Angular dependence of resonant inelastic x-ray scattering: a spherical tensor expansion

A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered photons. The expression presented in this paper differs from that of the influential article by Carra et al. (Phys. Rev. Lett. 74, 3700, 1995) because it does not omit interference terms between electric dipole and quadrupole contributions when coupling each photon to itself. Some specific cases of the spherical tensor expansion are discussed. For example the case of isotropic samples is considered and the cross-section is expressed as a combination of only three fundamental spectra for the situation where electric dipole or electric quadrupole transitions in the absorption process are followed by electric dipole transitions in the emission. This situation includes the case of untextured powder samples, which corresponds to the most frequent situation met experimentally. Finally, it is predicted that some circular dichroism may be observed on isotropic samples provided that the circular polarization of the scattered beam can be detected

Effect of vibrations on the pre-edge features of x-ray absorption spectra

The influence of atomic vibrations on x-ray absorption near edge structure (XANES) is calculated by assuming that vibrational energies are small with respect to the instrumental resolution. The resulting expression shows that, at the K-edge, vibrations enable electric dipole transitions to 3s and 3d final states. The theory is applied to the K-edge of Al in Al2O3 corundum and of Ti in TiO2 rutile and compared with experiment. At the Al K-edge, sizeable transitions towards 3s final states are obtained, leading to a clear improvement of the agreement with experimental spectra. At the Ti K-edge, electric dipole transitions towards 3d final states explain the temperature dependence of the pre-edge features.Comment: 4 pages, 2 figure

Structural relaxation around substitutional Cr3+ in MgAl2O4

The structural environment of substitutional Cr3+ ion in MgAl2O4 spinel has been investigated by Cr K-edge Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES) spectroscopies. First-principles computations of the structural relaxation and of the XANES spectrum have been performed, with a good agreement to the experiment. The Cr-O distance is close to that in MgCr2O4, indicating a full relaxation of the first neighbors, and the second shell of Al atoms relaxes partially. These observations demonstrate that Vegard's law is not obeyed in the MgAl2O4-MgCr2O4 solid solution. Despite some angular site distortion, the local D3d symmetry of the B-site of the spinel structure is retained during the substitution of Cr for Al. Here, we show that the relaxation is accomodated by strain-induced bond buckling, with angular tilts of the Mg-centred tetrahedra around the Cr-centred octahedron. By contrast, there is no significant alteration of the angles between the edge-sharing octahedra, which build chains aligned along the three four-fold axes of the cubic structure.Comment: 7 pages, 4 figure

First-principles calculations of X-ray absorption spectra at the K-edge of 3d transition metals: an electronic structure analysis of the pre-edge

International audienceWe first present an extended introduction of the various methods used to extract electronic and structural information from the K pre-edge X-ray absorption spectra of 3d transition metal ions. The K pre-edge structure is then modelled for a selection of 3d transition metal compounds and analyzed using first-principles calculations based on the density functional theory (DFT) in the local density approximation (LDA). The selected compounds under study are presented in an ascending order of electronic structure complexity, starting with the Ti K-edge of rutile and anatase, and finishing with the Fe K-edge of the cyanomet-myoglobin. In most cases, the calculations are compared to polarized experimental spectra. It is shown that DFT-LDA methods enable us to reproduce satisfactorily the experimental features and to understand the nature of the electronic transitions involved in the pre-edge region. The limiting aspects of such methods in modelling the core-hole electron interaction and the 3d electron-electron repulsion are also pointed out

Site symmetry and crystal symmetry: a spherical tensor analysis

The relation between the properties of a specific crystallographic site and the properties of the full crystal is discussed by using spherical tensors. The concept of spherical tensors is introduced and the way it transforms under the symmetry operations of the site and from site to site is described in detail. The law of spherical tensor coupling is given and illustrated with the example of the electric dipole and quadrupole transitions in x-ray absorption spectroscopy. The main application of the formalism is the reduction of computation time in the calculation of the properties of crystals by band structure methods. The general approach is illustrated by the examples of substitutional chromium in spinel and substitutional vanadium in garnet.Comment: 27 pages, 3 figure

Angular dependence of core hole screening in LiCoO2: A DFT+U calculation of the oxygen and cobalt K-edge x-ray absorption spectra

Angular dependent core-hole screening effects have been found in the cobalt K-edge x-ray absorption spectrum of LiCoO2, using high-resolution data and parameter-free GGA+U calculations. The Co 1s core-hole on the absorber causes strong local attraction. The core-hole screening on the nearest neighbours cobalt induces a 2 eV shift in the density of states with respect to the on-site 1s-3d transitions, as detected in the Co K pre-edge spectrum. Our DFT+U calculations reveal that the off-site screening is different in the out-of-plane direction, where a 3 eV shift is visible in both calculations and experiment. The detailed analysis of the inclusion of the core-hole potential and the Hubbard parameter U shows that the core-hole is essential for the off-site screening, while U improves the description of the angular dependent screening effects. In the case of oxygen K-edge, both the core-hole potential and the Hubbard parameter improve the relative positions of the spectral features

Structural relaxation around substitutional Cr3+ in pyrope garnet

The structural environment of substitutional Cr3+ ion in a natural pyrope Mg3Al2Si3O12 has been investigated by Cr K-edge Extended X-ray Absorption Fine Structure (EXAFS) and X-ray Absorption Near Edge Structure (XANES) coupled with first-principles computations. The Cr-O distance is close to that in knorringite Mg3Cr2Si3O12, indicating a full relaxation of the first neighbors. The local C3i symmetry of the octahedral Y site is retained during Cr-Al substitution. The second and third shells of neighbors (Mg and Si) relax only partially. Site relaxation is accommodated by strain-induced bond buckling, with angular tilts of the Si-centered tetrahedra around the Cr-centered octahedron, and by a radial deformation of the Mg-centered dodecahedra

Crystal structure of synthetic Mg3Cr2Si3O12, the high-pressure Cr end-member of the knorringite-pyrope garnet series

Knorringite, the Cr-end-member of the pyrope garnet series (Nixon et al. 1968), often occur in high proportions in kimberlite garnets and is thus used for tracing high-pressure deep-earth conditions favorable to the formation of diamonds, in which knorringite-rich garnet can occur as inclusions. However, although the synthesis of knorringite is reported in the literature (Ringwood 1977; Irifune et al. 1982; Taran et al. 2004), the structure of the pure end-member has not been yet determined from experimental data. In this study, the crystal structure of knorringite, Mg3Cr2(SiO4)3, has been refined from high resolution synchrotron X-ray powder diffraction data recorded under ambient conditions on a polycrystalline sample synthesized at 12 GPa in a multi-anvil apparatus. The structure is cubic, space group Ia-3d, a = 11.5935(1), V = 1558.27(4) {\AA}3, dcalc = 3.97 g.cm-3. The Cr-O distance of 1.957(2) {\AA} is consistent with EXAFS results on the same sample. This short distance indicates a substantial compression of the CrO6 octahedron, compared to ambient pressure Cr3+-minerals such as uvarovite ( = 1.99 {\AA}, Andrut and Wildner 2002). Our experimental results thus confirm early empirical predictions based on series of high-pressure Cr-garnet end-members (Fursenko 1981), showing that the values of the Cr-O distance and the Cr-O-Si angle decrease with the augmentation of pressure and with the diminution of the size of the divalent cation

Неоміфологія постсучасної особистості

У статті аналізуються тенденції деміфологізації та деконструкції особистісного буття в умовах сучасного технологічного суспільства. Результатом цих процесів стає підміна глибинності та ієрархічності особистісного само-визначення імітацією та симуляцією у різноманітних формах: імідж, маска, аватар.В статье анализируются тенденции деконструкции и демифологизации личностного бытия в условиях современного технологического общества. Результатом этих процессов стала подмена глубинности и иерархичности личностного самоопределения имитацией и симуляцией в разнообразных формах: имидж, маска, аватар.The trends of demythologization and reconstruction of personality existence in modern technological society circumstances are analyzed in the article. As a result of such processes, an imitation and simulation in their different forms, such as: image, mask, avatar — substitute the depth and hierarchy of personal self-determination

Utilisation des alliages ferreux dans la construction monumentale du Moyen Age. Etat des lieux de l'avancée des études métallographiques et archéométriques

L'étude métallographique des fers de construction mis en œuvre dans certains grands édifices français des périodes médiévales et modernes apporte de nombreuses informations sur les caractéristiques du matériau utilisé tout comme sur l'histoire de la métallurgie du fer, en même temps qu'elle soulève de nombreuses interrogations. Les résultats accumulés depuis quelques années permettent de mettre en valeur différents points. Tout d'abord, il semble que les grands édifices médiévaux sont pour la plupart renforcés uniquement avec du fer de réduction directe. En région rouennaise, la période de transition identifiée par analyse des inclusions se situe à la fin du XVe siècle, ce qui correspond à l'étude archivistique. Le fer employé, rempli d'inclusions, souvent phosphoreux, et n'ayant pas fait l'objet de traitement spécifique est un matériau standard pour la période médiévale ; de rares exceptions sont cependant à noter. Sont également évoquées les questions relatives aux différentes étapes du travail de forge, et en premier lieu celle de l'utilisation du marteau hydraulique pour faciliter la phase d'épuration de la loupe, opération longue et épuisante d'après les résultats d'archéologie expérimentale. Pour finir, la fréquente homogénéité de certains rapports dans les inclusions semble montrer que les hétérogénéités de la matrice, notamment la diversité des degrés de carburation, sont liées à l'hétérogénéité initiale de la loupe de fer, et non la marque d'une récupération par corroyage.The metallographic study of construction iron used in churches and other buildings during the Middle Ages and the modern period can provide a great deal of information on the characteristics of this material as well as on the history of iron and steel metalwor-king. At the same time the study of construction iron raises many questions. This paper discusses results accumulated from certain French monuments, these include: the cathedrals of Amiens and Rouen, the church Saint-Ouen of Rouen, the basilica of Saint-Denis, the Palais des Papes in Avignon and the dungeon of the Château de Vincennes. The analysis of the composition of slag inclusions entrapped in the metallic matrix allows differentiating iron of the direct process from iron that comes from finery. It seems that all these medieval buildings were essentially reinforced with bars of bloomery iron, and thus didn't really take advantage of the introduction of the blast furnace. In Normandy, where several buildings were studied, the results are compatible with that of the archives: a transition between the direct and indirect processes during the end of the 15thcentury. The metallographic analyses show that in general the iron used in those monuments is very heterogeneous, with no peculiar distribution of the iron and steel parts, numerous slag inclusions, and often a high content of phosphorus. Moreover, no specific forge treatment was observed. This material seems to be a random quality iron for these periods, but whose quality was always fairly sufficient according to its section and role. Certain bars of the Palais des Papes are the only exception to this picture so far. Questions related to the different stages of the smith's work at the forge are then evoked. Results from forge experiments, specifically on the cleansing operation that occurs between the reduction and the forming of the object, have been studied. Two phases have been identified in this stage: first compacting the bloom with a wooden hammer to reduce its porosity, second expelling the slag inclusions that arc still entrapped in the metal by folding the piece of metal and hammering it with a steel hammer. The experiment shows that this phase is particularly long and tiring: more than 4 hours to get an ingot out of a 14 kg bloom. Therefore it brings out the question of the use of hydraulic hammers to help the smith in the second phase of the cleansing. Finally, the analysis of the composition of the slag inclusions reveals that, in more than one case out of two, the ratios of certain elements (Al, Si, Ca) are stable in the whole sample. These elements arc a sort of chemical signature of the object resulting from the reduction. Therefore, it seems that all the heterogeneities seen above arc more likely to be linked to the original heterogeneity of the bloom and not the mark of recuperation by welding pieces of metal from different origins. Therefore brand new metal seems to take an important place in the supply of these monumental buildings. It is also sometimes possible to determine, through the slag inclusion analysis, that sand additions were made during the forging phase