Neutron cross sections for defect production by high energy displacement cascades in copper

1023

Journal of Nuclear Materials 122 & 123 (1984) 1023-1027 North-Holland, Amsterdam

NEUTRON CROSS SECTIONS

H. L. HEINISCH Hanford

FOR DEFECT PRODUCTION

BY HIGH ENERGY DISPLACEMENT

CASCADES

IN COPPER*

and F. M. MANN

Engineering

Development

Lab, Richland,

WA, 99352

Defect production cross sections for copper have been devised, based on computer simulations of displacement cascades. One thousand cascades ranging in energy from 200 eV to 200 keV were generated with the MARLOWE computer code. The cascades were subjected to a semi-empirical cascade quenching procedure and to short-term annealing with the ALSOME computer code. Functions were fitted to the numbers of defects produced as a function of primary knock-on atom (PKA) damage 1) the total number of point defects after quenching and energy for the following defect types: after short-term annealing, 2) the numbers of free interstitials and free vacancies after shortterm annealing, and 3) the numbers and sizes of vacancy and interstitial clusters after shortterm annealing. In addition, a function describing the number of distinct damage regions (lobes per cascade was fitted to results of a graphical analysis of the cascade configurations. The defect production functions have been folded into PKA spectra using the NJOY nuclear data processing code system with ENDF/B-V nuclear data to yield neutron cross sections for defect produc tion in copper. The free vacancy cross section displays much less variation with neutron energy than the cross sections for damage energy or total point defects.

4.

1. INTRODUCTION Defect production ter simulations development

functions

based on compu-

are a valuable

of correlation

Approximately

resource for the

Neutron

models.

one thousand

the number of distinct

cross-sections

for the production

cascades,

damage regions

(lobes) per cascade.

ranging

were then determined

of these defects.

The primary purpose of this paper is to pre-

in energy from 200 eV to 200 keV, were generated

sent the defect production

functions

in Cu with the MARLOWE computer

brief discussion

The models and com-

cascades were subjected cascade quenching

The

to a semi-empirical

procedure

annealing with the computer Functions

code.'

puter codes for generating,

and to short-term

short-term

code ALSOME.

discussed

were then fitted to the numbers of

defects produced

as a function of PKA damage

energy.

annealing

of the tabulated

functions

are described

here:

and a

quenching

the cascades

in detail elsewhere.2

and

have been Publication

neutron cross sections

with a broader discussion approximations

The following

of them.

employed

along

of the impact of the in the simulations

is

anticipated.

1. the total number of point defect pairs after quenching 2.

the numbers of free vacancies

interstitial 3.

and after short-term

atoms after short-term

annealing and free annealing

the numbers of vacancy and interstitial

clusters

after short-term

annealing,

and the

cluster sizes

*This work is sponsored #DE-AC06-76FF02170.

2. SIMULATIONS Displacement

cascades

stages: the collisional

is the athermal rearrangement the temperature

of the cascade

that of the crystal)

by the U.S. Department

0022-3 115/84/$03.00 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

are modeled

in three

stage, quenching

(which

of the defects as region approaches

and short-term

annealing

of Energy, Office of Fusion Energy, under Contract

1024

H.L. Heinisch. F.M. Mann /Neutron

(during which the defects rearrange through thermally

activated

the crystal temperature). short-term

cross sections for defect production

themselves

defect diffusion Both quenching

,

I

I

1

/

1

-QUENCHED(U4)

at

----SHORT-TERM ANNEALED(V&

and

annealing consist only of interac-

tions among the defects of a single isolated cascade. migrate

"Free defects"

are those which

far away from the boundaries

cascade region during short-term The cascades

are generated

ing atomic displacements temperature

of 300K.

of the

annealing.

in a crystal hav-

corresponding

Cascades

short-term

and quenching

annealing

During

the interstitials,

being

Although

of the temperature.

the precise temperature crystal temperature

is not important, the

for the functions

presented

here is assumed to be in the range where vacancies

are mobile but vacancy cluster

dissociation

is not activated

The results of the simulations

were tabula-

of the average PKA damage

energy

loss model.

larger than the damage energies

calculated

from

the Lindhard model. Quenching

annealing

gerated parameter

code, modified

and interaction values.

to allow

with exag-

The quenching

were chosen so that the number of

defect pairs remaining

after the quench was

equal to that extracted3 measurements

1

would remain

results,

labeled ~4, are what

irrmediately after quenching

temperature,

indefinitely

and short-term

of PKA damage energy.

at 4K where defects

The results

interstitials

are not

labeled v300 are the

numbers of defect pairs remaining of isolated

at a temperature

at any

or what would remain

after short-

individual cascades

where both vacancies

are mobile,

and

about 300K for Cu.

The points are the results of the simulations,

is simulated with the ALSOME

defect migration

perature

as a function

term annealing

The MARLOWE values are at most a few percent

parameters

after quenching

annealing

mobile.

in MARLOWE with a local-

ized (Firsov) electronic

short-term

remaining

crystal

energy as determined

60

!io

The average number of defect pairs per PKA remaining after quenching and short-term annealing of isolated cascades in copper as a function of PKA damage energy. The points are results of the simulations, the solid line is equation 1, and the dashed line under it is equation 2.

The quenching

during short-term

annealing.

ted as functions

40

30

FIGURE

through

stages.

more mobile, will act before the vacancies move, regardless

20

PKADAMAGEENERGY(keV)

are not very

sensitive to the crystal temperature the collisional

la

to a

using quenching

parameters

of energy above 1 keV.

that are independent

The quenching

of the

200 eV and 500 eV cascades was simulated simple recombination.

by

The curve for quenching

is the function extracted 3

from resistivity

measurements,

from resistivity

on copper irradiated

at low tem-

(4K).

3. RESULTS 3.1 Total Point Defect Production Figure 1 shows the numbers of point defects

v4 = 0,

T ( 17 eV

= (0.66 1nT + 3.82 x 10w3T -l.gZ)TU/T,

T _> 17 eV,

(1)

1025

H.L. Heinisch, F.M. Mann 1 Neutron cross sections for defect production

c

energy T.

I

FkEE VAkANClEA (n,)

-

where TD is the damage energy for a PKA of

---FREEiNTERSTlTlALS

It is given by the Robinson

(nil

/a/

formula,4 T= D

/

'

/

T 11 + 0.1583 g(c)j'

/

/

where for Cu, g(E) = 3.4008

E"~

+ 0.40244

c3'4 + E

and E = 4.452 x 10s6 T. The results after short-term were well described

annealing

throughout

by scaling the quenched

A /

at 300K /

the energy range

function

/

by the factor

0.78. v300

= 0.78 v4

/

(2)

3.2 Free Defects Free defects

region during short-term

rather than recombining

or clustering

within the cascade. Figure 2 shows the numbers of free vacancies and free interstitials function

per cascade as a

I

I

I

I

20

30

40

50

PKADAMAGEENERGY(keV) FIGURE 2 The average number of free defects per PKA after short-term annealing of individual cascades in copper at 300 K. The points are results of the simulations. The solid line is equation 3 and the dashed line is equation 4.

of PKA damage energy.

At PKA energies

The number of free interstitials

less than about 1 keV there

I

I

10

are the mobile defects which

escape the cascade annealing

0

per cascade

of damage energy TD is:

are too few defects to form imnobile clusters, hence the defects annealing

remaining

keV the free defects fraction

after short-term

are all free defects.

are a small constant

of the total defects remaining

short-term

annealing.

in determining

An additional

the quenching

was that the fractions short-term

annealing

parameter

1.1 x lo3 eV 5 TD 2 5 x lo4 eV

= 0.14 '4,

To > 5 x lo4 eV

be small, in agreement 3.3 Defect Clusters per cascade of

According

to the model, two defects of the

same type that find themselves TD < 500 eV

(3)

= (0.032 + 1274 TD -ls2) v4,

form a single cluster.

model does not contain information

500 eV 2 TD 5 5 x lo4 eV

sufficient

to realistically

This simple physical

simulate the

details of cluster or loop formation even sophisticated

TD > 5 x lo4 eV

within a criti-

cal reaction distance of each other will spontaneously

= 0.035 v4,

(4)

values

damage energy TD is: V

TD < 1.1 x lo3 eV

= (0.13 •t 720 TD -') v4,

constraint

of free defects after

The number of free vacancies

= 0.78 v4,

= 0.78 v4,

after

with experiments.5-7

n

"i

Above lo-20

molecular

(indeed,

dynamics cannot

1026

H. L. Heinisch,

simulate the quenching cascades). dependence

However,

original

of high energy

3.4 Lobes

In the energy range of lo-30 keV, cascades

this simple model may be

for predicting

Nevertheless,

or becoming information

the numbers and sizes of clusters, qualification

of the

as opposed

free defects. is presented

that the model

begin the frequent

production

of multiple

damage regions, the number of which increases

the fractions

point defects that cluster,

to recombining

cross .rections for defect production

because of the strong

of the results on the initial defect

configuration, sufficient

F.M. Mann / Neutron

with energy.

average size, independent 30 keV.

here on

given the

These lobes have a maximum

The potential

damage parameter

of energy above about

usefulness

for correlating

of lobes as a yield strength

changes has been demonstrated8.

is quite simple.

The number of lobes per cascade as a

The average number of vacancy clusters,

function of PKA damage energy

larger than size four, as a function of PKA

is

TB < 1.2 x lo4 eV

L=O

(9)

damage energy is =_ .353 + 5.88 x lO-5 To, TU < 300 eV

NV = 0,

TB21.2 (5)

= 3.3 x lO-4 TU - 0.10,

TB 2 300 eV

The average size of vacancy clusters than size four, as a function

larger

of PKA damage

with ENDF/B-V

Damage energies

nuclear data.

were calculated

using the Robinson

S, = 9.2 [l - 0.5 exp (-3.6 x 10s4 T,,)],

(6)

here

functions

The code was used to generate

cross sections with a neutron for interstitials,

weighting

appropriate

described

75 group

spectrum

for a thermal reactor

below 10 eV and constant TB < 790 eV

formula-

The HEATR module of NJOY was modified

tion.4

above 10 eV.

Figure 3 shows the neutron cross sections (7)

= 4.6 x 1O-4 T,, - 0.36

eV

3.5 Neutron Cross Sections

to use the defect production

Ni = 0,

4

The neutron cross sections were calculated 9 using the NJOY nuclear data processing code,

energy is

Similarly

x 10

T,,2 790 eV

copper for total point defect production free defect production displacements

in

and

at 300 K, as well as for

per atom (dpa).

The dpa curve

depends only on nuclear data and an assumed

and

effective Si = 5.7 [l - 0.14 exp (-9 x 10m5 TB)]

displacement

energey of 30 eV.

(8) 4. CONCLUSIONS

At PKA energies distributions independent

of cluster

of energy,

than 10 keV the cluster energy dependent, clusters energy.

become

Neutron cross sections for the production

greater than 10 keV, the sizes are essentially

but at energies

size distributions

primarily

various defects

in displacement

copper have been determined

less are

in that larger

less frequent with decreasing

computer

simulations.

simulation,

cascades

and short-term

annealing,

were used to determine

production

functions

clusters.

in

from the results of

The results of the

after quenching

of

the defect

for free defects and

1027

H.L. Heinisch, F.M. Mann / Neutron cross sections for defect production

1

8

a idl ii

1

a dpa b POINT DEFECTS c FREE INTERSTITIALS

I

I

I

work.

The energy dependence

of the neutron

for free vacancy production

cross sections correspondingly

different.

show much less variation

is

The present results

of the free vacancy

cross section with neutron energy.

ACKNOWLEDGEMENTS The authors gratefully contributions

acknowledge

the

of D.G. Doran and R.L. Simons to

this work.

d

NEUTRON

ENERGY,

eV

REFERENCES

FIGURE 3 Damage cross sections for copper as a function of neutron energy for (a) displacements per atom (dpa), (b) total point defect pairs, (c) free interstitials and (d) free vacancies after short-term annealing of individual cascades at 300 K. The dpa cross sections are in barns, while the remaining curves have been normalized to the dpa curve at low energies to emphasize their relative energy dependencies. Because of the simplicity cluster

information

of the models,

get annihilated,

are in clusters,

cascade

were used for defect production

3.

R. L. Simons, DAFS Quarterly Progress Report July-Sept. 1980, DOE/ER--0046/13, U.S. Dept. of Energy (1980) 41.

4.

M. T. Robinson, British Nuclear

5.

T. H. Blewitt, A. C. Klank, T. Scott and W. Weber, Proc. Int. Cont. Radiation-Induced Voids in Metals, Albany, NY, 1971, eds. J. W. Corbett and L. C. Ianiello, NTIS, CONF-710601 (1972).

6.

J.

7.

U. Theis and H. Wollenberger, Mater. 88 (1980) 121.

8.

H. L. Heinisch and R. L. Simons, DAFS Quarterly Progress Report Jan-Mar 1982, Pi;/ER-0046/g, U.S. Dept. of Energy (1982)

9.

R. E. MacFarlane. R. J. Barrett. D. W. Muir and R. B. Boccourt, The NJOY Nuclear Data Processing System, Vol. I: Users Manual, LA-7584-M, Los Alamos National Laboratory (1978).

10

D. G. Doran, R. L. Simons and W. N. McElroy, ASTM STP 570 (1975) 290.

or escape the

simulations cross

but they ignored the cascade

sections,"

stage and long replacement

during cascade PKA energies

generation.

pertinent

not explicitly

modeled

significant

numbers.

differences

between

present

H. L. Heinisch,

of defects

cascade.

quenching

2.

may do a good

what fractions

Earlier displacement

M. T. Robinson and I. M. Torrens, w. ARev B9 (1972) 5008.

simulations

fewer free vacancies

J. Nucl. Mater.

in press.

in Nuclear Fusion Reactors, Energy Sot. (1980).

the

should be used with some

The simulations

reservations.

job of determining

1.

sequences

Also, the higher

to fusion reactors were

A. Goldstone, D. M. Parkin and H. M. Simpson, J. Appl. Phys. 53 (1982) 4189. J. Nucl.

in statistically The most significant

the early work and the are the order of magnitude and the departure

damage energy proportionality

from

in the current