Simulation of displacement cascades in  -Fe and Fe-10% Cr

1. Simulation of displacement cascades in -Fe and Fe-10% Cr Terentiev Dmitry and Malerba Lorenzo

2. Simulation of displacement cascades and their analysis: Fe-Cr vs Fe Study of collisional stage: cascade core, peak time, volume and density vs PKA energy Control of cascade growth via direct visualization Study of final atomic configuration: distribution of defects, clustering, visualization Main Goals

3. Molecular Dynamics Microcanonical statistical ensemble Periodic boundary conditions Simulation cell size up to 1 000 000 atoms Simulation time up to 30 ps Either pure Fe or 10% Cr atoms in Fe matrix The interatomic potential EAM for ferromagnetic Fe-10%Cr Simulation technique

4. Distributions & Visualization Defects (Wigner-Seitz cell combined with linked cells method) vacancy - no atoms in the cell replacement - one atom, but number doesn’t correspond to initial interstitial - 2 atoms in one cell displacement = interstitials + replacements Clustering formation Vacancy cluster - distance is <= than 2nd nn Interstitial cluster - distance is <= than 3rd nn Cascade core – at maximum number of defects Cascade volume and density peak time Visualization of mobile defects, finding right criteria for SIA clustering Criteria for defect analysis

5. Simulation of collision cascades:Initial parameters • Recoil energies from 1 keV up to 40 keV (also < 1 keV) • Maximum size of simulation box: 80 l. u. side • Simulation scheme: Collisional stage: 50000.01 fs 20 Post collisional :10000.1 fs 90 Cooling 10001 fs 10 Total simulation time 30ps Table with cascade parameters

6. Predicted threshold displacement energies and other results Threshold displacement energies of Fe atom in pure Fe matrix at 300 K (all values are ±1eV) Average threshold displacement energies for Cr and Fe atoms in pure Fe and Fe-Cr (10% ) alloy.

7. Angle dependence of EDComparison P. Vajda: "Anisotropy of electron radiation damage", Rev. Mod. Phys., (1977) (origin work: Erginsoy et al (1964)) D.J. Bacon, A. F. Calder, J.M. Harder, S.J. Wooding “Computer simulation of low-energy displacement events in pure bcc and hcp metals”, Journal of nuclear materials,1993 [210], [221],[211] predicted correctly

8. Peak time distributions • no essential influence of Cr atoms on characteristics • pronounced increase of core density, cascade volume and peak time at 10keV – 20(30) keV and then slope changes • after 30 keV looks like cascade volume and density become saturated • these effects can be explained because above10-20 keV gradual subcascade splitting occurs and each of these is a replica of lower energy cascades

9. Evolution of collision cascades • Evolution of no. of displacements • Evolution of no. of Frenkel pairs • shift of maximum with rise of recoil energy • increase of Ndisp during post-collisional stage, while Nvac decreases

10. Evolution of collision cascades • Evolution of dumbbells • NFe-Fe > NFe-Cr but! only during collision stage • Nmix increases at the expense of Fe-Fe dumbbells • Fe-Fe/Fe-Cr replacement processes take place during cooling stage as well • rearrangement of dumbells distribution ~ 4.5 ps ~ 8 ps

11. Visualization of cascades initial PKA position 20 keV energy 1st snap shot after 50fs Film up to 3ps 135 direction 60 l.u.

12. Visualization of cascades 20 keV energy Particles energy – Evolution Film from 1ps up to 10 ps

13. Visualization of cascades The distribution of dumbells – red – Cr atoms, blue – Fe atoms, 60 l.u. – box size Configurations at the final stage of simulation 30ps. Simulation temperature - 300K 20 keV cascade Sim. Time from 5ps up to 30 ps

14. Final distributions of defects • NRT efficiency becomes stable at ~ 0.3 • Fraction of Cr ~ 0.65 in surviving dumbbells, whereas concentration is 10%, very small amount of Cr-Cr dumbbells, although Cr-Cr has MAX Ebind • Approximation of Fr; pairs gives 0.87 exponential factor, which is slightly higher than for pure Fe

15. Clustered fraction for vacancies and interstitials • significant influence of criteria for vacancy and interstitial clustering detection • considerable increase of clustering from 10 keV PKA energy for SIA clustering, but not regular • at the moment no essential influence of Cr component • despite that 65% of dumbbells contain Cr, only 20% of Cr atoms belong to big clusters (with size more than 5 atoms) • discrepancy between our results and other simulation results for pure Fe 3rd nn for SIA 2nd nn for vacancy

16. VisualizationSubcascade formation evidence Final assesment Final assesment

17. VisualizationDense cascade (affected by PBC) Final assesment Final assesment

18. The TDE predicted by the potential are in the correct range of values, considering the existing uncertainties. The evolution in time of the cascades is physically acceptable. Long lived cascades (Epka>10keV) may be connected with formation of dense cascades. With rising energy, this effect disappears, which could be connected with formation of subcascades (in some cases) The total number of Frenkel pairs obtained in displacement cascades is less than NRT (efficiency < 0.3 - asymptote). Quite stable after 10 kev PKA energy. During the post-cascade stage a tendency to increasing number of Fe-Cr dumbbells at the expense of Fe-Fe dumbbells was observed. In all considered cases the number of mixed dumbbells exceeds Fe-Fe dumbbells. Clustering in high energy cascades needs more detailed study and longer simulations, nevertheless there is evidence of big SIA cluster formation in the case of cascade splitting, while the formation of big vacancy clusters could be a product of dense cascades. After the cooling stage of the cascade, small vacancy clusters and sizeable interstitial were detected, this qualitatevly agrees with other calculations. But statistic is too poor to give a certain conclusion. Conclusions