Mechanisms of recovery of radiation damage based on the interaction - - PowerPoint PPT Presentation

Mechanisms of recovery of radiation damage based on the interaction of quodons with crystal defects

Vladimir Dubinko

NSC Kharkov Institute of Physics and Technology, Kharkov, Ukraine

OUTLINE

1. Driving forces of microstructure evolution 2. Void growth and shrinkage: MD simulation 3. Radiation-induced solubility limit: Focuson concept 4. Experimental evidence for the radiation-induced annealing of voids and dislocation loops 5. Theoretical estimates: the need for quodons 6. Quodon definition and discovery 7. Experimental evidence 8. Applications in physics of radiation effects: Swelling saturation and reduction with increasing irradiation dose Self-organization of voids Electron-plastic effect

Outstanding problems

Radiation-induced void swelling

1.2 MeV Cr 3+ → Ni (600oC, ~25 dpa) DOSE ATE:

3

7 10 / dpa s

−

×

Driving forces of microstructure evolution

SIA Crowdion Focuson VAC

_

Perfect crystal

PKA

a

SIA Crowdion Focuson PKA VAC

Crystal with ED

_ _ _ _ _

GB

b

Void

v

c D

Void Void

⎭ ⎬ ⎫ ⎩ ⎨ ⎧ kTR Dcth

v

γω 2 exp

Thermal treatment

v vc

D Irradiation

i ic

D ( ) ( )

R E E bl E E K Dc

v F F F d irr vR

,

0Φ

≈

HISTORY

“For many years already we study the void swelling in reactor materials, but to solve the problem one should know how the void shrink rather than grow…” Ilya Naskidashvilly, Winter School, Bakuriani, Georgia1980

20 years later…

MD simulation of point defects production in the vicinity of extended defects

Schematic representation of point defect formation near a void. Illustration of the final stages of collision cascade developments in the bulk (left) and near the void (right) at PKA energy 1 keV.

10 100 1000 5 10

FP in bulk Interstitials Vacancies Number of defects PKA Energy, eV

10 100 1000 20 40 60 80 100

In Bulk Near Void Number of displaced atoms PKA Energy, eV

In contrast to the Frenkel pair production in the bulk, the collision events in the vicinity of extended defects results in a biased formation of vacancies due to the lower energy barrier involved

• N. P. Lazarev, V. I. Dubinko,
• Radiat. Eff. Def. Solids 158 (2003) 803

Radiation-induced solubility limit

( ) ( ) ( )

K T c T c K T c

irr v th v eq v

, , + =

( )

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛− = T k E T c

B f v th v

exp

( ) ( )

( )

F SD v F d v F irr v

E E E E K T D Kbl K T c , , , Φ ≈

( )

dx E E x x E E

F SD v

E E SD v F F SD v

∫

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = Φ

1

ln ln ,

m v f v SD v

E E E + =

Self-diffusion activation energy

0.2 0.4 0.6 0.8 1.10 13 1.10 12 1.10 11 1.10 10 1.10 9 1.10 8 1.10 7 1.10 6 1.10 5 1.10 4 1.10 3 0.01 0.1 1

Thermal equilibrium Radiation-induced equilibrium Total equilibrium Steady-state

HOMOLOGICAL TEMPERATURE VACANCY CONCENTRATION

Ee = 1 MeV

Radiation-induced reduction in the void swelling

V.I. Dubinko, A.G. Guglya, E. Melnichenko, R. Vasilenko, EMRS 2008, Journal of Nuclear Materials, 385 (2009) 228-230

Cr 3+ → Ni (600oC, ~25 dpa) Cr 3+ → Ni (600oC, ~25 dpa) + Cr 3+ → Ni (450oC, ~25 dpa) Cr 3+ → Ni (600oC, ~25 dpa) + Cr 3+ → Ni (525oC, ~25 dpa)

1 3

10 7

− −

× = s K

1021 ions/m2 ION FLUENCE DOSE RATE

Radiation-induced void shrinkage

Experiment

1 2 3 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 Void density, x 1015 cm-3 Tipe of irradiation 1 - Cr3+ (600oC) 2 - Cr3+ (600oC + 525oC) 3 - Cr3+ (600oC + 450oC) 1 2 3 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 Void diamiter, nm Tipe of irradiation 1 - Cr3+ (1,2 MeV, 600oC, 1017ion/cm2) 2 - Cr3+ (600oC + 525oC ) 3 - Cr3+ (600oC + 450oC)

1 2 3 1 2 3 4 5 6 7 Swelling, % Tipe of irradiation 1 - C3+ (600oC) 2 - Cr3+ (600oC + 525oC) 3 - Cr3+ (600oC + 450oC)

DOSE RATE

1 3

10 7

− −

× = s K

H+(30 keV) - Ni, 600oC, 3 dpa, (1018 ion/cm2 600oC, 3 dpa + 450oC, 6 dpa

Proton irradiation of nickel samples

(Dubinko, Guglya, 2009)

0.0 0.5 1.0 1.5 2.0 2 4 6 8 10 12 14 16 18 20

Void size, nm Dose, x 10

18 ion/cm 2

Proton irradiation of nickel samples

(Dubinko, Guglya, 2009)

0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Void density, x 10

16 cm

• 3

Dose, x 10

18 ion/cm 2

0.0 0.5 1.0 1.5 2.0 1 2 3 4 5 6 7 8 9 10

Swelling, % Dose, x 10

18 ion/cm 2

Dose dependence of void size (a), void density (b) and swelling (c) in nickel irradiated by H+ ions ( 30 keV, 3 dpa (1018 ion/cm2)) at 600оС and 450оС.

Radiation damage and electron radiation induced recovery in ZnTe

Lu, Niu, Wang Radiation Effects and Defects in Solids, 116 (1991) 81 - 94

3,5 and 7 keV Ar ion irradiation produced defects in ZnTe crystals and their annealing are investigated using transmission electron microscopy. The defects are identified to be densely distributed small dislocation

• loops. Under electron beam irradiation (80-200 keV), these dislocation

loops are seen to reduced in density considerably. This electron beam induced defect annealing is explained qualitatively in terms of the non- radiative recombination of excited electron on the defects

Radiation-induced void shrinkage

theory ( )

[ ]

K T c D Z c D Z c D Z R dt dR

eq v v V v i i V i v v V v

, 1 − − =

700 800 900 1000 1100 1200 10 5 5 10 15 20 Breather range 10000 b Breather range 1000 b Focuson range 10 b ("classical" limit) Breather range 10000 b Breather range 1000 b Focuson range 10 b ("classical" limit) TEMPERATURE (K) VOID GROWTH RATE, nm/h

Temperature dependence of the Void growth/shrinkage rate in Ni for different ranges of breather propagation.

1 3

10 7

− −

× = s K

DOSE RATE

Quodon definition

As the incident focuson energy is dispersed but the available kinetic energy still far exceeds that of phonons, atoms experience large displacements from their equilibrium positions. Propagation of the corresponding lattice vibrations may be governed by nonlinear forces. This may result in formation of vibrational particle-like solitons, called discrete breathers (DBs) or quodons (QODs). According to molecular dynamic simulations, the DBs are mobile, highly anharmonic longitudinal vibrations that are sharply localized in longitudinal direction and practically across one atomic distance in the transverse direction. The main difference between focusons and breathers (quodons) is that the latter are stable against thermal motion.

Discrete breathers can move and transport coherently energy through the lattice: Interaction of moving discrete breathers with vacancies, J Cuevas, 1 JFR Archilla, B S´anchez-Rey, FR Romero, 2005

Energy density plot for the interaction moving breather–vacancy. The particle to the right of the vacancy is located at n = 0. In (a), the moving breather is reflected and the vacancy moves backwards, in (b) the breather is transmitted and the vacancy moves backwards.

F.M. Russell, J.C. Eilbeck, Evidence for moving breathers in a layered crystal insulator at 300 K,

Europhysics Letters 78, 10004, 2007.

Ejection of atoms at a crystal surface caused by energetic breathers which have travelled more than 107 unit cells in atomic chain directions. The breathers were created by bombardment of a crystal face with heavy ions. This effect was observed at 300K in the layered crystal muscovite, which has linear chains of atoms for which the surrounding lattice has C2 symmetry.

Swelling saturation and void ordering

Breather

Micrographs of bcc void lattices following ion irradiation in molybdenum, (111) projection [J.H. Evans, in Patterns, Defects and Materials Instabilities, 1990]. Dissolution of a void in the “interstitial” position due to the absorption of breathers coming from larger distances as compared to “regular” voids [V. Dubinko, Nuclear Inst. and Methods in Physics Research, 2009]

Vacancy voids have been produced in Ni by 1.2 MeV Cr

ion irradiation at 873 oK up to the ion fluence of 1021 ions m-2 Irradiation of specimens containing voids at 798 oK and 723oK has resulted in the radiation-induced annealing of voids . The experimental results may be explained in the framework of the rate theory taking into account the interaction of voids with long-propagating discrete breathers

• quodons.

SUMMARY #1

Outstanding problem: How to observe quodons in conventional MD ?

The energy relaxation simulations in Cu at T = 1 K,

Lazarev, Dubinko, 2003

INVESTIGATION OF THE ELECTRON-PLASTIC EFFECT

• In 60-70th of the last century a pioneering study

was made on the effect of electron beam on plastic deformation of some hcp and fcc metals. However, the underlying mechanisms of the

• bserved effects are still a subject of debates.
• In the present paper, we report on the effect of

electron beam of (0.5 MeV energy and 5х1013 сm-2s-1 density) on plastic deformation of polycrystalline aluminum (99,5%) and copper (99,5%) under uniaxial deformation at a rate of 1.6x10-4s-1 at room temperature.

Deformation hardening of aluminum samples (a) without irradiation (1) and under electron irradiation (2); It can be seen that irradiation results in the softening of the material. (b) Temperature increase due to electron beam was 20 to 40 oC, which was insufficient to explain the observed effects.

Experimental investigation of the electron-plastic effect under electron irradiation

Dubinko, Lebedev, Kushnir et al, NSC KIPT, 2008

Electron beam pulse parameters: Tпак = ( 1-3)x 10-6 s, wпак = 50 hz, φе = 5.1013 сm-2s-1

Experimental investigation of the electron-plastic effect under electric current

EPE dependence on the electric current density in Cu (99.5%) at 300 K and the strain rate is 2.7x10-4 s [Lebedev et al, Kharkov National University, 2008] The linear dependence can not be explained by Joule heating of the sample

Phonon distribution function calculated with increasing time under electric current pulse. Red curve is the equilibrium Bose- distribution function T= 20 K; Е = 94 V/сm

t

Electron distribution function calculated with increasing time under electric current pulse. Red curve is the equilibrium Fermi- distribution function. T= 20 K; Electric field, Е = 94 V/сm

Hypothesis:

If “hot” electrons can generate quodons under electron irradiation and under electric current pulse conditions, it may explain the EPE in both cases.

Outstanding problem: Quodon mechanism of the EPE

Summary

• Mechanical properties of materials under irradiation are different

from those under post-irradiation tests, which should be taken into account in forecasting the lifetime of nuclear power plants.

• Nonequilibrium

fluctuations of energy states of the atoms surrounding crystal defects arise as a result of their interaction with radiation-induced quodons. These fluctuations result in radiation- induced recovery processes such as the void shrinkage and

• rdering, saturation and even reduction of swelling, radiation-

induced softening. So the quodon mechanics should be taken into account in modeling of material response to irradiation.

THANK YOU FOR YOUR ATTENTION!