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We present an implementation of the Maxwell-Bloch (MB) formalism for the study of x-ray emission dynamics from periodic multilayer materials whether they are artificial or natural. The treatment is based on a direct Finite-Difference-Time-Domain (FDTD) solution of Maxwell equations combined with Bloch equations incorporating a random spontaneous emission noise. Besides periodicity of the material, the treatment distinguishes between two kinds of layers, those being active (or resonant) and those being off-resonance. The numerical model is applied to the problem of $K\alpha$ emission in multilayer materials where the population inversion could be created by fast inner-shell photoionization by an x-ray free-electron-laser (XFEL). Specificities of the resulting amplified fluorescence in conditions of Bragg diffraction is illustrated by numerical simulations. The corresponding pulses could be used for specific investigations of non-linear interaction of x-rays with matter.

Efficient multilayer optics for radiation in the water window range are difficult to manufacture due to extremely small layer thicknesses and severe intermixing of elements between the layers. Therefore, adequate analytics and short feedback loops are of utmost importance for manufacturers to improve performance and efficiency. We show the possibility for non-destructive elemental depth profiling with commercial laboratory equipment using four real-life CrSc multilayer samples. Comparative measurements at the laboratory of PTB at the synchrotron radiation facility BESSY II confirm the results and prove the potential of laboratory equipment for the reliable analysis of stratified materials with sub-nanometer layer thicknesses.

We present the observation of the angular distribution of a characteristic x-ray emission through a periodic multilayer. The emission coming from the substrate on which the multilayer is deposited is used for this purpose. It is generated upon proton irradiation through the multilayer and detected with an energy sensitive CCD camera. The observed distribution in the low detection angle range presents a clear dip at a position characteristic of the emitting element. Thus, such a device can be envisaged as a spectrometer without mechanical displacement and using various ionizing sources (electrons, x-rays, ions), their incident direction being irrelevant., Comment: 3 pages, 2 figures, 13 references

Pd/Y multilayers are high reflectance mirrors designed to work in the 7.5-11 nm wavelength range. Samples, prepared by magnetron sputtering, are deposited with or without B4C barrier layers located at the interfaces of Pd and Y layers to reduce interdiffusion, which is expected by calculating mixing enthalpy of Pd and Y. Grazing incident x-ray reflectometry is used to characterize these multilayers. B4C barrier layers are found effective on reducing the Pd-Y interdiffusion. Details of the composition of the multilayers are revealed by hard x-ray photoemission spectroscopy under x-ray standing waves effect. It consists in measuring the photoemission intensity from samples that perform an angular scan in the region corresponding to the multilayer period and the incident photon energy according to the Bragg law. The experimental result indicates that Pd does not chemically react with B nor C at the Pd-B4C interfaces while Y does at the Y-B4C interfaces. The formation of Y-B or Y-C chemical compound can be the reason why the interfaces are stabilized. By comparing the experimentally obtained angular variation of the characteristic photoemission with the theoretical calculation, the depth distribution of each component element can be interpreted., Comment: 13 pages, 8 figures, 1 tables, 19 references

The Kossel interferences generated by characteristic x-ray lines produced inside a periodic multilayer have been observed upon proton irradiation, by submitting a Cr/B4C/Sc multilayer stack to 2 MeV protons and observing the intensity of the Sc and Cr K$\alpha$ characteristic emissions as a function of the detection angle. When this angle is close to the Bragg angle corresponding to the emission wavelength and period of the multilayer, an oscillation of the measured intensity is detected. The results are in good agreement with a model based on the reciprocity theorem. The combination of the Kossel measurements and their simulation, will be a useful tool to obtain a good description of the multilayer stack and thus to study nanometer-thick layers and their interfaces.

The time-dependent Bragg diffraction by multilayer gratings working by reflection or by transmission is investigated. The study is performed by generalizing the time-dependent coupled-wave theory previously developed for one-dimensional photonic crystal [Andr{\'e} J-M and Jonnard P, J. Opt. 17, 085609 (2015)] and also by extending the Takagi-Taupin approach of the dynamical theory of diffraction. The indicial response is calculated. It presents a time-delay with a transient time that is a function of the extinction length for reflection geometry and of the extinction length combined with the thickness of the grating for transmission geometry.

We present the characterization of Mg-Co-Zr tri-layer stacks by using x-ray fluorescence induced by x-ray standing waves, both in the grazing incidence (GI) and grazing exit (GE) modes. The introduction of a slit in the direction of the detector improves the angular resolution by a factor 2 and significantly the sensitivity of the technique for the chemical characterization of the buried interfaces. By observing the intensity variations of the Mg Kalpha and Co Lalpha characteristic emissions as a function of the incident (GI mode) or detection (GE mode) angle, we show that the interfaces of the Si/[Mg/Co/Zr] x30 multilayer are abrupt, whereas in the Si/[Mg/Zr/Co] x30 multilayer a strong intermixing occurs at the Co-on-Zr interfaces. The explanation of this opposite behaviour of the Co-on-Zr and Zr-on-Co interfacesis given by the calculation of the mixing enthalpies of the Co-Mg, Co-Zr and Mg-Zr systems, which shows that the Co-Zr system presents anegative value and the two others positive values. Together with the difference of the surface free energies of Zr and Co, this leads us to consider the Mg/Zr/Co system as aMg/Co x Zr y bi-layer stack, with x/y estimated around 3.5., Comment: Published in Journal of Synchrotron Radiation 22, 1419 (2015)http://scripts.iucr.org/cgi-bin/paper?S1600577515016239

The time-dependence of the Bragg diffraction by one-dimensional photonic crystals and its influence on the short pulse reflection are studied in the framework of the coupled- wave theory. The indicial response of the photonic crystal is calculated and it appears that it presents a time-delay effect with a transient time conditioned by the extinction length. A numerical simulation is presented for a Bragg mirror in the x-ray domain and a pulse envelope modelled by a sine-squared shape. The potential consequences of the time-delay effect in time-dependent optics of short-pulses are emphasized.

Kossel diffraction under standing-wave excitation in a one-dimensional photonic crystal is investigated. It is shown that by combining the reciprocity theorem, the Fermi golden rule and the concept of density of photonic modes, it is possible to predict the behaviour of the Kossel diffraction in such a system.

We conducted an inter-laboratory study of a metallic glass whose main component is nickel. Two determinations of the mass fractions of the different elements present within the sample were asked to the participants: one at an acceleration voltage of 15 or 20 kV and another one at 5 kV. We compare the mass fractions obtained from wavelength dispersive (WDS) and energy dispersive spectrometries (EDS) and also try to find an influence of the kind of EDS detector and its entrance window, the background subtraction method, the use or not of standards as well as the quantification method. Both means of WDS and EDS mass fractions are close to the reference values. The dispersion of the results was larger at 5 kV than at 15-20 kV owing to the use of the L lines rather than K lines and to the lowest collected intensities. There is an exception with the case of boron because at the lowest voltage, the excitation condition is more favourable for the production of the K line. It appears that the dispersion of the results is larger with EDS than with WDS but it was not possible to find a correlation between the large dispersion and one of the considered experimental parameters and quantification factors. Thus, one can think that electron microprobes are inherently better for the determination of mass fractions or that the implementation of quantitative analysis must be optimized for some cases, especially in SEMs., Comment: Members of the GN-MEBA, SEMPA users group and Belgian laboratories coordinated by Universite Catholique de Louvain are thanked for their participation to this inter-laboratory study

We study the interface evolution of a series of periodic Co/Mo2C multilayers as a function of the annealing temperature up to 600{\textdegree}C. Different complementary techniques are implemented to get information on the phenomenon taking place at the interfaces of the stack. The periodical structure of Co/Mo2C multilayer is proven by Time-of-flight secondary ion mass spectrometry (ToF-SIMS) depth profiles which demonstrate the formation of an oxide layer at both air/stack and stack/substrate interfaces. From Nuclear magnetic resonance (NMR) spectra, we observed the intermixing phenomenon of Co and C atoms for the as-deposited sample, and then at annealing temperature above 300{\textdegree}C Co and C atoms separate from their mixed regions. Comparison of NMR results between Co/Mo 2 C and Co/C references confirms this phenomenon. This is in agreement with x-ray emission spectroscopy (XES) measurements. Furthermore the calculation of the Co-C, Co-Mo and Mo-C mixing enthalpy using Miedema's model gives a proof of the demixing of Co and C atoms present within the stacks above 300{\textdegree}C. From the transmission electron microscopy (TEM) analysis, we found the presence of some crystallites within the as-deposited sample as well as the mainly amorphous nature of all layers. This is confirmed using x-ray diffraction (XRD) patterns which also demonstrate the growth of crystallites induced upon annealing., Comment: Published in Applied Surface Science 331, 8-16 (2015). http://dx.doi.org/10.1016/j.apsusc.2014.12.055

We discuss the feasibility of a soft-x-ray distributed feedback laser (DFL) pumped by an x-ray free electron laser (X-FEL). The DFL under consideration is a Mg/SiC bi-layered Bragg reflector pumped by a single X-FEL bunch at 57.4 eV, stimulating the Mg L2,3 emission at 49 eV corresponding to the 3s-3d -> 2p1/2,3/2 transition. Based on a model developed by Yariv and Yeh and an extended coupled-wave theory, we show that it would be possible to obtain a threshold gain compatible with the pumping provided by available X-FEL facilities., Comment: This paper has 7 pages and is published in Laser Physics 24, 085001 (2014). The webpage of the editor is http://iopscience.iop.org/1555-6611/24/8/085001/

The valence states of Mg-Al alloys are compared to those of reference materials (pure Mg and Al metals, and intermetallics). Two methods based on X-ray emission spectroscopy are proposed to determine the phases and their proportion: first, by analyzing the Al valence spectra of the Mg-rich alloys and the Mg valence spectra of the Al-rich alloys; second, by fitting with a linear combination of the reference spectra the Al spectra of the Al-rich alloys and the Mg spectra of the Mg-rich alloys. This enables us to determine that Al and Al3Mg2 are present in the 0-43.9 wt% Al composition range and Mg and Al12Mg17 are present in the 62.5-100 wt% Al composition range. In the 43.9-62.5% Al range, the alloy is single phase and an underestimation of the Al content of the alloy can be estimated from the comparison of the bandwidth of the alloy spectrum to the bandwidths of the reference spectra., Comment: 10 pages. can also be found at: http://journals.cambridge.org/action/displayAbstract?fromPage=online\&aid=3416872

Using electron-induced X-ray emission spectroscopy (XES), we have studied two Al/Ni periodic multilayers that differ only by their annealing temperature: as-deposited and annealed at 115C. Our aim is to show that XES can provide further details about the chemistry at the metal-metal interface, in addition to what is obtained by X-ray diffraction. The distribution of valence states exhibiting Al 3p and Ni 3d character is determined from the analysis of the Al Kbeta and Ni Lalpha emission bands respectively. The multilayer emission bands are compared to those of reference materials: pure Al and Ni metals as well as Al3Ni, Al3Ni2 and AlNi intermetallics. We provide evidence that, for temperatures up to 115C, Al3Ni is the major component of the multilayer., Comment: 5 pages. Can also be found at : http://www.epjap.org/action/displayAbstract?fromPage=online\&aid=8011580

Periodic multilayers give rise to enhanced X-ray fluorescence when a regime of standing waves occurs within the structure. This regime may concern the primary radiation used to induce the fluorescence, the secondary radiation of fluorescence or both of them. Until now, existing models only dealt with standing wave regime of primary radiation. We present a theoretical approach based on the oscillating dipole model and the coupled-wave theory that can treat efficiently any standing wave regime. We compare our simulations to experimental data available in the literature.

Periodic multilayers are nowadays widely used to perform x-ray analysis in the soft x-ray range (photon energy lower than 1 keV). However, they do not permit to obtain high-resolution spectra like natural or synthetic crystals. Thus, multilayers cannot resolve interferences between close x-ray lines. It has been shown and demonstrated experimentally that patterning a grating profile within a multilayer structure leads to a diffractive optics with improved resolving power. We illustrate the use of a Mo/B4C multilayer grating in the Fe L and C K spectral ranges, around 700 eV and 280 eV respectively. First, in the Fe L range, the improved spectral resolution enables us to distinguish the Fe L\alpha and L\beta emissions (separated by 13 eV). In addition, using a sample made of a mix of LiF and an iron ore, we show that it is possible to easily resolve the F K and Fe L emissions. These examples demonstrate that an improved x-ray analysis can be obtained with multilayer gratings when there is the need to study samples having elements giving rise to close emission lines. Second, in the C K range, by comparing C K\alpha spectra from B4C and cellulose, we show that the shape of the emission band is sensitive to the chemical state of the carbon atom., Comment: 8 pages; published in X-ray Spectrometry 38, 117 (2009)

The resonant magnetic reflectivity of Co/Mg multilayers around the Co L2,3 absorption edge is simulated then measured on a specifically designed sample. The dichroic signal is obtained when making the difference between the two reflectivities measured with the magnetic field applied in two opposite directions parallel to the sample surface. The simulations show that the existence of magnetic dead layers at the interfaces between the Co and Mg layers leads to an important increase of the dichroic signal measured in the vicinity of the third Bragg peak that otherwise should be negligible. The measurements are in agreement with the model introducing 0.25 nm thick dead layers. This is attributed to the Co atoms in contact with the Mg layers and thus we conclude that the Co-Mg interfaces are abrupt from the magnetic point of view., Comment: 8 pages

A set of Mo/Si periodic multilayers is studied by non destructive analysis methods. The thickness of the Si layers is 5 nm while the thickness of the Mo layers changes from one multilayer to another, from 2 to 4 nm. This enables us to probe the effect of the transition between the amorphous to crystalline state of the Mo layers near the interfaces with Si on the optical performances of the multilayers. This transition results in the variation of the refractive index (density variation) of the Mo layers, as observed by x-ray reflectivity (XRR) at a wavelength of 0.154 nm. Combining x-ray emission spectroscopy and XRR, the parameters (composition, thickness and roughness) of the interfacial layers formed by the interaction between the Mo and Si layers are determined. However, these parameters do not evolve significantly as a function of the Mo thickness. It is observed by diffuse scattering at 1.33 nm that the lateral correlation length of the roughness strongly decreases when the Mo thickness goes from 2 to 3 nm. This is due to the development of Mo crystallites parallel to the multilayer surface.

The amorphous-to-crystalline transition in Al(1.0%wtSi)/Zr and Al(Pure)/Zr multilayers grown by direct-current magnetron sputtering system has been characterized over a range of Al layer thicknesses (1.0-5.0 nm) by using a series of complementary measurements including grazing incidence X-ray reflectometry, atomic force microscopy, X-ray diffraction and high-resolution transmission electron microscopy. The Al layer thickness transition exhibits the Si doped in Al could not only disfavor the crystallization of Al, but also influence the changing trends of surface roughness and diffraction peak position of phase Al<111>. An interesting feature of the presence of Si in Al layer is that Si could influence the transition process in Al(1%wtSi) layer, in which the critical thickness (1.6 nm) of Al(Pure) layer in Al(Pure)/Zr shifts to 1.8 nm of Al(1.0%wtSi) layer in Al(1.0%wtSi)/Zr multilayer. We also found that the Zr-on-Al interlayer is wider than the Al-on-Zr interlayer in both systems, and the Al layers do not have specific crystal orientation in the directions vertical to the layer from SAED patterns below the thickness (3.0 nm) of Al layers. Above the thickness (3.0 nm) of Al layers, the Al layers are highly oriented in Al<111>, so that the transformation from asymmetrical to symmetrical interlayers can be observed. Based on the analysis of all measurements, we build up a model with four steps, which could explain the Al layer thickness transition process in terms of a critical thickness for the nucleation of Al(Pure) and Al(1%wtSi) crystallites.

The effect of increasing temperature on the structural stability and interactions of two kinds of Al/Zr (Al(1%wtSi)/Zr and Al(Pure)/Zr) multilayer mirrors are investigated. All Al/Zr multilayers annealed from 200^{\circ}C to 500^{\circ}C, were deposited on Si wafers by using direct-current magnetron sputtering technology. A detailed and consistent picture of the thermally induced changes in the microstructure is obtained using an array of complementary measurements including grazing incidence X-ray reflectance, atomic force microscope, X-ray diffraction and high-resolution transmission electron microscopy. The first significant structural changes of two systems are observed at 250^{\circ}C, characterized by asymmetric interlayers appears at interface. At 290^{\circ}C, the interface consisted of amorphous Al-Zr alloy is transformed to amorphous Al-Zr alloy and cubic ZrAl3 in both systems. By 298^{\circ}C of Al(1%wtSi)/Zr and 295^{\circ}C of Al(Pure)/Zr multilayers, the interfacial phases of Al-Zr alloy transform completely into polycrystalline mixtures of hcp-ZrAl2 and cubic-ZrAl3, which smooth the interface boundary and lower the surface roughness in the multilayers. Up to 500^{\circ}C, the multilayer structure still exists in both systems, and the differences between the asymmetric interlayers are much larger in the multilayers. Finally, we discuss the transformation from symmetric to asymmetric in the annealing process for other systems.

Etched multilayers obtained by forming a laminar grating pattern within interferential multilayer mirrors are used in the soft x-ray range to improve the spectral resolution of wavelength dispersive spectrometers equipped with periodic multilayers. We describe the fabrication process of such an etched multilayer dispersive element, its characterization through reflectivity measurement and simulations, and its implementation in a high-resolution Johann-type spectrometer. The specially designed patterning of a Mo/B4C multilayer is found fruitful in the range of the C K emission as the diffraction pattern narrows by a factor 4 with respect to the non-etched structure. This dispersive element with an improved spectral resolution was successfully implemented for electronic structure study with an improved spectral resolution by x-ray emission spectroscopy. As first results we present the distinction between the chemical states of carbon atoms in various compounds, such as graphite, SiC and B4C, by the different shape of their C K emission band., Comment: 12 pages. Published in X-ray Spectrom. 41, 308 (2012)

We present the results of the characterization of Mg/Co periodic multilayers and their thermal stability for the EUV range. The annealing study is performed up to a temperature of 400\degree C. Images obtained by scanning transmission electron microscopy and electron energy loss spectroscopy clearly show the good quality of the multilayer structure. The measurements of the EUV reflectivity around 25 nm (~49 eV) indicate that the reflectivity decreases when the annealing temperature increases above 300\degreeC. X-ray emission spectroscopy is performed to determine the chemical state of the Mg atoms within the Mg/Co multilayer. Nuclear magnetic resonance used to determine the chemical state of the Co atoms and scanning electron microscopy images of cross sections of the Mg/Co multilayers reveal changes in the morphology of the stack from an annealing temperature of 305\degreee;C. This explains the observed reflectivity loss., Comment: Published in Applied Physics A: Materials Science \& Processing Published at http://www.springerlink.com.chimie.gate.inist.fr/content/6v396j6m56771r61/ 21 pages

We present the Cauchois and S\'en\'emaud Tables of X-ray emission lines and absorption edges. They are written both in French and English. They were published in 1978 by Pergamon Press and are insufficiently known. However they are of large interest because of their completeness. They comprise the energies of all the K, L, M, N and O emission lines of natural elements from lithium up to uranium as well as the energies of satellite emissions and absorption discontinuities. The more intense lines of radio-elements up to fermium (Z = 100) are also given. The Tables range from the hard X-rays (122 keV, 0.01 nm) to the extreme ultra-violet (12 eV, 102 nm). For each transition, the wavelength ({\AA} and uX) and energy (eV and Ry) are given and references are indicated. The transitions are grouped by increasing wavelength (decreasing photon energy) and also by element and spectral series. We present, as an example, the use of the Tables to identify the emissions of the molybdenum L spectrum. We decided to scan the Cauchois and S\'en\'emaud Tables and make them available for the scientific community. They are now available at the Website of our laboratory, http://www.lcpmr.upmc.fr/., Comment: The Cauchois and S\'en\'emaud Tables are now available at the following address : http://www.lcpmr.upmc.fr/themes-A2f.php The definitive version of the paper is available at www3.interscience.wiley.com X-Ray Spectrom. 2011, 40, 12-16

We use the Kramers-Kronig transform (KKT) with logarithmic kernel to obtain the reflection phase and, subsequently, the complex refractive index of a bulk mirror from reflectance. However, there remains some confusion regarding the formulation for this analysis. Assuming the damped Drude model for the dielectric constant and the oblique incidence case, we calculate the additional terms: phase at zero frequency and Blashke factor and we propose a reformulated KKT within this model. Absolute reflectance in the s-polarization case of a gold film is measured between 40 and 350 eV for various glancing angles using synchrotron radiation and its complex refractive index is deduced using the reformulated KKT that we propose. The results are discussed with respect to the data available in the literature., Comment: 18 pages, piblished in j. Mod. Opt. 57, 1504 (2010)

We study the introduction of a third material, namely Zr, within a nanometric periodic Mg/Co structure designed to work as optical component in the extreme UV (EUV) spectral range. Mg/Co, Mg/Zr/Co, Mg/Co/Zr and Mg/Zr/Co/Zr multilayers are designed, then characterized in terms of structural quality and optical performances through X-ray and EUV reflectometry measurements respectively. For the Mg/Co/Zr structure, the reflectance value is equal to 50% at 25.1 nm and 45deg of grazing incidence and reaches 51.3% upon annealing at 200deg C. Measured EUV reflectivity values of tri-layered systems are discussed in terms of material order within a period and compared to the predictions of the theoretical model of Larruquert. Possible applications are pointed out., Comment: 19 pages

The non-dispersed soft x-ray emission from a La/B4C periodic multilayer irradiated by monochromatic x-rays has been measured as a function of the incident photon energy in the 125-200 eV range for different scattering angles. We have observed a scattered intensity peak at incident energies which shift towards the low-energy side as the value of the scattering angle increases. These observations are interpreted as Raman scattering by the 5p level of lanthanum assisted by Bragg diffraction from the lattice of the periodic multilayer. A simple model based upon the laws of energy and momentum conservation enables us to account for the variation of the incident energy associated with the Bragg-Raman peak., Comment: 11 pages

The electronic structure of AlN in wurtzite and zinc-blende phases is studied experimentally and theoretically. By using x-ray emission spectroscopy, the Al 3p, Al 3s and N 2p spectral densities are obtained. The corresponding local and partial theoretical densities of states (DOS), as well as the total DOS and the band structure, are calculated by using the full potential linearized augmented plane wave method, within the framework of the density functional theory. There is a relatively good agreement between the experimental spectra and the theoretical DOS, showing a large hybridization of the valence states all along the valence band. The discrepancies between the experimental and theoretical DOS, appearing towards the high binding energies, are ascribed to an underestimation of the valence band width in the calculations. Differences between the wurtzite and zinc-blende phases are small and reflect the slight variations between the atomic arrangements of both phases.