Low Atomic Number Materials Research Articles

DETERMINATION RISK OF BREMSSTRAHLUNG RADIATION PRODUCED BY BETA-RAY

When interacting with absorption materials, beta rays, which are emitted by isotopes, are harmful because bremsstrahlung (braking) radiation is produced. Therefore, the efficiency of a shielding material can be improved by considering the bremsstrahlung radiation generated by the material’s beta ray absorption. In this study, to determine the risk of bremsstrahlung radiation produced by beta rays, the fractions of beta energy transformed into bremsstrahlung radiation were calculated for beta emitters in the energy ranges of 0.0026–0.1734, 0.205–0.694, and 0.9345–2.640 MeV, using five different absorption materials (13Al, 26Fe, 48Cd, 74W, and 82Pb). The relationship between the fractions of beta energy transformed into bremsstrahlung radiation by the five shielding materials and the maximum energies of some beta emitters was studied to determine the most suitable beta-ray shielding materials to effectively minimize bremsstrahlung radiation. The results showed that the fractions of beta energy transformed into bremsstrahlung radiation increased as the beta energy and the atomic number of the shielding material increased. The fraction of beta energy transformed into bremsstrahlung radiation in 13Al ˂ 26Fe ˂ 48Cd ˂ 74W ˂ 82Pb.Therefore, beta ray shields should be made with low atomic number materials to reduce the generation of bremsstrahlung radiation. Practically, beta shields made from materials with atomic numbers greater than 13 are rarely employed; notably, aluminum successfully decreased the production of bremsstrahlung radiation. However, it is also necessary to use materials with medium and high atomic numbers as secondary beta shields to reduce the effect of the bremsstrahlung radiation photons formed by the interaction between beta rays and shielding materials.

Abstract No. 527 CT-Guided Percutaneous Interventions: Reduction of Metal Needle-Tip (Beam-Hardening) Artifacts with Low Atomic Number Materials in Phantom and Porcine Models

Abstract No. 527 CT-Guided Percutaneous Interventions: Reduction of Metal Needle-Tip (Beam-Hardening) Artifacts with Low Atomic Number Materials in Phantom and Porcine Models

The study of X-ray full-field imaging method for low atomic number elements based on Compton scattering

Full-field X-ray fluorescence imaging cannot image low atomic number (Z < 12) materials because the characteristic X-ray fluorescence produced by low atomic number (Z < 12) materials is severely attenuated in air. In this paper, we propose a method to combine Compton scattering with full-field X-ray fluorescence imaging, which can realize the imaging of both metals (high atomic number) and organic materials (low atomic number), and compensate the defect that the conventional FF-XRFI technique cannot image materials with low atomic number such as organic materials. The imaging experiments were performed using two materials, zirconium metal and polyethylene, and the imaging results were optimized using a density filtering algorithm, and the results indicate that it is possible to use this method to image samples of high and low atomic number with resolution.

Design optimization of backscatter X-ray security scanner based on pencil-beam scanning

At national borders and high-security facilities, security screening is conducted to block the entrance of illicit goods such as weapons, explosives, and drugs. In the Republic of Korea, the Korea Customs Service currently conducts transmission X-ray security screening using fixed energy. However, the detection efficiency of this system for drugs or explosives composed of organic substances is rather low. Alternatively, the backscatter X-ray detection system is sensitive to materials of low atomic number; therefore, it can play an essential, complementary role in security screening. In the present study, the design of a pencil-beam-based backscatter X-ray security scanner was optimized and, subsequently, its performance was evaluated under various conditions using the Monte Carlo (MC) simulation technique. As for the X-ray generator, we optimized the tube voltage and the geometry of the chopper wheel collimator. Detector parameters including length, distance between detectors, and thickness also were optimized for detection efficiency. Finally, the performance of the optimized system was evaluated for various object conditions and postal phantoms.

Influence of multiple Coulomb scattering on accuracy of muon transmission imaging of small-scale matter

The muon transmission imaging method is a non-destructive detection imaging method and can obtain the internal density structure of the target object by analyzing the flux change of cosmic ray muon before and after passing through the target object. This method assumes that muon travels along a straight line in a lowatomic number material. However, the multiple Coulomb scattering causes the muon deviate from the straight line to a certain extent when penetrating the material, which may have a certain influence on the accuracy of muon transmission imaging. This study uses the Geant4 software package to carry out Monte Carlo simulation of muon transmission imaging. Object models with multiple density structures and several meters are used to analyze the effect of multiple scattering on the accuracy of transmission imaging. In the experiment, we set up a model in which muons of different energy vertically pass through a rock with a certain thickness, we can intuitively see the influence of scattering on the penetration path of muons. By setting up rock-water block models with thickness in a range of 0.8, 2.4 and 4.0 m, the effect of Coulomb scattering on the transmission imaging of small-scale material muons is analyzed. The results suggest that the muon transmission imaging method can well restore the geometric shape and spatial distribution characteristics of density anomalies for objects with several-meter scale for standard rock materials with a scale of several meters. However, the flux deviation caused by multiple Coulomb scattering on the muons in the near-vertical direction can reach 5%, and up to 13% in the boundary areas of the standard rock and air. We limit the scattering angle of the muon, and select the muon with a scattering angle of less than or equal to 1° for imaging. The results of transmission imaging by using the selected muon have improved. The image does not have the illusion of an abnormally increased flux around the model caused by scattering, but the muon flux in the model area is reduced even more, thereby affecting the accuracy of restoring the absolute density of an object using flux differences. Therefore, the effects of multiple Coulomb scattering should be considered for recovering more accurate absolute density in small-scale muon transmission imaging study.

Using Single-Crystal Graphene to Form Arrays of Nanocapsules Enabling the Observation of Light Elements in Liquid Cell Transmission Electron Microscopy.

We have designed and fabricated a TEM (transmission electron microscopy) liquid cell with hundreds of graphene nanocapsules arranged in a stack of two Si3N4-x membranes. These graphene nanocapsules are formed on arrays of nanoholes patterned on the Si3N4-x membrane by focused ion beam milling, allowing for better resolution than for the conventional graphene liquid cells, which enables the observation of light elements, such as atomic structures of silicon. We suggest that multiple nanocapsules provide opportunities for consecutive imaging under the same conditions in a single liquid cell. The use of single-crystal graphene windows offers an excellent signal-to-noise ratio and high spatial resolution. The motion of silicon nanoparticles (a low atomic number (Z) material) interacting with nanobubbles was observed, and analyzed, in detail. Our approach will help advance liquid-phase TEM observations by providing a straightforward method to encapsulate liquid between monolayers of various 2-dimensional materials.

Strategy for optimizing experimental settings for studying low atomic number colloidal assemblies using liquid phase scanning transmission electron microscopy

Observing processes of nanoscale materials of low atomic number is possible using liquid phase electron microscopy (LP-EM). However, the achievable spatial resolution (d) is limited by radiation damage. Here, we examine a strategy for optimizing LP-EM experiments based on an analytical model and experimental measurements, and develop a method for quantifying image quality at ultra low electron dose De using scanning transmission electron microscopy (STEM). As experimental test case we study the formation of a colloidal binary system containing 30 nm diameter SiO2 nanoparticles (SiONPs), and 100 nm diameter polystyrene microspheres (PMs). We show that annular dark field (DF) STEM is preferred over bright field (BF) STEM for practical reasons. Precise knowledge of the material's density is crucial for the calculations in order to match experimental data. To calculate the detectability of nano-objects in an image, the Rose criterion for single pixels is expanded to a model of the signal to noise ratio obtained for multiple pixels spanning the image of an object. Using optimized settings, it is possible to visualize the radiation-sensitive, hierarchical low-Z binary structures, and identify both components.

Two-dimensional parametric design of short pulse laser driven iron opacity experiments

High intensity short pulse lasers are commonly used to create high temperature and high density plasmas. These plasmas are used to study fundamental properties such as the equation of state and opacity. The targets often use small-diameter, thin buried layers of the materials of interest, surrounded by a tamper of low atomic number material such as plastic. Computational modeling is used to design and interpret experiments with short pulse lasers. Most of the modeling to date has assumed one-dimensional plane-parallel geometry. In this paper, the effects of radial gradients in the irradiation of thin planar targets are studied with one- and two-dimensional radiation/hydrodynamic simulations. It is found that the main effect of radial gradients is the averaging of plasma conditions and x-ray emission over the pattern of irradiation. Differences between one- and two-dimensional simulations arise because the plasma conditions and x-ray emission are, in general, nonlinear functions of the temperature of the plasma and thereby also nonlinear functions of the irradiation intensity. The differences increase with the ratio of the buried layer radius to the laser spot radius. The root mean square difference in the inferred iron L-shell opacity is less than 30% when the ratio is less than 1.0 and about 70% when the ratio is 1.5.

X-ray Compton backscattering imaging via structured light.

Compton backscattering imaging (CBI) is a technique that uses ionizing radiation to detect the presence of low atomic number materials on a given target. Unlike transmission x-ray imaging, the source and sensor are located on the same side, such that the photons of interest are scattered back after the radiation impinges on the body. Rather than scanning the target pixel by pixel with a pencil-beam, this paper proposes the use of cone-beam coded illumination to create the compressive x-ray Compton backscattering imager (CXBI). The concept was developed and tested using Montecarlo simulations through the Geant4 application for tomography emissions (GATE), with conditions close to the ones encountered in experiments, and posteriorly, a test-bed implementation was mounted in the laboratory. The CXBI was evaluated under several conditions and with different materials as target. Reconstructions were run using denoising-prior-based inverse problem algorithms. Finally, a preliminary dose analysis was done to evaluate the viability of CXBI for human scanning.

Effect of Ti content on preparation and properties of TiB&lt;sub&gt;2&lt;/sub&gt;-SiC-Ti materials

Since the 21st century, low atomic number material coating has been considered as one of methods for treating the first wall of controllable thermonuclear fusion device . The TiB&lt;sub&gt;2&lt;/sub&gt; material with high melting point, high hardness, low coefficient of thermal expansion, excellent wear resistance and low atomic number has entered into people’s field of vision. Single TiB&lt;sub&gt;2&lt;/sub&gt; is difficult to sinter and process into other products. Therefore, adding ceramic and metal additives to TiB&lt;sub&gt;2&lt;/sub&gt; matrix material to effectively improve the mechanical properties and processability of the material has become a research hotspot. On the basis of the existing researches of TiB&lt;sub&gt;2&lt;/sub&gt;-SiC, in the present work the metal Ti powder is added as the second additive to improve the properties of TiB&lt;sub&gt;2&lt;/sub&gt; composite. The TiB&lt;sub&gt;2&lt;/sub&gt; and SiC are mixed at a mass ratio of 2 to 3, then two kinds of TiB&lt;sub&gt;2&lt;/sub&gt;-SiC-Ti materials with different amounts of Ti content are prepared by spark plasma sintering (SPS) technology. The materials are irradiated by a He&lt;sup&gt;+&lt;/sup&gt; beam with energy of 60 keV and ion fluence of 2 × 10&lt;sup&gt;17&lt;/sup&gt; ions/cm&lt;sup&gt;2&lt;/sup&gt; at room temperature. The material is heat-treated at 1500 ℃ before and also after irradiation. The performances of prepared samples, the effect of irradiation on materials and the results of high temperature heat treatment are characterized by energy dispersive spectroscopy, Raman spectrum, grazing angle x-ray diffraction spectrum, Vickers hardness, wear resistance test, and scanning electron microscope. The results show that the surface morphology and toughness of TiB&lt;sub&gt;2&lt;/sub&gt;-SiC-Ti material with 3% Ti mass fraction are poor as shown in SEM images. The wear resistance test indicates that the material surface is seriously worn and the wear resistance is poor. The X-ray diffraction spectrum and Raman spectra show that the material is oxidized seriously at 1500 ℃, which is likely to be the cause of the poor compactness of materials. Raman spectra, Grazing angle X-ray diffraction spectrum and some Vickers hardness data before and after irradiation indicate that the material with low Ti content possess better crystal structure and weaker irradiation hardening. In conclusion, the TiB&lt;sub&gt;2&lt;/sub&gt;-SiC-Ti material with 3% Ti mass fraction exhibits lower density, poorer wear resistance and lower hardness, while the material with lower Ti mass fraction is more resistant to irradiation than the material with 6% Ti mass fraction at room temperature.

Development of Stochastic Voronoi Lattice Structures via Two-Photon Polymerization

ABSRACT Low-density polymer foams of varying sizes, shapes, and densities are of specific interest to the inertial confinement fusion (ICF) program and related high-energy density plasma physics research. Historically, these foams are comprised of polystyrene or other low atomic number materials and have densities in the 30 to 300 mg/cm3 range. However, at the lower end of this density range, these traditional polymer foams become fragile and difficult to cast and machine into the geometries needed. Recently, the need by experimentalists for materials with densities below 30 mg/cm3 has increased. To address these needs, we are developing three-dimensional (3-D) printing techniques to create high-precision, low-density, and repeatable complex lattice structures. Using two-photon polymerization 3-D printing, we recently developed the first 5 mg/cm3 low-density lattice structure having an annular hemispherical shape. These microscale to mesoscale structures were modeled and designed using the nTopology software, specifically utilizing the “Voronoi volume lattice” and “random points in body” option blocks. All printing operations were performed using the Nanoscribe Photonic Professional GT instrument. Characterization of these 3-D structures was conducted using various microscopic and X-ray tomographic imaging techniques. Overall printed part sizes ranged from 1 to 5 mm in diameter and were composed of lattice ligaments having thicknesses in the 3- to 5-µm range. These structures have been incorporated into ICF targets recently shot on both the University of Rochester’s Laboratory of Laser Energetics Omega laser and the National Ignition Facility.

(Invited) In Situ and Operando Synchrotron X-Ray Spectroscopy and Scattering Characterization of PEFC Cathode Catalysts

With wavelengths on the order of atomic dimensions and the ability to penetrate through low atomic number materials (e.g., Nafion® and carbon), hard X-rays, particularly those arising from synchrotron sources with high brilliance, are ideal for the atomic-level characterization of polymer electrolyte fuel cell (PEFC) catalysts in situ, in aqueous environments that mimic PEFC conditions, and operando, in the membrane-electrode assembly (MEA) environment. Two particularly valuable X-ray techniques for this purpose are X-ray absorption spectroscopy (XAS) and small angle X-ray scattering (SAXS) or anomalous SAXS (ASAXS), which allows discrimination of scattering from the absorbing element. Analysis of the X-ray spectrum near the absorption edge of interest (i.e., the near edge or XANES region) provides information on the oxidation state and electronic structure (e.g., d-band vacancy) of the material, properties that have been associated with catalyst activity. The extended region of the XAS spectrum (EXAFS) yields information on the atomic structure and coordination environment of the absorbing element (i.e., number and identity of nearest neighbors and distances between atoms). Unlike X-ray diffraction, XAS is particularly useful for characterization of platinum nanoparticle catalysts and of single-site platinum-group metal-free catalysts, such as Fe-N-C catalysts. However, EXAFS can be limited in the information it can provide regarding the bonding geometries, but absorption in the pre-edge region, which is sensitive to bonding geometry, can provide this essential information. SAXS and ASAXS are well-established techniques for probing particle sizes and particle size distributions on the nanometer level. While not as widely-used in the fuel cell community as XAS, SAXS and ASAXS are well-suited to examining nanoparticle fuel cell catalysts, which typically have particle diameters of 2-5 nm.This presentation will discuss the information that can be obtained from X-ray spectroscopy and scattering techniques and provide examples of application of these techniques to the study of platinum and platinum alloy nanoparticle catalysts and atomically-dispersed Fe-N-C and Co-N-C PEFC cathode catalysts. The utility of using a combination of XAS and ASAXS to study platinum alloy catalyst degradation and of the combination of information from XANES, EXAFS, and XAS pre-edge data to an Fe-N-C catalyst will be presented.Acknowledgements:This research was supported by the U.S. Department of Energy (DOE), Energy Efficiency and Renewable Energy, Hydrogen and Fuel Cell Technologies Office (HFTO), through the Electrocatalysis Consortium (ElectroCat). This research used resources of the Advanced Photon Source (APS), a U.S. Department of Energy (DOE) Office of Science User Facility, operated for the DOE Office of Science by Argonne National Laboratory under Contract DE-AC02-06CH11357. The authors thank Hoon Chung of Los Alamos National Laboratory for providing the Fe-N-C catalyst and Johnson Matthey Fuel Cells for providing the Pt and PtCo catalysts. This work was conducted at Argonne National Laboratory, a U.S. DOE Office of Science Laboratory operated for the U.S. DOE by UChicago Argonne, LLC, under Contract DE-AC02-06CH11357.

Observation of Hydrogen-Induced Dzyaloshinskii-Moriya Interaction and Reversible Switching of Magnetic Chirality

The Dzyaloshinskii-Moriya interaction (DMI) has drawn great attention as it stabilizes magnetic chirality, with important implications in fundamental and applied research. This antisymmetric exchange interaction is induced by the broken inversion symmetry at interfaces or in non-centrosymmetric lattices. Significant interfacial DMI was found often at magnetic / heavy-metal interfaces with large spin-orbit coupling. Recent studies have shown promise of induced DMI at interfaces involving light elements such as carbon (graphene) or oxygen. Here we report direct observation of induced DMI by chemisorption of the lightest element, hydrogen, on a ferromagnetic layer at room temperature, which is supported by density functional theory calculations. We further demonstrate a reversible chirality transition of the magnetic domain walls due to the induced DMI via hydrogen chemisorption/desorption. These results shed new light on the understanding of DMI in low atomic number materials and design of novel chiral spintronics and magneto-ionic devices.

Empirical beam hardening and ring artifact correction for x-ray grating interferometry (EBHC-GI).

Talbot-Lau grating interferometry enables the use of polychromatic x-ray sources, extending the range of potential applications amenable to phase contrast imaging. However, these sources introduce beam hardening effects not only from the samples but also from the gratings. As a result, grating inhomogeneities due to manufacturing imperfections can cause spectral nonuniformity artifacts when used with polychromatic sources. Consequently, the different energy dependencies of absorption, phase, and visibility contrasts impose challenges that so far have limited the achievable image quality. The purpose of this work was to develop and validate a correction strategy for grating-based x-ray imaging that accounts for beam hardening generated from both the imaged object and the gratings. The proposed two-variable polynomial expansion strategy was inspired by work performed to address beam hardening from a primary modulator. To account for the multicontrast nature of grating interferometry, this approach was extended to each contrast to obtain three sets of correction coefficients, which were determined empirically from a calibration scan. The method's feasibility was demonstrated using a tabletop Talbot-Lau grating interferometer micro-computed tomography (CT) system using CT acquisitions of a water sample and a silicon sample, representing low and high atomic number materials. Spectral artifacts such as cupping and ring artifacts were quantified using mean squared error (MSE) from the beam-hardening-free target image and standard deviation within a reconstructed image of the sample. Finally, the model developed using the water sample was applied to a fixated murine lung sample to demonstrate robustness for similar materials. The water sample's absorption CT image was most impacted by spectral artifacts, but following correction to decrease ring artifacts, an 80% reduction in MSE and 57% reduction in standard deviation was observed. The silicon sample created severe artifacts in all contrasts, but following correction, MSE was reduced by 94% in absorption, 96% in phase, and 90% in visibility images. These improvements were due to the removal of ring artifacts for all contrasts and reduced cupping in absorption and phase images and reduced capping in visibility images. When the water calibration coefficients were applied to the lung sample, ring artifacts most prominent in the absorption contrast were eliminated. The described method, which was developed to remove artifacts in absorption, phase, and normalized visibility micro-CT images due to beam hardening in the system gratings and imaged object, reduced the MSE by up to 96%. The method depends on calibrations that can be performed on any system and does not require detailed knowledge of the x-ray spectrum, detector energy response, grating attenuation properties and imperfections, or the geometry and composition of the imaged object.

Estudio de la emisión de radiación de frenado mediante simulaciones mixtas con el código Monte Carlo PENELOPE

El método Monte Carlo permite la descripción precisa de las propiedades de la radiación de frenado, la cual se emplea en medicina para radiodiagnóstico o radioterapia. El código PENELOPE descansa en la implementación de historias condensadas para el transporte de partículas cargadas y permite al usuario adaptar el grado de detalle de las simulaciones mediante los parámetros de simulación. La variación de estos parámetros puede afectar a las distribuciones de partículas obtenidas al simular radiación de frenado producida en blancos gruesos. En este trabajo se analizan las diferencias entre simulaciones con distinto grado de detalle mediante la reproducción con PENELOPE de experimentos publicados de producción de radiación de frenado con electrones de alta y baja energía. Para ello se varían los parámetros de simulación C1 y C2 hasta alcanzar un valor a partir del cual los resultados de las simulaciones son estadísticamente equivalentes. Se ha observado que una inadecuada elección de los parámetros de simulación conlleva una reproducción inexacta de las características del haz de frenado. Se necesita mayor grado de detalle para simular electrones de alta energía en un material de alto número atómico que para electrones de baja energía en un material de bajo número atómico.

Imaging and analysis of low atomic number materials in the STEM

Imaging and analysis of low atomic number materials in the STEM

Thermal shaping of thin glass panels for hard X-ray telescope optics

We present a process for thermal forming of thin glass panels of borosilicate glass to produce mirror segments for X-ray telescope optics. The mirror segments are required to be shaped in a parabolic and hyperbolic shape in accordance with Wolter-I type design of X-ray telescope optics. Thermal forming of glass is a low-cost method to produce light-weight mirror segments. The process makes use of a semi-cylindrical quartz mold having surface roughness of the order of 1 nm. Flat glass sheets of 0.2 mm and 0.3 mm thickness are placed on the diametric edges of the mold. With a suitable thermal cycle, the glass sheets are thermally formed as per the shape of the mold. The shape of these formed glass sheets was measured using a non-contact optical setup. The surface quality measurements of the formed glass sheets were performed using atomic force microscope and they were found to be in the range of 0.04–0.33 nm. Once tested for acceptance, these glass sheets are coated using sputter deposition of multi-layers of high and low atomic number materials for hard X-ray reflection. Such mirror segments do not require polishing of the surface before being coated with multi-layers.

Evaluation of Testis functioning during Pelvic Radiotherin the presence of testis lead shield

Introduction: Rectal and bladder cancer are the most common disease among young man. Although External Radiotherapy (EBRT) is one of the most effective treatment options introduced so far, the testis undesired radiation dose increases the risk of infertility and hormonal malfunctioning. The testicles are usually outside of the radiation field, but they can be exposed either to scattered and or direct radiation pending on the distance of radiation field, patient thickness and radiation beam energy. To evaluate testis functioning, the LH, FSH and testosterone levels in rectal and bladder carcinoma and effect of testicular shielding in sex hormonal level during external beam radiotherapy were evaluated. In order to control neutron dose received to the region of interest, shield optimization through Geant4 simulation toolkit was also investigated. Materials and Methods: Thirty patients with bladder and rectal adenocarcinoma received pelvic radiotherapy. All patients received 5040-Gy radiation dose ,1.8Gy/fraction and five days per week. 15 patients were treated without testicular shielding and others received radiotherapy with testicular shielding made of 1.5 centimeter lead. Blood tests were performed before and after radiotherapy for both group. The head of Simens Primus were simulated using Geant4 code. For verification of the simulated linac’s head, the percentage depth doses (PDDs) and Profiles were compared with the corresponding measurements. CT- Structure And Plan Dicom files were then imported to the code and the testicular shield was modelled. Results: Based on the Gamma Index results in the first step and evaluation of optimized shielding, testis dose is minimum. Conclusion: Although the application of routine shield apparently reduces the radiation dose, the neutron dose should also be taken into account. The modified shield including low atomic number materials reduces the radiation dose and improving hormonal functioning.

A compact, high resolution tracker for cosmic ray muon scattering tomography using semiconductor sensors

A semiconductor tracker for muon scattering tomography is presented. The tracker contains silicon strip sensors with an 80 μm pitch, precision mechanics and integrated cooling. The electronic readout of the sensors is performed by a scalable, inexpensive, flexible, FPGA-based system, which is demonstrated to achieve an event rate of 30 kHz. The tracker performance is compared with a Geant4 simulation. A scattering angle resolution compatible with 1.5 mrad at the 4 GeV average cosmic ray muon energy is demonstrated. Images of plastic, iron and lead samples are obtained using an Angle Statistics Reconstruction algorithm. The images demonstrate good contrast between low and high atomic number materials.

Analysis of stabilization of photon beam softening with off-axis distance for filtration system enhancement to increase dosimetry in radiotherapy

Beam softening is depending on the material atomic number and photon beam energy for photon beam filtration; the filtration quality is essential to producing a clinical beam in external radiotherapy. Beam softening analysis is done using Monte Carlo method. The Monte Carlo model was performed for 6 MV photon beam produced by Varian Clinac 2100 with flattening filter thereafter the flattening filter was removed and replaced by slab of aluminum and copper with different thickness. The purpose of this study is to analyze the photon beam softening with off-axis distance for the reference field size of 10 × 10 cm2; the beam softening is studied in terms of tow coefficients a1 and a2.Inside the irradiation field, for aluminum slab, the coefficient a1 varied in interval from −1.2 cm−1 to 1.7 cm−1 and it has big fluctuations with off-axis distance. For copper, a1 varied from 0 cm−1 to 1.5 cm−1 and it has small fluctuations with off-axis distance. The coefficient a2, for aluminum slab, varied from −1 cm−2 to 0.4 cm−2 with big fluctuations. For copper slab, a2 varied from −0.9 cm−2 to 0 cm−2 with small fluctuations. We conclude that the beam softening is very stabilized for copper than aluminum in despite of copper attenuate more photons than aluminum for same slab thickness when they are used in photon beam filtration. To increase dosimetry in radiotherapy, the flattening filter should be constructed based on low atomic number materials but with high stabilization of beam softening with off-axis distance.