Neutron Radiation Damage Studies in the Structural Materials of a 500 Mwe Fast Breeder Reactor Using DPA Cross-Sections from ENDF/B-VII.1

Pramana – J. Phys. (2018) 90:46 © Indian Academy of Sciences https://doi.org/10.1007/s12043-018-1536-y

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 SAHA1 ,∗,KDEVAN1, ABHITAB BACHCHAN1, G PANDIKUMAR1 and S GANESAN2

1Reactor Neutronics Division, Reactor Design Group, Indira Gandhi Centre for Atomic Research, Homi Bhabha National Institue, Kalpakkam 603 102, India 2Bhabha Atomic Research Centre, Mumbai 400 085, India ∗Corresponding author. E-mail: [email protected]

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 28.41.−i; 28.41.Ak; 28.41.Qb; 28.50.Ft

1. Introduction required to knock off a lattice atom, called lattice displacement energy, is usually in the range of 20Ð100 eV It is well known that interaction of neutrons or ionis- in metals and its alloys. It is material-dependent. The ing particles with the nuclear materials for a prolonged atom that is hit by a neutron is known as primary-knock- period of time results in radiation damage by continu- on atom (PKA). If a PKA has enough kinetic energy, it ously dislodging atoms from their normal lattice sites. can knock off another lattice atom (called secondary Because of energy transfer due to interaction, a suffi- knock-on atom) during its movement beyond a lattice ciently energetic particle incident on a target displaces distance, and this mechanism may lead to a cascade an atom from its lattice site to an interstitial posi- of displacements. Part of PKA energy is lost in elec- tion, leaving behind a vacant lattice position [1,2]. In tronic excitation, and the rest, known as the damage a nuclear reactor, such damage happens mainly due to energy, builds up the displacement cascade. When the (a) elastic and inelastic collisions of neutrons with the cascade cools down, many of the displaced atoms return nuclei, (b) recoil of a nucleus on emission of an ener- to their original sites or vacant sites elsewhere in the getic particle after neutron absorption and (c) energy lattice (recombination). A large number of atom replace- transfer by the replaced atoms and other secondary par- ments reduce the actual number of defects that could ticles with the lattice atoms. The minimum energy Ed be produced by atom displacements. This is only a 46 Page 2 of 15 Pramana – J. Phys. (2018) 90:46 fraction of the initially displaced atoms, known as IAEA-CRP on primary radiation damage cross-sections damage efficiency. The complex process of primary [17]. radiation damage and its evolution are explained sat- At Indira Gandhi Centre for Atomic Research isfactorily by observing the changes in macroscopic (IGCAR), the codes RECOIL (ORNL) [18], based on properties of irradiated materials, viz. swelling, creep, ENDF/B-IV (1974) and SPECTER (ANL) [19], based embrittlement, stress corrosion cracking etc. and corre- on ENDF/B-V (1979) are being used for radiation lating them with radiation dose. Two parameters, fluence damage studies in fast reactors. These two codes have and absorbed dose, are used to characterise the effects their own in-built database of neutron cross-sections of neutron irradiations in a nuclear reactor. The spec- and PKA spectra for all relevant reactions in multi- trum details of incident neutrons are considered only in group forms which are not amenable to update by the the latter one. The fluence approach is hence not suited user. These codes work satisfactorily, but they have for irradiations in the fields of varying neutron spectrum; limitations in group structure and the data are three- damage cascade being very sensitive to the energy spec- decade-old. Though, all fast reactor core neutronics trum of PKAs which in turn is dependent on the incident calculations are done using cross-section sets based on neutron energy and the type of interaction with the tar- more recent libraries, viz. ENDF/B-VII.1, JEFF-3.1, get material. The radiation damage due to absorbed dose JENDL-4.0 etc., three-decade-old displacement cross- in structural materials is often quantified by a parame- sections from RECOIL code are still continued to be ter called displacement per atom (dpa) which means the used for the prediction of dpa in structural materials, average number of times an atom is displaced from its due to the non-availability of computer code to compute lattice site during the period of irradiation. It is a measure dpa cross-sections from the above files. Compared to of the energy deposited in the material by the interacting the previous libraries, the recent libraries are evaluated particles which is correlated well with the damage- with improved nuclear reaction models and state-of-the- related parameters. It can be applied in high-energy ion art experimental data. In the evaluation of the resonance and electron irradiation experiments to simulate neu- parameters, the present approach is to use ReichÐMoore tron damage in shorter time periods [3Ð5]. However, the formalism instead of the MLBW approach followed in dpa lacks information about the structural composition the past. In these files, the ranges of resolved resonances of the defects induced by radiation. The concentra- are extended to the unresolved resonance region. More tion of freely migrating defects is sometimes used importance is given to quantify and tabulate the covari- to incorporate diffusion effects of defects at elevated ance data. In particular, the database in ENDF/B-VII.1 temperatures [6]. (which is being considered in the present work) has Since 1975, the secondary displacement model of the data representing energy and angle information of Norgett, Robinson and Torrens, called simply as NRT secondary particles in a reaction. More features of the model, has been used as the standard to compute the latest evaluated libraries can be found in [20] and other number of stable defects in nuclear materials exposed related references. More accurate anisotropic scatter- to high-energy particles [7]. In this model, the par- ing and recoil energy distribution data in these libraries titioning of PKA energy and estimation of damage are expected to have significant impact on dpa cross- energy are done by using the Robinson’s partition sections. Though, the HEATR module of the NJOY function [8], which is based on the theory of Lind- code [21] has the capability to process these files, it hard et al [9,10].TheNRTmodelisanimprove- was not licensed to India till February 2017. Further, ment over the KinchinÐPease (KP) atom displace- this module also has the limitations of (a) explicitly ment model [11]. It is observed that under various not giving the PKA spectra of all partial reactions and physical conditions, the number of existing defects (b) not implementing the latest damage models like observed is very less compared to the original number arc-dpa for dpa cross-sections. Also the dpa cross- of displacements produced [12]. Molecular dynamics section obtained from HEATR deviates slightly from (MD) simulations and cryogenic irradiation experi- NRT definition (discussed later). These shortfalls in ments have shown that the number of stable vacan- the above modules/codes have motivated us in devel- cies and interstitials existing in irradiated materials is oping an indigenous computer code to calculate dpa about 20Ð40% of the NRT value [12Ð15]. Recently, cross-sections from the recent evaluated libraries for fast more advanced displacement damage models are devel- reactor applications. Since radiation damage in struc- oped with more insight into the physical processes tural materials limits the fuel burn-up and plant life in that occur during the evolution of the secondary col- fast reactors, establishing the capability of more realistic lision cascade [16]. The replacement per atom (rpa) estimation of radiation damage in nuclear materials is model and athermal recombination-corrected dpa (arc- an important step to realise India’s future programme of dpa) model are the two major outcomes of the recent sodium-cooled fast reactors with improved economics, Pramana – J. Phys. (2018) 90:46 Page 3 of 15 46 ERmax safety and reliability. In this paper, we mainly report σ t ( ) = σ i ( ) i ( , )ν[ ( )]. D E E dER K E ER T ER the details of developing a code called computation of 0 radiation damage (CRaD) and its application to var- i ious studies for PFBR core structural materials. The (2.3) importance of PKA spectra is highlighted by comput- i ( , ) ing the average energy of PKA for different neutron The function K E ER is the kernel of energy trans- flux spectra. The relative contributions of various neu- fer ER to the PKA through a nuclear reaction of type i σ i tron reactions to total dpa cross-sections are discussed, with cross-section (E). The kernel of energy transfer with Fe-56 as an example. A comparative study of NRT- for each reaction depends on the kinematics of neutronÐ dpa for Fe from CRaD is made with other sources of nucleus reaction. These are briefly given in ‘Appendix data, viz. RECOIL, SPECTER, NJOY-2016 and ASTM A’. The damage energy T corresponds to the effective E693-12. Total dpa of D-9 alloy corresponding to PFBR energy available for damage production after correct- spectra for 540 days of full power operation are cal- ing for the energy losses due to electronic excitation ν[ ( )] culated and compared. The arc-dpa model-based dpa and ionisation. T ER is the secondary displacement ( ) cross-sections of Fe are found using CRaD and its damage function. Here the damage energy T ER is impact on total dpa estimation in PFBR is also seen. found from Robinson partition function [8]givenin eqs (2.4a)and(2.4b):

E T (E ) = R , (2.4a) 2. Method of computing displacement per atom R 1 + FG(ε) cross-sections where F, G and ε are defined as The fundamental quantity that is required to estimate dpa rate in a known neutron flux field is dpa cross- . 2/3 1/2( + )3/2 0 0793Z1 Z2 A1 A2 section, σ (E). It gives the chance estimate for an atom F = , D 2/3 + 2/3 3/4 3/2 1/2 to get displaced from its lattice site. Total dpa in a mate- Z1 Z2 A1 A2 / / rial at a particular reactor location is found by integrating G = 3.4008ε1 6 + 0.40244ε3 4 + ε, σD(E) over the entire neutron energy fluence at the loca- E ε = R . tion. The value of σD(E) is computed by convoluting 2/3 2/3 1/2 30.724Z1 Z2 Z + Z (A1 + A2)/A2 the PKA energy spectrum (σPKA(E, ER)) and the sec- 1 2 ondary damage function ν[T (ER)] (of damage energy (2.4b) T ) over the whole range of recoil energy ER. PKA spectrum is the fundamental quantity dictating the radiation Here Z and A with suffixes 1 and 2 denote the atomic effects in a material. It is discussed below. The rate of and mass numbers of the recoil and lattice nuclei respec- atomic displacements in a material due to exposure to tively. The number of displacements undergone per neutrons of energy E can be expressed as atom is found from the NRT displacement damage model function ν(T ). R(E) = NσD(E)ϕ(E), (2.1) where N is the atom density (number of atoms per unit 2.1 The NRT model 2 volume), ϕ(E) is the neutron flux (n/cm /s) and σD(E) is the displacement per atom cross-section (cm2).The The NRT displacement damage model function ν(T ) to quantity R(E)/N gives the number of displacements per compute the number of defects is given by atom per second (dpa/s) caused by neutrons of energy ⎧ E. The total dpa in the material due to neutron irradiation ⎨ 0; T < Ed ϕ( ) ν( ) = ; ≤ < /β . with a flux spectrum of E for a time period of t T ⎩ 1 Ed T 2Ed (2.5) seconds is βT/2Ed; T ≥ 2Ed/β Emax = φ( )σ t ( ), Here, β is the damage efficiency (arising from the poten- DPA t dE E D E (2.2) Emin tial scattering of atoms) which is equal to 0.8. It is independent of PKA energy and the target material. In σ t ( ) = σ i ( ) where D E i D E is the total dpa cross-section this model, the material is assumed to be monoatomic which is equal to the sum of displacement cross-sections with atomic number Z and atomic mass A. Ed is the σ i ( ) = due to all possible neutron interactions, D E , of type lattice displacement energy. It is to be noted that Ed i. It is estimated as 40 eV, irrespective of the target, as the NRT standard. 46 Page 4 of 15 Pramana – J. Phys. (2018) 90:46

2.2 Athermal recombination-corrected displacement values −0.568 (±0.020) and 0.286 (±0.005) for bad per atom (arc-dpa) model and cad respectively [16].

The KP or NRT dpa model is known to overestimate the number of Frenkel pairs in metals. These models assume 2.3 Primary knock-on atom (PKA) spectra that damage occurs linearly with deposited energy. But MD simulation and experimental evidences show that The neutron interaction cross-section σi (E) for the the damage is less than what is expected from these reaction i multiplied with the kernel of energy transfer models when the deposited energy is well above the from E to ER, Ki (E, ER), gives the differential recoil threshold displacement energy [13,22]. The displaced energy transfer cross-section dσi (E)/dER or PKA spec- atoms have sufficient kinetic energies so that vacancies trum for the reaction. Ki(E, ER) gives the probability and interstitials recombine and the final damage pro- that a nucleus will recoil with energy ER, after undergo- duced is less than the initial displacements produced. ing a reaction of type i (i = (n, n); (n, n); (n, 2n); (n, 3n); This phenomenon is independent of thermal-assisted (n, p); (n, α); etc.) with a neutron of energy E.Total defect migration and can occur even at 0 K. Hence the recoil spectra are obtained by adding the contribution damage efficiency reduces from 0.8 considered in NRT from all partial reactions. From eq. (2.3), it can be seen model. It is actually energy-dependent varying from 0.5 that the dpa cross-section is obtained by integrating the to 0.2, with majority of experiments agreeing at 0.3 [23]. displacement damage function over recoil atom spec- The arc-dpa model has been developed to address the trum. The two-body collision kinematics (see ‘Appendix shortcomings of the NRT model. The damage efficiency A’) and the data from ENDF/B-VII.1 library are used function ξ, which is defined as the ratio of true defects for its computation. Total PKA spectrum is a function to number of defects predicted by the NRT model is of recoil atom energy which depends on the incident obtained by performing MD simulations [16]. The num- neutron energy and the energy and angular distributions ber of displacements in this model is given as ⎧ of ejected secondary particles (neutrons, charged particles). The total dσ/dER of each isotope is calculated ⎨ 0; T < Ed ν( ) = ; ≤ < /β and then they are added with respective abundances to T ⎩ 1 Ed T 2Ed (2.6) βT ξ(T )/2E ; T ≥ 2E /β get overall contribution in iron. Total PKA spectrum d d averaged over a neutron flux spectrum φ(E) due to all where possible reaction channels is 1 − c ad bad ξ(T ) = T + cad. (2.7) bad E i (2Ed/β) max dσ (E, E ) R φ(E)dE Therefore, in the arc-dpa formalism three material- dσ(E ) i dE R = Emin R . specific parameters Ed, bad and cad are required to be dE Emax R φ( ) known. Here bad and cad are dimensionless parame- E dE ters obtained by fitting the results from MD simulations Emin and experiments. From [16], it is noted that the num- (2.8) ber of Frenkel pairs follows a power-law relation with the damage energy at intermediate energies. As energy The neutron spectrum-averaged energy of the primary increases, the cascades tend to split either completely recoil atoms is calculated as or incompletely into several subcascades, indicating a linear scaling with damage energy. The parameter bad E E max Rmax dσ(E, ER) gives the point where the cascade behaviour changes dEϕ(E) dER ER E E dER from the power law to linear scaling. In a way, it tells ( )ϕ = min Rmin . ER avg how rapidly the residual damage approaches the sat- Emax ERmax σ( , ) ϕ( ) d E ER uration value by athermal recombination beyond the dE E dER E E dER onset of the formation of subcascades. The saturation min Rmin (2.9) is dictated by the parameter cad. A low value of this parameter (typical in high-density low-melting point materials) signifies that the interstitials transport less The PKA spectrum per unit interaction averaged over efficiently to the outer periphery of the displacement the incident neutron energy spectrum ϕ tells about the cascade and recombination is more likely to take place. recoil atoms at a particular energy ER and carries the A LevenbergÐMarquardt least squares fit to the experi- information of the incident neutrons [24]. It is defined mental and MD data in the case of iron has resulted in by Pramana – J. Phys. (2018) 90:46 Page 5 of 15 46

2 3. CRaD code 10

1 The main objective of the CRaD code is to compute 10 the PKA spectra and dpa cross-sections due to neutron interactions by using the data from the recent evaluated 0 10 nuclear data libraries like ENDF/B-VII.1. It is writ- ten in FORTRAN 95. Subsequently, its scope will be -1 (barns/ eV) R 10 extended to the estimation of various allied quantities in the radiation damage study, like radiation heating,

/ dE -2

σ 10

d etc. The relevant data, viz. neutron interaction cross- 10 7 -3 Iron section, angle of scattering, secondary energy distri- 10 -2 -1 10 6 10 0 bution, scattering anisotropy, secondary energyÐangle 10 10 1 10 2 distribution, etc. are extracted from the basic/processed 10 3 10 5 10 4 / 10 5 ENDF B-VII.1 library. Each neutronÐnucleus interac- Recoil Energy (eV) 10 6 10 tion is treated separately to compute its contribution Neutron Energy (eV) to the dpa cross-section. The dpa cross-section from a reaction is found at all neutron energies for which Figure 1. A typical PKA spectrum matrix for Fe. the reaction cross-sections are available. The total dpa Emax cross-section is computed by adding the contribution of i i dEσ (E)ϕ(E)K (E, ER) all partial reactions in a union energy grid. The CRaD i ( ) = Emin . gives dpa cross-section data both in point-wise and in K ER Emax multigroup forms. For multigrouping, a few in-built dEσ i (E)ϕ(E) i standard weighting functions and group structures are Emin (2.10) provided. The groups structures considered are: SAND- II extended (640 groups), VITAMIN-J (175 groups), The fraction of recoil atoms above some energy ER is DLC-2 (100 groups), ABBN-93 (26 groups). A few then estimated by eq. (2.11), which gives the compara- results from CRaD are discussed below. tive estimates of recoils having different energies due to the neutrons in the full energy range. 3.1 Primary knock-on atom spectra Fraction of recoils above energy (E ) R ERmax A neutron of energy E can produce a recoil atom with a K (ER)dER range of energies depending upon the type of interaction = ER . it undergoes. Here we have calculated the group-to- E (2.11) Rmax group recoil spectrum matrices K a→b due to various K (ER)dER ij reaction channels, represented as a → b. The incident ERmin

101 13 MeV Neutron 100 total

10-1 n, n

-2 n, n' (barns/eV) 10 R / dE -3 σ 10 d threshold reactions (n, x)*10000 10-4 (n, 2n)*10000

10-5 0.0 2.0x105 4.0x105 6.0x105 8.0x105 1.0x106 Recoil Energy (eV)

Figure 2. PKA spectra for various interactions of neutron with a 56Fe nucleus. 46 Page 6 of 15 Pramana – J. Phys. (2018) 90:46

1020

-s) PFBR Core Centre 19 2 10 PFBR Radial Blanket 1018 PFBR Grid Plate Top 1017 PFBR Lattice Plate 1016 1015 1014 1013 1012 1011 1010 109 108 107 Neutron Flux per Unit Lethargy (eV/cm

10-3 10-2 10-1 100 101 102 103 104 105 106 107 Neutron Energy (eV)

Figure 3. 175-group neutron ﬂux per unit lethargy at different locations of PFBR. neutron and recoil energy groups are represented by 100

the indices i and j respectively. Each of them uses a ) VITAMIN-J 175-group structure. A typical 3D plot of R PKA spectrum matrix for Fe is shown in figure 1.A 56 snap-shot of PKA spectra in Fe for a 13 MeV incident 10-1 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 -2 10 PFBR Core Centre plotted in figure 4. The spectrum of the recoil nucleus PFBR Radial Blanket due to radiative capture of neutrons is not included here.

Fraction of Recoils Above (E PFBR Grid Plate Top At neutron energies lower than Ed, the recoil due to PFBR Lattice Plate γ (n, ) reaction can give rise to recoil to the residual 10-3 nucleus, but it is not very significant in the intermediate 10-2 10-1 100 101 102 103 104 105 106 and higher neutron energies. From figure 4, it is seen Recoil Energy (eV) that the fraction of higher energy recoil atoms at the core centre is comparatively more than what is found Figure 4. Fraction of recoil atoms in Fe above certain recoil at other three locations. While about 54% of the recoils energy for different flux spectra at different locations in PFBR. are above 24.5keV in the core centre, it is about 50, 24 and 20% in the radial blanket, grid plate top and lattice anisotropy in scattering reactions are accounted in the plate locations respectively. The average PKA energies calculation. The anisotropy in neutron scattering is estimated using eq. (2.9) for the neutron fluxes at vari- seen to play an important role in lowering the dpa ous locations of the PFBR is shown in figure 5.Average cross-section [25,26]. This case of elastic scattering energy of PKA is 35.9 keV at the core centre and at the of neutrons in 56Fe is illustrated in figure 6. Inelastic grid plate location it is 5.9 keV. It is observed in the case scattering and other high-energy reactions also show of iron, that the average recoil energy from (n, γ ) reac- anisotropy, but to a very small extent. From figures 7 and tion is rather small, compared to other partial reactions. 8, it can be seen that in the low-energy region the recoil It is also to be noted that the actual rate of production of of the nucleus following radiative capture of neutrons recoils depends on the absolute value of neutron flux. is the sole contributor to dpa cross-section. The contribution from neutron-induced elastic scattering starts 3.2 Displacement per atom cross-section from around hundreds of eV of incident neutron energies and remains over the whole energy range. In the In CRaD, the contributions from all the important MeV region, as scattering becomes anisotropic, its con- neutronÐnucleus interactions including the effect of tribution slightly decreases. In these energies, inelastic Pramana – J. Phys. (2018) 90:46 Page 7 of 15 46

35.94 35

30 25.67 25

10 7.73 5.86 Average PKA Energy (keV) 5

0 Core Centre Radial Blanket Grid Plate Top Lattice Plate Location

Figure 5. The average recoil energies in Fe at different core locations of PFBR.

105

104

103

102

101 DPA Cross Section (barns) 100 56Fe Isotropic Elastic Scattering Anisotropic Elastic Scattering 10-1 102 103 104 105 106 107 108 Neutron Energy (eV)

Figure 6. The effect of anisotropic scattering on dpa cross-section in 56Fe. scattering and other non-elastic reactions have signifi- and neutron flux spectrum. The correlation of radia- cant contributions. Isotope-wise dpa cross-section of Fe tion effects are beyond the scope of this procedure. The is shown in figure 9. The dpa cross-section of Fe is com- ASTM NRT-dpa cross-sections were processed from puted by weighting with the abundance of its constituent ENDF/B-VI library by using NJOY code in the 640 isotopes. extended SAND-II group structure. There is not much change in the iron cross-sections of ENDF/B-VI and 3.3 Comparison of Fe dpa cross-section with ASTM VII.1 libraries. No reference is provided for the mate- E693-12 standard rial temperature, self-shielding effect and the weighting function. For comparing with ASTM NRT-dpa cross- The dpa cross-sections of Fe from CRaD are compared sections, we have assumed a constant weighting flux in with the latest, ASTM (American Society for Test- eq. (A.1) for averaging dpa cross-sections of Fe at room ing and Materials) dpa cross-sections. ASTM E-693-12 temperature. The ASTM and CRaD dpa cross-sections [27] gives a standard practice for characterising neu- for iron are shown in figure 10. The spikes seen in the tron exposures in iron and low alloy steels in terms of ratio plot around the energy region where contribution displacement per atom (dpa). The application of this from elastic scattering starts is primarily due to numer- practice requires the knowledge of total neutron fluence ical errors involved in predicting too small values of 46 Page 8 of 15 Pramana – J. Phys. (2018) 90:46

103 n, n n, n'

2 n, g 10 n, 2n other threshold 101 total

100

10-1

10-2 DPA Cross Section (barns)

10-3 Fe 56

10-4 101 102 103 104 105 106 107 Neutron Energy (eV)

Figure 7. dpa cross-sections due to partial neutron interactions in 56Fe.

1.0

Fe 56 0.8

0.6 n, n n, n' n, g 0.4 n, 2n other threshold

Fractional Contribution total 0.2

0.0 101 102 103 104 105 106 107 Neutron Energy (eV)

Figure 8. Relative contributions of partial reactions to the total dpa cross-section of 56Fe.

dpa cross-sections; the difference of dpa cross-sections only one atom if damage energy lies between Ed and between these two sources ranges from 0.02 to 0.1 barns 2Ed/β. This is the methodology followed in CRaD, in these few energy points. whereas in NJOY, dpa cross-section is computed by multiplying the damage energy cross-section by a fac- 56 3.4 Comparison of Fe dpa cross-section with torequalto0.8/2Ed. For Fe with Ed = 40 eV, this is NJOY-2016 equivalent to dividing the damage energy cross-section by 100 to get the dpa cross-section. So, according to Total dpa cross-sections of 56Fe from ENDF/B-VII.1, the NRT model, recoils with damage energies between computed by using CRaD and NJOY-2016, are given 40 and 100eV (corresponding to incident neutrons of in figure 11. The dpa cross-section due to elastic and energy between ∼500 and 1500eV) produce exactly inelastic scattering reactions in 56Fe are shown in figure one secondary displacement, whereas it ranges from 0.4 12. The spikes seen in the ratio plots in figures 11 and 12 to 1, if NJOY data are used. Thus, the underprediction around 1keV energy region can be explained by using of dpa cross-sections with NJOY-2016 around 1 keV the NRT function in eq. (2.5). The second condition in is because of neglecting the second condition of NRT this function says that there can be a displacement of function. It is to be noted that the ASTM standard uses Pramana – J. Phys. (2018) 90:46 Page 9 of 15 46

103 Fe 54 Fe 56 Fe 57 102 Fe 58 Fe

101

100

10-1 Total DPA Cross Section (barns)

10-2 100 101 102 103 104 105 106 107 Neutron Energy (eV)

Figure 9. Total dpa cross-sections of Fe and its isotopes from ENDF/B-VII.1 with CRaD.

10 3 ASTM E693-12 (ENDF/B-VI) CRaD (ENDF/B-VII.1) 10 2

10 1

10 0

10-1 Iron 10-2 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 Total DPA Cross Section (barns)

1.4 1.2 CRaD / ASTM 1.0 Ratio 0.8 0.6

10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 Neutron Energy (eV)

Figure 10. dpa cross-section of Fe in 640 energy groups: CRaD vs. ASTM E693-12. the complete NRT function for computing dpa cross- of these core components. The grid plate at the core bot- section. tom 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 3.5 Displacement rates in structural materials at very critical components like thermocouples, neutron different core locations of PFBR detectors and control rod drive mechanisms. The displacement rates in Fe, Cr and Ni at these selected core The elements Fe, Cr and Ni form important constituents locations of PFBR is compared in table 2 by using the in different types of structural steels. In PFBR [28], the NRT-dpa cross-sections from NJOY-2016 and CRaD. clad and wrapper materials of the fuel and the blanket For Fe, the comparison is also made with ASTM stan- assemblies are made of D-9 steel, which contains about dard dpa cross-sections. At the core centre, Ni is found 66.1% of Fe, 14% of Cr and 15% of Ni (table 1). The to have higher dpa rates than the other two elements grid plate and control plug of PFBR use SS-316-LN type because of higher dpa cross- sections. It is to be noted steel. The reactor life is decided mainly based on the that the fuel and the blanket assemblies are replaced after cumulative radiation damage on the structural materials 540 days of full power operation. The dpa cross-sections 46 Page 10 of 15 Pramana – J. Phys. (2018) 90:46

103 NJOY 2016 CRaD 102

101

100

10-1 Fe 56

10-2 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 Total DPA Cross Section (barns)

2.8 2.4 CRaD / NJOY 2016 2.0 1.6

Ratio 1.2 0.8 0.4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 Neutron Energy (eV)

Figure 11. dpa cross-section of 56Fe: CRaD vs. NJOY-2016. of D-9 steel are computed by weighting the dpa cross- numbers are directly calculated by performing simula- sections of its constituent elements with their elemental tions. In general, the low-energy PKAs will be simulated compositions. Since 26 group (ABBN-93) 3-D diffu- by MD and PKAs with higher energies (approximately sion theory calculations are performed for estimating greater than 1 keV) by the BCA method. It is seen from core neutronics parameters in PFBR, the dpa cross- table 4 that NRT model overpredicts the total dpa in Fe sections are also computed in this group structure for compared to the MD-BCA and arc-dpa approaches. The estimating dpa in core structural elements. The core- difference between arc-dpa and MD-BCA results (about 1 flux is used to collapse the point dpa cross-sections. 28%) could be due to the differences in the methodology From table 3, it is interesting to note that the total dpa of calculations noted above and errors in the element- in D-9 steel at PFBR core centre is the lowest (79 dpa specific fitted parameters in arc-dpa model. 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 4. Summary and conclusions are consistently higher by about 35, 36.8 and 38.8% respectively than that by RECOIL code. Similar trends It is vital to estimate the important radiation damage are seen in other locations also. parameters properly to assess the performance of structural materials in nuclear reactors. As noted earlier that 3.6 The athermal recombination-corrected DPA the existing tools to quantify radiation damage have model some shortcomings, an effort was initiated to develop an indigenous computer code CRaD for the purpose. We have estimated the dpa cross-section of iron by The PKA spectra for Fe and dpa cross-sections of CRaD using this model and compared with NRT-dpa structural materials are computed from ENDF/B-VII.1 in figure 13. The arc-dpa parameters used are Ed = library by using CRaD. All the partial neutron nucleus 40 eV, bad =−0.568 and cad = 0.286. The com- reactions, including their anisotropy effects from 0 to bined MD-BCA dpa cross-sections from the IAEA CRP 20 MeV, are taken into account in the calculations. [29] are also included in the comparison. The dpa in The general agreement between results of CRaD and iron, estimated for 540 days with core-1 flux in PFBR well-established code NJOY 2016 is found to be good. isgivenintable4. It can be noted that a difference The Fe dpa cross-sections from CRaD are also found exists between the arc-dpa and MD-BCA methods of to compare well with the ASTM standard data. The calculations. While an analytic function derived from a NRT model gives an upper bound of the dpa cross- series of experimental and MD simulation results [16] sections. Improved model, like the arc-dpa, developed is used to calculate the number of stable defects in the from the available experimental data and MD simula- arc-dpa method, in the MD-BCA approach [29] these tions for realistic prediction of dpa cross-sections is also Pramana – J. Phys. (2018) 90:46 Page 11 of 15 46

102

100

10-2 NJOY 2016 10-4 n,n reaction in Fe 56 CRaD

-6

DPA Cross Section (barns) 10 102 103 104 105 106 107 108 3 CRaD / NJOY 2016 2

Ratio 1 0

102 103 104 105 106 107 108 Neutron Energy (eV) (a)

103

102

NJOY 2016 1 10 CRaD

n,n' reaction in Fe 56 0 DPA Cross Section (barns) 10 106 107 1.2 CRaD / NJOY 2016

1.0 Ratio

10 6 10 7 Neutron Energy (eV) (b)

Figure 12. dpa cross-section of 56Fe 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% 66.080 14.0 15.0 2.250 2.0 0.043 0.625 0.002 implemented in CRaD. It is worthwhile here to men- The ENDF/B-VII.1-based NRT-dpa cross-sections tion that although the estimate of damage from such from CRaD are applied for the damage assessment advanced models and MD-BCA simulations compare in the structural materials of the upcoming 500 MWe closely to what is observed practically, a conservative PFBR. The dose limit of 85 dpa [28] was used for the approach has to be followed for selection of materials design of clad and wrapper materials in PFBR with D- and deciding life of FBRs. The higher value of predicted 9 steel, based on the experimental correlations of dpa dpa is safer. Hence, the NRT-dpa as standard is prefer- with the radiation damage. For this, the dpa estimation able from design considerations. was made using the dpa cross-sections from RECOIL 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−06 5.753E−10 3.864E−12 2.109E−07 CRaD 2.081E−06 5.525E−10 3.815E−12 2.085E−07 NJOY 2.077E−06 5.478E−10 3.773E−12 2.080E−07 Ni CRaD 2.587E−06 1.012E−09 6.750E−12 2.855E−07 NJOY 2.586E−06 1.003E−09 6.668E−12 2.850E−07 Cr CRaD 2.279E−06 6.349E−10 3.766E−12 2.262E−07 NJOY 2.280E−06 6.312E−10 3.735E−12 2.260E−07

Table 3. Estimation of dpa in D9 steel in PFBR for three cycles (cycle length = 180 efpd). Neutron ﬂux Total dpa for 540 effective full power days of operation RECOIL SPECTER NJOY-2016 CRaD (ENDF/B-IV) (ENDF/B-V) (ENDF/B-VII.1) (ENDF/B-VII.1) Averaged over inner core 51.168.669.870.8 Inner core maximuma 78.9 106.2 107.9 109.5 Outer core maximum 54.272.974.175.3 Radial blanket maximum 12.516.716.917.2 aPeak ﬂux is 8E+15 n/cm2/s

NRT Model (CRaD) 3 10 ARC-DPA Model (CRaD) Combined MD-BCA (IAEA-CRP)

102

101

100

10-1 Iron Total DPA Cross Section (barns)

10-2 10-4 10-3 10-2 10-1 100 101 102 103 104 105 106 107 Neutron Energy (eV)

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 Ð CRP CRaD CRaD ASTM NJOY SPECTER RECOIL (Combined MD-BCA) (ARC-DPA) (NRT) (NRT) (NRT) (NRT) (NRT) Iron 27.3 34.9 103.9 105.7 103.7 101.04 73.2 code. In the present analysis, it is found that dpa in D- of renormalisation of experimental correlations of dpa 9 steel, with CRaD, SPECTER and NJOY-2016 codes, and radiation damage to ensure consistency of dam- is overpredicted by about 35% with respect to RECOIL age prediction with ENDF/B-VII.1 library for PFBR code. This observation clearly highlights the importance applications. In the case of accelerator-driven systems, Pramana – J. Phys. (2018) 90:46 Page 13 of 15 46 components like target window experience more than where Q is the Q-value for discrete inelastic scattering 100 dpa [30]. The nuclear data needs of such systems to take place from a particular level. μ is the centre of have been discussed in [31]. The finding in our present mass cosine of angle of scattering of the neutron. The work for fast reactors, such as PFBR, that the dpa with incident energy-secondary angular parameters, al (E) or the use of nuclear data from ENDF/B-VII.1 differs from the full summation in eq. (A.3) are given in file 4 section the older dpa calculations is generic and may apply 2 for elastic scattering. For discrete inelastic scattering to assessments or predictions of radiation damage to al(E) are given in sections 51Ð91 of either file 4 or file components in fusion reactors and accelerator-driven 6. subcritical systems [32,33]. A.2.2 Continuum inelastic scattering and (n, 2n) reaction. The secondary particle energy distribution is Acknowledgements either given in file 5 or file 6. File 6 may also contain the product energy-angle distribution and recoil energy The authors gratefully acknowledge Dr V Gopalakr- distribution for these reactions. If the recoil energy dis- ishnan, former Head, Nuclear Data Section, Reactor tribution is available, then these data are used from the Design Group, IGCAR, for his keen interest and the file. If such data are not available, evaporation model initiatives made for developing an Indian radiation dam- of nuclear reaction is adapted. In this model, the energy age code for fast reactor applications. His guidance and transfer kernel is given as follows: encouragement for this work are also acknowledged. A.2.2.1 Continuum inelastic scattering. E max Appendix A f (E, E ) K (E, E ) = dE . (A.4) R 1 ( )1/2 0 4 A+1 EE A.1 Group averaging point dpa cross-section The maximum value of E is The point dpa cross-section is group-averaged into a A A E = Ql + E , neutron group structure using eq. (A.1). This expression A + 1 A + 1 shows the total multigrouped dpa cross-section in the gth neutron group. where Ql is the Q-value for the lowest level. The distribution function f (E, E) represents the probability that Eg(max) a neutron of energy E in the centre of mass frame is σ t ( )ϕ( ) D E E dE evaporated from the compound nucleus. In the centre σ t , = Eg(min) . D g (A.1) of mass frame it is given as the Maxwellian of nuclear Eg(max) = ϕ(E)dE temperature ED kT: E ( ) g min E − / f (E, E ) = e E ED , (A.5) I (E) A.2 Reaction kinematics where max The energyÐcross-section data for different reactions i E − max/ ( ) = 2 − + E ED / I E ED 1 1 e (A.6) are given in different sections of file 3 of ENDF B-VII.1 ED tape for the material. The kernel of energy transfer for is a normalization factor such that each reaction depends on the kinematics of neutronÐ E max nucleus reaction. These are briefly given below [5,18, dE f (E, E ) = 1. (A.7) 19,21,24,34,35]. 0 A.2.2.2 (n, 2n) Reaction. A.2.1 Elastic and resolved level inelastic scattering. Emax E − / ( , ) = E ED AE 2 K E ER e ER = (1 − 2Rμ + R ), (A.2) I (E) (A + 1)2 0 E−E E − / (A + 1)(−Q) e E ED dE dE , (A.8) R = 1 − , I (E, E) AE 0 max NL where I (E) is given by eq. (A.6) with E = E and 1 2l + 1 ( , ) max K (E, ER) = al(E)Pl (μ), (A.3) I E E isgivenbyeq.(A.6) with E replaced by 2π 2 max = l=0 E EÐE . 46 Page 14 of 15 Pramana – J. Phys. (2018) 90:46

The recoil energies in these two reactions can be found References by √ [1] F Seitz, Discuss. Faraday Soc. 5, 271 (1949) 1 [2] W S Snyder and J Neufeld, Phys. Rev. 97, 1636 ER(E, E ,μ)= (E − 2μ EE + E ), (A.9) A (1955) where μ is the laboratory cosine of the angle of emission [3] F A Garner, Comprehens. Nucl. Mater. 4, 33 (2012) of secondary neutron. [4] L R Greenwood, J. Nucl. Mater. 216, 29 (1994) [5] Gary S Was, Fundamentals of radiation materials science (Springer, New York, 2007) A.2.3 Threshold n, particle reactions. File 6 of the [6] L I Ivanov and Yu M Platov, Radiation physics of metals ENDF/B-VII.1 tape for the material may contain the and its applications (Cambridge International Science recoil energy distribution for these reactions in specific Publishing, 2004) pp. 5Ð11 sections. These data are used when available. If such [7] M J Norgett, M T Robinson and I M Torrens, Nucl. Eng. data are not available, then the recoil energy is found Des. 33, 50 (1975) from the following equations: [8] M T Robinson and I M Torrens, Phys. Rev. B 9, 5008 (1974) 1 ∗ [9] J Lindhard, V Nielsen, M Scharff and P V Thomsen, E = (E − 2 aE∗ E cos φ + aE ), (A.10) R A + 1 p p Mat. Fys. Medd. Dan. Vid. Selsk. 33(10) (1963) [10] J Lindhard, M Scharff and H E Schi¿tt, Mat. Fys. Medd. where a is ratio of the emitted particle mass to neutron Dan. Vid. Selsk. 33(14), 1 (1963) mass, [11] G H Kinchin and R S Pease, Rep. Prog. Phys. 18(1),1 (1955) (A + 1 − a) E∗ = E [12] D J Bacon, F Gao and Yu N Osetsky, Nucl. Instrum. A + 1 Methods 153, 87 (1999) and energy of the emitted particle E is approximately [13] R S Averback, R Benedek and K L Merkle, Phys. Rev. p B 18, 4156 (1978) chosen as the smaller value between the available energy [14] J H Kinney, M W Guinan and Z A Munir, J. Nucl. Mater. AE 122–123, 1028 (1984) Q + [15] P Jung, J. Nucl. Mater. 117, 70 (1983) A + 1 [16] Kai Nordlund et al, Primary radiation damage in mate- and the Coulomb barrier energy rials, Report Nuclear Science NEA/NSC/DOC (2015) 9, OECD/NEA, 2015 1.029 × 106zZ [17] R E Stoller, L R Greenwood and S P Simakov, Pri- in eV a1/3 + A1/3 mary radiation damage cross sections, Report INDC (NDS)-0691 (IAEA Headquarters, Vienna, Austria, z and Z being charges of the emitted particle and the 2015) target respectively. [18] T A Gabriel, J D Amburgey and N M Greene, Radi- The energy transfer kernel in this case (considering ation damage calculations: Primary recoil spectra, isotropic emission of recoil atom) is displacement rates, and gas production rates, Report ORNL/TM-5160 (Oak Ridge National Laboratory, 1 K (E, E ) = . 1976) R ( ) − ( ) (A.11) ERmax E ERmin E [19] L R Greenwood and R K Smither, SPECTER: Neu- tron damage calculations for materials irradiations, Report ANL/FPP/TM-197 (Argonne National Labora- A.2.4 (n, γ ) reaction. tory, 1985) [20] M B Chadwick et al, Nuclear Data Sheets 112, 2887 2 E E Eγ (2011) E = − 2 cos φ [21] A C Kahler, The NJOY nuclear data processing system, R + + ( + ) 2 A 1 A 1 2 A 1 mc Version 2016, Report LA-UR-17-20093 (Los Alamos 2 Eγ National Laboratory, 2016) + . [22] R S Averback and K L Merkle, Phys. Rev. B 16, 3860 2 (A.12) 2(A + 1)mc (1977) 2 [23] L Malerba, J. Nucl. Mater. 351, 28 (2006) The average of Eγ is evaluated from the gamma yield [24] J D Jenkins, Nucl. Sci. Eng. 41, 155 (1970) data given in file 12 for discrete gamma and distri- [25] W Sheely, Nucl. Sci. Eng. 29, 165 (1967) bution given in file 15 for continuum gamma. The [26] Uttiyoarnab Saha and K Devan, Proceedings of the damage energy from this reaction is calculated from DAE-BRNS Symp. on Nucl. Phys. (2016) Vol. 61, pp. recoil energy considering isotropic gamma emission. 644Ð645 Pramana – J. Phys. (2018) 90:46 Page 15 of 15 46

[27] ASTM E693-12, Standard practice for charactersing [32] A Bouhaddane et al, J. Phys.: Conf. Ser. 516, 012024 neutron exposures in iron and low alloy steels in terms (2014) of displacements per atom (DPA), E 706 (ID) [33] V Kumar, Harphool Kumawat and Manish Sharma, Pra- [28] P Puthiyavinayagam et al, Development of fast breeder mana – J. Phys. 68, 315 (2007) reactor technology in India, progress in nuclear energy [34] ENDF-6 Formats Manual, CSEWG Document ENDF- (2017), https://doi.org/10.1016/j.pnucene.2017.03.015 102, Report BNL-90365-2009 Rev.1 [29] https://www-nds.iaea.org/CRPdpa/ [35] Junhyun Kwon, Yong Hee Choi and Gyeong-Geun [30] P Satyamurthy, L M Gantayet and A K Ray, Pramana – Lee, 2nd Research coordination meeting on primary J. Phys. 68, 343 (2007) radiation damage cross-Section (Vienna, Austria, June [31] S Ganesan, Pramana – J. Phys. 68, 257 (2007) 29ÐJuly 2, 2015)