A.V. Kozlov , I.A. Portnykh, V.L. Panchenko

A.V. Kozlov, I.A. Portnykh, V.L. Panchenko

FSUE «INM», 624250, Box 29, Zarechny, Sverdlovsk region, RussiaCorresponding author. fax: +7-34377-33396; e-mail: [email protected], [email protected]

A model of influence of A model of influence of radiation damage rate on radiation damage rate on

formation and evolution of formation and evolution of radiation defects in radiation defects in

austenitic steelsaustenitic steels..

Fast neutron reactorFast neutron reactorG G 10 10--66 dpa/sdpa/s

2IntroductionIntroduction

Correctness ?

Correctness ?

Thermal reactorThermal reactorG G 10 10--881010--77 dpa/sdpa/s

Results of fast neutron Results of fast neutron reactor irradiationreactor irradiation

G G 10 10--66 dpa/sdpa/s

Results of an Results of an accelerating irradiation accelerating irradiation

G G ≥≥ 10 10-4-4 dpa/sdpa/s predictpredict

predictpredict

predictpredict

3

The purpose of the workThe 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.

Basic positions of modelBasic 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:

Gg xx

x

xx

x cG

dtdc

5

Объект исследованияОбъект исследованияBasic positions of model; Basic positions of model; examined temperature range examined temperature range

Middle Temperature Middle Temperature Irradiation (MTO-2)Irradiation (MTO-2)

Low Temperature Low Temperature Irradiation (LTO)Irradiation (LTO)

ii –mobile - dissociate from –mobile - dissociate from cascade areas and freely cascade areas and freely diffuse in matrix diffuse in matrix ((ii=1);=1);

vv - - remain in cascade remain in cascade formation area, formation area,

transformed into compact transformed into compact energy-binding energy-binding

configurations - vacancy configurations - vacancy clusters clusters ((vv=0)=0)..

ii –mobile - dissociate –mobile - dissociate from cascade areas and from cascade areas and freely diffuse in matrixfreely diffuse in matrix;;

vv - - dissociate from dissociate from clusters and diffuse in clusters and diffuse in

matrix. matrix.

Low Temperature Irradiation (LTO). Model.Low Temperature Irradiation (LTO). Model.6

Diffused interstitials migrate to three type of sink: grain boundary, dislocations and inside clusters.

Grain boundaryGrain boundaryDislocationDislocation

Interstitial-vacancy recombination Interstitial-vacancy recombination process leads to cluster vanish. The process leads to cluster vanish. The

cluster size doesn’t change at the cluster size doesn’t change at the recombination process.recombination process.

Cluster evolutionCluster evolution

Cluster after thermodynamic Cluster after thermodynamic stabilizationstabilization

Low Temperature Irradiation (LTO). Model.Low Temperature Irradiation (LTO). Model.7

Calculation resultsCalculation results8

Where dg – grain size;d - dislocation density;nc – clusters concentration;rc – average size of clusters.

Formula for diffusion time of interstitials:

222

_

))10/210/2/(20)/exp(3

arnadakTE

ccdg

mii

For ChS-68 steel at For ChS-68 steel at GG221010-7-7 dpa/s and dpa/s and Т Т300 300 КК

ii 1010--11 s s


Interstitials concentration: )/exp(1 iii tGс

Fig. 1. Time dependence of interstitials concentration in ChS-68 steel at neutron irradiation at G210-7 dpa/s and Т300 К.

0,0

0,4

0,8

1,2

1,6

2,0

0 0,5 1 1,5 2Time, s

Inte

rstit

ial c

once

ntra

tion,

10-8


Where m0 - average amount of vacancies in cluster at formation moment.

Average lifetime of clusters:

For ChS-68 steel at For ChS-68 steel at GG221010-7-7 dpa/s and dpa/s and Т Т33110 0 КК

Average lifetime of clusters Average lifetime of clusters 101033-10-1044 сс

cc

dgc n

rad

Gmat 2

03 )2/(10

4

Calculation resultsCalculation results 11

Clusters concentration:

Fig. 2. Time dependence of radiation clusters concentration in ChS-68 steel at neutron irradiation at G210-7 dpa/s and Т300 К.

)12

1( tg

nc

Clusters generation rate: 3

0

4amGg

2

)2/(10

c

dg

rad

0,00,20,40,60,81,01,21,41,6

0 1 2 3 4Time, 104 s

Clu

ster

s con

cent

ratio

n,

1023

m-3


Fig. 3. Time dependence of average vacancy concentration in cluster for various damage dose rates in ChS-68 steel at neutron irradiation at Т310 К.

0,09

0,10

0,11

0,12

0,13

0,14

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0Time, 104 s

Vaca

ncy

conc

entra

tion

in

clus

ter

G=1E-8 G=5E-8 G=1E-7 G=2E-7 G=1E-6

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Calculation resultsCalculation results

The irradiation with lower damage The irradiation with lower damage dose rate leads to more strong dose rate leads to more strong

radiation damages, than at higher radiation damages, than at higher damage dose rate (at the same damage dose rate (at the same

damage dose).damage dose). !!

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Low Temperature Irradiation (LTO) – Experimental dataLow Temperature Irradiation (LTO) – Experimental data

The experimental examinations after The experimental examinations after irradiation and post annealing of two irradiation and post annealing of two austenitic steels ChS-68 (16Cr-15Ni-austenitic steels ChS-68 (16Cr-15Ni-

2Mo-2Mn-Si-Ti) in a state after final 20 2Mo-2Mn-Si-Ti) in a state after final 20 % cold work and EI-844 (16Cr-15Ni-% cold work and EI-844 (16Cr-15Ni-

2Mo-Mn-Si-Nb) in austenitic state were 2Mo-Mn-Si-Nb) in austenitic state were carried out. The irradiation was carried carried out. The irradiation was carried out at temperature 310 K to damage out at temperature 310 K to damage

dose 0.0007 dpa for ChS-68 and 0.007 dose 0.0007 dpa for ChS-68 and 0.007 dpa for EI-844 steels.dpa for EI-844 steels.

Comparing calculated and experimental dataComparing calculated and experimental data 15

TableTable 1 – 1 – Relative sizeRelative size changes changes (%) (%) of ChS-68 and EI-844 of ChS-68 and EI-844 steel specimens irradiated at temperaturesteel specimens irradiated at temperature 310 К, 310 К, caused by caused by

an annealing of radiation clustersan annealing of radiation clusters..

Material Dilatometry data Calculated data

ChS-68 0.012 0.007

EI-844 0.010 0.006

Middle Temperature Irradiation (MTO). Model.Middle Temperature Irradiation (MTO). Model.16

Average diffusion time of interstitials and vacancies was calculated by the same methodic:

dtc

Gdс

i

ii )(

_

dtc

Gdс

v

vv )(

_

)( vi cf

Formulas for vacancy diffusion time and interstitial diffusion time was obtained.

For ChS-68 steel at For ChS-68 steel at GG111010--66 dpa/s and dpa/s and Т Т70700 0 КК

vv 101033 s, s, ii 1010--33 s s

0,00,5

1,01,5

2,02,53,0

3,54,0

4,55,0

-8 -7 -6 -5 -4


Fig. 6. Dependence of quasi-equilibrium vacancy concentration on irradiation damage rate in ChS-68 steel irradiated at different temperatures.

LgG

Vac

ancy

con

cent

ratio

n, ×

10-5

600 K

700 K

800 K

05

101520253035404550

-8 -7 -6 -5 -4


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

Inte

rstit

ials

con

cent

ratio

n, ×

10-1

0

0

20

40

60

80

100

-8 -7 -6 -5 -4


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

Cve

/Cie, ×

105

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Middle Temperature Irradiation (MTO). Middle Temperature Irradiation (MTO). Model.Model.

It is incorrectly to use plainly the It is incorrectly to use plainly the results obtained at high damage results obtained at high damage

dose rate irradiation for prediction dose rate irradiation for prediction influence of low damage dose rate influence of low damage dose rate

irradiation on material structure irradiation on material structure changes.changes.

!!

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ConclusionsConclusionsThe 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.

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ConclusionsConclusions

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.

Thank you for Thank you for attention and attention and

patiencepatience

A.V. Kozlov , I.A. Portnykh, V.L. Panchenko

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