### CLUSTER DYNAMICS STUDY OF EFFECT ON THE TEMPERATURE CHANGE ON THE NEUTRON EMBRITTLEMENT OF α-IRON

#### Abstract

The actual issue of using data of neutron embrittlement of reactor materials received under the study of witness-samples, installed at selected points of the atomic reactor, to the assessment of the actual neutron embrittlement of the reactor is considered. Significant difference in the mechanical properties, including neutron embrittlement, of the predicted values based on the

results of examination of witness-samples and the results of examinations of the reactor pressure vessel of the nuclear power plant Graiswald (Germany) after its closure in 1990, was found experimentally in 2010-2013 years. Here, the mechanical properties have been measured and the small-angle neutron scattering method has been used to determine the size and density of nano-defects with a size of up to 3 nm, namely clusters of point defects (vacancy clusters and clusters of interstitial atoms), copper precipitates, and clusters composed of point defects and alloying elements of the reactor pressure vessel steel. In the proposed study, one of the possible causes of the mentioned discrepancy is considered, namely, the difference in the surveillance temperature of the reactor (300 °C) and the temperature of the witness-sample (123 °C), which is irradiated for about one year in the reactor, and then extracted from it during routine shutdowns, for example, when replacing nuclear fuel. In order to simplify, we study the effect of temperature change not on reactor steel, but on commercial pure α -iron (carbon content is less than 30 ppm). The distribution functions of vacancy clusters and clusters of self-interstitial atoms respect to the number of monomers have been calculated by means of cluster dynamics calibrated by experimental data of small-angle neutron scattering, transmission electron microscopy and positron annihilation spectroscopy of commercially pure α - iron neutron irradiated in the research reactor BR-2 (Belgium, Mol). The mean cluster size and the number density of clusters are used to estimate the increase of the yield strength of Δσ of α - iron due a neutron irradiation. This value is usually interpreted as a quantitative characteristic of neutron embrittlement. It is shown that the contribution of vacancy clusters to the value of Δσ of the studied α -iron can be neglected while the contribution from clusters of self-interstitial atoms decreases with increasing time during which the temperature of the reactor was reduced.

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#### References

Gokhman A., Bergner F. (2010). Cluster dynamics simulation of point defect clusters in neutron irradiated pure iron. Radiation Effects and Defects in Solids: Incorporating Plasma Science and Plasma Technology, 165, 216–226.

Shu S., Almirall N, Wells P., Yamamoto T., Odette G., Morgan D. (2018). Precipitation in Fe-Cu and Fe-Cu- Mn model alloys under irradiation: Dose rate effects. Acta Materialia, 157, 72-82.

Bergner F., Gillemot F., Hernández-Mayoral M., Serrano M., Török G., Ulbricht A., Altstadt E. (2015.) Contributions of Cu-rich clusters, dislocation loops and nanovoids to the irradiation-induced hardening of Cu-bearing low-Ni reactor pressure vessel steels, Journal of Nuclear Materials, 461, 37–44.

Meslin E., Lambrecht M, Hernandez-Mayoral M, Bergner F. (2010). Characterization of neutron-irradiated ferritic model alloys and RPV steel from combined APT, SANS, TEM and PAS analyses, Journal of Nuclear Materials, 406, 73-83.

Jumel S., Duysen Van J. (2007), Simulation of irradiated effects in light water reactor vessel steels – experimental validation of RPV-1, Journal of Nuclear Materials, 366, 256-265

Ulbricht A., Altstadt E., Bergner F., Viehrig H., Keyderling U. (2011). Small-angle neutron scattering investigation of as-irradiated, annealed and reirradiated reactor pressure vessel weld material of decommissioned reactor, Journal of Nuclear Materials, 416, 111-116.

Kondria M., Gokhman A. Cluster dynamics simulation of the flux effect for neutron irradiated pure iron, in print

Becker J., Becker E., Brandes Re. (1961). Reactions of Oxygen with Pure Tungsten and Tungsten Containing Carbon, J. Appl. Phys., 32, 411-423.

Odette G. R. (1998). Neutron irradiation effects in rea pressure vessel steels and weldments. In: Davies, M.(Ed.), Modeling Irradiation Embrittlement in Reactor Pressure Vessel Steels. Vienna, 438-530.

Hindmarsh A. C. (1983) ODEPACK. A Systematized Collection of ODE Solvers. Scientific Computing, R. S. Stepleman et al. (eds.), North-Holland, Amsterdam, Vol. 1 (of IMACS Transactions on Scientific Computation), 55-64.

Petzold L. R. (1983). Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. Siam J. Sci. Stat. Comput, Vol. 4, P. 136-148.

The NAG Fortran Library www.nag.co.uk https://www.nag.co.uk/nag-fortran-library

LSODA is part of the ODEPACK provided by Alan C. Hindmarsh (1984) on the CASC server of the Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Amosov A. A., Kopchenova N. V., Dubinsky Yu. A. (1994). Computational methods for engineers, M .: Higher School, 544 p.

Hardouin Duparc A,. Moingeon C., Smetaninsky-de-Grande N., BarbuA. (2002). Microstructure modelling of ferritic alloys under high flux 1MeV electron irradiations, Journal of Nuclear Materials, 302, 143–155.

Bergner F., Almazouzi A., Hernandez-Mayoral M., Lambrecht M., Ulbricht A. (2008) In Combined TEM, PAS and SANS Investigations of Neutron Irradiated Pure Iron WorkshopProceedings Karlsruhe, Germany, 2007, June 4–6, Nuclear Energy Agency, 260, OECD, 283–290.