Transcript Заголовок слайда отсутствует

A.V. Kozlov, I.A. Portnykh,
V.L. Panchenko
A model of influence of
radiation damage rate on
formation and evolution of
radiation defects in
austenitic steels.
FSUE «INM», 624250, Box 29, Zarechny, Sverdlovsk region, Russia
Corresponding author. fax: +7-34377-33396;
e-mail: [email protected], [email protected]
Introduction
Results of an
accelerating irradiation
G ≥ 10-4 dpa/s
Fast neutron reactor
G  10-6 dpa/s
predict
Results of fast neutron
reactor irradiation
G  10-6 dpa/s
Thermal reactor
G  10-810-7 dpa/s
2
3
The 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:
gx  x   G
Change of point defect concentration in matrix:
dc x
cx
 x   G 
dt
x
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).
Basic positions of model;
Объект
исследования
examined temperature range
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).
Middle Temperature
Irradiation (MTO-2)
i –mobile - dissociate
from cascade areas and
freely diffuse in matrix;
v - dissociate from
clusters and diffuse in
matrix.
5
Low Temperature Irradiation (LTO). Model.
Diffused interstitials migrate to three type of sink: grain
boundary, dislocations and inside clusters.
Dislocation
Grain boundary
6
Low Temperature Irradiation (LTO). Model.
7
Cluster after thermodynamic
Interstitial-vacancy recombination
stabilization
process leads to cluster vanish. The
cluster size doesn’t change at the
recombination process.
Cluster evolution
8
Calculation results
Formula for diffusion time of interstitials:
3  exp( Emi / kT )
i 
2
2
2
20  (a / d g  2 d  a / 10  2nc  rc  a / 10 ))
_
Where dg – grain size;
d - dislocation density;
nc – clusters concentration;
rc – average size of clusters.
For ChS-68 steel at G210-7 dpa/s and Т300 К
i  10-1 s
9
Calculation results
Interstitials concentration:

сi    G i  1  exp(t / i )

Interstitial concentration, 10
-8
2,0
1,6
1,2
0,8
0,4
0,0
0
0,5
1
1,5
2
Time, s
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
Average lifetime of clusters:

a 3  m0  10 /( 2d g )   d  a

tc 


n
c

4  G 
rc2

Where m0 - average amount of vacancies in cluster at
formation moment.
For ChS-68 steel at G210-7 dpa/s and Т310 К
Average lifetime of clusters
103-104 с
11
Calculation results
nc    ( 1 
Clusters concentration:
4  G
g
3
m0  a
Clusters
generation rate:
2g

 
 t  1)
10 /( 2d g )  d  a
rc2
Clusters concentration,
1023 m-3
1,6
1,4
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.
1,2
1,0
0,8
0,6
0,4
0,2
0,0
0
1
2
3
4
4
Time, 10 s
12
Vacancy concentration in
cluster
Calculation results
0,14
0,13
0,12
0,11
0,10
0,09
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
Time, 104 s
G=1E-8
G=5E-8
G=1E-7
G=2E-7
G=1E-6
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
Calculation 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).
!
Low Temperature Irradiation (LTO) – Experimental data
The experimental examinations after
irradiation and post annealing of two
austenitic steels ChS-68 (16Cr-15Ni2Mo-2Mn-Si-Ti) in a state after final 20
% cold work and EI-844 (16Cr-15Ni2Mo-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.
14
Comparing calculated and experimental data
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.
Material
Dilatometry data
Calculated data
ChS-68
0.012
0.007
EI-844
0.010
0.006
15
Middle Temperature Irradiation (MTO). Model.
Average diffusion time of interstitials and vacancies was
calculated by the same methodic:
dс i  (  G 
ci
_
i
)dt
dс v  (  G 
cv
_
v
)dt
 i  f (cv )
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  103 s, i  10-3 s
16
600 K
700 K
800 K
Vacancy concentration, ×10-5
Middle Temperature Irradiation (MTO). Model.
5,0
4,5
4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
-8
-7
-6
-5
-4
LgG
Fig. 6. Dependence of quasi-equilibrium vacancy concentration on
irradiation damage rate in ChS-68 steel irradiated at different
temperatures.
17
600 K
700 K
800 K
Interstitials concentration, ×10-10
Middle Temperature Irradiation (MTO). Model.
18
50
45
40
35
30
25
20
15
10
5
0
-8
-7
-6
-5
LgG
Fig. 7. Dependence of quasi-equilibrium interstitials concentration
on irradiation damage rate in ChS-68 steel irradiated at
different temperatures.
-4
19
Middle Temperature Irradiation (MTO). Model.
100
600 K
700 K
800 K
Cve/Cie, ×105
80
60
40
20
0
-8
-7
-6
-5
-4
LgG
Fig. 8. Dependence of ratio vacancies concentration to interstitials
concentration on irradiation damage rate in ChS-68 steel
irradiated at different temperatures.
Middle 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.
!
20
Conclusions
21
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.
Conclusions
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.
22
Thank you for attention
and patience