Neutron radiation damage studies in the structural materials of a 500 MWe fast breeder reactor using DPA cross-sections from ENDF/B-VII.

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1 Pramana J. Phys. (2018) 90:46 Indian Academy of Sciences Neutron radiation damage studies in the structural materials of a 500 MWe fast breeder reactor using DPA cross-sections from ENDF/B-VII.1 UTTIYOARNAB SAHA 1,,KDEVAN 1, ABHITAB BACHCHAN 1, G PANDIKUMAR 1 and S GANESAN 2 1 Reactor Neutronics Division, Reactor Design Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institue, Kalpakkam , India 2 Bhabha Atomic Research Centre, Mumbai , India Corresponding author. uttiyoarnabsaha@gmail.com MS received 18 May 2017; revised 20 October 2017; accepted 31 October 2017; published online 23 February 2018 Abstract. The radiation damage in the structural materials of a 500 MWe Indian prototype fast breeder reactor (PFBR) is re-assessed by computing the neutron displacement per atom (dpa) cross-sections from the recent nuclear data library evaluated by the USA, ENDF/B-VII.1, wherein revisions were taken place in the new evaluations of basic nuclear data because of using the state-of-the-art neutron cross-section experiments, nuclear model-based predictions and modern data evaluation techniques. An indigenous computer code, computation of radiation damage (CRaD), is developed at our centre to compute primary-knock-on atom (PKA) spectra and displacement cross-sections of materials both in point-wise and any chosen group structure from the evaluated nuclear data libraries. The new radiation damage model, athermal recombination-corrected displacement per atom (arc-dpa), developed based on molecular dynamics simulations is also incorporated in our study. This work is the result of our earlier initiatives to overcome some of the limitations experienced while using codes like RECOIL, SPECTER and NJOY 2016, to estimate radiation damage. Agreement of CRaD results with other codes and ASTM standard for Fe dpa cross-section is found good. The present estimate of total dpa in D-9 steel of PFBR necessitates renormalisation of experimental correlations of dpa and radiation damage to ensure consistency of damage prediction with ENDF/B-VII.1 library. Keywords. Primary-knock-on atom spectra; displacement per atom; displacement per atom cross-section; computation of radiation damage; molecular dynamics simulation; renormalisation. PACS Nos i; Ak; Qb; Ft 1. Introduction It is well known that interaction of neutrons or ionising particles with the nuclear materials for a prolonged period of time results in radiation damage by continuously dislodging atoms from their normal lattice sites. Because of energy transfer due to interaction, a sufficiently energetic particle incident on a target displaces an atom from its lattice site to an interstitial position, leaving behind a vacant lattice position [1,2]. In a nuclear reactor, such damage happens mainly due to (a) elastic and inelastic collisions of neutrons with the nuclei, (b) recoil of a nucleus on emission of an energetic particle after neutron absorption and (c) energy transfer by the replaced atoms and other secondary particles with the lattice atoms. The minimum energy E d required to knock off a lattice atom, called lattice displacement energy, is usually in the range of ev in metals and its alloys. It is material-dependent. The atom that is hit by a neutron is known as primary-knockon atom (PKA). If a PKA has enough kinetic energy, it can knock off another lattice atom (called secondary knock-on atom) during its movement beyond a lattice distance, and this mechanism may lead to a cascade of displacements. Part of PKA energy is lost in electronic excitation, and the rest, known as the damage energy, builds up the displacement cascade. When the cascade cools down, many of the displaced atoms return to their original sites or vacant sites elsewhere in the lattice (recombination). A large number of atom replacements reduce the actual number of defects that could be produced by atom displacements. This is only a

2 46 Page 2 of 15 Pramana J. Phys. (2018) 90:46 fraction of the initially displaced atoms, known as damage efficiency. The complex process of primary radiation damage and its evolution are explained satisfactorily by observing the changes in macroscopic properties of irradiated materials, viz. swelling, creep, embrittlement, stress corrosion cracking etc. and correlating them with radiation dose. Two parameters, fluence and absorbed dose, are used to characterise the effects of neutron irradiations in a nuclear reactor. The spectrum details of incident neutrons are considered only in the latter one. The fluence approach is hence not suited for irradiations in the fields of varying neutron spectrum; damage cascade being very sensitive to the energy spectrum of PKAs which in turn is dependent on the incident neutron energy and the type of interaction with the target material. The radiation damage due to absorbed dose in structural materials is often quantified by a parameter called displacement per atom (dpa) which means the average number of times an atom is displaced from its lattice site during the period of irradiation. It is a measure of the energy deposited in the material by the interacting particles which is correlated well with the damagerelated parameters. It can be applied in high-energy ion and electron irradiation experiments to simulate neutron damage in shorter time periods [3 5]. However, the dpa lacks information about the structural composition of the defects induced by radiation. The concentration of freely migrating defects is sometimes used to incorporate diffusion effects of defects at elevated temperatures [6]. Since 1975, the secondary displacement model of Norgett, Robinson and Torrens, called simply as NRT model, has been used as the standard to compute the number of stable defects in nuclear materials exposed to high-energy particles [7]. In this model, the partitioning of PKA energy and estimation of damage energy are done by using the Robinson s partition function [8], which is based on the theory of Lindhard et al [9,10]. The NRT model is an improvement over the Kinchin Pease (KP) atom displacement model [11]. It is observed that under various physical conditions, the number of existing defects observed is very less compared to the original number of displacements produced [12]. Molecular dynamics (MD) simulations and cryogenic irradiation experiments have shown that the number of stable vacancies and interstitials existing in irradiated materials is about 20 40% of the NRT value [12 15]. Recently, more advanced displacement damage models are developed with more insight into the physical processes that occur during the evolution of the secondary collision cascade [16]. The replacement per atom (rpa) model and athermal recombination-corrected dpa (arcdpa) model are the two major outcomes of the recent IAEA-CRP on primary radiation damage cross-sections [17]. At Indira Gandhi Centre for Atomic Research (IGCAR), the codes RECOIL (ORNL) [18], based on ENDF/B-IV (1974) and SPECTER (ANL) [19], based on ENDF/B-V (1979) are being used for radiation damage studies in fast reactors. These two codes have their own in-built database of neutron cross-sections and PKA spectra for all relevant reactions in multigroup forms which are not amenable to update by the user. These codes work satisfactorily, but they have limitations in group structure and the data are threedecade-old. Though, all fast reactor core neutronics calculations are done using cross-section sets based on more recent libraries, viz. ENDF/B-VII.1, JEFF-3.1, JENDL-4.0 etc., three-decade-old displacement crosssections from RECOIL code are still continued to be used for the prediction of dpa in structural materials, due to the non-availability of computer code to compute dpa cross-sections from the above files. Compared to the previous libraries, the recent libraries are evaluated with improved nuclear reaction models and state-of-theart experimental data. In the evaluation of the resonance parameters, the present approach is to use Reich Moore formalism instead of the MLBW approach followed in the past. In these files, the ranges of resolved resonances are extended to the unresolved resonance region. More importance is given to quantify and tabulate the covariance data. In particular, the database in ENDF/B-VII.1 (which is being considered in the present work) has the data representing energy and angle information of secondary particles in a reaction. More features of the latest evaluated libraries can be found in [20] and other related references. More accurate anisotropic scattering and recoil energy distribution data in these libraries are expected to have significant impact on dpa crosssections. Though, the HEATR module of the NJOY code [21] has the capability to process these files, it was not licensed to India till February Further, this module also has the limitations of (a) explicitly not giving the PKA spectra of all partial reactions and (b) not implementing the latest damage models like arc-dpa for dpa cross-sections. Also the dpa crosssection obtained from HEATR deviates slightly from NRT definition (discussed later). These shortfalls in the above modules/codes have motivated us in developing an indigenous computer code to calculate dpa cross-sections from the recent evaluated libraries for fast reactor applications. Since radiation damage in structural materials limits the fuel burn-up and plant life in fast reactors, establishing the capability of more realistic estimation of radiation damage in nuclear materials is an important step to realise India s future programme of sodium-cooled fast reactors with improved economics,

3 Pramana J. Phys. (2018) 90:46 Page 3 of safety and reliability. In this paper, we mainly report the details of developing a code called computation of radiation damage (CRaD) and its application to various studies for PFBR core structural materials. The importance of PKA spectra is highlighted by computing the average energy of PKA for different neutron flux spectra. The relative contributions of various neutron reactions to total dpa cross-sections are discussed, with Fe-56 as an example. A comparative study of NRTdpa for Fe from CRaD is made with other sources of data, viz. RECOIL, SPECTER, NJOY-2016 and ASTM E Total dpa of D-9 alloy corresponding to PFBR spectra for 540 days of full power operation are calculated and compared. The arc-dpa model-based dpa cross-sections of Fe are found using CRaD and its impact on total dpa estimation in PFBR is also seen. 2. Method of computing displacement per atom cross-sections The fundamental quantity that is required to estimate dpa rate in a known neutron flux field is dpa crosssection, σ D (E). It gives the chance estimate for an atom to get displaced from its lattice site. Total dpa in a material at a particular reactor location is found by integrating σ D (E) over the entire neutron energy fluence at the location. The value of σ D (E) is computed by convoluting the PKA energy spectrum (σ PKA (E, E R )) and the secondary damage function ν[t (E R )] (of damage energy T ) over the whole range of recoil energy E R. PKA spectrum is the fundamental quantity dictating the radiation effects in a material. It is discussed below. The rate of atomic displacements in a material due to exposure to neutrons of energy E can be expressed as R(E) = Nσ D (E)ϕ(E), (2.1) where N is the atom density (number of atoms per unit volume), ϕ(e) is the neutron flux (n/cm 2 /s) and σ D (E) is the displacement per atom cross-section (cm 2 ).The quantity R(E)/N gives the number of displacements per atom per second (dpa/s) caused by neutrons of energy E. The total dpa in the material due to neutron irradiation with a flux spectrum of ϕ(e) for a time period of t seconds is DPA = t Emax deφ(e)σd t (E), (2.2) E min where σd t (E) = i σ D i (E) is the total dpa cross-section which is equal to the sum of displacement cross-sections due to all possible neutron interactions, σd i (E), of type i. It is estimated as σ t D (E) = i ERmax σ i (E) de R K i (E, E R )ν[t (E R )]. 0 (2.3) The function K i (E, E R ) is the kernel of energy transfer E R to the PKA through a nuclear reaction of type i with cross-section σ i (E). The kernel of energy transfer for each reaction depends on the kinematics of neutron nucleus reaction. These are briefly given in Appendix A. The damage energy T corresponds to the effective energy available for damage production after correcting for the energy losses due to electronic excitation and ionisation. ν[t (E R )] is the secondary displacement damage function. Here the damage energy T (E R ) is found from Robinson partition function [8] givenin eqs (2.4a) and(2.4b): T (E R ) = E R 1 + FG(ε), (2.4a) where F, G and ε are defined as 2/ Z1 Z 1/2 2 (A 1 + A 2 ) 3/2 F = ( 2/3 Z 1 + Z 2/3 ) 3/4 3/2 2 A 1 A 1/2, 2 G = ε 1/ ε 3/4 + ε, ε = E R ( 2/ Z 1 Z 2 Z 1 + Z 2/3 ) 1/2(A A 2 )/A 2 (2.4b) Here Z and A with suffixes 1 and 2 denote the atomic and mass numbers of the recoil and lattice nuclei respectively. The number of displacements undergone per atom is found from the NRT displacement damage model function ν(t ). 2.1 The NRT model The NRT displacement damage model function ν(t ) to compute the number of defects is given by 0; T < E d ν(t ) = 1; E d T < 2E d /β. (2.5) βt/2e d ; T 2E d /β Here, β is the damage efficiency (arising from the potential scattering of atoms) which is equal to 0.8. It is independent of PKA energy and the target material. In this model, the material is assumed to be monoatomic with atomic number Z and atomic mass A. E d is the lattice displacement energy. It is to be noted that E d = 40 ev, irrespective of the target, as the NRT standard.

4 46 Page 4 of 15 Pramana J. Phys. (2018) 90: Athermal recombination-corrected displacement per atom (arc-dpa) model The KP or NRT dpa model is known to overestimate the number of Frenkel pairs in metals. These models assume that damage occurs linearly with deposited energy. But MD simulation and experimental evidences show that the damage is less than what is expected from these models when the deposited energy is well above the threshold displacement energy [13,22]. The displaced atoms have sufficient kinetic energies so that vacancies and interstitials recombine and the final damage produced is less than the initial displacements produced. This phenomenon is independent of thermal-assisted defect migration and can occur even at 0 K. Hence the damage efficiency reduces from 0.8 considered in NRT model. It is actually energy-dependent varying from 0.5 to 0.2, with majority of experiments agreeing at 0.3 [23]. The arc-dpa model has been developed to address the shortcomings of the NRT model. The damage efficiency function ξ, which is defined as the ratio of true defects to number of defects predicted by the NRT model is obtained by performing MD simulations [16]. The number of displacements in this model is given as 0; T < E d ν(t ) = 1; E d T < 2E d /β (2.6) βt ξ(t )/2E d ; T 2E d /β where ξ(t ) = 1 c ad (2E d /β) b T b ad + c ad. (2.7) ad Therefore, in the arc-dpa formalism three materialspecific parameters E d, b ad and c ad are required to be known. Here b ad and c ad are dimensionless parameters obtained by fitting the results from MD simulations and experiments. From [16], it is noted that the number of Frenkel pairs follows a power-law relation with the damage energy at intermediate energies. As energy increases, the cascades tend to split either completely or incompletely into several subcascades, indicating a linear scaling with damage energy. The parameter b ad gives the point where the cascade behaviour changes from the power law to linear scaling. In a way, it tells how rapidly the residual damage approaches the saturation value by athermal recombination beyond the onset of the formation of subcascades. The saturation is dictated by the parameter c ad. A low value of this parameter (typical in high-density low-melting point materials) signifies that the interstitials transport less efficiently to the outer periphery of the displacement cascade and recombination is more likely to take place. A Levenberg Marquardt least squares fit to the experimental and MD data in the case of iron has resulted in values (± 0.020) and (± 0.005) for b ad and c ad respectively [16]. 2.3 Primary knock-on atom (PKA) spectra The neutron interaction cross-section σ i (E) for the reaction i multiplied with the kernel of energy transfer from E to E R, K i (E, E R ), gives the differential recoil energy transfer cross-section dσ i (E)/dE R or PKA spectrum for the reaction. K i (E, E R ) gives the probability that a nucleus will recoil with energy E R, after undergoing a reaction of type i (i = (n, n); (n, n); (n, 2n); (n, 3n); (n, p); (n, α); etc.) with a neutron of energy E. Total recoil spectra are obtained by adding the contribution from all partial reactions. From eq. (2.3), it can be seen that the dpa cross-section is obtained by integrating the displacement damage function over recoil atom spectrum. The two-body collision kinematics (see Appendix A ) and the data from ENDF/B-VII.1 library are used for its computation. Total PKA spectrum is a function of recoil atom energy which depends on the incident neutron energy and the energy and angular distributions of ejected secondary particles (neutrons, charged particles). The total dσ /de R of each isotope is calculated and then they are added with respective abundances to get overall contribution in iron. Total PKA spectrum averaged over a neutron flux spectrum φ(e) due to all possible reaction channels is dσ (ER ) = de R i Emax dσ i (E, E R ) φ(e)de E min de R. Emax E min φ(e)de (2.8) The neutron spectrum-averaged energy of the primary recoil atoms is calculated as (E R ) ϕ avg = Emax E min Emax E min ERmax deϕ(e) deϕ(e) dσ(e, E R ) de R E R E Rmin de R ERmax. dσ(e, E R ) de R E Rmin de R (2.9) The PKA spectrum per unit interaction averaged over the incident neutron energy spectrum ϕ tells about the recoil atoms at a particular energy E R and carries the information of the incident neutrons [24]. It is defined by

5 Pramana J. Phys. (2018) 90:46 Page 5 of dσ / de R (barns/ ev) 10-3 Recoil Energy (ev) Iron Figure 1. A typical PKA spectrum matrix for Fe. K (E R ) = i Emax deσ i (E)ϕ(E)K i (E, E R ) E min Emax. deσ i (E)ϕ(E) i E min (2.10) The fraction of recoil atoms above some energy E R is then estimated by eq. (2.11), which gives the comparative estimates of recoils having different energies due to the neutrons in the full energy range. Fraction of recoils above energy (E R ) = ERmax E R ERmax E Rmin K (E R )de R. (2.11) K (E R )de R 3. CRaD code The main objective of the CRaD code is to compute the PKA spectra and dpa cross-sections due to neutron interactions by using the data from the recent evaluated nuclear data libraries like ENDF/B-VII.1. It is written in FORTRAN 95. Subsequently, its scope will be extended to the estimation of various allied quantities in the radiation damage study, like radiation heating, etc. The relevant data, viz. neutron interaction crosssection, angle of scattering, secondary energy distribution, scattering anisotropy, secondary energy angle distribution, etc. are extracted from the basic/processed ENDF/B-VII.1 library. Each neutron nucleus interaction is treated separately to compute its contribution to the dpa cross-section. The dpa cross-section from a reaction is found at all neutron energies for which the reaction cross-sections are available. The total dpa cross-section is computed by adding the contribution of all partial reactions in a union energy grid. The CRaD gives dpa cross-section data both in point-wise and in multigroup forms. For multigrouping, a few in-built standard weighting functions and group structures are provided. The groups structures considered are: SAND- II extended (640 groups), VITAMIN-J (175 groups), DLC-2 (100 groups), ABBN-93 (26 groups). A few results from CRaD are discussed below. 3.1 Primary knock-on atom spectra A neutron of energy E can produce a recoil atom with a range of energies depending upon the type of interaction it undergoes. Here we have calculated the group-togroup recoil spectrum matrices Kij a b due to various reaction channels, represented as a b. The incident dσ / de R (barns/ev) 10-3 total 13 MeV Neutron n, n n, n' 10-4 (n, 2n)*10000 threshold reactions (n, x)* x x x x x10 6 Recoil Energy (ev) Figure 2. PKA spectra for various interactions of neutron with a 56 Fe nucleus.

6 46 Page 6 of 15 Pramana J. Phys. (2018) 90:46 Neutron Flux per Unit Lethargy (ev/cm 2 -s) PFBR Core Centre PFBR Radial Blanket PFBR Grid Plate Top PFBR Lattice Plate Figure group neutron flux per unit lethargy at different locations of PFBR. neutron and recoil energy groups are represented by the indices i and j respectively. Each of them uses a VITAMIN-J 175-group structure. A typical 3D plot of PKA spectrum matrix for Fe is shown in figure 1. A snap-shot of PKA spectra in 56 Fe for a 13 MeV incident neutron is shown in figure 2. The 175-group neutron fluxes at four different locations of the prototype fast breeder reactor (PFBR) are shown in figure 3. The fraction of recoils above different recoil energies for Fe is plotted in figure 4. The spectrum of the recoil nucleus due to radiative capture of neutrons is not included here. At neutron energies lower than E d, the recoil due to (n, γ ) reaction can give rise to recoil to the residual nucleus, but it is not very significant in the intermediate and higher neutron energies. From figure 4, it is seen that the fraction of higher energy recoil atoms at the core centre is comparatively more than what is found at other three locations. While about 54% of the recoils are above 24.5 kev in the core centre, it is about 50, 24 and 20% in the radial blanket, grid plate top and lattice plate locations respectively. The average PKA energies estimated using eq. (2.9) for the neutron fluxes at various locations of the PFBR is shown in figure 5.Average energy of PKA is 35.9 kev at the core centre and at the grid plate location it is 5.9 kev. It is observed in the case of iron, that the average recoil energy from (n, γ ) reaction is rather small, compared to other partial reactions. It is also to be noted that the actual rate of production of recoils depends on the absolute value of neutron flux. 3.2 Displacement per atom cross-section In CRaD, the contributions from all the important neutron nucleus interactions including the effect of Fraction of Recoils Above (E R ) 10-3 PFBR Core Centre PFBR Radial Blanket PFBR Grid Plate Top PFBR Lattice Plate Recoil Energy (ev) Figure 4. Fraction of recoil atoms in Fe above certain recoil energy for different flux spectra at different locations in PFBR. anisotropy in scattering reactions are accounted in the calculation. The anisotropy in neutron scattering is seen to play an important role in lowering the dpa cross-section [25,26]. This case of elastic scattering of neutrons in 56 Fe is illustrated in figure 6. Inelastic scattering and other high-energy reactions also show anisotropy, but to a very small extent. From figures 7 and 8, it can be seen that in the low-energy region the recoil of the nucleus following radiative capture of neutrons is the sole contributor to dpa cross-section. The contribution from neutron-induced elastic scattering starts from around hundreds of ev of incident neutron energies and remains over the whole energy range. In the MeV region, as scattering becomes anisotropic, its contribution slightly decreases. In these energies, inelastic

7 Pramana J. Phys. (2018) 90:46 Page 7 of Average PKA Energy (kev) Core Centre Radial Blanket Grid Plate Top Lattice Plate Location Figure 5. The average recoil energies in Fe at different core locations of PFBR DPA Cross Section (barns) Fe Isotropic Elastic Scattering Anisotropic Elastic Scattering Figure 6. The effect of anisotropic scattering on dpa cross-section in 56 Fe. scattering and other non-elastic reactions have significant contributions. Isotope-wise dpa cross-section of Fe is shown in figure 9. The dpa cross-section of Fe is computed by weighting with the abundance of its constituent isotopes. 3.3 Comparison of Fe dpa cross-section with ASTM E standard The dpa cross-sections of Fe from CRaD are compared with the latest, ASTM (American Society for Testing and Materials) dpa cross-sections. ASTM E [27] gives a standard practice for characterising neutron exposures in iron and low alloy steels in terms of displacement per atom (dpa). The application of this practice requires the knowledge of total neutron fluence and neutron flux spectrum. The correlation of radiation effects are beyond the scope of this procedure. The ASTM NRT-dpa cross-sections were processed from ENDF/B-VI library by using NJOY code in the 640 extended SAND-II group structure. There is not much change in the iron cross-sections of ENDF/B-VI and VII.1 libraries. No reference is provided for the material temperature, self-shielding effect and the weighting function. For comparing with ASTM NRT-dpa crosssections, we have assumed a constant weighting flux in eq. (A.1) for averaging dpa cross-sections of Fe at room temperature. The ASTM and CRaD dpa cross-sections for iron are shown in figure 10. The spikes seen in the ratio plot around the energy region where contribution from elastic scattering starts is primarily due to numerical errors involved in predicting too small values of

8 46 Page 8 of 15 Pramana J. Phys. (2018) 90:46 DPA Cross Section (barns) 10 3 n, n n, n' n, g n, 2n other threshold total 10-3 Fe Figure 7. dpa cross-sections due to partial neutron interactions in 56 Fe. 1.0 Fractional Contribution Fe 56 n, n n, n' n, g n, 2n other threshold total Figure 8. Relative contributions of partial reactions to the total dpa cross-section of 56 Fe. dpa cross-sections; the difference of dpa cross-sections between these two sources ranges from 0.02 to 0.1 barns in these few energy points. 3.4 Comparison of 56 Fe dpa cross-section with NJOY-2016 Total dpa cross-sections of 56 Fe from ENDF/B-VII.1, computed by using CRaD and NJOY-2016, are given in figure 11. The dpa cross-section due to elastic and inelastic scattering reactions in 56 Fe are shown in figure 12. The spikes seen in the ratio plots in figures 11 and 12 around 1 kev energy region can be explained by using the NRT function in eq. (2.5). The second condition in this function says that there can be a displacement of only one atom if damage energy lies between E d and 2E d /β. This is the methodology followed in CRaD, whereas in NJOY, dpa cross-section is computed by multiplying the damage energy cross-section by a factorequalto0.8/2e d. For Fe with E d = 40 ev, this is equivalent to dividing the damage energy cross-section by 100 to get the dpa cross-section. So, according to the NRT model, recoils with damage energies between 40 and 100 ev (corresponding to incident neutrons of energy between 500 and 1500 ev) produce exactly one secondary displacement, whereas it ranges from 0.4 to 1, if NJOY data are used. Thus, the underprediction of dpa cross-sections with NJOY-2016 around 1 kev is because of neglecting the second condition of NRT function. It is to be noted that the ASTM standard uses

9 Pramana J. Phys. (2018) 90:46 Page 9 of Total DPA Cross Section (barns) 10 3 Fe 54 Fe 56 Fe 57 Fe 58 Fe Figure 9. Total dpa cross-sections of Fe and its isotopes from ENDF/B-VII.1 with CRaD. Total DPA Cross Section (barns) 10 3 Iron ASTM E (ENDF/B-VI) CRaD (ENDF/B-VII.1) Ratio CRaD / ASTM Figure 10. dpa cross-section of Fe in 640 energy groups: CRaD vs. ASTM E the complete NRT function for computing dpa crosssection. 3.5 Displacement rates in structural materials at different core locations of PFBR The elements Fe, Cr and Ni form important constituents in different types of structural steels. In PFBR [28], the clad and wrapper materials of the fuel and the blanket assemblies are made of D-9 steel, which contains about 66.1% of Fe, 14% of Cr and 15% of Ni (table 1). The grid plate and control plug of PFBR use SS-316-LN type steel. The reactor life is decided mainly based on the cumulative radiation damage on the structural materials of these core components. The grid plate at the core bottom houses all the fuel and blanket assemblies and also the primary sodium pumps, whereas the control plug is positioned above the core subassemblies that contain very critical components like thermocouples, neutron detectors and control rod drive mechanisms. The displacement rates in Fe, Cr and Ni at these selected core locations of PFBR is compared in table 2 by using the NRT-dpa cross-sections from NJOY-2016 and CRaD. For Fe, the comparison is also made with ASTM standard dpa cross-sections. At the core centre, Ni is found to have higher dpa rates than the other two elements because of higher dpa cross- sections. It is to be noted that the fuel and the blanket assemblies are replaced after 540 days of full power operation. The dpa cross-sections

10 46 Page 10 of 15 Pramana J. Phys. (2018) 90:46 Total DPA Cross Section (barns) 10 3 NJOY 2016 CRaD Fe Ratio CRaD / NJOY Figure 11. dpa cross-section of 56 Fe: CRaD vs. NJOY of D-9 steel are computed by weighting the dpa crosssections of its constituent elements with their elemental compositions. Since 26 group (ABBN-93) 3-D diffusion theory calculations are performed for estimating core neutronics parameters in PFBR, the dpa crosssections are also computed in this group structure for estimating dpa in core structural elements. The core- 1 flux is used to collapse the point dpa cross-sections. From table 3, it is interesting to note that the total dpa in D-9 steel at PFBR core centre is the lowest (79 dpa for three cycles of operation) with ENDF/B-IV based RECOIL dpa cross-sections. However, the predictions for this location by SPECTER, NJOY-2016 and CRaD are consistently higher by about 35, 36.8 and 38.8% respectively than that by RECOIL code. Similar trends are seen in other locations also. 3.6 The athermal recombination-corrected DPA model We have estimated the dpa cross-section of iron by CRaD using this model and compared with NRT-dpa in figure 13. The arc-dpa parameters used are E d = 40 ev, b ad = and c ad = The combined MD-BCA dpa cross-sections from the IAEA CRP [29] are also included in the comparison. The dpa in iron, estimated for 540 days with core-1 flux in PFBR isgivenintable4. It can be noted that a difference exists between the arc-dpa and MD-BCA methods of calculations. While an analytic function derived from a series of experimental and MD simulation results [16] is used to calculate the number of stable defects in the arc-dpa method, in the MD-BCA approach [29] these numbers are directly calculated by performing simulations. In general, the low-energy PKAs will be simulated by MD and PKAs with higher energies (approximately greater than 1 kev) by the BCA method. It is seen from table 4 that NRT model overpredicts the total dpa in Fe compared to the MD-BCA and arc-dpa approaches. The difference between arc-dpa and MD-BCA results (about 28%) could be due to the differences in the methodology of calculations noted above and errors in the elementspecific fitted parameters in arc-dpa model. 4. Summary and conclusions It is vital to estimate the important radiation damage parameters properly to assess the performance of structural materials in nuclear reactors. As noted earlier that the existing tools to quantify radiation damage have some shortcomings, an effort was initiated to develop an indigenous computer code CRaD for the purpose. The PKA spectra for Fe and dpa cross-sections of structural materials are computed from ENDF/B-VII.1 library by using CRaD. All the partial neutron nucleus reactions, including their anisotropy effects from 0 to 20 MeV, are taken into account in the calculations. The general agreement between results of CRaD and well-established code NJOY 2016 is found to be good. The Fe dpa cross-sections from CRaD are also found to compare well with the ASTM standard data. The NRT model gives an upper bound of the dpa crosssections. Improved model, like the arc-dpa, developed from the available experimental data and MD simulations for realistic prediction of dpa cross-sections is also

11 Pramana J. Phys. (2018) 90:46 Page 11 of DPA Cross Section (barns) Ratio NJOY 2016 n,n reaction in Fe 56 CRaD CRaD / NJOY (a) DPA Cross Section (barns) Ratio NJOY 2016 CRaD n,n' reaction in Fe CRaD / NJOY (b) Figure 12. dpa cross-section of 56 Fe due to (a) elastic and (b) inelastic scattering of neutrons. Table 1. Elemental composition in D9 steel. Element Fe Cr Ni Mo Mn C Si B wt% implemented in CRaD. It is worthwhile here to mention that although the estimate of damage from such advanced models and MD-BCA simulations compare closely to what is observed practically, a conservative approach has to be followed for selection of materials and deciding life of FBRs. The higher value of predicted dpa is safer. Hence, the NRT-dpa as standard is preferable from design considerations. The ENDF/B-VII.1-based NRT-dpa cross-sections from CRaD are applied for the damage assessment in the structural materials of the upcoming 500 MWe PFBR. The dose limit of 85 dpa [28] was used for the design of clad and wrapper materials in PFBR with D- 9 steel, based on the experimental correlations of dpa with the radiation damage. For this, the dpa estimation was made using the dpa cross-sections from RECOIL

12 46 Page 12 of 15 Pramana J. Phys. (2018) 90:46 Table 2. Comparison of dpa rates in Fe, Cr and Ni at selected core locations of PFBR. Element Code Core centre Grid plate top Lattice plate Radial blanket Fe ASTM 2.095E E E E 07 CRaD 2.081E E E E 07 NJOY 2.077E E E E 07 Ni CRaD 2.587E E E E 07 NJOY 2.586E E E E 07 Cr CRaD 2.279E E E E 07 NJOY 2.280E E E E 07 Table 3. Estimation of dpa in D9 steel in PFBR for three cycles (cycle length = 180 efpd). Neutron flux RECOIL (ENDF/B-IV) Total dpa for 540 effective full power days of operation SPECTER (ENDF/B-V) NJOY-2016 (ENDF/B-VII.1) CRaD (ENDF/B-VII.1) Averaged over inner core Inner core maximum a Outer core maximum Radial blanket maximum a Peak flux is 8E+15 n/cm 2 /s Total DPA Cross Section (barns) 10 3 NRT Model (CRaD) ARC-DPA Model (CRaD) Combined MD-BCA (IAEA-CRP) Iron Figure 13. Total dpa cross-section of Fe from different models. Table 4. Comparison of dpa in iron for three cycles (cycle length = 180 efpd). Element IAEA CRP (Combined MD-BCA) CRaD (ARC-DPA) CRaD (NRT) ASTM (NRT) NJOY (NRT) SPECTER (NRT) RECOIL (NRT) Iron code. In the present analysis, it is found that dpa in D- 9 steel, with CRaD, SPECTER and NJOY-2016 codes, is overpredicted by about 35% with respect to RECOIL code. This observation clearly highlights the importance of renormalisation of experimental correlations of dpa and radiation damage to ensure consistency of damage prediction with ENDF/B-VII.1 library for PFBR applications. In the case of accelerator-driven systems,

13 Pramana J. Phys. (2018) 90:46 Page 13 of components like target window experience more than 100 dpa [30]. The nuclear data needs of such systems have been discussed in [31]. The finding in our present work for fast reactors, such as PFBR, that the dpa with the use ofnucleardata fromendf/b-vii.1 differs from the older dpa calculations is generic and may apply to assessments or predictions of radiation damage to components in fusion reactors and accelerator-driven subcritical systems [32,33]. Acknowledgements The authors gratefully acknowledge Dr V Gopalakrishnan, former Head, Nuclear Data Section, Reactor Design Group, IGCAR, for his keen interest and the initiatives made for developing an Indian radiation damage code for fast reactor applications. His guidance and encouragement for this work are also acknowledged. Appendix A A.1 Group averaging point dpa cross-section The point dpa cross-section is group-averaged into a neutron group structure using eq. (A.1). This expression shows the total multigrouped dpa cross-section in the gth neutron group. σ t D, g = Eg(max) E g(min) Eg(max) E g(min) σ t D (E)ϕ(E)dE ϕ(e)de A.2 Reaction kinematics. (A.1) The energy cross-section data for different reactions i are given in different sections of file 3 of ENDF/B-VII.1 tape for the material. The kernel of energy transfer for each reaction depends on the kinematics of neutron nucleus reaction. These are briefly given below [5,18, 19,21,24,34,35]. A.2.1 Elastic and resolved level inelastic scattering. E R = AE (A + 1) 2 (1 2Rμ + R2 ), (A.2) (A + 1)( Q) R = 1, AE K (E, E R ) = 1 NL 2l + 1 a l (E)P l (μ), (A.3) 2π 2 l=0 where Q is the Q-value for discrete inelastic scattering to take place from a particular level. μ is the centre of mass cosine of angle of scattering of the neutron. The incident energy-secondary angular parameters, a l (E) or the full summation in eq. (A.3) are given in file 4 section 2 for elastic scattering. For discrete inelastic scattering a l (E) are given in sections of either file 4 or file 6. A.2.2 Continuum inelastic scattering and (n, 2n) reaction. The secondary particle energy distribution is either given in file 5 or file 6. File 6 may also contain the product energy-angle distribution and recoil energy distribution for these reactions. If the recoil energy distribution is available, then these data are used from the file. If such data are not available, evaporation model of nuclear reaction is adapted. In this model, the energy transfer kernel is given as follows: A Continuum inelastic scattering. E max K (E, E R ) = de f (E, E ) 0 4 A+1 1. (A.4) (EE ) 1/2 The maximum value of E is E = A ( Q l + A ) A + 1 A + 1 E, where Q l is the Q-value for the lowest level. The distribution function f (E, E ) represents the probability that a neutron of energy E in the centre of mass frame is evaporated from the compound nucleus. In the centre of mass frame it is given as the Maxwellian of nuclear temperature E D = kt: f (E, E ) = E I (E) e E /E D, where [ I (E) = ED 2 1 (1 + E max E D is a normalization factor such that E max 0 de f (E, E ) = 1. A (n, 2n) Reaction. K (E, E R ) = E max 0 E E 0 E I (E) e E /E D ) e E max /E D ] (A.5) (A.6) (A.7) E I (E, E ) e E /E D de de, (A.8) where I (E) is given by eq. (A.6) with E max = E and I (E, E ) isgivenbyeq.(a.6) with E max replaced by E max = E E.

14 46 Page 14 of 15 Pramana J. Phys. (2018) 90:46 The recoil energies in these two reactions can be found by E R (E, E,μ)= 1 A (E 2μ EE + E ), (A.9) where μ is the laboratory cosine of the angle of emission of secondary neutron. A.2.3 Threshold n, particle reactions. File 6 of the ENDF/B-VII.1 tape for the material may contain the recoil energy distribution for these reactions in specific sections. These data are used when available. If such data are not available, then the recoil energy is found from the following equations: E R = 1 A + 1 (E 2 ae E p cos φ + ae p ), (A.10) where a is ratio of the emitted particle mass to neutron mass, E (A + 1 a) = E A + 1 and energy of the emitted particle E p is approximately chosen as the smaller value between the available energy Q + AE A + 1 and the Coulomb barrier energy zz a 1/3 + A 1/3 in ev z and Z being charges of the emitted particle and the target respectively. The energy transfer kernel in this case (considering isotropic emission of recoil atom) is K (E, E R ) = A.2.4 (n, γ ) reaction. E R = 1 E Rmax (E) E Rmin (E). E E A A + 1 E 2 γ 2(A + 1)mc 2 cos φ (A.11) Eγ 2 + 2(A + 1)mc 2. (A.12) The average of Eγ 2 is evaluated from the gamma yield data given in file 12 for discrete gamma and distribution given in file 15 for continuum gamma. The damage energy from this reaction is calculated from recoil energy considering isotropic gamma emission. References [1] F Seitz, Discuss. Faraday Soc. 5, 271 (1949) [2] W S Snyder and J Neufeld, Phys. Rev. 97, 1636 (1955) [3] F A Garner, Comprehens. Nucl. Mater. 4, 33 (2012) [4] L R Greenwood, J. Nucl. Mater. 216, 29 (1994) [5] Gary S Was, Fundamentals of radiation materials science (Springer, New York, 2007) [6] L I Ivanov and Yu M Platov, Radiation physics of metals and its applications (Cambridge International Science Publishing, 2004) pp [7] M J Norgett, M T Robinson and I M Torrens, Nucl. Eng. Des. 33, 50 (1975) [8] M T Robinson and I M Torrens, Phys. Rev. B 9, 5008 (1974) [9] J Lindhard, V Nielsen, M Scharff and P V Thomsen, Mat. Fys. Medd. Dan. Vid. Selsk. 33(10) (1963) [10] J Lindhard, M Scharff and H E Schiøtt, Mat. Fys. Medd. Dan. Vid. Selsk. 33(14), 1 (1963) [11] G H Kinchin and R S Pease, Rep. Prog. Phys. 18(1), 1 (1955) [12] D J Bacon, F Gao and Yu N Osetsky, Nucl. Instrum. Methods 153, 87 (1999) [13] R S Averback, R Benedek and K L Merkle, Phys. Rev. B 18, 4156 (1978) [14] J H Kinney, M W Guinan and Z A Munir, J. Nucl. Mater , 1028 (1984) [15] P Jung, J. Nucl. Mater. 117, 70 (1983) [16] Kai Nordlund et al, Primary radiation damage in materials, Report Nuclear Science NEA/NSC/DOC (2015) 9, OECD/NEA, 2015 [17] R E Stoller, L R Greenwood and S P Simakov, Primary radiation damage cross sections, Report INDC (NDS)-0691 (IAEA Headquarters, Vienna, Austria, 2015) [18] T A Gabriel, J D Amburgey and N M Greene, Radiation damage calculations: Primary recoil spectra, displacement rates, and gas production rates, Report ORNL/TM-5160 (Oak Ridge National Laboratory, 1976) [19] L R Greenwood and R K Smither, SPECTER: Neutron damage calculations for materials irradiations, Report ANL/FPP/TM-197 (Argonne National Laboratory, 1985) [20] M B Chadwick et al, Nuclear Data Sheets 112, 2887 (2011) [21] A C Kahler, The NJOY nuclear data processing system, Version 2016, Report LA-UR (Los Alamos National Laboratory, 2016) [22] R S Averback and K L Merkle, Phys. Rev. B 16, 3860 (1977) [23] L Malerba, J. Nucl. Mater. 351, 28 (2006) [24] J D Jenkins, Nucl. Sci. Eng. 41, 155 (1970) [25] W Sheely, Nucl. Sci. Eng. 29, 165 (1967) [26] Uttiyoarnab Saha and K Devan, Proceedings of the DAE-BRNS Symp. on Nucl. Phys. (2016) Vol. 61, pp

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