1. Introduction
Radiation (energetic gammas, neutrons, and other particles) is emitted during fission and fusion reactions which occur in nuclear reactors and throughout the process of radioactive decay. Primary Knock-on Atoms (PKAs) are created as a result of a collision between radiation-atoms. Exposure to radiation can induce changes in material properties. The aforesaid changes are a function of the number of atoms that have been displaced from lattice equilibrium sites [1].
The main cause of damage in the environment of fission reactors is the displacement of atoms due to neutron collisions. Kinetic energy is transported to target atoms during neutron collision. As a result, pairs are created between the vacancy and interstitial atoms. They are called "Frankel Pairs" (FP). The FP formation time is about 10-11 s after the collision. Consequently, microstructure changes and defected clusters are created by the FPs. The formation of the defects stated above influences the chemical, mechanical and other physical properties (growth, segregation, swelling, phase change, defect clustering, dissolution rate, and bubble formation) of irradiated materials [1-5].
Several methods are used to predict and compute the evolution, formation rate, and behavior of radiation damages, namely, the binary collision approximation (BCA), the molecular dynamics (MD) and the kinetic Monte Carlo (KMC) methods [1]. Economical, safe and reliable operation of nuclear power plants requires knowledge of the factors that may affect the material properties of the facility during its lifetime.
Graphite has been used in the nuclear industry from the time of establishment of the first critical reactors (Chicago pile-1) to fully commercialized reactors. It is used as a reflector, moderator [6-8] in fission reactors and divertor in plates [6, 9] of fusion reactors. Proper specification of graphite (high-temperature thermal, mechanical stability, superior-moderation properties, easy machinability, cost-effectiveness, high scattering and low neutron capture cross-section) is identified as the reason behind its use as a structural material and moderator in nuclear reactors [10-13]. Large specification changes occur due to imposition of gross microstructure evolution under neutron irradiation [8, 14]. Although, graphite has been used in the nuclear industry since the usage of the first graphite pile, there is a deficiency of holistic perception about its properties which is mainly due to the hardship associated with neutron-irradiation experiments and its very complex microstructure [15].
The method for calculation of dpa in nuclear reactors is discussed in some papers [16, 17] where it is shown that atom displacement depends on the flux value and neutron spectrum [18, 19] of the materials. While, other papers have shown the effects of neutron damage on graphite [20-25]. Wigner energy is created in graphite as a result of irradiation with neutrons in power and research reactors [26]. However, the aforementioned phenomenon is not the subject of this study. Graphite is used as a reflector to increase the neutron flux in TRR core [27]. These calculations are very important for the reactor safety, power plant management and any experimental test.
The purpose of this paper is to estimate the radiation damage in dpa units; that is, the average number of times an atom is displaced from its lattice site during the period of irradiation [28]. Two codes were used for the aforesaid purpose; namely, SRIM and SPECTER codes. In all techniques, MCNPX 2.6 code was used with ENDF/B-VI library to locate the region characterized by the maximum neutron flux in TRR core [29]. Following the calculation of neutron flux using the abovementioned code, radiation damage in the graphite box (GR) was calculated by using the SRIM 2013 computer program which is developed by Biersack, Zieglar, and others. SRIM is a Monte Carlo software based on the BCA method. It can be used for simulating the ion and neutron irradiation experimentations. For simulating neutron irradiation, the SRIM code uses of the file titled TRIM.DAT which contains the kinetic information (type, energy, collision position, and movement angle data) of PKAs. This file can be produced by the AMTRACK [30] code using the MCNPX code. A graphical user interface, a wide range of collision particles and graphical output are the benefits of the SRIM code. The SRIM code can calculate the ion distribution, ionization, and energy lost by phonons at different depths of the target.
In the second method, an estimate of radiation damage was computed by using the SPECTER code and the result was compared with the previous method. This code was developed by L.R. Greenwood[31] to easily calculate the damage incurred by any specified neutron irradiation. Unlike the other code, which is used for computing dpa rate, this code uses the Monte Carlo method for computing the aforementioned parameter [32].
In the last method, NRT model was used to calculate the damage rate and the result was compared with those obtained through other methods. This model was developed by Norgett, Robinson, and Torrens for calculating the damage rate of a PKA with a given energy [33]. The international radiation effects community adopted the NRT model as a standard model for calculating damage rate [34].
In the final section of the article, hydrogen retention is obtained as a function of the irradiation time. The radiation damage rate in the Tehran reactor has been calculated for the first time. Due to the long life of the reactor, these calculations and establishment of a material specification database are essential for long term management of the reactor.
2. Material and methods
2.1. Dpa calculation
Tehran Research Reactor (TRR) is a 5 MWt pool-type, light-water, moderated reactor. It is operated with U3O8 enrichment (20%) fuels chiefly for the purpose of research, training, irradiation experiments and production of radioisotopes. TRR core consists of two types of fuel assemblies, namely, Standard Fuel Element (SFE) and Control Fuel Element (CFE). Nuclear grade graphite which is protected by an external aluminum box (Gr) is used as a neutron reflector. Material irradiation is conducted in IR-Box positions [27]. Fig. 1 shows a planar view of the TRR core configuration as simulated by the MCNPX code.
In the first method, SPECOMP 2002 code [35] was used to calculate the displacement cross section of graphite. While, neutron flux was calculated by the MCNPX code. These results are used to evaluate the dpa by using the SPECTER code. In addition, material composition was also measured by using the Inductively Coupled Plasma Emission Spectrometer (ICP-AES) method. The calculated composition was used as inputs for the MCNPX and SPECOMP codes. Fig. 2 shows the flow chart of the radiation damage calculation process followed by the SPECTER code.
In the second method, neutron radiation damage on the graphite and rate of dpa are evaluated by using the SRIM/TRIM computer code. The SRIM code requires the kinetic information of the atoms for calculating neutron radiation damage. The latter is required to start the recoil cascades that should be extracted from the file titled, TRIM.DAT. AMTRACK is used to obtain the aforementioned file from the MCNPX-PTRAC (Particle Track) output file[30]. AMTRACK can reform the MCNPX-PTRAC output file whose code is written by using the MATLAB software [29]. PTRAC file has energy before and after collision, the particle type, position of reaction, reaction type and movement angle data [29]. Flowchart of the radiation damage calculation process followed by the SRIM code is displayed in Fig. 2.
The concentration of impurities in the graphite before irradiation was measured through the ICP-AES (VARIAN, LIBERTY50AX TURBO, Australia) method. Type and amount of impurities were specified by using the x-ray fluorescence (XRF) method. For preparing the ICP-AES solution, 0.549 gram of graphite powder was dissolved in 100 ml of p.a. grade 2 % nitric acid (for 72 h). Nitric acid (2 % Vol.) was prepared by diluting 65 % nitric acid manufactured by the Merck Company in distilled water. After dissolving the graphite powder sample in the acid, the solution was passed through a Whatman filter which was manufactured by the Sigma-Alderich Company. The resulting solution was analyzed by using the ICP-AES [36]. The material composition of the sample is shown in Table 1.
| Element | Al* | Si* | Ca* | Na* | S | B | Fe |
|---|---|---|---|---|---|---|---|
| Graphite | 0.311 | 0.306 | 0.331 | 0.084 | 0.026 | 4.86×10-3 | 4.32×10-3 |
After calculating the number of atom displacements from the SRIM code and the neutron flux from the MCNPX code, Eq.(1) can be used to calculate the damage rate in dpa/s unit:
where
where t(s) is the time of radiation.
2.2. Relationship between hydrogen retention and radiation
Hydrogen atoms may be trapped in two sites during the irradiation of graphite namely, interstitial cluster loop edge sites (trap 1) and carbon dangling bonds at edge surfaces of crystallites (trap 2). A study had shown that neutron irradiation creates 1 trap site at upper fluence with more than 0.017 dpa [25]. Hydrogen retention of neutron-irradiated graphite as well as the relationship between fluence (dpa) and hydrogen retention for the different kinds of trapping sites are shown for different neutron damage in Fig. 3. Using numerical interpolation, the relationship between fluence (dpa) and hydrogen retention (hydrogen retention per unit mass (H/C)) for different kinds of trapping sites can be obtained as follows:
where D is radiation damage in dpa unit and HT, H1, H2, are total hydrogen retention, hydrogen retention of trap 1 and trap 2, respectively.
3. Results and discussion
3.1. Calculation of neutron flux in GR-Box using MCNPX code
Alike other transport codes, MCNPX uses the density of simulated objects to calculate the mean free path of the traced particles in the media and track them over a wide range of energies. The computational model was built as per the information available from the final safety analysis report (FSAR). The MCNPX code was used to simulate neutron transport in the core as well as to calculate neutron fluxes and neutron flux spectra [27, 29]. The reactor was critical and control rods were 50% immersed into the core (core No. 83). The core contained 0.0435 ton of Uranium. Considering the different burn up of each fuel assembly, different materials were recommended for each one of the assemblies used in the MCNPX simulation. Burn up of each fuel assembly is shown in Fig. 4.
In addition, the flux of every graphite box was calculated by using F4 tally (Track length estimate of cell flux) and it is shown in Fig. 4. In MCNPX code, F4 tally determines the flux in any given volume. This tally calculates the neutron flux through a certain area or the number of neutron in a particular energy interval. MCNPX tallies were normalized to per starting particle [29]. As seen in the figure, graphite box in C9 position has the maximum total flux which measures up to 6.46×1013 n/ (cm2·s). Statistical uncertainties were less than 0.7 % in the calculated fluxes.
Figre 5 shows the axial flux on C9 graphite box. It can be seen that higher neutron flux exists between a height of 20 cm and 30 cm (about 8.5×1013 n/ (cm2·s)). Thus, this position was selected to calculate the radiation damage of GR-BOX. Neutron spectrum (69 groups) was calculated by using F2 tally in MCNPX code; since, this spectrum is suitable for simulation in TRR [27]. Spectrum was extracted from Ref [38] to calculate dpa in graphite box. Additionally, peak flux was used on the graphite box surface to calculate the dpa caused by neutron encounter in the graphite box of TRR core. This computation was conducted by using Eq.1.
3.2. Calculation of dpa rate using SPECOMP/SPECTER codes
Neutron radiation damage can simply be calculated by using the SPECTER computer code for any specified neutron irradiation. In the aforementioned code, recoil spectra, total damage energy (kerma) and gas production are computed too. The library files of the SPECTER code are very extensive. The dpa cross section for new material can be calculated by using SPECOMP code. It is appended to COMPOUND.DAT file. SPECOMP can be utilized for the materials which have five of the 38 elements contained in the SPECTER code [35]. The material composition of graphite is presented in Table 1. It should be noted that only C, Al, Si, Ca and Na elements are chosen to model graphite in the SPECOMP code. Fig. 6 shows the displacement cross section for graphite that has been calculated by using the SPECOMP code. The physical parameters which were used in the SPECOMP code are shown in Table 2. MCNPX code was used to evaluate the neutron flux on the graphite box surface. Consequently, the peak flux area was specified. Finally, the SPECTER code was used to calculate the dpa rate.
| Parameter | C[32] | A[39] | S[40] | C[41] | N[41] |
|---|---|---|---|---|---|
| Displacement energy (eV) | 28 | 25 | 15 | 40 | 25 |
| Effective gamma damage energy (eV) | 671 | 674 | 596 | 388 | 618 |
3.3. Calculation of dpa rate using SRIM/TRIM code
Ion distribution profiles of material irradiation can be calculated by using the SRIM (also known as TRIM) which is a Monte Carlo simulation code. Degree of ion penetration in a material is calculated through the Binary Collision Approximation (BCA) method in the SRIM. SRIM code uses material composition and density for describing a material. The TRIM.DAT file contains the kinetic information of atoms and it starts recoil cascades in neutron damage simulation [32].
An element with 1×1×1 cm3 dimensions (target) was utilized to extract PTRAC file from the MCNPX code. The file contains data about energies before and after the collision, the particle type, position and type of reaction as well as movement angle. The aforesaid information was utilized for calculating the dpa using the SRIM code. Fig. 7 shows the neutron spectrum output of the target.
Table 3 demonstrates the nuclear reaction occurring in the specimen. Transmutation reaction, 12C (n, γ) 13C and 13C (n, γ) 14N, occur due to thermal neutron capture. While, 12C (n, α) 9Be reaction is performed for releasing high energy neutron (E > 7MeV) [42].
| Target atom | Reaction and production | Un-normalized production (Atom/cm3s) |
|---|---|---|
| C | 12C (n, γ) 13C | 8.39×10-5 |
| 12C (n, α) 9Be | 4.93×10-5 | |
| 13C (n, γ) 14N | 3.66×10-7 |
PTRAC file was used to create TRIM.DAT file using AMTRACK (intermediate computer program). The latter is needed to simulate neutron radiation damage while using the SRIM code. Finally, SRIM uses the abovementioned file along with the material composition (Table 1) information to calculate the dpa. Fig. 8 shows the PKA spectrum which is calculated by AMTRAC. Simulation is performed by approximately 100000 ions.
SRIM has two methods for simulating the radiation damage evolution namely, "Ion distribution and quick calculation of damage" (QD) and "Detailed calculation with full damage cascades" (FC). In the QD method, the code uses the Kinchin-Pease equation for estimating the number of defects on each primary knock-on atom based on its recoil energy and the trajectories of primary ions only. Subsequently, primary knock-on atoms (PKAs) are produced. In the FC method, the total collision cascade is calculated for less than 1 eV energy by applying the BCA. In addition, track of all displaced atoms and their count is also evaluated. In this method, "replacement collisions" reduce the vacancy number [43, 44]. Studies have shown that the QD method has more reliable results [45].
The physical parameters which were used for SRIM simulation are shown in Table 4. Lattice binding energy is the energy that every recoiling target atom loses when it leaves its lattice site and recoils in the target. Surface binding energy is the energy that target atoms must absorb to leave the surface of the target and displacement energy (Ed) is the minimum energy that an atom needs to be displaced from its lattice site [32]. If the lattice atom receives less than Ed energy, the struck atom undergoes large amplitude vibrations within its site but remains in its location and vacancy is not created [17].
Table 5 compares the rate of dpa in the SPECTER and SRIM codes. The obtained results are also compared with the ones derived from the NRT method. The calculation procedure used in the NRT method had been discussed by Stoller et al [45] and Saha et al [30]. The rate of damage incurred while conducting the reactor function on full power for one day had been obtained. The results obtained from the two codes and the NRT method were consistent with each other. Similar results had been obtained in the previous researches [44]. The results obtained through the QD method had a lower difference with the results derived from the SPECTER code and the NRT method. The QD and NRT methods for graphite calculated a damage level of about 171 vacancies/ion and 175 vacancies/ion, respectively.
| Code/model | Damage Level(Vacancies/ ion) | Damage rate (dpa/s) | dpa/EFPD* | |
|---|---|---|---|---|
| SRIM 2013 | QD | 171 | 1.567×10-8 | 1.3538×10-3 |
| SPECTER | - | 1.507×10-8 | 1.3020×10-3 | |
| NRT | 175 | 1.603×10-8 | 1.3849×10-3 | |
The QD mode calculated a damage rate of 1.567×10-8 dpa/s. While, the dpa calculated by the QD mode for one Effective Full Power Day (EFPD) was 1.3538×10-3 displacements. The SPECTER code calculated 1.507×10-8 dpa/s as the rate of damage and the dpa/EFPD equaled to 1.302×10-3 displacements. Through the NRT method, the values of 1.603×10-8 dpa/s and 1.3849×10-3 were obtained for the damage rate and dpa/EFPD, respectively.
Table 6 presents the output parameters of the SRIM code. Displacement occurs when the energy of struck atom (E2) is greater than the displacement energy (Ed). "Total displacements" is equal to the total rate of these displacements. If both atoms (incident and struck atoms) have enough energy (E1 > Ed & E2 > Ed) to leave the lattice site, a vacancy is created. The "total vacancies" parameter shows the total number of the vacancies mentioned earlier. "Replacement collisions" is the rate with which incident atom ejects struck atom from the original lattice site and stays in its location. "Total ionization" is the energy lost by electrons. In addition, "total phonons" expresses the energy lost by the target phonons [32].
| Parameter | QD |
|---|---|
| Total displacements (dpa/s) | 1.567×10-8 |
| Total vacancies (dpa/s) | 1.567×10-8 |
| Replacement collisions (dpa/s) | 0 |
| Total ionization (keV/PKA) | 17244.4 |
| Total phonons (KeV/PKA) | 2642.1 |
Fig. 9 presents the "PKAs trajectory" and "transverse view" of neutron spectrum of 69 groups which was considered for QD method. Fig. 10 shows the "PKAs distribution" and "PKAs ranges" for all PKAs in the neutron spectrum of 69 groups, that had stopped within the graphite during the QD method. Figs. 9 and 10 illustrate a nearly uniform PKAs distribution. The lack of peak in the distribution of PKAs in material causes a uniform change in the material specification. The uniform distribution was consistent with the results stated in the references [1].
Fig. 11 shows the vacancy distributions calculated by using the SRIM code. Fig. 12 shows the total displacements and vacancy distributions per ion collision in 3D which were derived from neutron spectrum of 69 groups. A nearly uniform area was obtained for vacancy and atom distributions. The aforesaid observation is consistent with previous researches. Uniform distribution is created by collisions of neutron with atoms [1]. The QD method for graphite had obtained a damage rate of 1.567×10-8 dpa/s and the dpa calculated through the QD method for one Effective Full Power Day (EFPD) was 1.3538×10-3 displacements.
3.4. Hydrogen retention calculation
Fig. 13 illustrates the dependency of hydrogen retention on the irradiation time for the different types of trapping sites. The starting point for the trapping of hydrogen in interstitial cluster loop edge sites is after about one day of irradiation. As visible in the figure, the hydrogen trapping begins to saturate after a time; These results are similar to the ones obtained by other researches [9, 25].
4. Conclusion
In this study, the core of TRR was simulated by using MCNPX code and the location with the highest neutron flux was identified. The radiation damage rate in the Tehran reactor was calculated for the first time. The calculation of the radiation damage rate is essential for any empirical assay in this field. In the case of the aforementioned location, the dpa value was estimated for the graphite box using two SPECTERs and SRIM codes as well as the NRT method for neutron spectrum of 69 groups. The material composition of graphite was measured using the ICP-AES method and it was used in the above-listed codes. The results obtained through the "Quick calculation of damage" method by using SRIM code were in agreement with the SPECTER and NRT model results. The maximum radiation damage rate of 1.567×10-8 dpa/s was obtained for graphite in TRR core. These results serve as evidence to the almost uniform distribution of PKAs in the material, which causes a uniform change in the material specification in neutron radiation. Using the experimental data, the equation for hydrogen retention changes was also obtained. Dependency of hydrogen retention on the irradiation time was calculated for the different types of trapping sites present in the environmental conditions of the Tehran reactor. It was observed that hydrogen retention begins to saturate after a certain period of time. This observation is similar to the results of other studies.
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