2137-32 Joint ICTP-IAEA Advanced Workshop on Multi-Scale Modelling for Characterization and Basic Understanding of Radiation Damage Mechanisms in Materials 12-23 April 2010 MD simulation of interaction between radiation damages and microstructure: voids, helium bubbles and grain boundaries N. Lazarev Akhiezer Institute for Theoretical Physics Kharkov Ukraine
MD simulation of interaction between radiation damages and microstructures: voids, helium bubbles and grain boundaries n.lazarev@kipt.kharkov.ua
Collaboration Anatole A. Turkin Vladimir I. Dubinko Kharkov Institute of Physics and Technology, Ukraine Robin Schäublin EPFL SB CRPP Groupe Matériaux, PSI, Switzerland ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 2
Motivation = α κ + + = α κ + + κ = κ κ = κ = 0 α = 4π + It is assumed that under irradiation, Frenkel pairs of vacancies and SIAs are created in the bulk and annihilated at extended defects, such as dislocations, grain boundaries, cavities and the like, which are thus considered primarily as the sinks for point defects. However, extended defects can act also as the radiation-induced sources of point defects, which can result in a new driving force of the microstructural evolution. ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 3
Motivation External surface 10 kev, Au M. Ghaly and R.S. Averback, Phys. Rev. Lett. 72 (1994) 364. Bilayer interfaces 5 kev, Co/Cu K. Nordlund and R. S. Averback, Phys. Rev. B59 (1999) 20. Grain boundaries 20 kev, Ni M. Samaras, P. M. Derlet, H. Van Swygenhoven, M. Victoria, Phys. Rev. Lett. 88 (2002) 125505. ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 4
Motivation Kai Nordlund et al, Nature 398 (1999) 6722 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 5
Motivation M. Samaras, W. Hoffelner, M. Victoria, J. Nucl. Mat. 352 (2006) 50 56 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 6
Outline ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 7
Simulation method U = V ( r + ij ) F( ρi ) ρ = ij i i φ( r ij ) j ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 8
Defect production close to voids in Cu N. P. Lazarev, V. I. Dubinko, Radiat. Eff. & Def. Solids 158 (2003) 803. V.I. Dubinko, N.P. Lazarev, Nucl. Instr. Meth. Phys. Res. B 228 (2005) 187 SIA PKA Void Vacancy ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 9
Displacement threshold energy in bulk Cu at T = 4 K E d pc, ev N. P. Lazarev, V. I. Dubinko, Radiat. Eff. & Def. Solids 158 (2003) 803. D. J. Bacon, H. F. Deng, F. Gao, J. Nucl. Mater. 205 (1993) 84. 100 [322] [311] 80 [520] [221] [211] 60 [720] 40 [110] [810] [111] 20 [210] [100] [441] [100] 0 0 20 40 60 80 100 120 140 Angle, deg ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 10
A biased formation of vacancies in the vicinity of void 10 Number of defects 1 0.1 Vacancies FP in bulk SIAs 10 100 1000 PKA Energy, ev ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 11
Simulation of void dissolution by subthreshold irradiation R 2 δ R 1 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 12
Time of thermal dissolution of void ( ) 0 = 4 π = exp( 2γ ) γ = σω / 0 ( 1 exp(2 / ) ) / = γ τ = 3 0 0 2γ 0 ( 2 + exp(2γ / )) τ ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 13
Time dependence of void size during irradiation 15 T = 1000 K E K = 18 ev >5000 cascades R, A 12 9 6 V 0 =1004ω 3 0 50 100 150 200 Time, ns ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 14
Different stages of void dissolution ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 15
ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 16 Void dissolution rate due to radiation emission of vacancies α R r = 2 2 * 1 1 2 ), ( ), ( Δ + < < = 0,, ), ( 0 + Δ Δ 2 2 0 π ) / exp(2 4 0 γ π = γ = σω / ) ( 4 ) / exp(2 ~ 0 2 0 + Δ Δ + = γ
Void dissolution rate due to radiation or thermal vacancies 10-2 Dose rate, K 10-4 10-6 10-8 Irradiation dissolution Thermal dissolution 10-10 300 400 500 600 Temperature, o C ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 17
Critical size of a void vs temperature and dose rate 10 3 R c, A 10 2 K = 10-8 10-6 10-4 10-3 10 1 10 0 300 400 500 600 700 Temperature, o C ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 18
Diffusion and primary damages in Fe 10-4 D, cm 2 /s 10-5 10-6 10-7 V SIA 0.5 1.0 1.5 2.0 2.5 3.0 3.5 1000/T, K -1 i v ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 19
Primary damages in displacement cascades ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 20
Variable time step. E PKA = 20 kev, T = 900 K K max, ev ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 21
Point defect distribution, E PKA = 20 kev, T = 900 K SIAs SIA disl. loop Vacancy clusters vacancies ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 22
Cascade evolution in time. 1 frame per 500 MD time steps ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 23
Cascade evolution in time, another view ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 24
Defect production in perfect crystal at T = 300K 100 10 1 0.1 0.1 1 10 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 25
Number of Frenkel pairs vs. PKA energy at T = 900K 100 10 1 0.1 0.1 1 10 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 26
Effect of cascade defects annealing at high temperature 10 1 0.1 1 10 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 27
Survived point defects fraction ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 28
Distribution of cluster sizes 20 15 10 5 0 0 10 20 30 40 20 15 10 5 0 0 10 20 30 40 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 29
Defects production near voids ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 30
Some final states of cascade development near voids SIAs vacancies Void ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 31
Cascade evolution near a void. 1 frame per 500 MD time steps ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 32
Cascade evolution near void. 1 frame per 500 MD time steps ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 33
Defect production near voids at T = 300K 100 10 1 0.25 0.5 1 2 4 8 16 32 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 34
Defect production near voids at T = 900K 100 10 1 0.25 0.5 1 2 4 8 16 32 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 35
Melting temperature of He vs pressure 10-1 P, ev/a 3 10-2 10-3 10 1 10 2 10 3 T m, K ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 36
Equation of state for Helium 50 40 800K 600K 50 40 V a, A 3 30 20 10 300K 100K V, A 3 30 20 10 0 10-3 10-2 10-1 P, ev/a 3 0 0 10 20 30 40 kt/p, A 3 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 37
Defects production near He bubbles ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 38
Cascade evolution near bubble. 1 frame per 500 MD time steps ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 39
Cascade evolution near bubble. 2-nd example ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 40
Defect production near bubbles at T = 300K 100 300K 10 1 0.25 0.5 1 2 4 8 16 32 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 41
Defect production near bubbles at T = 900K 100 900K 10 1 0.25 0.5 1 2 4 8 16 32 ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 42
Simulation of recrystallization under irradiation ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 43
Homogeneous irradiation of polycrystal ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 44
Heterogeneous irradiation of polycrystal ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 45
Heterogeneous irradiation of polycrystal ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 46
Conclusion ICTP/IAEA Workshop on Multi-Scale Modelling, Trieste 12-23 April 2010 47