- Università di Bologna, Representacion en Buenos Aires, Department Memberadd
- Radiation Physics, Boltzmann Transport equation for photons, Monte Carlo Simulation, Theoretical Model, X Rays, Polarization, and 10 moreX-Ray Fluorescence (XRF) Spectroscopy, X-ray Physics, Material Caracterization X ray (SAXS WAXS PDF XRF..), XRF Spectroscopy, Análisis XRF, portable XRF (PXRF) in Archaeology and Museum Science, XRF, XRFS, Pigments (Chemistry), and Interdisciplinary Engineeringedit
- Jorge Eduardo Fernandez is professor of Radiation Transfer and Particle Transport and is Director of the Alma Mater S... moreJorge Eduardo Fernandez is professor of Radiation Transfer and Particle Transport and is Director of the Alma Mater Studiorum University of Bologna - Representacion en la Republica Argentina, the Argentinian branch of the University of Bologna. He obtained his PhD in Physics at the Universidad Nacional de Córdoba, Argentina in 1985, with a theoretical–experimental dissertation on a spectroscopic absolute method of analysis with nuclear techniques. He has authored some 120 publications in high-ranked scientific journals, several of them as invited contributions and numerous invited talks worldwide. His main research interests are: X-ray interactions, X- and Gamma-Ray photon transport with deterministic and Monte Carlo methods, multiple scattering of photons, polarization effects, detailed description of the X-ray spectrum, detailed description of the detector response function, and spectrum unfolding from detector influence. He is Editor of "Applied Radiation and Isotopes" and "X-Ray Spectrometry", serves as Secretary of the International Radiation Physics Society (IRPS) and is a member of many relevant committees and panels.edit
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ABSTRACT It is well known that the polarisation state of the source radiation influences the behaviour of the photons in their interaction with the matter. The most important phenomena in the energy range of x-rays, photoelectric effect,... more
ABSTRACT It is well known that the polarisation state of the source radiation influences the behaviour of the photons in their interaction with the matter. The most important phenomena in the energy range of x-rays, photoelectric effect, coherent (or Rayleigh) scattering and incoherent (or Compton) scattering, are differently influenced by such a polarisation state. Photoelectric effect does not feel the effect of the polarisation and has an isotropic cross-section. Rayleigh and Compton scattering instead, are strongly influenced by both, the polarisation state and the scattering geometry. In particular, when a linearly polarised beam, whose electric field is parallel to the scattering plane, scatters at 90 degrees, both Rayleigh and Compton scattering tend to vanish for a single scattering. In fact, this paradigmatic behaviour allows us to eliminate the ‘noise’ due to scattering and to collect only the signal produced by the photoelectric effect. These phenomena are more complex in the presence of the multiple scattering: for the same geometry, the total scattering is no longer zero even if it remains considerably reduced. In order to study this phenomenon, the following configuration is proposed. (figure) Using the Monte Carlo code MCSHAPE [1], some simulations have been made by varying the angle between the scattering plane with the incident beam (defined by the incident beam and the beam 1) and the scattering plane of the collision with the second target (defined by beam 1 and the outgoing beam). The code MCSHAPE, in fact, can simulate the behaviour of arbitrarily polarised photons and it follows the evolution of their polarisation state after the interaction with the atoms. The polarisation state of the photons is described, in the code, thanks to the Stokes parameters I, Q, U and V, having the dimension of an intensity and containing all the physical information about the polarisation state. Simulated experiments with a monochromatic unpolarised source of 59,54 keV (main gamma line of 241-Am) and with an x-ray tube source have been considered. In the first case, the results of the simulations show that, after the 90° scattering in the first target, a part of the scattered beam (beam 1) is polarised (the degree of polarisation is a function of energy, and as it is shown, for some energies, 90% of the beam is polarised), but it is not fully polarised as for the single scattering (this is an effect of the multiple scattering in the target).The intensity collected by the detector, after the scattering with the second target, depends on the rotation between the first and the second pieces of the tube. The scattering is drastically reduced for a rotation angle around 90°, even if, due to multiple scattering, it is not zero. This behaviour is tested also with polychromatic excitation. An experimental apparatus is being developed in order to investigate in detail the rotational dependence of this configuration. [1] J.E. Fernandez, V.G. Molinari, M. Bastiano and V. Scot. Diffusion of photons with arbitrary state of polarisation: the Monte Carlo code MCSHAPE. Nuclear Instruments and Methods B 213 (2004) 105-107 (see also http://shape.ing.unibo.it)
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ABSTRACT The vector equation is the best model known for describing the diffusion of incoherent photon beams. In this article, a brief overview of the Boltzmann transport equation (scalar and vector) will be given. Then, it will be... more
ABSTRACT The vector equation is the best model known for describing the diffusion of incoherent photon beams. In this article, a brief overview of the Boltzmann transport equation (scalar and vector) will be given. Then, it will be described the state-of-the-art of the transport codes we developed at Bologna based on this model. Finally, the application of the codes will be illustrated with some examples.
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In this paper the 3D photon transport equation is considered to give a detailed description of the fluorescence photon emission from a homogeneous slab. As an example we study, with a complete 3D spatial description in plane geometry,... more
In this paper the 3D photon transport equation is considered to give a detailed description of the fluorescence photon emission from a homogeneous slab. As an example we study, with a complete 3D spatial description in plane geometry, the distribution both in physical and momentum space of the primary photons, induced by a radiation beam crossing the slab. Then we will see how the 3D geometry influences the shape of the continuous spectra due to a second Compton collision which modifies the distribution of the primaries due to photoelectric effect. The possibility of isolating the effect of a particular interaction is one of the strength points of the multiple-scattering scheme in the framework of transport techniques, which allows a better understanding of the photon diffusion. In order to evaluate the effects of the boundary conditions, we will use the integral transport equation instead of the integro-differential one, which has the advantage of treating the flow of the photons from the outer space as an external source. The results will be compared with those obtained in the case of a half-infinite medium uniformly irradiated with a plane infinite slant source of monochromatic photons previously solved in 1D.
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X-ray photons - as many other particles - interact with matter producing secondary radiation that carries useful information about the atoms comprising the target. The availability of intense sources of highly monochromatic X-rays and the... more
X-ray photons - as many other particles - interact with matter producing secondary radiation that carries useful information about the atoms comprising the target. The availability of intense sources of highly monochromatic X-rays and the great improvement in detector technology intensified research in X-ray spectrometry in the last twenty years. New techniques allowed the attenuation coefficients and the physics of the atom to be better known: Extended X-ray Absorption Fine Structure (EXAFS), X-ray Absorption Near Edge Structure (XANES), and Inelastic X-ray Scattering Spectroscopy (IXSS). Old techniques, like X-ray Fluorescence (XRF), gained in precision thus extending the horizon of applicability to new elements and energy ranges, and consequently Energy Dispersive X-ray Fluorescence (EDXRF) and Synchrotron Radiation X-ray Fluorescence (SRXRF) were evolved. Particle induced X-ray emission spectroscopy also benefited from this improvement. The field of application of X-ray spectrometry has grown from atomic, to nuclear, to plasma physics, to astrophysics. In this work the authors summarize the knowledge recently gained about how the intensity due to multiple scattering perturbs the first-order terms of the three processes of main interest in X-ray spectrometry between 1 keV and 100 keV: the photoelectric, the Rayleigh and the Compton effects. They show that the contribution of a few orders of scattering, calculated in the frame of transport theory, allows the construction of a theoretical X-ray spectrum that matches well experimental data from targets of homogeneous composition and infinite thickness. 99 refs., 15 figs.
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The Compton effect is a potential ionization mechanism of atoms. It produces vacancies in inner shells that are filled with the same mechanism of atomic relaxation as the one following photo-absorption. This contribution to X-ray... more
The Compton effect is a potential ionization mechanism of atoms. It produces vacancies in inner shells that are filled with the same mechanism of atomic relaxation as the one following photo-absorption. This contribution to X-ray fluorescence emission is frequently neglected because the total Compton cross-section is apparently much lower than the photoelectric one at useful X-ray energies. However, a more careful analysis suggests that is necessary to consider single shell cross sections (instead of total cross sections) as a function of energy. In this article these Compton cross sections are computed for the shells K, L1-L3 and M1-M5 in the framework of the impulse approximation. By comparing the Compton and the photoelectric cross-section for each shell it is then possible to determine the extent of the Compton correction to the intensity of the corresponding characteristic lines. It is shown that for the K shell the correction becomes relevant for excitation energies which are too high to be considered in X-ray spectrometry. In contrast, for L and M shells the Compton contribution is relevant for medium-Z elements and medium energies. To illustrate the different grades of relevance of the correction, for each ionized shell, the energies for which the Compton contribution reaches the extent levels of 1, 5, 10, 20, 50 and 100% of the photoelectric one are determined for all the elements with Z = 11–92. For practical applications it is provided a simple formula and fitting coefficients to compute average correction levels for the shells considered.
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Secondary electrons produced by Compton scattering and photoelectric effect contribute to the photon field through conversion mechanisms like bremsstrahlung and inner-shell impact ionization (ISII). Because electrons interact... more
Secondary electrons produced by Compton scattering and photoelectric effect contribute to the photon field through conversion mechanisms like bremsstrahlung and inner-shell impact ionization (ISII). Because electrons interact continuously, the solution of the coupled transport problem is complex and time consuming. For this reason, photon transport codes frequently neglect the effects due to secondary electrons. Both of these contributions have been computed by means of the ad hoc code KERNEL that uses the Monte Carlo code PENELOPE specific for coupled transport. The correction on the intensity of the characteristic lines due to ISII was treated in a recent paper of our group. This paper adds the continuous contribution to the radiation field due to bremsstrahlung by secondary electrons. The bremsstrahlung emission is studied in terms of angle, space, and energy. The continuous contribution is stored in a data library for selected photon source energies in the interval 1–150 keV and for all the elements Z = 1–92. For intermediate source energies, the single element contribution is obtained by interpolating the data library. An example is presented on how to use the data library to include bremsstrahlung in the simulation of a synchrotron experiment.
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ABSTRACT In every X-ray spectroscopy measurement the influence of the detection system causes loss of information. Different mechanisms contribute to form the so-called detector response function (DRF): the detector efficiency, the escape... more
ABSTRACT In every X-ray spectroscopy measurement the influence of the detection system causes loss of information. Different mechanisms contribute to form the so-called detector response function (DRF): the detector efficiency, the escape of photons as a consequence of photoelectric or scattering interactions, the spectrum smearing due to the energy resolution, and, in solid states detectors (SSD), the charge collection artifacts. To recover the original spectrum, it is necessary to remove the detector influence by solving the so-called inverse problem. The maximum entropy unfolding technique solves this problem by imposing a set of constraints, taking advantage of the known a priori information and preserving the positive-defined character of the X-ray spectrum. This method has been included in the tool UMESTRAT (Unfolding Maximum Entropy STRATegy), which adopts a semi-automatic strategy to solve the unfolding problem based on a suitable combination of the codes MAXED and GRAVEL, developed at PTB. In the past UMESTRAT proved the capability to resolve characteristic peaks which were revealed as overlapped by a Si SSD, giving good qualitative results. In order to obtain quantitative results, UMESTRAT has been modified to include the additional constraint of the total number of photons of the spectrum, which can be easily determined by inverting the diagonal efficiency matrix. The features of the improved code are illustrated with some examples of unfolding from three commonly used SSD like Si, Ge, and CdTe. The quantitative unfolding can be considered as a software improvement of the detector resolution.
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The detector response function of X-ray and gamma-ray detectors is obtained from the convolution of the energy deposition spectrum with the detector resolution function. The energy deposition spectrum can be computed by using... more
The detector response function of X-ray and gamma-ray detectors is obtained from the convolution of the energy deposition spectrum with the detector resolution function. The energy deposition spectrum can be computed by using deterministic or Monte Carlo codes, while the energy resolution depends specifically on the detection mechanism, which is characteristic of the single detector. In a first approximation, the energy resolution can be modeled using a normalized Gaussian distribution having its full width at half maximum expressed in terms of specific semiempirical formulas for solid-state detectors, scintillators, and gas proportional counters. However, this approach is not sufficient with some solid-state detectors. It is frequent to find that the peaks show a deviation from the Gaussian shape: a long flat shelf structure from the peak centroid to the lower energies and an asymmetry that can be described with an exponential decay on the left side of the peak. These two effects have been introduced in the new tool RESOLUTION by adapting empirical models found in literature. RESOLUTION can be tailored to the specific detector by analyzing measured monochromatic peaks by means of the following strategies: (1) in a first approximation, a Gaussian shape is assumed in order to determine the full width at half maximum parameters, (2) if it is noted a flat background on the left side of the peak, then a shelf function is added, and (3) if a departure of the Gaussian is observed, then an exponential tail function is added. RESOLUTION gives a very precise description of the line shape. Copyright © 2015 John Wiley & Sons, Ltd.
MCSHAPE is a general purpose Monte Carlo code developed at the University of Bologna to simulate the diffusion of X- and gamma-ray photons with the special feature of describing the full evolution of the photon polarization state along... more
MCSHAPE is a general purpose Monte Carlo code developed at the University of Bologna to simulate the diffusion of X- and gamma-ray photons with the special feature of describing the full evolution of the photon polarization state along the interactions with the target. The prevailing photon-matter interactions in the energy range 1–1000 keV, Compton and Rayleigh scattering and photoelectric effect, are considered. All the parameters that characterize the photon transport can be suitably defined: (i) the source intensity, (ii) its full polarization state as a function of energy, (iii) the number of collisions, and (iv) the energy interval and resolution of the simulation. It is possible to visualize the results for selected groups of interactions. MCSHAPE simulates the propagation in heterogeneous media of polarized photons (from synchrotron sources) or of partially polarized sources (from X-ray tubes). In this paper, the main features of MCSHAPE are illustrated with some examples and a comparison with experimental data.
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Compton and Rayleigh scattering peak intensities and their ratio are used in reflection and transmission experiments to obtain information about the density of the investigated specimen. The ratio is preferred because it allows the... more
Compton and Rayleigh scattering peak intensities and their ratio are used in reflection and transmission experiments to obtain information about the density of the investigated specimen. The ratio is preferred because it allows the reduction of the errors due to attenuation and geometry. In all cases it is fundamental to predict their angular distributions in order to design the optimal experiment for a given material. The code SAP (Scattering Angular distribution Plot) is a graphical tool to compute and plot Rayleigh and Compton differential cross-sections (atomic and electronic), form factors and incoherent scattering functions. In this work, the code is improved by adding the computation of Rayleigh and Compton first-order peak fluxes and intensities, and the Rayleigh-to-Compton peak ratio, in both, reflection and transmission geometries, for single elements, compounds and mixture of compounds, for monochromatic excitation in the range of 1-1000 keV. The new characteristics of the code are illustrated with some examples.
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MCSHAPE is a Monte Carlo code for the simulation of gamma and X-ray diffusion in matter which gives a general description of the evolution of the polarisation state of the photons. The model is derived from the so-called 'vector'... more
MCSHAPE is a Monte Carlo code for the simulation of gamma and X-ray diffusion in matter which gives a general description of the evolution of the polarisation state of the photons. The model is derived from the so-called 'vector' transport equation. The three-dimensional (3D) version of the code can accurately simulate the propagation of photons in heterogeneous media originating from either polar-ised (i.e. synchrotron) or unpolarised sources, such as X-ray tubes. Photoelectric effect, Rayleigh and Compton scattering, the three most important interaction types for photons in the considered energy range (1–1000 keV), are included in the simulation with the state-of-art extent of detail. In this paper, the 3D version of the code MCSHAPE is presented. The sample is described using the so-called voxel model. Results from the validation studies and applications of the code to scanning XRF and XRF tomography experiments are discussed.
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In x-ray fluorescence spectroscopy, a photon beam is focused on the sample to stimulate the emission of characteristic radiation. Even if a qualitative interpretation of the measurements is simple, a quantitative analysis is not... more
In x-ray fluorescence spectroscopy, a photon beam is focused on the sample to stimulate the emission of characteristic radiation. Even if a qualitative interpretation of the measurements is simple, a quantitative analysis is not straightforward because the primary photons are produced deep in the target and the properties of the radiation that reaches the detector are modified significantly by the interactions undergone before leaving the specimen. Understanding how the emission spectra are influenced by interactions with matter is a central problem in fluorescence analysis. In this work, by using the 3D transport equation, we found that not only the composition of the specimen but also the geometry of the system plays an important role in determining the properties of the radiation field, denoting by geometry the shape of the target, the direction of the incoming beam and the observation angle.
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In this paper a practical solution to perform spectral analysis of diagnostic X-ray beams is described, based on a miniaturized Compton selection chamber (CSC) using a Si-PIN detector. Results are compared with those obtained with a first... more
In this paper a practical solution to perform spectral analysis of diagnostic X-ray beams is described, based on a miniaturized Compton selection chamber (CSC) using a Si-PIN detector. Results are compared with those obtained with a first prototype of CSC based on nitrogen cooled high purity germanium (HPGe) detector. With this method, the direct X-ray spectrum is Compton scattered inside the CSC, collected by a solid-state detector and reconstructed using a simplified scattering matrix experimentally determined. The results obtained will be compared with a reference standard, represented by direct spectra acquired with an HPGe detector in a laboratory facility, not applicable for on-field measurements.
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When X-rays penetrate in the matter, they interact with the atoms, producing secondary radiation that carries important information about the composition of the target. The polarization state is one of the properties of the incoming... more
When X-rays penetrate in the matter, they interact with the atoms, producing secondary radiation that carries important information about the composition of the target. The polarization state is one of the properties of the incoming photons which changes as a consequence of the number and the type of the undergone interaction. Therefore, to study properly the atomic properties of a material, it is necessary to consider the evolution of the polarization state of radiation. It is presented MCSHAPE, a Monte Carlo code developed to describe the evolution of the polarization state of X-ray photons as a consequence of the multiple scattering collisions undergone during the diffusion into the sample. In order to study properly the transport of photons with an arbitrary state of polarization, the model adopted in this code is derived from the so called ÔvectorÕ transport equation [Radiative Transfer, Chapter 1, Section 15, Clarendon, Oxford, 1950; Nucl. Instr. and Meth. B 73 (1993) 341]. Using the Stokes parameters I, Q, U and V , having the dimension of an intensity and containing all the physical information about the polarization state, MCSHAPE simulates the full state of polarization of the photons at any given position, wavelength and solid angle.