An integrated model for materials in a fusion power plant: transmutation, gas production, and helium embrittlement under neutron irradiation

Summary

This study presents an integrated computational framework combining neutron-transport calculations (MCNP), material inventory burn-up modeling (FISPACT), and electronic-structure density functional theory (DFT) to evaluate material degradation in the DEMO fusion reactor. It investigates spatial variations of neutron spectra, gas production (helium and hydrogen), and atomic displacements across structural and plasma-facing components. A simple physics-based model is used to predict critical helium-induced grain-boundary embrittlement lifetimes for candidate fusion materials including iron, tungsten, and beryllium.

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Title, Authors, Abstract, and Section 1: Introduction

IOP PUBLISHING and INTERNATIONAL ATOMIC ENERGY AGENCY NUCLEAR FUSION Nucl. Fusion 52 (2012) 083019 (12pp) doi:10.1088/0029-5515/52/8/083019

An integrated model for materials in a fusion power plant: transmutation, gas production, and helium embrittlement under neutron irradiation

M.R. Gilbert, S.L. Dudarev, S. Zheng, L.W. Packer and J.-Ch. Sublet EURATOM/CCFE Fusion Association, Culham Centre for Fusion Energy, Abingdon, Oxfordshire OX14 3DB, UK E-mail: [email protected]

Received 16 January 2012, accepted for publication 11 July 2012 Published 1 August 2012 Online at stacks.iop.org/NF/52/083019

Abstract The high-energy, high-intensity neutron fluxes produced by the fusion plasma will have a significant life-limiting impact on reactor components in both experimental and commercial fusion devices. As well as producing defects, the neutrons bombarding the materials initiate nuclear reactions, leading to transmutation of the elemental atoms. Products of many of these reactions are gases, particularly helium, which can cause swelling and embrittlement of materials. This paper integrates several different computational techniques to produce a comprehensive picture of the response of materials to neutron irradiation, enabling the assessment of structural integrity of components in a fusion power plant. Neutron-transport calculations for a model of the next-step fusion device DEMO reveal the variation in exposure conditions in different components of the vessel, while inventory calculations quantify the associated implications for transmutation and gas production. The helium production rates are then used, in conjunction with a simple model for He-induced grain-boundary embrittlement based on electronic-structure density functional theory calculations, to estimate the timescales for susceptibility to grain-boundary failure in different fusion-relevant materials. There is wide variation in the predicted grain-boundary-failure lifetimes as a function of both microstructure and chemical composition, with some conservative predictions indicating much less than the required lifetime for components in a fusion power plant.

Introduction In magnetic-confinement fusion devices a large number of high-energy neutrons are generated in the plasma by deuterium–tritium fusion reactions. These neutrons escape from the plasma and irradiate the materials that make up the reactor vessel. One of the key outstanding issues for the fusion materials programme is in the understanding of how neutrons influence the properties of materials over the projected lifetime of a fusion power plant. Not only do the incident neutrons cause atomic displacements within the materials, leading to the generation and accumulation of radiation defects, which cause hardening, embrittlement, and irradiation creep, but they also initiate non-elastic nuclear reactions that alter the nature of the constituent atoms. This process, known as transmutation or burn-up, changes the chemical composition of materials, leading in turn to measurable changes in structural and mechanical properties.

Perhaps even more problematic are the nuclear reactions initiated by fusion neutrons that give rise to the transmutation production of gas atoms, such as helium (He) and hydrogen (H). These reactions, which include neutron capture followed by α-particle (4He2+) emission, often written as (n,α), and neutron capture and proton (1H+) emission (n,p), generally occur less frequently than the major (n,γ) reactions, but have a much more significant effect on properties of materials, particularly metals and alloys. Even at low concentrations, gas particles can have severe life-limiting consequences for materials, with He being a particular problem because, with its low solubility in the crystal lattice, it forms clusters and accumulates at defects, dislocations and at grain boundaries, leading to swelling or embrittlement.

In fusion, the issue of transmutation gas production is likely to be a more significant problem than in fission because of the higher neutron fluxes and higher average neutron energies. For example, in figure 1 where a fission spectrum for a fuel assembly of a 3.8 GW (gigawatts of thermal power) LWR-P4 reactor in Paluel, France, is compared to a fusion spectrum computed for the first wall (FW) armour of the 3.0 GW DEMO concept reactor described later, the fluxes of neutrons per lethargy interval are greater in the fusion spectrum at all but thermal energies.

Section 2: Neutron-induced transmutation of materials and Section 2.1

Figure 1 compares the neutron-energy spectra in fission (PWR) and fusion (DEMO FW) reactors. For fission the average neutron spectrum in the fuel assembly of a PWR reactor is shown, while the equatorial FW armour spectrum for the DEMO model in figure 2 is representative of fusion.

Many of the gas-producing nuclear reactions exhibit cross section thresholds, which means that for incident neutrons below a particular energy the reaction either does not occur or has a very low probability. Thus, in fusion, while the higher neutron fluxes compared to fission would increase the total number of reactions in irradiated components, the larger fraction of neutrons at higher energies would also tend to raise the proportion of those reactions which lead to helium and hydrogen gas production.

Since experimental testing of materials in a fully realistic fusion neutron-irradiation environment is not currently possible, simulation and theory has a vital role in providing predictions for material response as a result of neutron bombardment and the corresponding build-up of elemental impurities.

This paper gives an example of an integrated approach involving neutron-transport simulations, calculations of the evolution in material composition, and atomic level modelling of the changes to material properties caused by the various aspects of transmutation. For the present study, the last of these three components is only concerned with modelling of helium-induced grain-boundary embrittlement, producing, in combination with knowledge of transmutation response, estimates of the timescales for the loss of structural integrity of components due to grain-boundary failure. As this integrated approach develops in the future, perhaps with an additional step involving the creation and modification of a reactor’s design, other more realistic and relevant models of the consequences of irradiation damage and transmutation could be applied.

Neutron-induced transmutation of materials In a previous study [1], we considered the transmutation response of various materials under identical FW conditions for both a power plant design (PPCS model B [2]) and for the ITER device, which is presently under construction. While this provided significant insight into the differing behaviour of materials under neutron irradiation, particularly with regard to He/H gas production, it is important to appreciate the limitations of the approach. Specifically, not all the components of a fusion reactor will experience the same flux and spectrum of neutrons as that seen in the FW armour. In fact, the FW environment will be the worst in terms of transmutation and gas production due to the high neutron fluxes and energies, and conditions elsewhere may be significantly different.

2.1. Geometry dependence of neutron flux and energy spectrum Figure 3 shows neutron spectra calculated for different regions of a recent design, developed at CCFE in 2009, for the DEMO reactor, which is planned as the last step after ITER before progression to commercial fusion power generation. This particular design is helium cooled with a Li/Be tritium-breeding blanket and a W divertor. EUROFER is the primary in-vessel structural steel. A model geometry of the design (figure 2) was created using the HERCULES code [3, 4], and neutrons were transported through it using the MCNP code [5]. Only the major structures were included in the design, with homogeneous material compositions taken as the average composition of all of the materials present in a particular component.

Section 2.1: Geometry dependence (cont.) and Figures 2-3

Figure 2 depicts a toroidal section through the simplified, homogeneous, DEMO model used in MCNP simulations to obtain neutron fluxes and spectra, indicating First wall & blanket, Shielding & backplates, Vessel Walls, Coils, Divertor, and plasma locations (A, B, C, D, E, F, G).

Figure 3 shows a comparison of the neutron-energy spectra in DEMO: (a) as a function of depth into the vessel from the plasma-facing wall at the equatorial position A; and (b) in the first two layers of the divertor as a function of position (E–G).

Neutron trajectories were tracked with MCNP. The flux results (n cm-2 per source neutron ns) were multiplied by 9.576 × 10^20 ns s^-1 corresponding to the 2.7 GW expected plasma thermal power (producing 14.1 MeV neutrons), reaching 3.0 GW total thermal power output including exothermic blanket reactions.

As shown in Figure 3(a), the neutron spectra and fluxes change dramatically over depth: from 8.36 × 10^14 n cm^-2 s^-1 in the first centimetre of the equatorial blanket at position A (depth 2–3 cm) to 3.9 × 10^13 n cm^-2 s^-1 in the final five cm (depth 57–62 cm), a drop of >95% due to Be moderation and 6Li neutron absorption.

In the divertor (Figure 3(b)), fluxes at point E (7.1 × 10^14 n cm^-2 s^-1 in armour, 5.6 × 10^14 n cm^-2 s^-1 in structure) are roughly twice as high as at point G (3.6 × 10^14 n cm^-2 s^-1 in armour, 2.4 × 10^14 n cm^-2 s^-1 in structure).

Section 2.1: NRT dpa Calculations and Figure 4

The high concentration of W in the divertor causes self-shielding in the lower-energy regions of the neutron spectra (resonances around 10 eV). Displacements per atom (dpa) per second were calculated using NJOY and the NRT method:

σd(En) = ∑_j σj(En) Ej(En) (1) σdpa(En) = 0.8 σd(En) / (2 Ed) (2) NRT dpa per second = ∑_i^(Ng) φi σdpa_i (3)

Threshold displacement energies Ed used: 31 eV for Be; 40 eV for Fe, Cr, V, Nb, Zr; 60 eV for Mo; and 90 eV for W and Ta.

Figure 4 displays the defect production rates in dpa/year as a function of depth into the FW armour and blanket at position A for Fe, Cr, Be, and W. In the 2 cm FW armour layer, dpa/year values are 14.4 for Fe, 15.0 for Cr, 7.2 for Be, and 4.4 for W.

Section 2.2: Influence on transmutation and gas production (Fe)

FISPACT inventory calculations were performed using the European Activation File (EAF-2003) to model activation and transmutation for Fe, W, and Be.

Figure 5 shows the variation in (a) He and (b) H concentrations in pure Fe as a function of time (1, 3, 5 years) for the spectra at different FW armour positions (A, B, C, D) in DEMO along with equivalent dpa/year.

Total fluxes in the 2 cm FW armour are: 8.25 × 10^14 n cm^-2 s^-1 at A; 6.97 × 10^14 n cm^-2 s^-1 at B; 8.04 × 10^14 n cm^-2 s^-1 at C; and 7.94 × 10^14 n cm^-2 s^-1 at D. Threshold reactions 56Fe(n,α)53Cr (threshold ~3.7 MeV) and 56Fe(n,p)56Mn (threshold ~2.9 MeV) are significantly reduced at position B due to a softer spectrum above 1 MeV.

Section 2.2.1: Fe (cont.) and Section 2.2.2: W

Figure 6 displays the high-energy part of the neutron spectra for the 2 cm FW armour layer at positions A, B, C, and D. Figure 7 shows the variation in He concentration in pure Fe after a 5-year irradiation across the depth into the FW armour and blanket at position A, alongside total dpa.

After 5 years, He in Fe reaches 709 appm at A, 365 appm at B, 734 appm at C, and 586 appm at D. Across the depth at A, He falls from ~700 appm in the FW armour to only 3 appm at 57–62 cm depth.

Section 2.2.2 Tungsten (W): In the divertor armour (0–2 cm), 5-year He generation in pure W varies from 15 appm at E to <1 appm at G. Hydrogen generation is approximately twice that of He. In the FW armour, 5-year W transmutation produces ~30,000 appm (3 at%) Re at position A, while in the divertor armour at E it reaches ~10,000 appm (1 at%). Tantalum (Ta) production is ~5470 appm at A and ~4940 appm at E.

Figure 8 and Section 2.2.3: Beryllium (Be)

Figure 8 shows the variation in concentrations of (a) He, (b) Re, and (c) Ta produced in pure W under neutron irradiation across divertor positions (E, F, G) and FW armour (A) for 1, 3, and 5 years.

Section 2.2.3 Beryllium (Be): Beryllium in the blanket produces significant quantities of helium. In the first 1 cm of the equatorial blanket at A, He reaches 19,300 appm after 5 years (~320 appm/month), falling to 200 appm in the final 5 cm (depth 57–62 cm), as shown in Figure 9. Hydrogen production in Be is much lower (~475 appm after 5 years at position A).

Figure 9 and Section 3: Modelling of He accumulation at grain boundaries

Figure 9 shows He concentration and total dpa in pure Be after 5-year irradiation as a function of depth into the DEMO blanket at position A.

Section 3: Modelling of He accumulation at grain boundaries Assuming cubic crystal grains of linear size a: N_He ≈ a^3 n G_He (4) ν_He = (a / 3) n G_He (5)

Boundary destabilization occurs when stored energy equals surface formation energy: E_He^sol ν_He^c ≈ 2 ε_surf (6) G_He^c = 3 ν_He^c / (a n) (7)

Where E_He^sol is the solution energy of a substitutional He atom, ε_surf is the average surface energy, and n is the atomic density.

Table 1, Table 2, and Grain-boundary Failure Discussion

Table 1: Basic quantities used for evaluating critical helium grain-boundary concentrations:

Fe: ρRT = 7.87 g/cm3, n = 8.5 × 10^22 cm^-3, E_He^sol = 4.34 eV, ε_surf = 2.4 J/m2
V: ρRT = 6.11 g/cm3, n = 7.2 × 10^22 cm^-3, E_He^sol = 4.81 eV, ε_surf = 2.6 J/m2
Cr: ρRT = 7.19 g/cm3, n = 8.3 × 10^22 cm^-3, E_He^sol = 5.20 eV, ε_surf = 2.3 J/m2
Mo: ρRT = 10.22 g/cm3, n = 6.4 × 10^22 cm^-3, E_He^sol = 4.65 eV, ε_surf = 3.0 J/m2
Nb: ρRT = 8.57 g/cm3, n = 5.6 × 10^22 cm^-3, E_He^sol = 4.55 eV, ε_surf = 2.7 J/m2
Ta: ρRT = 16.65 g/cm3, n = 5.5 × 10^22 cm^-3, E_He^sol = 4.82 eV, ε_surf = 3.0 J/m2
W: ρRT = 19.25 g/cm3, n = 6.3 × 10^22 cm^-3, E_He^sol = 4.77 eV, ε_surf = 3.5 J/m2
Be: ρRT = 1.85 g/cm3, n = 1.2 × 10^23 cm^-3, E_He^sol = 3.46 eV, ε_surf = 2.2 J/m2
Zr: ρRT = 6.51 g/cm3, n = 4.3 × 10^22 cm^-3, E_He^sol = 3.08 eV, ε_surf = 2.0 J/m2

Table 2 summarizes calculated ν_He^c, G_He^c, and critical embrittlement lifetimes t^c and dpa in FW armour and blanket (depth 17–19 cm) for grain sizes a = 5 µm and a = 0.5 µm.

Fe (5 µm): G_He^c = 48.8 appm; FW t^c = 4 months (4.79 dpa); blanket t^c = 2 years (9.57 dpa)
Fe (0.5 µm): G_He^c = 488.0 appm; FW t^c = 4 years (57.47 dpa); blanket t^c = 18 years (86.13 dpa)
Be (5 µm): G_He^c = 38.5 appm; FW t^c = 4 days (0.08 dpa); blanket t^c = 11 days (0.09 dpa)
Be (0.5 µm): G_He^c = 385.2 appm; FW t^c = 1 month (0.60 dpa); blanket t^c = 4 months (1.00 dpa)
W (5 µm): G_He^c = 87.2 appm; FW t^c = 20 years (88.89 dpa); blanket t^c = 228 years (357.37 dpa)
W (0.5 µm): G_He^c = 871.5 appm; FW t^c > 300 years (>1333 dpa); blanket t^c > 300 years (>470 dpa)

Section 4: Summary, Acknowledgments, and References

Summary The combined MCNP neutron-transport simulations and FISPACT inventory calculations demonstrate that transmutation and gas accumulation rates vary dramatically by position in DEMO. Helium production in Fe is severe at the first wall but drops rapidly across the breeding blanket, posing minimal threat in outer shield and vacuum vessel structures. In W, He production is negligible, meaning displacement cascades and non-gas transmutants (Re, Ta, Os) will govern lifetime. In Be, extreme He production and swelling gradients represent a major engineering challenge.

Grain-boundary embrittlement models indicate that smaller grain sizes (e.g. 0.5 µm in Fe) can extend structural lifetimes to commercially viable durations (~4 years in FW), whereas Be exhibits rapid predicted embrittlement failure unless mitigation strategies are implemented.

Acknowledgments The authors acknowledge discussions with R.G. Odette, M. Rieth, T. Yamamoto, D. Nguyen-Manh, and P. Karditsas. Funded by EURATOM/CCFE and RCUK Energy Programme Grant EP/I501045.

References include works on FISPACT, EAF-2003, NJOY, EUROFER metallurgy, and DFT simulations of defects in fusion materials (Gilbert & Sublet 2011, Maisonnier et al 2005/2006, Rieth et al 2008, Yamamoto et al 2006, Becquart & Domain 2006, Fu & Willaime 2005/2007, etc.).