ISO/DIS 19226:2026(en)

ISO/TC 85/SC 6

Secretariat: DIN

Date:2025-11-10

Nuclear energy — Determination of neutron fluence and displacement per atom (dpa) in reactor vessel and internals

Energie nucléaire — Détermination de la fluence neutronique et des déplacements par atome (dpa) dans la cuve et les internes de réacteur

© ISO 2026

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Foreword

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This document was prepared by Technical committee ISO/TC 85, Nuclear energy, nuclear technologies, and radiological protection, Subcommittee SC 6, Reactor Technology.

This document is based on the ANSI/ANS 19.10-2024 but extends to cover the evaluation of irradiation damage due to neutron fluence.

Introduction

This document is intended for use by

a) those involved in the determination of exposure parameters for the prediction of irradiation damage to the vessel and to the internals of a nuclear reactor, where the exposure parameters can be neutron fluence and/or displacements per atom (dpa),

b) those involved in the determination of material properties of irradiated reactor vessels and reactor internals,

c) regulatory agencies in licensing actions such as the writing of Regulatory Guides, analysis of reports concerning the integrity and material properties of irradiated pressure vessels and reactor internals.

Nuclear energy — Determination of neutron fluence and displacement per atom (dpa) in reactor vessel and internals

This document provides a procedure for the evaluation of irradiation data in the region between the reactor core and the inside surface of the containment vessel, through the pressure vessel and the reactor cavity.

NOTE These irradiation data could be neutron fluence or displacements per atom (dpa), and Helium production.

The evaluation employs both neutron flux computations and measurement data from in-vessel and cavity dosimetry, as appropriate. This document applies to pressurized water reactors (PWRs), boiling water reactors (BWRs), and pressurized heavy water reactors (PHWRs).

This document also provides a procedure for evaluating neutron damage properties at the reactor pressure vessel and internal components of PWRs, BWRs, and PHWRs. Damage properties are focused on atomic displacement damage caused by direct displacements of atoms due to collisions with neutrons and indirect damage caused by gas production, both of which are strongly dependent on the neutron energy spectrum. Therefore, for a given neutron fluence and neutron energy spectrum, calculations of the total accumulated number of atomic displacements are important data to be used for reactor life management.

The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.

ANSI/ANS 19.10, Methods for determining neutron fluence in BWR and PWR pressure vessel and reactor internals

ASTM E170-16a, Standard Terminology Relating to Radiation Measurements and Dosimetry

For the purposes of this document, the terms and definitions given in ANSI/ANS 19.10, ASTM E170-16a and the following apply.

ISO and IEC maintain terminological databases for use in standardization at the following addresses:

— ISO Online browsing platform: available at https://www.iso.org/obp

— IEC Electropedia: available at https://www.electropedia.org/

3.1

accuracy of a measured/calculated value

difference between the “real” and the measured/calculated value, typically due to systematic errors in the measurement/calculation procedure

3.2

benchmark experiment

well-defined set of physical experiments with results judged to be sufficiently accurate for use as a calculational reference point

Note 1 to entry: The judgment is made by a group of experts in the subject area.

3.3

best-estimate fluence

most accurate value of the fluence based on all available measurements, calculated results, and adjustments based on bias estimates, least-squares analyses, and engineering judgment

3.4

calculational methodology

mathematical equations, approximations, assumptions, associated parameters, and calculational procedure that yield the calculated results

Note 1 to entry: When more than one step is involved in the calculation, the entire sequence of steps comprises the “calculational methodology.”

3.5

code benchmark

comparison to the results of another code system that has been previously validated against experiment(s)

3.6

continuous-energy cross-section data

cross-section data that are specified in a dense point-wise manner that comprises the energy range

3.7

dosimeter reaction

neutron-induced nuclear reaction with a product nuclide having sufficient activity to be measured and related to the incident neutron fluence

3.8

displacements per atom (dpa)

Consequence-based radiation exposure measurement unit representing the total number of displacements per atom of a material as a result of neutron irradiation over a specified time

3.9

least-squares adjustment procedure

method for combining the results of neutron transport calculations and the results of dosimetry measurements that provides an optimal estimate of the fluence by minimizing, in the least-squares sense, the calculation-to-measurement differences

3.10

multigroup cross-section data

cross-section data that have been determined by averaging the continuous-energy cross-section data over discrete energy intervals using specified weighting functions to preserve reaction rates

3.11

neutron fluence

time-integrated and energy-integrated neutron fluence rate (i.e. the time-integrated and energy-integrated neutron flux) as expressed in neutrons per square centimeter

3.12

precision of a measured/calculated value

standard deviation (if available from a set of repeated measurements/calculations) of the distribution of the measured or calculated physical value

3.13

reactor internals

reactor structure components that are within the pressure vessel such as the core baffle, core barrel, thermal shield, lower and upper core plates in PWRs and BWRs

3.14

solution variance

measure of the statistical variance of the Monte Carlo transport solution due to a finite number of particle histories

Note 1 to entry: Mathematically, it is the second central moment of the distribution about the mean value, which is used to measure the dispersion of the distribution about the mean.

The transport calculations need to be able to determine accurately the neutron flux or fluence distributions, and/or other response parameters such as reaction rates or dpa for the analysis of integral dosimetry measurements and for the prediction of irradiation damage to reactor pressure vessels and its internals.

Calculation methodologies described in this document focus on neutron fluence for determining radiation embrittlement of reactor vessel materials.

While neutron fluence (E > 1,0 MeV) (where neutron fluence (E > 1,0 MeV) represents the fluence of neutrons with energy above 1,0 MeV) has frequently been selected as the exposure parameter for determining radiation embrittlement of reactor vessel materials, the procedures in this document extend to include fluence spectrum above 0,1 MeV, in addition to thermal fluence below 0,625 eV.

Some parameters of the calculations would be determined based on

— direct use of the results: design or comparison to measurements (which imply envelope or best-estimate results, respectively),

— required response functions: (E > 1,0 MeV) neutron flux, (E > 0,1 MeV) neutron flux, thermal neutron flux (E < 0,625 eV), dpa/s, dosimeter reaction rates;

NOTE The figures for flux, given as examples of upper or lower limit, depend on the application.

— location(s) of interest: fineness of the spatial meshing.

In the practice suggested in this document, a source distribution throughout the core is prepared using the results of core physics calculations; multidimensional transport theory calculations then are performed to propagate the neutrons to regions outside the core.

This document uses codes based on transport theory to determine multigroup three-dimensional flux distributions and to evaluate the reaction rates of dosimetry materials or dpa properties through proper use of response functions or cross sections.

Transport theory calculations should be performed using deterministic discrete ordinates (S_N)^[2] or statistical Monte Carlo^[3] approaches as discussed in 4.2.2 and 4.2.3, respectively. Other transport methods may be used if they are part of a benchmarked methodology.

The four major types of input required are.

a) Material composition:

The material compositions should represent the physical configuration as closely as practical. Material compositions and densities (consistent with the geometric model), coolant and moderator density (consistent with operating conditions associated with temperature) are required.

b) Geometric model:

The geometric model should represent the physical configuration as closely as practical, including hot dimensions. Otherwise, “as-built” dimensions of the reactor configuration should be used when available.

c) Cross-section data:

Appropriate cross-section data should be used. Cross-section sets may be used if they are part of a benchmarked methodology. Major considerations include:

1) the pertinence of the data evaluation (ENDF/B, JEFF, JENDL…);

2) the energy group structure;

3) the order of the scattering anisotropy (i.e. P_n expansion);

4) the method used for group-collapsing.

d) Core neutron source:

The determination of the neutron source should include the temporal, spatial, angular and energy dependence together with the absolute source normalization. The spatial distribution(s) of sources shall be representative of the integrated or averaged distribution(s) during the considered irradiation duration(s). The angular distribution can be considered as isotropic. The neutron distribution should be accurate especially at the periphery of the core, in order to properly determine the fluence on the Reactor Pressure Vessel. Also, the neutron source spectrum (spectra) shall be determined and the average number(s) of neutrons produced per fission, ν, shall be selected. All these parameters are to be chosen with regards to the calculated data: representative of irradiation conditions (in case of comparisons to measurements), or enveloping (in case of design phase for internals and/or vessel analyses).

In order to ensure an accurate representation of three-dimensional effects, three-dimensional discrete ordinates transport calculations should be used when practical. These calculations can be based on methods such as finite differences, finite elements or method of characteristics (MOC). When three-dimensional calculations are not practical, a synthesis method may be used to determine the three-dimensional flux or fluence distribution. In this approach, the fluence distribution is determined by synthesizing the results of one- and two-dimensional discrete ordinates solutions (see References [4] and [29]). The results depend on the specific locations where the neutron flux/fluence has to be determined (location of interest), i.e., not only at the core mid-plane, in general. Note that the use of synthesis technique may lead into inaccurate results if the material and/or source distributions are highly three dimensional.

In addition to the considerations a) to d) in 4.2.1, the Monte Carlo model construction could require a technique to reduce the score variance. The geometric model used in the Monte Carlo analyses should reflect the actual physical configuration. The great flexibility in typical Monte Carlo codes allows a very detailed representation, and this should be used to represent all the important features of the geometry under consideration and precise dosimeter location. Typically, Monte Carlo codes allow use of either multigroup or continuous-energy cross sections. Continuous-energy cross sections are recommended. Variance-reduction techniques that have been validated for these applications may be used to reduce the variance in the Monte Carlo calculation (some of them are presented in the References [3] and [5]). Techniques that may be used to improve the statistics at locations far from the core include the following, provided that preliminary checking especially on potential bias on the score has been done:

a) source biasing;

b) splitting with Russian roulette which can be based on weight windows or Adaptive Multilevel Splitting (AMS);

c) surface restarts;

d) Exponential biasing.Adjoint neutron transport calculations

Adjoint calculations may be performed:

— as upstream calculations, to estimate the space- and energy- dependent importance of the core neutrons to a specific location (on the vessel or on the considered internal), in order to determine the variance reduction parameters used in the subsequent Monte Carlo simulation step;

— or else, to replace multiple transport calculations in direct mode:

Because the reactor conditions are generally dependent on the fuel cycle, multiple transport calculations are required to track the fluence during plant operation. However, when the operating conditions that affect the transport calculation (e.g. downcomer and core bypass coolant densities, core mechanical design) remain the same, multiple transport calculations may be replaced by a single adjoint calculation^[6].

The adjoint is calculated for an adjoint source located at the vessel or other location of interest that is taken to be proportional to the energy-dependent response cross section. Typically, in the case of flux and/or fluence (E > 1 MeV), the source is taken to be unity above 1,0 MeV and zero below 1,0 MeV. When a dosimeter reaction rate is required, the source typically is taken to be equal to an energy-dependent dosimeter cross section. The fluence (or reaction rate response) at the location of interest is then determined for each cycle by integrating the cycle-specific core neutron source over the calculated adjoint function.

If Monte-Carlo method is used, and if adjoint mode is not available in the code, there may exist options in direct mode that identify the originated sources (spatially and in energy).

Prior to performing transport calculations for a particular facility, the calculational methodology shall be validated by:

a) comparing results with benchmarked calculations and measurements, and

b) demonstrating that it accurately determines appropriate benchmark results.

Calculational uncertainties associated with the methodology for predicting neutron fluence typically include the following:

a) nuclear data (e.g. transport cross sections, dosimeter reaction cross sections, and fission spectra);

b) geometry (e.g. locations of internals and deviations from the nominal dimensions);

c) isotopic composition of material (e.g. density and composition of coolant water, vessel internals, the core barrel, thermal shielding, the pressure vessel with cladding, and concrete shielding);

d) neutron sources (e.g. space and energy distribution depending on fuel burnup);

e) methods error (e.g. mesh density, angular expansion, convergence criteria, macroscopic group cross sections, fluence perturbation by surveillance capsules, spatial synthesis, and cavity streaming).

These uncertainties should be evaluated before and/or when performing transport calculations for a particular facility.

Accurate neutron dosimetry provides reasonable assurance that predictions of the reactor vessel neutron fluence at any critical location are accurate and reliable. In this regard, ratios of the calculated to the measured dosimeter response are determined for each dosimeter. The measured to calculated (M/C) ratios are then used to assess the existence of any biasing mechanisms operative within the calculational process.

Specific procedures identified in applicable standards on neutron metrology published by ASTM International should be followed (see References [7] to [20]). The general requirements for neutron monitors used for reactor pressure vessel dosimetry are outlined below, as are several specific requirements unique to stable-product neutron dosimeters:

a) Types of activation dosimeters:

The recommended set of activation and fissile dosimeters covering the spectral energy range from ~0,08 MeV to 10,0 MeV includes ²³⁷Np, ²³⁸U, ⁵⁸Ni, ⁵⁴Fe, ⁴⁶Ti, ⁶³Cu, and possibly ⁹³Nb. Additional ⁵⁹Co dosimeters enable to determinate the thermal contribution of the response in fast dosimeters, especially fission due to ²³⁵U present as traces in ²³⁸U dosimeters. Cobalt is generally diluted with aluminium in order to reduce the overall activity of the dosimeter.

b) Nuclear and material properties of dosimeters:

The physicochemical properties shall be compatible with the prevailing service conditions; for example, the dosimeter should not melt and should be chemically stable and corrosion resistant. Basic nuclear properties to be considered when implementing fissionable dosimeters include activation product half-life, reaction cross-section, gamma-ray yield, and fission yield.

c) Dosimeter mass and isotopic composition:

Dosimeters shall be of high isotopic purity and sufficient mass for adequate activation. The impact of impurities should be evaluated.

d) Dosimeter geometry and configuration:

In general, dosimeters are in the form of thin activation foils, although other shapes are available. The foil thickness is an important consideration for self-shielding during irradiation and photon absorption or fission-product loss from recoil during counting.

e) Spectral coverage:

Neutron dosimeters should possess adequate spectral coverage. In particular, the dosimeter should enable separate benchmarking calculations of the neutron fluence in the relevant energy ranges: <0,625 eV, >0,1 MeV, and >1,0 MeV.

f) Selection of alternative combinations of dosimeters:

ASTM E844-14^[14] and ASTM E1005-16^[15] provide guidance on composing an appropriate dosimetry package.

g) Nuclear data library:

The nuclear data library must contain the specific neutron cross section for metrology applications. For example, the IRDFF library can be used.

h) Irradiation geometry and dosimeter location:

Dosimeters should be placed in locations demonstrated to be representative of the location of interest. The dosimeter location should be determined accurately and recorded. Structures and materials surrounding a dosimeter that can influence its response should be avoided when possible. When these structures or materials are present, their effect should be assessed and included within the overall fluence determination.

i) Dosimeter encapsulation:

Neutron dosimeters are often placed within some form of encapsulating neutron filters or within the in-vessel surveillance capsule. The filter and capsule design should minimize perturbations to the neutron flux and spectrum. Such perturbations should be assessed and included within the overall fluence determination.

j) Irradiation parameters:

Exposure time, the associated power history, and the effects of dosimeter burnout should be accurately determined.

k) Dosimeter analysis:

Radio assay of active species is most commonly done by direct nuclear counting with a high-resolution gamma-ray spectrometer (usually Li-drifted Ge detectors). When conditions preclude direct counting, one can employ radiochemical dissolution (e.g. for Nb dosimeter). In either case, a complete description of the gamma-ray spectrometer and the counting techniques employed should be included as part of the dosimetry documentation.

l) Spectrum unfolding:

From measured reaction rates given by different foils, the more representative spectrum of the whole irradiation should be calculated using suitable unfolding codes.

Reactor vessel material test specimens along with neutron monitors are installed within surveillance capsules that are mounted in capsule holders at predetermined locations within the vessel but external to the core. These capsules are used as the primary means of monitoring of reactor pressure vessel (RPV) materials behavior under the effects of neutron irradiation.

Ex-vessel neutron dosimetry can provide an extended region of coverage for use in augmenting information from an in-vessel surveillance capsule program by providing data to benchmark the variation in axial and azimuthal flux as well as the attenuation through the reactor vessel wall.

In addition to radiometric dosimeters, stable product neutron dosimeters also are used for reactor fluence determinations. These devices include solid-state track recorders (SSTRs) and helium accumulation fluence monitors (HAFMs). These devices provide a permanent measurement record because of their stable responses. The provisions of ASTM standards ASTM E854-03^[17] for SSTRs and ASTM E910-07^[18] for HAFMs should be observed.

The ex-vessel dosimetry is usually mounted in the air annulus between the reactor vessel’s thermal insulation and the biological shield. Generally, the monitoring period is short term relative to that of the in-vessel surveillance capsules.

a) The neutron monitors should be encapsulated in a neutron-transparent material such as aluminum and suspended by high purity stainless steel bead chains or wires. The suspending material can be used to provide axial shape information.

b) The dosimetry should be placed azimuthally to assure full coverage consistent with the degree of the core symmetry and allow for cross-core comparisons.

c) The placements of neutron monitors should consider the effect that differences in coolant loop inlet temperatures and core structures, such as former bolts, may have on the interpretation of measured results.

d) The use of structural landmarks outside of the reactor vessel are key to the correct placement of the dosimetry with respect to the active core. The neutron monitor's actual position should be determined to be within 1 inch of an established reference point such as the mid-plane of the core barrel.

The accuracy of positioning of the in-vessel capsules and ex-vessel dosimeters can significantly impact the measurement uncertainty due to flux gradients. Consequently, the axial position of capsules or dosimeters should be kept within a region that is 80 % of the core height centered about the core mid-plane. Similarly, keeping the azimuthal position of the dosimetry closer to the expected peak or minimum fluence will have less of an adverse effect on the measured results. However, it is recognized that it is inevitable to place dosimetry in high gradient fluence regions to benchmark for the extended beltline region and reactor internals components directly above and below the active core.

In order to affect a meaningful comparison between measured results and the corresponding calculated quantities, the uncertainty and bias associated with the measurement process shall be carefully evaluated. Sources of uncertainty include the following: dosimeter physical parameters, irradiation characteristics (e.g. reactor power history and decay times), nuclear data (e.g. decay constants, fission yields, nuclear cross sections, and photon attenuation coefficients), and the nuclear counting process. Additional uncertainty sources may be present, and their presence should be investigated on a case-by-case basis.

Because dosimetry measurements are used to validate the calculational methodology, the measurement process shall be validated by performing dosimetry measurements with dosimeters that are identical to those exposed to certified fluences in standard neutron fields. Aspects of measurement validation in standard neutron fields are discussed in ASTM E2006-16^[19].

As discussed in Clause 4, dosimeter response should be calculated and compared to the measured values described in section 5. The M/C ratio can be used to validate the calculational methodology. If the measurement data are of sufficient quality and quantity to allow a reliable estimate of the calculational bias and the uncertainty is within the acceptable limits (i.e. they represent a statistically significant measurement database), the comparisons to measurements may be used to modify the calculation to account for bias by applying a correction, by adjusting the model, or both. Several methods of comparison may be used to validate the calculated results. When applying these methods it should be verified that the uncertainties associated with modelling, such as the spatial location of the detectors within the reactor vessel, are negligible as it is commonly assumed.When this is not the case, the effect of these uncertainties on the comparisons should be addressed.

One method of comparison is to directly compare the calculated dosimeter-specific activities at the end of irradiation with the corresponding measured dosimeter activities. This method enables various segments of the irradiation to be summed to get the total activity. The disadvantage is that experimental results from different irradiations cannot be directly compared without the introduction of transport theory calculations. An overall comparison of calculated and measured activities can be made by using a suitable weighted average of the M/C ratios. The weighting of individual sensor comparisons should include the uncertainties associated with measured activities as well as the energy spectrum coverage provided by each sensor.

The second method of comparison is to derive the average full-power reaction rate for each sensor using the irradiation history of the dosimeter set. After a sufficient operating duration, these reaction rates are independent of both the length of the irradiation and the time at less than full-power operation. The advantage of this approach is that the reaction rate comparisons permit direct comparisons of measured results from different reactors and different cycles of irradiation within the same reactor. Further, comparisons of measured spectral indices (ratios of reaction rates from different sensors) provide comparisons of the energy spectra at different measurement locations. As discussed in 6.2, an overall M/C comparison can be made using a suitably weighted average of the reaction rate data.

Another method of comparison to obtain a suitable weighting of the uncertainties in the measurements and calculations as well as the spectral coverage of the individual sensors is to apply least-squares adjustment procedures. Least-squares methods provide the capability of combining the measurement data with the neutron transport calculations resulting in an adjusted neutron energy spectrum with associated uncertainties.

The computed value of neutron exposure, produced with the guidance in Clause 4 to calculate the best-estimate values of fluence, is considered acceptable for safety analysis provided that both of the following are true:

a) The calculation has been validated as described in Clause 6;

b) The validation was based on a qualified database from measurements performed as described in Clause 5.

Neutrons from fission events cover a wide range of energies. These neutrons when interacting with elements along their transport paths could cause atom displacements directly or indirectly, creating displacement cascades, areas of low atomic density (high vacancy concentration), and of high atomic density (interstitial atoms), resulting in a change in the microstructure of the material which is commonly referred to as material damage.

Although the notion of displacements per atom of material from their normal lattice sites (dpa) is not a physical quantity and cannot be measured (there is not a simple correspondence between dpa and a particular change in a material property), dpa may be one of the exposure parameters of interest for users to evaluate embrittlement (see 4.1.1).

Hence, an appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation. This can be expressed as the total number of displaced atoms per atom of the material. The number of dpa associated with a particular irradiation depends on the primary knock-on atom (PKA) spectra in the material by the neutrons, and hence, depends on the material itself and on the neutron spectrum.

One can consider three major different metrics for dpa estimation; the original Kinchin-Pease,^[21] the frequently used Norgett Robinson and Torrens^[22] and the more recent and sophisticated Athermal Recombined Corrected.^[23] All of them are the effective estimation of Frenkel pairs in materials by model equivalence (accurate molecular dynamics for the latter). A drawbacks of these metrics is that they can only be used for model materials with a nominal factor applied to address some degree of cascade efficiency. The calculations apply to the number of displaced atoms that participates in the cascade rather than the number of displaced atoms at the end of the cascade that constitutes lattice defects like interstitial or vacancies.The calculation of the number of displaced atoms that are effective in altering a material's properties involves further study using molecular and cluster dynamics. In some cases diffusional rate-theory can be used to calibrate the net damage based on some measured property changes (swelling or radiation-induced element segregation for instance). Users shall indicate which metric and associated parameters (displacement energy for instance) they account for dpa calculations.

Damage cross-sections to be folded by neutron spectrum are often performed by a processing code in which the electronic screening is described by a partition function (Lindhard for instance in the NJOY/HEATR processing code^[24]). Users shall indicate which processing code (or partition function) and which nuclear data library is used for the calculation of such damage isotopic cross sections.

Users should note the possibility of the use of reduced dpa cross section in order to account for self-shielding corrections and that dpa response functions can have limitations/biases and associated uncertainties^[25]. The calculation method of dpa should be subject to periodic review..

Lattice defects are generally dominated by the interaction of fast (high energy) neutrons because they create atoms with high recoil energy within the interacting material; this is referred as direct radiation damage. However indirect radiation damage due to recoil from (n,2n), (n,γ), (n,p), and (n,α) reactions, for example, can be a significant fraction of the total number of displaced atoms. Of these reactions the (n,α) is perhaps the most important in creating high energy recoils (due to the mass and energy of the emitted α-particle).

Whereas most common engineering alloys used in nuclear reactors (steels and Ni-alloys containing Fe, Cr and Ni) are prone to damage production from the various recoil reactions, especially at high neutron energies (>5 MeV), these recoil reactions can occur over a very wide range of neutron energies in Ni-containing alloys in particular. Ni is a special case, where thermal neutrons become very effective contributors to radiation damage production through a two-stage process involving transmutation of the most common Ni isotope. The main isotope in Ni, ⁵⁸Ni, has a high thermal neutron capture cross-section creating ⁵⁹Ni. The ⁵⁹Ni, in turn has very high (n,γ), (n,p), and (n,α) reaction cross-sections over a very large range of neutron energies (especially at thermal neutron energies). In addition to the enhanced displaced atom production, helium generated from thermal (n,α) reactions is an important contributor to materials degradation. These reactions need to be considered, when a component is subjected to high thermal neutron fluence with significant percentage of nickel in the alloy. To this end standardized codes and procedures have been developed that allow a user to calculate dpa due to direct atomic displacement by neutrons and from various reactions of the type described here (see for instance References [26], [27] and [28]). More recent codes can also be used for these applications^[30].

Materials that are made of high nickel content under significant thermal neutron fluence can experience a considerable amount of atom displacements causing premature stress relaxation. Stress relaxation is undesirable for components such as bolts and tie-rods but can also be beneficial by reducing internal stresses, in welds for example, that could alleviate irradiation-assisted stress corrosion cracking. However, the biggest impact of the ⁵⁹Ni is swelling and embrittlement due to He production in areas of the reactor with high thermal neutron fluxes that can have serious consequences for components that operate for long periods in the reactor core region.

To have a proper assessment of the material damage properties inside the reactor vessel, an account of the helium production is required, which is strongly dependent on the thermal neutron fluence at the location of the component.

Other (n,α) reactions may also be considered, such as the (n,α) production in the boron of control rods. And other effects caused by the gas generation reaction may also be considered, such as steel swelling caused by Helium at high temperatures.

Bibliography

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[2] LEWIS E.E., MILLER W.F. Computational Methods of Neutron Transport. John Wiley and Sons, New York, 1984

[3] LUX I., KOBLINGER L. Monte Carlo Particle Transport Methods: Neutron and Photon Calculations. CRC Press, Boca Raton, Florida, 1990

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[5] X-5 MONTE CARLO TEAM. MCNP — A General Monte Carlo N-Particle Transport Code, Version 5, Volume I: Overview and Theory, LA-UR-03-1987, Ed. Los Alamos National Laboratory, April 24, 2003 (Revised 2/1/2008)

[6] S. Bourganel, O. Petti, C. M. Diop, Three-Dimensional Particle Transport Using Green’s functions in TRIPOLI-4 Monte Carlo Code: Application to PWR Neutron Fluence and Ex-Core Response Studies, Nucl. Technol, 184(2024), 1952-1974

[7] ASTM E705-13a, Standard Test Method for Measuring Reaction Rates by Radioactivation of Neptunium-237

[8] ASTM E1297-08 (Reapproved 2013), Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Niobium

[9] ASTM E704-13, Standard Test Method for Measuring Reaction Rates by Radioactivation of Uranium-238, ASTM International (2013)

[10] ASTM E264-08 (Reapproved 2013), Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Nickel

[11] ASTM E263-13, Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Iron, ASTM International (2013)

[12] ASTM E526-08 (Reapproved 2013), Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Titanium

[13] ASTM E523-16, Standard Test Method for Measuring Fast-Neutron Reaction Rates by Radioactivation of Copper

[14] ASTM E844-14, Standard Guide for Sensor Design and Irradiation for Reactor Surveillance

[15] ASTM E1005-16, Standard Test Method for Application and Analysis of Radiometric Monitors for Reactor Vessel Surveillance

[16] ASTM E181-10, Standard General Methods for Detector Calibration and Analysis of Radionuclides

[17] ASTM E854-03 (Reapproved 2009), Standard Test Method for Application and Analysis of Solid State Track Recorder (SSTR) Monitors for Reactor Surveillance

[18] ASTM E910-07 (Reapproved 2013), Standard Test Method for Application and Analysis of Helium Accumulation Fluence Monitors for Reactor Vessel Surveillance, E 706 (IIIC)

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