Comments on dpa calculation methods for ion beam driven simulation irradiations

The methodology of application of computer simulation technique to the NSC KIPT advanced simulation studies of radiation materials science at charged particles accelerators is considered with due account of the conformance of simulation methods and algorithms to the working standards of nuclear engi...

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Datum:	2013
Hauptverfasser:	Bratchenko, M.I., Bryk, V.V., Dyuldya, S.V., Kalchenko, A.S., Lazarev, N.P., Voyevodin, V.N.
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Sprache:	Russian
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2013
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Физика радиационных повреждений и явлений в твердых телах
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spelling	nasplib_isofts_kiev_ua-123456789-1116862025-02-09T09:50:47Z Comments on dpa calculation methods for ion beam driven simulation irradiations Зауваження до методів розрахунку з.н.а. щодо імітаційних опромінювань на пучках іонів Замечания о методах расчёта с.н.а. в имитационных облучениях на пучках ионов Bratchenko, M.I. Bryk, V.V. Dyuldya, S.V. Kalchenko, A.S. Lazarev, N.P. Voyevodin, V.N. Физика радиационных повреждений и явлений в твердых телах The methodology of application of computer simulation technique to the NSC KIPT advanced simulation studies of radiation materials science at charged particles accelerators is considered with due account of the conformance of simulation methods and algorithms to the working standards of nuclear engineering. The ambiguities of dpa calculations by means of the SRIM code are demonstrated and analyzed using complementary simulations by means of the RaT Monte-Carlo code. The refined guideline of the SRIM dpa calculations is presented. Методологія застосування методів комп’ютерного моделювання до імітаційних експериментів радіаційного матеріалознавства на прискорювачах заряджених частинок, що розвиваються у ННЦ ХФТІ, розглянута з особливою увагою до відповідності методів й алгоритмів моделювання до діючих стандартів атомної науки і техніки. Продемонстровані неоднозначності у розрахунках з.н.а. засобами коду SRIM. Їх аналіз проведений шляхом додаткового моделювання Монте-Карло-кодом RaT. Представлена вдосконалена методика розрахунків з.н.а. пакетом SRIM. Методология применения методов компьютерного моделирования к развиваемым в ННЦ ХФТИ имитационным экспериментам радиационного материаловедения на ускорителях заряженных частиц рассмотрена с особым вниманием к соответствию методов и алгоритмов моделирования действующим стандартам атомной науки и техники. Продемонстрированы неоднозначности в расчетах с.н.а. средствами кода SRIM. Проведен их анализ путем дополнительного моделирования Монте-Карло-кодом RaT. Представлена усовершенствованная методика расчетов с.н.а. пакетом SRIM. Authors are very grateful to Dr. Frank A. Garner for valuable discussions. 2013 Article Comments on dpa calculation methods for ion beam driven simulation irradiations / М.И. Братченко, В.В. Брык, С.В. Дюльдя, А.С. Кальченко, Н.П. Лазарев, В.Н. Воеводин // Вопросы атомной науки и техники. — 2013. — № 2. — С. 11-16. — Бібліогр.: 25 назв. — рос. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/111686 620.187:621.039.531 ru Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	Russian
topic	Физика радиационных повреждений и явлений в твердых телах Физика радиационных повреждений и явлений в твердых телах
spellingShingle	Физика радиационных повреждений и явлений в твердых телах Физика радиационных повреждений и явлений в твердых телах Bratchenko, M.I. Bryk, V.V. Dyuldya, S.V. Kalchenko, A.S. Lazarev, N.P. Voyevodin, V.N. Comments on dpa calculation methods for ion beam driven simulation irradiations Вопросы атомной науки и техники
description	The methodology of application of computer simulation technique to the NSC KIPT advanced simulation studies of radiation materials science at charged particles accelerators is considered with due account of the conformance of simulation methods and algorithms to the working standards of nuclear engineering. The ambiguities of dpa calculations by means of the SRIM code are demonstrated and analyzed using complementary simulations by means of the RaT Monte-Carlo code. The refined guideline of the SRIM dpa calculations is presented.
format	Article
author	Bratchenko, M.I. Bryk, V.V. Dyuldya, S.V. Kalchenko, A.S. Lazarev, N.P. Voyevodin, V.N.
author_facet	Bratchenko, M.I. Bryk, V.V. Dyuldya, S.V. Kalchenko, A.S. Lazarev, N.P. Voyevodin, V.N.
author_sort	Bratchenko, M.I.
title	Comments on dpa calculation methods for ion beam driven simulation irradiations
title_short	Comments on dpa calculation methods for ion beam driven simulation irradiations
title_full	Comments on dpa calculation methods for ion beam driven simulation irradiations
title_fullStr	Comments on dpa calculation methods for ion beam driven simulation irradiations
title_full_unstemmed	Comments on dpa calculation methods for ion beam driven simulation irradiations
title_sort	comments on dpa calculation methods for ion beam driven simulation irradiations
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2013
topic_facet	Физика радиационных повреждений и явлений в твердых телах
url	https://nasplib.isofts.kiev.ua/handle/123456789/111686
citation_txt	Comments on dpa calculation methods for ion beam driven simulation irradiations / М.И. Братченко, В.В. Брык, С.В. Дюльдя, А.С. Кальченко, Н.П. Лазарев, В.Н. Воеводин // Вопросы атомной науки и техники. — 2013. — № 2. — С. 11-16. — Бібліогр.: 25 назв. — рос.
series	Вопросы атомной науки и техники
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fulltext	ISSN 1562-6016. ВАНТ. 2013. №2(84) 11 УДК 620.187:621.039.531 COMMENTS ON DPA CALCULATION METHODS FOR ION BEAM DRIVEN SIMULATION IRRADIATIONS M.I. Bratchenko, V.V. Bryk, S.V. Dyuldya, A.S. Kalchenko, N.P. Lazarev, V.N. Voyevodin National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine The methodology of application of computer simulation technique to the NSC KIPT advanced simulation studies of radiation materials science at charged particles accelerators is considered with due account of the conformance of simulation methods and algorithms to the working standards of nuclear engineering. The ambiguities of dpa calcula- tions by means of the SRIM code are demonstrated and analyzed using complementary simulations by means of the RaT Monte-Carlo code. The refined guideline of the SRIM dpa calculations is presented. 1. INTRODUCTION Ion beam simulation irradiation of structural materi- als is used in NSC KIPT [1–3] and worldwide [4] as a valuable technique of express assessment of their radia- tion stability under nuclear reactor (n,γ) irradiation. The established standard practice of simulation studies [5] prescribes the calculation of the number of atomic dis- placements per atom (dpa defined [5] as “a unit of ra- diation exposure giving the mean number of times an atom is displaced from its lattice site”) as an adopted metric of correlation of the radiation damage relevant effects in metals and alloys subjected to different irradi- ation environments. This allows comparison of the re- sults of accelerator and reactor based irradiations as well as of those of different experimental groups [4, 5]. The quantification of spatially dependent dpa is a complicated radiation transport problem mostly solved by means of the Monte Carlo (MC) modeling software. The SRIM package [6] is a publicly available [7] practi- cally standard [5] user-friendly tool of such kind of cal- culations applicable to ~10(0…4) keV ion beams irradia- tion of planar layered targets. The TRIM MC code of the SRIM package simulates depth profiles of irradia- tion induced vacancy-interstitial Frenkel pairs (FPs) us- ing the binary collisions approximation (BCA) method. Under the assumption that each FP arises in a single ato- mic displacement, a common practice is to scale dpa at a given ion fluence Φ, cm–2, with the vacancy profile the TRIM code outputs in the VACANCY.TXT file. The present paper addresses the known issue of this code application to dpa calculations. TRIM offers two options for the FP distributions simulation. The express “quick damage” (QD) method simulates only the trajec- tories of primary ions and the production of primary knock-on atoms (PKAs). The total FP production rate is then calculated analytically within the scope of the mo- dified Kinchin-Pease (K–P) [8, 9] model of the seconda- ry displacement function (SDF) ν(T), the number of the secondary knock-on atoms (SKAs) produced by a PKA of energy T at a user-supplied value of a stable FP pro- duction threshold energy Ed. The alternative “full casca- des” (FC) damage MC simulation method simulates the overall collision cascade explicitly down to certain cut- off energy Efin ~ 1 eV of BCA applicability. The num- bers of FPs and atomic replacements are scored collisi- on-by-collision according to certain decision rules based on the values of Ed and the lattice binding energy Eb. The issue consists in the about twofold discrepancy of the vacancies (and thus dpa) profiles simulated by means of the FC and QD methods (Fig. 1). The ratio is too high to rate it as a reasonable scattering of the esti- mate of the same physical quantity. It is very probable that the FC/QD methods deviate systematically. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0 1.5 2.0 2.5 3.0 re l.u n. Depth (μm) "full cascades" to "quick damage" (NRT) ratio 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 "full cascades" SRIM2006.021.8 MeV Cr3+ HT-9 alloy V ac an ci es (1 04 /μ m -io n) "quick damage" (NRT) Fig. 1. Depth profiles of the total number of vacancies produced under irradiation of ferritic-martensitic steel HT-9 by 1.8 MeV Chromium ions at the NSC KIPT ESUVI accelerator [2] as calculated using two alterna- tive damage simulation methods of the TRIM BCA code Neither SRIM manuals [7] nor the ASTM simulation standard [5] comment the origin of this difference. The TRIM simulation method (FC/QD) is seldom specified in publications of experimentalists. This is fraught with misinterpretation of the measured irradiation effect (e.g. swelling) in terms of the calculated dpa, esp. significant for the topical case of ultra-high (300…600 dpa) dam- age dose irradiation [2] of prospective reactor materials. The goals of the present paper are: (i) to uncover physical and algorithmic reasons of the observed discre- pancy and (ii) to refine a guideline of the dpa rate calcu- lations by means of the TRIM BCA code. In sec. 2, we outline the meaning of dpa in radiation material science (RMS) R&D and the methods/models implemented in various codes (incl. TRIM) for dpa cal- culations. Since TRIM is not an open-source software, certain fine details of its algorithms (the calculated dpa seem to be sensitive to) are only poorly documented in [6,7,10] and subjected to changes from one version of the code to another. However, they are extractable from 12 ISSN 1562-6016. ВАНТ. 2013. №2(84) the deep analysis of the code operation. This way is adopted in sec. 3. Here we present the novel SRIM compatible modification [11] of the in-house developed CERN GEANT4 Toolkit [12] based multi-purpose MC code RaT 3.1 [13] and show its capability of reproduc- tion of TRIM FC/QD simulations of both damage pro- files and SDF. We juxtapose them with the controllable algorithms of the RaT code and give a quantitative mea- sure of the procedural sensitivity of dpa calculations. In sec. 4, this grounds the conclusions on the preferred op- tions of SRIM dpa calculations in conformity to the working standard [5] of ion beams driven RMS simula- tion studies. We end the paper with the prospects of fur- ther developments in view of recent IAEA supported ac- tivities [14] directed toward the long-expected refine- ment of radiation damage simulation standards. 2. A SURVEY OF DPA CALCULATION METHODS AND SOFTWARE When applying computer codes to the RMS relevant studies, one should clearly distinguish between the si- mulations of radiation damage and dpa. These physical- ly closely related problems differ methodologically. The ultimate goal of the radiation damage simulation is an ab initio prediction/explanation of the observed changes of macroscopic properties of irradiated materi- als (swelling, creep, embrittlement, stress corrosion cra- cking, etc.). The regularities of these phenomena are ve- ry complicated [1, 4] subject to the kind (neutrons, ions, electrons), intensity, energy spectrum, temperature and stress conditions of irradiation as well as to the evolving chemistry (nuclear transmutation) and microstructure of materials (vacancies and self-interstitial atoms (SIA) re- combination and annealing, diffusion and clustering, nu- cleation and evolution of voids, precipitates and disloca- tion loops). The driving forces of these changes spread over an extremely broad time scale starting from the pri- mary development and athermal quenching of displace- ment cascades (~10–(13…11) s) [15] through the kinetic stage of short-term (~10–(11…6) s) defects recovery up to the rate theory [16] described diffusion stage (>10–6 s) of structural and phase transformations. By reason of a limited computer power, it is out of the current agenda to integrate the models of all theses stages into a self- consistent software. Instead, the coherent concept of multiscale modeling [1, 4, 14–16] of radiation damage is developing for harmonization of inputs and outputs of successive tiers of simulation codes. Among them, only the earliest ballistic stage (~ps) deals with dpa relevant atomic displacements well described by the stable mo- lecular dynamics (MD) [15]. The most computationally efficient BCA method of the MARLOWE [17] or TRIM codes is in fact the extremely degenerated MD. Later the Recoil Interaction Approximation MD (RIA-MD) was proposed [18] to upgrade BCA toward an adequate treatment of collective lattice-driven effects (focusing, channeling) without visible loss of efficiency. RIA-MD software (like our MICKSER code [19]) is capable of precise atomistic calculations of ion induced dpa rates. However, the principal application of the dpa con- cept is far from such an atomistic modeling. It covers the routine tasks of nuclear reactor dosimetry of radiati- on damage [1, 4, 14] by means of the industry-grade MC codes like MCNP(X), MCU, MVP, KENO, etc. Such codes succeed in detailed 3D calculations of neu- tron and gamma fluxes inside and beyond a reactor core but do not attempt to simulate displacement cascades atomistically. The atomic displacements are considered “parasitically” as a particular case of primary irradiation induced secondary effects of finite microscopic cross- sections. The dpa rate is calculated as follows: ( ) ( ) ( )( )∑ ∫ ⋅⋅= i E ii i ii i EEEn t d;dpa d d Dσφ rr , (1) where n (atoms·cm–3) is the number density of a mate- rial, i enumerates the kind of primary radiation, φ is the energy E spectrum of the correspondent MC simulated flux (cm–2·s–1) in a point r, σD is the effective cross-sec- tion of displaced atoms production by each specific kind of radiation. The latter function is in turn a convolution of the PKA energy T spectrum σPKA and the SDF ν ( ) ( ) ( ) ( ) TTETE ET E d, max d PKAD νσσ ∫ ⋅= (2) over the whole range of T above the production thresh- old Ed. The MC code applies the precomputed damage- energy cross-sections 2Ed·σD(E) (eV·barn) which are practically independent on Ed (at least for neutrons) and are also referred as the displacement kerma factors. They are calculated off-line from the evaluated nuclear data by the data processing software (e.g., the HEATR module of the NJOY package [20]). Besides, the displa- cement kerma databases are incorporated into the wide- spread end-user utilities (like ENDF/B-V based code SPECTER [21] or the JENDL based code NPRIM [22]) for express calculations of dpa in reference neutron en- vironments of different nuclear reactors. Within this approach, the dynamics of displacement damage is concentrated in the model representation of the SDF ν(T) thus omitting all the above-mentioned di- versity of primary irradiation effects and reducing them to the production of elementary point defects (FPs). This is inherited from the very early stage of radiation damage theory (prior to the disclosure of swelling or ra- diation induced segregation) considered FPs as the only consequence of irradiation. The simplicity of this as- sumption gave rise to a set of exactly solvable models. For instance, the elementary balance equation ( ) ( ) ( ) ( )[ ]∫ =−−+⋅ T TTP 0 0dτντντντ (3) with the hard-sphere energy transfer p.d.f. P(τ)dτ = dτ/T and the boundary conditions ν(Ed) = 0, ν(2Ed) = 1 yields ( ) d d d KP d c d c c d 0, , (4.1) 1, 2 , (4.2) , 2 , (4.3)2 , , (4.4)2 T E E T E TT E T EE E T EE ν <⎧ ⎪ ≤ ≤⎪⎪= < ≤⎨ ⎪ ⎪ >⎪⎩ where Ec is the upper cut-off energy of discrimination of elastic (T < Ec) and inelastic (i.e. electronic, T > Ec) en- ergy losses of cascade atoms. Eq. (4) was first obtained by Kinchin and Pease in 1955 [8]. Numerous refine- ments of the K–P model were obtained in 1960-70s with the more accurate account for the detailed energy bal- ance, the anisotoropy of screened Coulomb scattering, ISSN 1562-6016. ВАНТ. 2013. №2(84) 13 the realistic partitioning of nuclear and electronic stop- ping and the impact of directional effects of channeling and focusing (see chap. 2 of ref. [2] for further details). In general, the predictions of all these models were found to scatter within ~100%. For practical purposes, this stimulated the elaboration, in 1975, of the synoptic model of SDF known as the NRT standard [9]. Norgett, Robinson and Torrens [9] proposed the fol- lowing general form of SDF: ( ) ( ) d D NRT 2E TET κν = , (5) where κ = 0.8 is the PKA mass and target temperature independent efficiency factor following from the atomic scattering anisotropy in the screened interaction poten- tial. Its value (0.8) was obtained as an appropriate fit of the results of a series of MARLOWE BCA code calcu- lations undertaken for Cu, Fe, Au and W targets [17]. For T > 2Ed/κ, it was found to be the PKA energy inde- pendent while κ = κ(T) due to lattice-driven effects at lower T. The ED(T) is the “damage energy” (or the “non-inelastic energy loss”, NIEL) available to produce displacements. To obtain it, the total electronic energy loss in a cascade is subtracted from the PKA energy. The standard adopts Robinson’s parameterization to the LSS [23] energy loss partitioning function. This yields ( ) ( )⎪ ⎪ ⎪ ⎩ ⎪⎪ ⎪ ⎨ ⎧ > + =≤≤ < = )3.6(,2, 1 (6.2),5.2 2 , 2 (6.1),,0 d L d d d d d D κε κκ ET gk T E E TE E ET TE where ( )2 TF 2 ZeTa=ε is the Lindhard’s reduced ener- gy of PKA with atomic and mass numbers Z and A, res- pectively, BTF 3 1 0.6262 aZa −= is the screening length, aB is the Bohr atomic radius, AZZk 6 1 1337.0L = and ( ) 6 1 4 3 40086.340244.0 εεεε ++=g . The formulae emphasize that this treatment is a particular case of LSS theory rigorously applicable only to a single-component material. When applying to multi-component materials, effective Z and A and the same value of the threshold energy Ed shall be used for all atomic species (typically, Ed = 40 eV for structural steels and alloys). These limitations of the NRT standard are evident. Much more serious restrictions cover the disregard of recombination, subcascades and other effects which ap- pear in MD modeling and essentially determine the dis- placement efficiency [15, 24]. Now the ~40 years old NRT standard looks outdated and shall be revised and upgraded in the near future [14]. However, its merit consisted in a closed, simple, and general form equally suitable for both analytical calculations and implemen- tations into computer codes. As a result, all industry- standard reactor MC codes make use of the NRT stan- dard displacement model to calculate dpa. They differ only in the SDF treatment details in the vicinity of Ed. Let’s summarize the difference of the considered approaches with the following intermediate conclusions. An atomistic MD, RIA-MD and BCA simulations at- tempt to model atomic displacements and radiation de- fects in materials as close as possible to the experimen- tally observed picture. From the other hand, dpa calcu- lated by the computational dosimetry relevant software is never observable experimentally. Currently it has the exclusive meaning of the NRT standard supplied do- simetric quantity, a conventional unit of measurement of irradiation impact. Just in this sense NRT dpa is men- tioned in the ASTM standard practice [5]. The physical adequacy of NRT dpa is thus of less value then the co- herence of their use in different simulation studies. 3. INTERROGATION OF THE TRIM CODE DPA CALCULATIONS ALGORITHMS To rationalize the observed behavior of the FC/QD algorithms (see Fig. 1), we perform calculations in par- allel by means of the TRIM and RaT 3.1 codes. Similar to NJOY/MCNP, the RaT can calculate and use nuclear heating and displacement kerma factors for reactor do- simetry relevant MC simulations [25]. Their NRT stan- dard (5–6) specific version is compared with the QD op- tions of TRIM. Moreover, RaT is currently the only ge- neral-purpose MC 3D radiation transport code capable of explicit atomistic BCA modeling of collision casca- des [11] using the “universal” Ziegler-Biersack-Litt- mark (ZBL) interaction potential and the electronic stopping power database of the SRIM package [6] (for details, see [11]). At its validation [11], the TRIM FC SDFs for He, Ni, and Xe irradiation of Nickel were re- produced within ~5% in a broad range of energies. Thus the RaT’s “explicit cascade” mode is expected to qual- ify the FC mode of TRIM. In fact, Fig. 2 clearly shows an excellent agreement of the results of TRIM and RaT calculation for both FC and QD modes of TRIM. 0.0 0.2 0.4 0.6 0.8 1.0 0 1x104 2x104 3x104 4x104 5x104 RaT 3.1 SRIM 2011 D is pl ac em en ts p er μ m -I on Depth (μm) Cr → X18H10T E = 1.8 MeV "fu ll d am age" ca sca de "quick damage" NRT 0 1 2 3 4 Io n di st rib ut io n (μ m -1 ) Fig. 2. Doping and damage profiles calculated for the case of the simulation irradiation [3] using the FC and QD options of TRIM (dotted curves) and the appropri- ate algorithms of the RaT MC code (solid curves) [11] The difference between QD/FC simulated damage profiles (see Figs. 1, 2) is not only inherent to irradia- tions by heavy ions. The RaT code simulates radiation damage produced in 3D targets by a great variety of primary radiations (n, p, α, e±, γ) with complex energy spectra. Fig. 3 [11] shows that the ~50 % difference of the explicitly calculated and NRT predicted dpa profiles also takes place at materials irradiation by relativistic electrons of the NSC KIPT LPE-10 linac. 14 ISSN 1562-6016. ВАНТ. 2013. №2(84) 0 1 2 3 4 5 6 7 8 0.0 0.5 1.0 1.5 2.0 2.5 full cascades NRT damage D is pl ac em en ts /m m p er e le ct ro n Depth (mm) e− → Inconel 690 E = 10 MeV 0.0 0.1 0.2 0.3 RaT 3.1 E le ct ro n di st rib ut io n (m m -1 ) Fig. 3. Deposition and damage profiles of the LPE-10 linac 10 MeV electrons in a slab of Ni–Cr alloy 690. A comparison of the explicit and NRT models predictions Fig. 4 clearly demonstrates that the FC/QD discrep- ancy is common to the overall topical range of PKA en- ergies (from Ed = 40 eV up to 2 MeV) where the SDFs ν in Iron calculated using both codes are well agreed. It is evident that the QD option is in the closest agreement with the predictions of the NRT standard SDF (5, 6). For FC mode, the deviation arises in the TRIM data ex- tracted from the VACANCY.TXT file (Nv, the number of vacancies) and in the summarized number of atomic displacements: Nd = Nv + Nr where Nr is the total num- ber of atomic replacements per PKA (a file NOVAC.TXT). 0.1 1 10 100 1000 0.1 1 10 100 1000 10000 ν( Τ ) PKA energy T (keV) NRT standard TRIM RaT "quick damage" "full cascades" (displacements) "full cascades" (vacancies) "full cascades" (damage energy) Iron Ed = 40 eV Fig. 4. PKA energy dependencies of the SDF in Iron calculated using various methods of the TRIM BCA (open markers) and RaT 3.1 MC (bold markers) codes as compared to the NRT standard SDF (dashed curve) However, there exists an undocumented way to ob- tain the NRT compatible data from the results of TRIM FC modeling. The non-ionizing energy losses of PKA and SKA are after all dissipated to phonons. TRIM ac- cumulates them in the PHONON.TXT file as a function of depth. Obviously, these data represent the profile of NIEL or damage energy ED. Thus one can calculate the SDF (5) directly from the PHONON.TXT data without reference to the LSS partitioning function (6). The re- sults are tagged in fig. 4 as a “damage energy” method. RaT uses NIEL to obtain the compatible data. The data of Fig. 4 are normalized to the NRT SDF (5–6) in Fig. 5. Here one can see that RaT reproduces all SRIM data to a few percents relative precision. NRT- based models (QD and damage-energy/NIEL) deviate from the standard values not more then by 10…20 % for all energies of interest (T > 100 eV). However, the FC- based methods manifest in this range of T the energy de- pendent 200…250 % high excess over the NRT stan- dard. Now we focus on the origin of this deviation. Note that it well agrees with the ratio (=2) of the me- an number (T/Ed) of displacing collisions and the K–P model (4.3) predicted number of FP, T/2Ed. One should be aware that both K–P and NRT models counts vacan- cies (or FPs), but not displacements. The difference be- tween them falls on replacement collisions (in TRIM, displacements = vacancies + replacements [7]). 0.1 1 10 100 1000 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 TRIM RaT "quick damage" TRIM RaT "full cascades" displacements (E2>Ed) TRIM vacancies ((E2>Ed) & (E1>Efin)) K-P vacancies ((E2>Ed) & (E1>Ed)) damage energy NIEL Iron Ed = 40 eV ν( T) /ν N R T(T ) PKA energy T (keV) Fig. 5. The ratios of the simulated and NRT SDFs of Iron according to the data of Fig. 4 The FC algorithm scores displacements, vacancies and replacements by the analysis of energy transfers at each binary collision in a cascade. It apply energy-based criteria to identify the type of produced damage. Sup- pose E1,2 are the energies of scattered and struck atoms after a collision. TRIM [7] (as well as MARLOWE [17] and other BCA codes) identifies displacement if E2 > Ed irrespectively of E1. The K–P model (4) produces a va- cancy from displacement only when E1 > Ed. This is the meaning of the boundary condition ν(2Ed) = 1 of Eq. 3. Otherwise (E1 < Ed) the vacancy is immediately anne- aled by the incident atom, and the replacement occurs. This scenario corresponds to the “K–P vacancies” curve of Fig. 5 obtained by the RaT code modeling. Evidently, it strongly deviates of the “TRIM vacancies” data. TRIM manuals (SRIM-08, p. 8-10, SRIM-09, p. 9- 34 [7]) declare the conformity of the replacements iden- tification rule to the above described K–P scenario and supplement it with the condition of identity of scattered and struck atoms (K–P was written for a single specie case). However, page 3 of the SRIM Tutorial 4, “Target Damage” states the another replacement rule, E1 < Efin where Efin << Ed is the cut-off energy of moving atom “below which it is considered to be stopped”. The spe- cific value of Efin ~ 1 eV is undocumented and cannot be accessed or altered by users. Moreover, it seems to be material specific. RaT fits TRIM at Efin = 4 eV for Iron. Therefore, the excess of vacancy production rate is mainly caused by the underestimation of replacements with respect to those assumed in K–P model and NRT. In comparison with the requirements of the NRT standard, the working version of the TRIM FC algo- ISSN 1562-6016. ВАНТ. 2013. №2(84) 15 rithm tries to simulate the collision cascade in much more details. Sub-threshold atoms can leave a vacancy when they escape from the target surface. Therefore, SRIM FC simulations are self-consistent. However, the concerned user must be aware that the FC produced “TRIM vacancies” are not the same that the “NRT dpa”. It is very probable that the correlation of this metric with the experimentally observed irradiation effects should be not worse then the NRT dpa. Fig. 6 shows that the ratios of the FC calculated SDFs (explicit to ef- fective damage energy derived) is only a weak function of PKA energy. Thus, “TRIM vacancies” (or “TRIM FC dpa”) is simply an another unit of measurement. 0.1 1 10 100 1000 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 ν(k) NRT(T)=0.8·E(k) D (T)/2Ed k = TRIM,RaT "full cascades" displacements (E2>Ed) TRIM vacancies ((E2>Ed) & (E1>Efin)) K-P vacancies ((E2>Ed) & (E1>Ed)) Iron, Ed = 40 eV ν( T) /ν (k ) N R T(T ) PKA energy T (keV) Fig. 6. The SDF ratios calculated using the algo- rithms of explicit cascade modeling and the NRT- compatible methods of damage energy calculation 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 150 keV 1 MeV "quick damage" "full cascades" (damage energy) "full cascades" (vacancies) SRIM2012.01 Fe → Fe Ed = 40 eV V ac an ci es (1 04 /μ m -io n) Depth (μm) Fig. 7. The TRIM calculated damage profiles for 150 keV and 1 MeV Fe self-ions irradiation of Iron The FC “damage energy” metric (that follows from the analysis of the PHONON.TXT file) can provide ex- perimentalists with (almost) NRT-compatible data on dpa profiles (Fig. 7). Since ion-target interactions are simulated more accurately in the FC mode, this can im- prove the prediction of the expected dpa profiles at planning of ion beam simulation irradiation, especially with multi-component targets. 4. CONCLUSIONS The SRIM package is a well approved and powerful tool suitable for atomistic simulation of ion beam inter- action with solid, ion implantation, sputtering, and the production of radiation defects. However, when applied to the reactor materials science relevant computational dosimetry of ion beam driven simulation irradiations, it must be used with caution. The parameters and the set- tings of the BCA simulation have to be chosen accord- ingly to the specific goal of computer modeling and ir- radiation experiment, and should not be omitted in pub- lications of simulation results. Different regimes of the code operation output phy- sically reasonable but semantically different dosimetric quantities. To compare with the reactor damage dosime- try data, the “quick damage” simulation option is the preferred one since its results are found to be the most closely conformant with the “NRT standard dpa” pre- scribed by the standard practice of simulation studies. The application of other options deviates the results from the working standards. One is free to use them for “what-if” and sensitivity analyses. But an uncritical use of the “full cascade” option outputs can result in over- estimation of the expected NRT dpa. This can be especi- ally critical in the case of ultrahigh-dose irradiations when considering the dpa dependent threshold effects (e.g. swelling). These conclusions are based on current regulations and are subject to change at the expected refinements of the NRT standard. The new generation GEANT4 based multi-purpose Monte Carlo radiation transport code RaT successfully reproduces the results of atomistic SRIM simulations. Due to its flexibility and capability of con- sistent simulation of coupled neutron-gamma, electron and ion beam relevant irradiations, it is a prospective platform for incorporation of new standards in the com- putational support of radiation materials science studies. Authors are very grateful to Dr. Frank A. Garner for valuable discussions. REFERENCES 1. V.N. Voyevodin, I.M. Neklyudov. Evolution of the structure-phase state and radiation resistance of structural materials. Kyiv: “Naukova dumka”, 2006, 376 p. (in Russian). 2. O.V. Borodin, V.V. Bryk, V.N. Voyevodin, A.S. Kalchenko, Yu.E. Kupriyanova, V.V. Melni- chenko, I.M. Neklyudov, A.V. Permyakov. Radiation swelling of ferritic-martensitic steels EP-450 and HT-9 under irradiation by metallic ions to super-higher doses // PAST. Ser. “Rad. Dam. Phys. and Rad. Mat. Sci.”. 2011, iss. 2(97), p. 10-15 (in Russian). 3. O.V. Borodin, V.V. Bryk, A.S. Kalchenko, V.V. Melnichenko. Influence of 5% cold-worked de- formation on behavior of 18Cr-10Ni-Ti steel under ion irradiation // PAST. Ser. “Rad. Dam. Phys. and Rad. Mat. Sci.”. 2011, iss. 4(98), p. 9-13 (in Russian). 4. G.S. Was. Fundamentals of radiation materials science: Metals and Alloys. Berlin, Heidelberg: Sprin- ger-Verlag, 2007, 827 p. 5. ASTM E521-96. Standard practice for neutron Radiation damage simulation by charged-particle irra- diation. Annual Book of ASTM Standards, vol. 12.02. American Society for Testing and Materials, Philadel- phia, PA, USA, 1996, p. 141-160. 16 ISSN 1562-6016. ВАНТ. 2013. №2(84) 6. J.F. Ziegler, J.P. 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Symposium on Reactor Do- simetry, Brussels, Belgium, Aug. 18-23, 2002. Singa- pore: World Sci. Publ., 2003, p. 84-92. 23. J. Lindhard, M. Scharff, H.E. Schiøtt. Range concepts and heavy ion ranges (notes on atomic collisi- ons, II) // Mat.-fys. Medd.r-Kong. Danske Vid. Selsk., KDVSA. 1963, v. 33, No. 14, p. 1-42. 24. C.H.M. Broeders, A.Yu. Konobeyev. Defect production efficiency in metals under neutron irradia- tion // JNM. 2004, v. 328, N 2-3, p. 197-214. 25. S.V. Dyuldya, M.I. Bratchenko. Nuclear re- sponses functions of Hastelloy Ni-Mo alloys // Proc. of ICPRP-XVIII, Alushta, Sept. 8–13, 2008. Kharkov: NSC KIPT, 2008, p. 83-84 (in Russian). Статья поступила в редакцию 20.03.2013 г. ЗАМЕЧАНИЯ О МЕТОДАХ РАСЧЁТА С.Н.А. В ИМИТАЦИОННЫХ ОБЛУЧЕНИЯХ НА ПУЧКАХ ИОНОВ М.И. Братченко, В.В. Брык, С.В. Дюльдя, А.С. Кальченко, Н.П. Лазарев, В.Н. Воеводин Методология применения методов компьютерного моделирования к развиваемым в ННЦ ХФТИ имита- ционным экспериментам радиационного материаловедения на ускорителях заряженных частиц рассмотрена с особым вниманием к соответствию методов и алгоритмов моделирования действующим стандартам атом- ной науки и техники. Продемонстрированы неоднозначности в расчетах с.н.а. средствами кода SRIM. Про- веден их анализ путем дополнительного моделирования Монте-Карло-кодом RaT. Представлена усовершен- ствованная методика расчетов с.н.а. пакетом SRIM. ЗАУВАЖЕННЯ ДО МЕТОДІВ РОЗРАХУНКУ З.Н.А. ЩОДО ІМІТАЦІЙНИХ ОПРОМІНЮВАНЬ НА ПУЧКАХ ІОНІВ М.І. Братченко, В.В. Брик, С.В. Дюльдя, О.С. Кальченко, М.П. Лазарєв, В.М. Воєводін Методологія застосування методів комп’ютерного моделювання до імітаційних експериментів радіацій- ного матеріалознавства на прискорювачах заряджених частинок, що розвиваються у ННЦ ХФТІ, розглянута з особливою увагою до відповідності методів й алгоритмів моделювання до діючих стандартів атомної нау- ки і техніки. Продемонстровані неоднозначності у розрахунках з.н.а. засобами коду SRIM. Їх аналіз прове- дений шляхом додаткового моделювання Монте-Карло-кодом RaT. Представлена вдосконалена методика розрахунків з.н.а. пакетом SRIM.

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