1. A.V. Kozlov, I.A. Portnykh, V.L. Panchenko FSUE «INM», 624250, Box 29, Zarechny, Sverdlovsk region, Russia Corresponding author. fax: +7-34377-33396; e-mail: sfti@uraltc.ru, AlexTIM@uraltc.ru A model of influence of radiation damage rate on formation and evolution of radiation defects in austenitic steels.

2. Fast neutron reactor G  10 -6 dpa/s 2Introduction Correctness ? Thermal reactor G  10 -8  10 -7 dpa/s Results of fast neutron reactor irradiation G  10 -6 dpa/s Results of an accelerating irradiation G ≥ 10 -4 dpa/s predict predict predict

3. 3The purpose of the work Creation of quantitative model of influence of radiation damage rate on both formation and evolution of radiation defects in austenitic steels and its experimental checkout.

4. Basic positions of model Entering rate of point defect from cascade to matrix: Where  х - coefficient of point defect get out from cascade area to matrix;  - cascade efficiency; G – irradiation damage rate; t – current value of time;  x - diffusion time of х-type point defect (x=i – for interstitials, x=v – for vacancies). 4 Change of point defect concentration in matrix:

5. 5 Объект исследования Basic positions of model; examined temperature range Middle Temperature Irradiation (MTO-2) Low Temperature Irradiation (LTO) i –mobile - dissociate from cascade areas and freely diffuse in matrix (  i =1); v - remain in cascade formation area, transformed into compact energy-binding configurations - vacancy clusters (  v =0). i –mobile - dissociate from cascade areas and freely diffuse in matrix; v - dissociate from clusters and diffuse in matrix.

6. Low Temperature Irradiation (LTO). Model. 6 Diffused interstitials migrate to three type of sink: grain boundary, dislocations and inside clusters. Grain boundary Dislocation

7. Interstitial-vacancy recombination process leads to cluster vanish. The cluster size doesn’t change at the recombination process. Cluster evolution Cluster after thermodynamic stabilization Low Temperature Irradiation (LTO). Model. 7

8. Calculation results 8 Where d g – grain size;  d - dislocation density; n c – clusters concentration; r c – average size of clusters. Formula for diffusion time of interstitials: For ChS-68 steel at G  2  10 -7 dpa/s and Т  300 К  i  10 -1 s

9. Calculation results 9 Interstitials concentration: Fig. 1. Time dependence of interstitials concentration in ChS-68 steel at neutron irradiation at G  2  10 -7 dpa/s and Т  300 К.

10. Calculation results 10 Where m 0 - average amount of vacancies in cluster at formation moment. Average lifetime of clusters: For ChS-68 steel at G  2  10 -7 dpa/s and Т  310 К Average lifetime of clusters 10 3 -10 4 с

11. Calculation results 11 Clusters concentration: Fig. 2. Time dependence of radiation clusters concentration in ChS-68 steel at neutron irradiation at G  2  10 -7 dpa/s and Т  300 К. Clusters generation rate:

12. Calculation results 12 Fig. 3. Time dependence of average vacancy concentration in cluster for various damage dose rates in ChS-68 steel at neutron irradiation at Т  310 К.

13. 13Calculation results The irradiation with lower damage dose rate leads to more strong radiation damages, than at higher damage dose rate (at the same damage dose). !

14. 14 Low Temperature Irradiation (LTO) – Experimental data The experimental examinations after irradiation and post annealing of two austenitic steels ChS-68 (16Cr-15Ni- 2Mo-2Mn-Si-Ti) in a state after final 20 % cold work and EI-844 (16Cr-15Ni- 2Mo-Mn-Si-Nb) in austenitic state were carried out. The irradiation was carried out at temperature 310 K to damage dose 0.0007 dpa for ChS-68 and 0.007 dpa for EI-844 steels.

15. Comparing calculated and experimental data 15 Table 1 – Relative size changes (%) of ChS-68 and EI-844 steel specimens irradiated at temperature 310 К, caused by an annealing of radiation clusters. MaterialDilatometry dataCalculated data ChS-680.0120.007 EI-8440.0100.006

16. Middle Temperature Irradiation (MTO). Model. 16 Average diffusion time of interstitials and vacancies was calculated by the same methodic: Formulas for vacancy diffusion time and interstitial diffusion time was obtained. For ChS-68 steel at G  1  10 -6 dpa/s and Т  700 К  v  10 3 s,  i  10 -3 s

17. 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 5,0 -8-7-6-5-4 Middle Temperature Irradiation (MTO). Model. 17 Fig. 6. Dependence of quasi-equilibrium vacancy concentration on irradiation damage rate in ChS-68 steel irradiated at different temperatures. LgG Vacancy concentration, ×10 -5 600 K 700 K 800 K

18. Middle Temperature Irradiation (MTO). Model. 18 Fig. 7. Dependence of quasi-equilibrium interstitials concentration on irradiation damage rate in ChS-68 steel irradiated at different temperatures. 600 K 700 K 800 K LgG Interstitials concentration, ×10 -10

19. Middle Temperature Irradiation (MTO). Model. 19 Fig. 8. Dependence of ratio vacancies concentration to interstitials concentration on irradiation damage rate in ChS-68 steel irradiated at different temperatures. 600 K 700 K 800 K LgG C ve /C ie, ×10 5

20. 20Middle Temperature Irradiation (MTO). Model. It is incorrectly to use plainly the results obtained at high damage dose rate irradiation for prediction influence of low damage dose rate irradiation on material structure changes. !

21. 21Conclusions The quantitative model of point defect evolution is created. It allows in any cases to describe point defect evolution in dependence on temperature, dose and damage dose rate of neutron irradiation. The dependences of interstitials concentration, vacancy clusters concentration and average vacancy amount in a cluster are obtained for low temperature and low dose irradiation. It’s shown irradiation at low damage dose rate lead to more strong distraction than irradiation at high damage dose rate when irradiation doses are equal. The calculation results of size changes of EI-844 and ChS-68 steel specimens irradiated at 310 K to low damage dose and annealed are correlate to the obtained experimental data.

22. 22Conclusions It’s shown by the model vacancy and interstitial quasi-equilibrium concentrations are established at irradiation temperatures 600 – 800 K during the fix time. The time is about 1 hour for vacancies and 10 -3 s for interstitials in ChS-68 steel irradiated in fast neutron reactor. The dependences of vacancy and interstitial concentrations on damage dose rate for irradiation temperatures 600 K, 700 K, 800 K were obtained. It’s shown the less damage dose rate leads to stronger radiation swelling.

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