Electron and positron contributions to the displacement per atom profile in bulk multi-walled carbon nanotube material irradiated with gamma rays



Electron and positron contributions to the displacement per atom profile in bulk multi-walled carbon nanotube material irradiated with gamma rays

Aporte de electrones y positrones al perfil de desplazamientos atómicos en materiales masivos de nanotubos de carbono de paredes múltiples irradiados con rayos gamma.                                  


Antonio Leyva Fabelo, Ibrahin Piñera Hernández, Diana Leyva Pernía, Yamiel Abreu Alfonso y Carlos M. Cruz Inclán 

Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN)
Calle 30, No. 502, entre 5ta y 7ma, Miramar, Playa, La Habana, Cuba





The electron and positron contributions to the effective atom displacement cross-section in multi-walled carbon nanotube bulk materials exposed to the gamma rays were calculated. The physical properties and the displacement threshold energy value reported in literature for this material were taken into account. Then, using the mathematical simulation of photon and particle transport in matter, the electron and positron energy flux distributions within the irradiated object were also calculated. Finally, considering both results, the atom displacement damage profiles inside the analyzed bulk carbon nanotube material were determined. The individual contribution from each type of secondary particles generated by the photon interactions was specified. An increasing behavior of the displacement cross-sections for all the studied particles energy range was observed. The particles minimum kinetic energy values that make probabilistically possible the single and multiple atom displacement processes were determined. The positrons contribution importance to the total number of point defects generated during the interaction of gamma rays with the studied materials was confirmed.

Key words: carbon nanotubes, gamma radiation, atomic displacements, cross section, monte carlo method, simulation.


Se presentan los resultados del cálculo de las contribuciones de los electrones y los positrones a la sección eficaz de desplazamiento de los átomos de carbono en materiales masivos constituidos por nanotubos de paredes múltiples. Para ello se tomaron en consideración las propiedades físicas y la energía umbral de desplazamiento del carbono reportadas en la literatura para este material. Se calculó también la distribución espacial de los flujos energéticos de los electrones y positrones dentro del blanco irradiado utilizando la simulación matemática del transporte de los fotones y las partículas en la materia. Considerando ambos resultados, se determinaron los perfiles de daño por desplazamientos atómicos dentro del material masivo analizado, particularizando el aporte de cada tipo de partícula secundaria generada por la interacción de los fotones. Los resultados mostraron el comportamiento creciente de las secciones eficaces de desplazamiento en todo el rango de energía cinética evaluado. Se determinaron los valores de energías cinéticas de electrones y positrones a partir de los cuales son probabilísticamente posible los procesos de desplazamientos atómicos simples y múltiples. Se confirmó la importancia del aporte de los positrones al número total de defectos puntuales generados durante la interacción de los rayos gamma con el material estudiado.

Palabras claves: nanotubos de carbono, radiación gamma, desplazamientos atómicos, sección eficaz, método de Monte Carlo, simulación.




The irradiation techniques are an effective method for the controlled generation of defects in carbon nanostructured materials. They are used in order to modify its properties, or to facilitate some processes such as coalescence, functionalization, formation of tunneling barriers, couplings creation and some others [1-5]. It is well known that the formation of radiation-induced defects in carbon nanostructures change their mechanical and electronic properties and may even cause catastrophic structural alterations [6, 7]. In this sense, understanding the formation of radiation-induced defects in these materials and its quantification is essential for the so-called defect-assisted engineering of nanomaterials [8]. These studies are also very important for the development of other applications related to nuclear, aerospace and medical technologies, where devices and materials based on carbon nanostructures are habitually exposed to aggressive radiation environments. Examples of these applications could be radiation detectors, solar cells, batteries, electronic microcircuits, etc. [9-12]. The thorough knowledge of the radiation response of these materials and devices, its radiation resistance and the dose thresholds is decisive for the modern and future science and technology.

For the present study, the gamma rays have been selected as radiation source due to its high penetration capability and its ability to generate stable point defects through the emitted secondary particles [7, 13, 14]. Gamma rays are often present in any nuclear facility, either for research, energy generation or medical therapy purposes. Moreover, in outer space this radiation forms part of an energetic and dense radiation background.

Although in the scientific literature the study of gamma rays effects on different carbon nanostructures are reported, see for example [2, 7, 15], the influence of gamma radiation on defects generation in bulk multi-walled carbon nanotubes (B-MWCNT) materials is investigated for the first time. In particular, the carbon atom displacement cross-section for electrons and positrons had not been reported. Neither, the sample in-depth distribution of the generated displacements per atom total number and its electron and positron contributions had been studied.

Knowledge of these data and facts provides new evidences to the understanding of the gamma radiation damage phenomenon in advanced materials, such as B-MWCNT, which is essential for safe and reliable exploitation and generalization of its applications.




The studied samples consist of B-MWCNT with mass densities of 1.36 g and 1.45 g , which correspond to 24.4% and 19.4% porosities respectively. These values were experimentally measured in B-MWCNT samples fabricated by spark plasma sintering [16].

The effective atom displacement cross-sections were calculated using the MCCM (Monte Carlo assisted Classical Method) algorithm. This software takes into account the McKinley-Feshbach approach [17] with the Kinchin-Pease approximation [18] for the damage function. A more complete and detailed explanation of this procedure can be found in [19].

Figure 1 shows a graphical representation of the simulated experiment. A multi-walled carbon nanotubes cylindrical shaped sample (100 µm diameter and 10 µm thickness) is irradiated with monochromatic photons of given energies. These photons impact perpendicularly and homogeneously distributed over top surface of the cylinder. The atom displacement profile determination is performed in a 10 μm x 10 μm x 10 μm voxel located in the center of the cylinder.

The energy fluxes of electrons and positrons were calculated at different depths within the selected voxel. This calculation was accomplished with the use of MCNPX (Monte Carlos n - Particles Transport Code) software [20], which simulates the transport of photons and particles in matter. The obtained energy fluxes results were processed by the MCCM program to determine the number of atom displacements with depth in the selected voxel for each kind of secondary particle.

All simulation results are reported with a relative statistical error lower than 1%, which was ensured using a large number (10 million) of simulated incident photons and its secondary particles.

The displacement threshold energy, , is an important characteristic describing the radiation hardness of the material. It is related not only to the bond energy but also to the local chemical bonding, to the availability of open space in the structure, and it may depend on the system geometry (e.g. diameter of a nanotube, incidence angle of radiation). Due to this, the determination of is complicated, and for our target material a wide range of values are reported in the literature. This threshold energy interval is usually between 15 and 20 eV [21, 22]. For this work was selected the average value = 19.3 eV reported in [23], where the authors studied the angular dependence of the threshold energy using molecular-dynamics simulations.




Gamma radiation is not able to directly transfer the energy needed to produce atom displacements, therefore the products of its interaction with matter (electrons and positrons) are responsible for this process. If the kinetic energy transferred from particle to the nucleus is higher than , a carbon atom can leave its initial position to form a metastable structural defect on a subpicosecond time scale. The probability of this atom displacement process is determined by the displacement cross section, calculated using the previously explained methodology. Displacement cross section dependences with the secondary electron and positron kinetic energies are shown in figure 2. The behaviors of these two plots are similar, increasing with energy within the entire studied energy interval. Values of σdpa calculated for electrons are lightly higher than those of positrons, but no more than 3.36% in average.

As can be accurately observed in the inset graph of figure 2 (magnification of the low energy region, ≤ 1 MeV) the atom displacements processes are energetically possible for particle energy ≥ 100 keV.

If the primary rejected atom has enough energy to displace another atom by atom-atom collisions, then the multiple atoms displacements may take place. The multilayer structure and the bulk character of the studied sample increases the probabilities of occurring cascades processes. The precise moment when the multiple atoms displacements processes begin is observable in figure 2 at the point where an abrupt curves slope change takes place. As seen, the energy at which the atom displacement cascades begin is ~ 500 keV for both, electrons and positrons.

Figure 3 shows the calculation results for the total number of displacements per atom as a function of the incident photon energy for two mass density values. Here, denotes the sum of all the involved particles contributions to dpa in the whole voxel volume. In this figure is observed that behaviors with the photon energy are monotonous increasing in the whole studied energy range. For photon energies higher than 20 MeV, difference between the two distributions is almost constant, being approximately 6% superior for the sample with = 1.45 g .

The behaviors of the total number of atom displacements with depth inside the sample for both analyzed mass densities are presented in figure 4. Here, reported values refer to the total number of stable defects generated in a 1 µm thick layer within the voxel shown in figure 1. These layers are located parallel at different depths in a continuous arrangement and perpendicularly to the incident photons direction.

For both analyzed sample mass densities, the in-depth dependences increase monotonically along the entire sample, thus showing inhomogeneous volume distribution within the sample for all studied energies. The highest values are located near to the sample surface opposite to the incidence surface.

Taken as reference the values generated by the low-energy photons (1 MeV), the number of point defects produced by the other examined energies (20, 50, 75 and 100 MeV) were found to be higher by about 180, 1400, 3500 and 6600 times respectively, regardless of the depth where the events take place and the mass density of the studied samples.

At first sight the differences between the profiles presented in figures 4 (a) and (b) are not observable. Detailed analysis showed that the distributions corresponding to the higher mass density sample were on average 6.59% higher than those ones belonging to the lighter sample. This small difference between the defects numbers created in the sample volume is closely related to the ratio between the two mass densities (6.62%). This result is reasonable because the density parameter appears as a linear factor in the used formalism for calculating the dpa and it is the one parameter that changes in the simulated experiment.

Figures 5 (a) and (b) present the results of the decomposition in its two components, the electron and the positron contributions. The first conclusion from the analysis of these two figures is that the relationship between partial contributions dependence to the mass density is negligible.

As can be seen for both figures, at low energies the positrons contribution to the stable structural point defects formation is significantly lower than the electrons one. For photons energies lower than 1.02 MeV positrons contribution is completely absent, as expected.

With increasing photon energy the occurrence probability of the pair formation phenomenon growths generating a larger number of positrons and increasing their maximum kinetic energies. The positron displacement cross section (see figure 2) and the particle range also rise with the particle energy.

All this leads to the observed behaviors in figures 5 (a) and (b); with increasing photon energy, the weight of the positron component grows up to close to the electronic component. The positrons contribution to the total number of dpa generated in the sample were found to be 3.8%, 11.4%, 35.5% and 41.8% for photon energies of 5, 10, 50 and 100 MeV respectively.

As can be seen, positrons contribute substantially to the total number of atom displacements in the analyzed structure exposed to radiation. This fact contradicts the affirmation made by some authors whom claim that, since the generated positron subsequently annihilates by combining with an electron, its effect on atom displacement is negligibly small, and they does not included it in the calculation. For example, in [24] the authors present the results in the determination of the displacement cross section in various materials including C for gamma energies up to 14 MeV, avoiding in all the cases the positron contributions to the displacement damage. Following the used methodology, we have determinate that for 14 MeV gamma energy the positron contribution to the total displacement number in B-MWCNT sample (carbon allotrope) is about 16%, value which cannot be considered negligible. In previous studies, where bulk fullerene C60 [25] and YBCO superconducting materials [26] where studied following the same procedure as here, similar results were obtained. In summary, these results prove that the positron contribution cannot be ignored, and it takes a significant importance when increasing the photon energy.




The atom displacement cross section dependences with the secondary electron and positron kinetic energies for B-MWCNT were calculated in the energy range up to 100 MeV. Both behaviors are increasing with the energy and the values obtained for electrons are on average 3.36% higher than for positrons. The displacements processes start at particle energy ~ 100 keV and the multiple atoms displacements begin at energy close to 500 keV for both electrons and positrons. The total number of displacements per atom as a function of the incident photon energy was determined for two mass densities. These profiles show a monotonous increasing behavior in all the energy range, with values which are 6.6% higher for the sample with greater mass density. The dependence with depth of the total number of atom displacements is also monotonically increasing along the entire sample, with slopes growing up with photon energy. The electron and positron contributions to the as a function of photon energy were presented, showing that the relationship between partial contributions dependence to the mass density is negligible. At very low energies the positrons contribution to the is small, but its role increases with photon energy, reaching the 3.8%, 11.4%, 35.5% and 41.8% for photon energy of 5, 10, 50 and 100 MeV respectively. This behavior is independent of the B-MWCNT target mass density. These results confirm once again that the positron contribution to the atom displacements in materials should be considered, taking more importance when increasing the incident photon energy.



This work was supported by the AENTA of Cuba through the project PRN/6-2/3.




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Recibido: 10 de diciembre de 2012
25 de abril de 2013