patterns when a spherical strain field was assumed in the crystal. The volume change of the lattice caused by the strain center was estimated to correspond to a sphere with a radius of 10 µm.