Evaluation of neutron radiation damage on gold microstructure using MCNP

The effects of radiation interaction with materials have been studied over the years on metals, semiconductors, and other alloys. The result of these interactions constitutes microstructural effects, like point defects, dislocation loops, and void swellings. The accumulation of these defects results to damage on the macroscopic scale. This study is aimed to predict the magnitude of radiation damage in gold sample due to neutron irradiation. Neutron flux, displacement-per-atom rate, as well as heat deposition, were calculated in MCNP6.2, using the SAFARI-1 reactor model. The total neutron flux and dpa rate in the gold sample were determined to be 2.262 × 1011 n.cm−2.s−1 and 5.209 × 10−7 s−1 respectively. Also, the total heat deposition due to neutrons and photons was 2.515 × 10−6 W.g−1 and 0.513 W.g−1, respectively. Hence, the predicted neutron dpa and flux for the gold sample in this study suggest a heavy damage regime.


Introduction
Radiation damage in crystalline materials starts from a single point defect at the microstructure level when a material is exposed to radiation such as neutrons and photons.Radiation effects on the microstructure can over time, translate into observable defects in the form of physical property changes [1].The formation of interstitial-vacancy (Frenkel) pairs evolves from 0dimensional (point defects) to 3-dimensional defects (voids, cavities, and precipitates) in the material after exposure to a high dose of radiation.These constitute microstructural damage in crystalline solids [2].To quantify the level of damage in materials, a radiation exposure quantity is essential as a standard.Universally, the quantity used to correlate displacement damage in materials is known as displacement per atom (dpa), which can be defined as the ratio of the number of atoms displaced to the number of material atoms in the same volume for a given fluence of radiation [3].It offers the basis for calculating other radiation effects on crystalline materials since radiation-induced changes in the microstructure are a function of the dpa [3,4].It is also a measure for comparing radiation effects for different types of radiation (neutrons, photons, electrons, ions) quantitatively.Research on the effect of damage in crystalline materials has been conducted for many decades, driven by the need to control the radiation-induced degradation of materials in reactors and the response of the material to harsh radiation environments.Such research has been beneficial for nuclear material development and other applications, particularly in assessing the capabilities of materials that can be considered for different purposes in reactor engineering or other high-radiation environments, based on radiation damage resilience.Gold is utilized for different applications in radiation environments.These may include reactor flux monitoring studies and advanced space and satellite detector applications [5,6].Within these applications, interactions of the material with high-energy particles can occur, leading to microstructural defects.This work aimed to predict the level of neutron radiation damage in gold sample using the Monte Carlo N-Particle Transport code (MCNP 6.2) [7].MCNP solves transport problems by tracking particles' life histories using natural stochastic processes.Hence, in reactor-type analyses, the code enables coupled neutronphoton transport calculations that predict very well the real behaviour of particles in such complex geometries.

Methodology 2.1. Material description and MCNP model
The sample used for the simulation was 99.9% pure gold ( 197 Au) foil of thickness 0.0064 mm and radius 0.55 cm.The sample was simulated at the D6 NW3 position of the Isotope Production Rig (IPR) as illustrated in the SAFARI-1 MCNP Model in Figure 1a.This IPR position has a neutron flux of order 10 14 n.cm −2 .s−1 in the SAFARI-1 reactor core.Extract of position D6, which housed the gold sample enclosed with aluminium canister mimicking the actual experimental setup is shown in Figure 1b.

Calculation of energy-dependent flux
The energy-dependent flux was calculated using the 172 energy groups in the XMAS structure [9].The XMAS structure was used to generate the energy-dependent flux spectrum at the D6 NW3 position.This structure is a spectrum of 80 thermal, 47 epithermal, and 45 fast neutron energies ranging from 1.10 × 10 −10 to 19.6 MeV.The track length estimator F4 cell flux tally was applied to simulate the energy-dependent flux.Choosing the F4 neutron flux tally was based on the assumption that the neutron collisions with the material emanate isotropically from the fuel assemblies surrounding the D6 IPR position shown in Figure 1a.Data of neutron flux obtained from the MCNP tally were normalized to the SAFARI-1 reactor power using Equation 1 [10,11].
where F lux is the normalized neutron flux.Other parameters used for the flux normalization are summarized in Table1.

Displacement Per Atom Calculation Method
A useful parametric quantity, the displacement per atom (dpa), has been modeled to ascertain the level of radiation damage in a material.These models include the Kinchin and Pease (KP) model and the Norgett-Robinson-Torrens(NRT) dpa model [3], among others.Whereas, this present work makes use of the NRT-dpa model in conjunction with MCNP6.2 which provides necessary neutron-induced dpa results.In order to evaluate the dpa rate for the material, a tally multiplier is applied to the standard flux in the MCNP code.The number of atoms displaced is related to the total available neutron energy E a and is given by Equation 2 in Ref. [12,13]: where η is the efficiency correction factor and E d is the atomic displacement energy for the material.To tally the dpa rate, the NJOY [13,14] code was used to process the defect production cross-sections (DPCS) in the Evaluated Nuclear Data Files (ENDF/B-VII) libraries into suitable formats accessible by MCNP input file.Damage cross-section and Kinetic Energy Released in Materials (KERMA) are produced in the HEATR function within NJOY.The F4 neutron tally (F4:N) was used with FM tally multipliers to estimate the dpa rate as shown in Equation 3.
where FM4 is the F4 tally multiplier which performs the integration of Equation 2 implicitly during simulation, when the F4 tally is called.M T =444 is the material reaction, c is the cell number for the Au sample, m is the material number, and K is the kinetic energy released in materials (KERMA) [13] given by: where ρ m is the atomic number density of the material m in atoms.b−1 .cm−1 and η = 0.8 is the efficiency correction factor obtained from binary collision approximations.

Calculation of heat energy deposition
Associated heat deposition for both neutrons and photons on the gold sample was calculated using F6 card tallies.The F6 tally was used to estimate the neutron and photon heating because it evaluates the true heat deposition from neutrons and photons in the material [15].Individual particle's heat deposition tallies are given in Equations 6 and 7 for neutrons and photons respectively [10,15].
where E is the energy of the incident neutron, P (E) i is the probability for the reaction i at the incident energy E of a neutron, Ēout i is the mean exiting energy of the neutron for the reaction i at incident energy E with Q-value Q i and Ēi,γ(E) is the mean exiting γ energy for the reaction i at neutron incident energy E.
where n represents the number of photon reactions i under consideration.The three reactions considered are i = 1 representing incoherent Compton scattering, i = 2 for pair production, and i = 3 for photoelectric absorption.The Ēi,out (E) is the mean exiting γ energy for the reaction at neutron incident energy E, and P i (E) is the probability of the reaction at γ incident energy E.

Simulation of radiation damage in gold sample
Simulation of damage was done using the model based on the SAFARI-1 research reactor shown in Figure 1a.The geometries of all reactor core components and the sample were coded in the cell and surface input cards.MCNP uses tallies to track and record the interactions between particles and the target material.The simulations were conducted using the beginning of the cycle (BOC) state C1601-1, which represents the normal reactor cycle for SAFARI-1 reactor.A total of 2500 kcode active and 250 inactive cycles were performed.Each cycle employed nominally 100,000 histories to ensure sufficient statistics and convergence of the results.The acceptable success criteria for MCNP uncertainties is to have a tally fluctuation chart (TFC) with a constant value figure of merit (FOM), a relative error, and a variance of variance (VOV) of less than 0.1.

Results and Discussion
The Results presented in the figures and tables below are based on flux, dpa values, as well as heat deposition for both neutrons and photon interactions with the Au sample studied.Uncertainty checks were performed inherently by MCNP and are also reported.The uncertainties reported along the results are fractional standard deviations (fsd).

Neutron Flux and dpa rate
The normalized neutron flux-energy profile is presented in Figure 2, depicting a total neutron flux of (2.262 ± 0.048) × 10 11 n.cm −2 .s−1 .Figure 3 shows the dpa rates-energy profile for the Au sample while the contribution of the thermal, epithermal and fast regimes dpa rates is (3.176, 0.0093 and 1.939) ×10 −7 dpa.s −1 respectively with a total dpa rate estimated to be (5.21 ± 0.15) ×10 −7 dpa.s −1 .It can be observed that there is a higher occurrence of dpa at the thermal energy range, followed by the fast energy range.Since the dpa depends on the neutron flux and the incident neutron energy, this result follows the flux-energy response.The large thermal cross-section for neutron capture in Au could be responsible for the damage accumulation in the thermal energy regions.2, the mean heat deposition due to photons and neutrons was estimated at 0.513± 0.011 W.g −1 and (2.515±0.121)×10−6 W.g −1 , respectively.Heat energy absorbed from radiation types, especially for crystalline materials relates to the thermal heating of the materials.The result of heat deposition by neutrons in the sample material is infinitesimal compared to the heat deposition by photons.At the same time, the fast energy range contributed solely to the heat deposition by photons as is evident in Figure 4.This heat production by photons at the fast regime could be attributed to the fast capture reactions.3 shows the calculations of neutron fluence and dpa up to an irradiation time of 1 year.This study predicted a dpa ranging from 0.23 -0.9 within one irradiation cycle.The microstructural characteristics of most pure metals are altered by a dpa value greater than 0.1 [1].Hence, the dpa values predicted in this work are capable of inducing microstructural changes to the Au foil sample placed under these irradiation conditions.The results also confirm the linear dependence of total dpa with irradiation time.

Conclusion
In this work, an estimation of neutron radiation damage to the microstructure of the Au sample using MCNP6.2 has been reported.All MCNP6.2 tally calculations exhibited random behaviour, and maintained a constant value of the figure of merit (FOM) with a relative error and variance of variance (VOV) of less than 0.1.The calculated dpa values relate to fairly heavy damage in the microstructure of the gold sample.Heat deposition due to neutrons and photons is not significant to result in material property changes, excessive heating leading to long cooling time after sample irradiation, or an addition to the total reactor power.The dpa values, however, are capable of inducing changes in the microstructural properties of the Au foil when exposed to neutron radiation during flux monitoring over time.Also, since some components of spaceships are made of gold material, dpa values reported in this study may be used as a reference for inferring possible damage over long-term exposures of such components to radiations of comparable exposure levels.Neutron dpa rates calculated in this present study will be an addition to the database of radiation damage studies for the gold material.

Figure 1a .Figure 1 .
Figure 1a.Reactor core configuration Figure 1b.D6 IPR position Figure 1.SAFARI-1 MCNP Model [7] (a) Core configuration showing the fuel assemblies and IPR positions.A grid of rows labeled A-H and columns 1-9 is shown to enhance the identification of the core structural components.(b) represents an extract of D6 position illustrating the sample irradiation position

Figure 4 .
Figure 4. Neutron and photon heat deposition spectra.Note that neutron heat deposition values are scaled up by 10 5 to enable comparison with the photon heat deposition, especially in the higher neutron energy region

Table 1 .
Flux normalization for Au sample

Table 2 .
Average heat deposition in the energy regimes

Table 3 .
Neutron fluence and dpa