Characterization and annealing behavior of voids in neutron-irradiated nickel

CHARACTERIZATION AND ANNEALING NEUTRON-IRRADIATED G. L. KULCINSKI,

B. MASTEL

BEHAVIOR NICKEL*

OF VOIDS

IN

and H. E. KISSINGER?

Transmission electron microscopy (TEM) and small angle scattering (SAS) techniques were used to determine the size and density of voids in high purity nickel that had been irradiated to 3 x 10zl n/cm2 (>O.l MeV) at 450°C and subsequently annealed for 2 hr at 650, 800, 900, 975, 1050 and 1150°C. The as-irradiated material contained 1.8 x lOI truncated octahedral voids cma whose average size was 400 A. TEM revealed that the dissolution of the voids during high temperature anneals was rather inhomogeneous with those voids nearest the grain boundaries disappearing first. This resulted in a grain boundary denuded zone whose width depended on temperature, varying from 1 p at 650°C to 15 ,LL at 975°C and complete “denuding” at 1050°C. Both TEM and SAS revealed that the voids in the center of the grains did not coarsen during annealing, and the average size remained at -400 A up to the temperature of complete annealing (1050°C). Such behavior has been predicted for voids that are partially gas-filled, and annealing studies at 1050 and 1150°C did indeed reveal gas bubbles at the recrystallized grain boundaries. Microhardness measurements were also made on the samples after various anneals, and a good correlation was found between the hardness increase, AH, and the quantity (Nd)liz, where N is the number of voids/cma and d is their diameter. More specifically, AH = 6 ,&(Nd)‘lz, where p is the shear modulus and b is the burgers vector. CARACTERISATIOX

ET

COMPORTEMENT AU RECUIT DES IRRADIE AUX NEUTRONS

VIDES

DANS

LE

NICKEL

La microscopic Qlectronique par transmission (TEM) et la diffraction aux petits angles (SAS) ont Bti: utilisbes pour determiner la taille et la densite des vides dans du nickel de haute puret& ayant BtB irradib Zt 3 x 10zl n/cm2 ( >O,l MeV) it 450°C puis recuit pendant deux heures B 650, 800, 900, 975, 1050 et 1150°C. Le mat&iau irradie contient I,8 x 1Ol4 vides octahbdriquas tronqu& par cm3, dont la taille moyenne est de 400 A. La microscopic Blectronique montre que la dissolution des vides au tours des recuits It haute temperature est plut6t inhomogbne, les vides situ& le plus p&s des joints de grains disparaissant les premiers, ceci produisant une zone denudbe aux joints de grains dont la grandeur dBpend de la tempbrature, variant de 1 p It 660°C B 15 p B 975”C, et &ant compl&ement d&ud&e it 1050°C. La microscopic ainsi que la diffraction montrent que les vides situ& aux centres des grains ne grossissent pas au tours du recuit, et que la taille moyenne reste de 400 A environ jusqu’h la temperature de complet recuit (1050°C). Un comportement tel que oelui-ci a 6tB p&vu pour les vides partiellement remplis de gaz, et des expbrienoes de recuit B 1050 et 1150°C r&&lent en effet la presence de bulles de gaz aux joints de grains recristalli&s. Des mesures de microdurete ont 6th effectubes Bgalement sur les Ochantillons apres diff&ents recuits, et l’augmentation de duret8, AH, est libe de fapon simple it la qua&it& (NcZ)‘/~ oti N est le nombre de vides/cms et d leur diametre; c.a.d. AH = 6 ,&(Nd), oil p est le module de cisaillement et b le vecteur de Burgers. UNTERSUCHUNG

DES CHARAKTERS (VOIDS)

IN

UND

DES ANLADVERHALTENS

NEUTRONENBESTRAHLTEM

VON HOHLRdUMEN

NICKEL

Gr613e und Dichte der Hohlriiume (Voids) in hochreinem mit 3 x 20z1 Neutronen/cmZ ( >O,l MeV) bei 450°C bestrahltem und anschliel3end 2 Stunden bei 650,800,900,975,2050 und 1150°C angelassenem Nickel wurden mit Hilfe der Durchstrahlungselektronenmikroskopie (TEM) und der Kleinwinkelstreuung (SAS) bestimmt. Das bestrahlte Material enth< 1,8 x 1Ol4 oktaedrische Hohlr(iume pro cm3 mit einer durchschnittlichen GraBe von 400 A: TEM zeigte, da0 die AuflGsung der Hohlriiume in Hochtemperatur-AnlaBversuchen inhomogen erfolgte, wobei die am niichsten an den Korngrenzen Dabei entstanden entlang der Korngrenzen verarmte gelegenen Hohlriiume zuerst verschwanden. Bei 1050°C verschwanden alle Hohlriiume. Sowohl Zonen : 1 ,u breit bei 650°C und 15 ,u bei 950°C. TEM als such SAS ergaben, daB die GrijDenverteiluung der Hohlriiume in den Kornmitten wahrend des Anlassens nicht grBber wurde und daB die mittlere KorngrGl3e bis zur Temperatur vollst&ndiger Ausheilung (1050°C) ~400 A blieb. Dieses Verhalten war fiir teilweise gasgeftillte Hohlriiume vorhergesagt worden und in Anlanversuchen bei 1050°C und 1150°C wurden tatsiichlich Gasblasen (bubbles) an den rekristallisierten Korngrenzen beobaohtet. An verschieden angelassenen Proben wurde die Mikrohiirte gemessen. Zwischen der Zunahme der Hiirte AH und der GriiBe (Nd)‘j2 ergab sich folgender Zusammenhang AH == 6 ,&(Nd)ll”. Dabei ist N die Zahl der Hohlriiume pro cm3, d ihr Durchmesser, p der Schubmodul und b der Burgersvektor.

1. INTRODUCTION

Swelling temperature

of

non-fissionable neutron irradiation

austenitic stainless steels, to less than 10 per cent of the target fluence (10z4 n/cm2) of future fast breeder

metals during high is a serious materials

reactors

in design of future fast breeder reactors.(1*2)

problem

The magnitude

of the problem

considers

irradiation

that

of

is evident one

when one

particular

alloy,

METALLURGICA,

VOL.

19, JANUARY

1971

in a volume

increase

of 8 per

introduces probof cooling chan-

nels, and it can also impose severe stresses on reactor components. The observable

* Received April 4, 1970. This paper is based on work performed under United States Atomic Energy Commission Contract AT(45-l)-1830. t Battelle Memorial Institute, Pacific Northwest Laboratory, Richland. Washington. ACTA

has resulted

cent.t3) This dimensional instability lems with respect to the constriction

swelling

is a direct

result

of the

agglomeration of irradiation-produced vacancies into three-dimensional voids. The factors which govern 27

ACTA

“8

the production,

growth

must be understood operated

and stability

of these voids

if future fast reactors

in a safe and economical

metal,

namely

Ni, during

are to be

manner.

This paper deals with the stability The voids

METALLURGICA,

of voids in one

postirradiation

were characterized

annealing.

by both

transmission

electron

microscopy

and small angle scattering

niques.

In addition,

the effect of voids on the micro-

tech-

hardness of the nickel was investigated. 2. EXPERIMENTAL

The impurity used

content

for this experiment

specimens

were in the form

11 mm in diameter After

is given

dynamic

vacuum

starting

in Table

stock 1.

of polycrystalline anneal

of 2 x lo-‘torr,

size was 45 ,LLand the resistivity

All foils,

at 700°C in a

the average grain ratio, R,,,/R,,,,

was

111. The foils were encapsulated cans

containing

oxygen)

and

high

in 304 stainless

purity

irradiated

sodium

at 450°C

in

irradiation

gamma

temperature

was

steel

(
ppm

EBR-I1

reactor to a fast fluence of 3 x 10zl n/cm2 00.1 The

MeV).

calculated

from

heating rates along with a knowledge

of the

After

irradiation, annealed

temperatures: Both

a different

set of samples

was

for 2 hr at each of the following

650, 800, 900, 975, 1050 and 1150°C.

irradiat’ed

and control

samples

were included

The hardness values of the samples were determined before and after irradiation treatment

with

and after each annealing

a

Vickers

Microhardness

Tester.

of 5-10

indents

were measured

on each

specimen. TABLE 1. Impurity concentration nickel starting stock

ppm (wt.)

Element


Mg Al Si K Ca Cr Fe co CU Zn As Zr Sn C : H Total Xi purity

in

(wt. %)

A: 50 <2 1.5 99.98

the

was performed

on the

foil

thinning in a 70-30 mixture

of methanol

acid at -40°C.

samples

and nitric

used for the microscopy

small angle X-ray The length voids

scattering

was determined

graphs.

The

same

were used for the

measurements.

(1) of the (110) edge of the octahedral

Normally,

from

180,000 x photomicro-

200-300

voids

The average

by 1 IN,/2

were

measured

octahedral

edge was

N,, where N, is the number

of voids with (110) edge equal to 1. The

void

ference

density

was determined

fringe technique

graphs.

Accurate

of 500-700

from

thickness

by noting operating

by

71,000 x

the inter-

photomicro-

values were determined

diffraction

vector

9. An average

voids were counted for the density measure-

ments. The per cent volume voids

was

calculated

change to be expected

A V/V,,= 0.47

by

where N,, is the number

of voids/cm3

for the

(z Z3N,,),

with an edge

equal to 1. The average void diameter was also determined by small angle scattering measurements with monochromatic

copper

between

Ku

radiation.

at 1 min angular 8-60

min from

Rigaku-Denki

Intensities

intervals

beam

goniometer.

time at each angular setting was 500 sec. were corrected

for the background

The small angle scattering

scattering

of a sphere with volume

equal to that of a regular

corrections

were made.

Four methods

Their

of interpreting

of the methods, are

methods

scattering

those employ

curve.

on

The diameter

of edge 1is 0.961; accordingly,

parameters,

a

caused

data were analyzed

octahedron

Two

with

Counting The data

from the specimens.

the basis of spherical scattering centers.

used.

were

in the range

the primary

small-angle

by radioactivity

in each set.

An average

microscopy

measured

ambient, reactor sodium temperature. vacuum

Electron

samples after electrolytic

determined

by 0.075 mm thick.

a 2 hr preirradiation

19, 1971

for each sample.

PROCEDURE

of the nickel

VOL.

of

appropriate

the X-ray

which

yield

Guinierc4)

approximations

The Guinier method

data were single size

and

Pored.(s)

to the true approximates

the intensity in the low-angle portion of the scattering curve by i(h) = exp for

spherical

particles

R2h2/5

of radius

R.

(1) The

intensity

i(h) is the normalized intensity scattered at angle h = 2n sin 012. The size determined by the Guinier approximation

is actually

a mean size weighted

the square of the volume(6) true mean size.

by

and is larger than the

The Porod approximation is applicable to the highangle tails of the scattering curve. This approximation,

KULCINSKI

et al.:

as given by Gerald,“)

ANNEALISG

(2)

>

where S, == surface area of scattering I’, == volume The method to

distribution. by Roess given

of scattering

of Roess that

calculated distribution

N(D)

centers,

centers.

matching

Two

and Shull:

by

NE E 5 v, z z I"

and Shull@) uses the entire

curve and involves

scattering

VOIDS

IN

NEUTRON-IRRADIATED

for

the observed

an assumed

functions

(1) a Maxwellian

= A(D/D,)”

by experiment;

distribution,

where N(D)

= 0 elsewhere,

determined

exp -

90

CONTROLVALUES

70

0.2

distribution

(D/D,J2,

UNIRRADIATED ,' ,.

5l-

size

were used

0.4

I 0

where

= 1 between

and

constant.

cc is an

Finally

aD,

and D,,

experimentally

the method

I

gated. Void

to

a

distribution

densities

were

data by ext#rapolating zero angle,

estimated

was investi-

from

the

X-ray

the Guinier approximation

This provides

of scattering

function

centers,

an estimate of the number

since

phase in the forward

to

all elect,rons

direction

scatter

with intensity

in

given

byCIO'

where

I(0)

= absolute

intensity

(3) scattered

in

the

power of a single electron =

7.9 x 10W6 cm2,

scattering equal

= mean square of the number of electrons

according

to

void and matrix.

Babinet’s

in electron

principle(“) density

is

between

Therefore, the voids were considered

to act as scattering of 2.5/A3 (electron

centers with an electron density

Figure

in nickel)

electron microscopy

2 shows

after irradiation

density

in a matrix

of

zero electron density.

the microstructure

RESULTS

AND

OBSERVATIONS

(a) Mierohadness The

results

does not change

during

with the observations

annealing

and have

anneals

at

of the voids

and is consistent

made by Brimhall and Mastel.03)

The voids are octahedral

in shape, bounded

various

{loo} planes. Table 2 summarizes

degrees

the data

An important

by (111)

of truncation obtained

from

on the

result is that the voids

did not disappear homogeneously

and the voids relatively

throughout the speci-

Those voids that were near

in the center of the grains remained

unchanged

typical

the nickel

up to 975°C.

boundary

zones

after irradiation

at 650, 800 and 900°C.

and after

asymmetry

measurements,

shown in Fig. 1, reveal that the hardness increase due to irradiation is quite stable during postirradiation annealing up to 975°C (~0.7T,). Above that temperature, it rapidly recovers to the unirradiated value, and after annealing at 105O”C, the microhardness

of voids

in

2 hr anneals

After irradiation,

at 650°C caused asymmetric This

Figure 3 displays

denuded

zone was on the order of 0.1-0.2

the denuded

,u wide, and annealing denuding

is indicative

of

of up to 1 ,u.

grain

boundary

Annealing a different sample at 800°C motion. resulted in a greater asymmetry (as much as 0.3-3 p), zone

(on a separate

sample) was 2-3 ,U wide but symmetric.

The denuded

zone grew quite rapidly

After

anneal of the microhardness

of the nickel

The morphology

while after 900°C the denuded 3.

(TEM)

and after 2 hr vacuum

800, 900 and 975°C.

some

the voids contain no electrons, their effective

to the difference

samples are the

grain boundaries were the only ones which disappeared,

per particle. Although

1200

and control

men during the anneals.

n := number of particles, 5

(b) Transmission

TEM studies.

forward direction, I,(O) = scattering

1

I

same.

planes,

I(0) = IJO)nNz,

0. 8

400 800 TEMPERATURE,'C

values of the irradiated

employed

0.6

T/T,

FIG. 1. Recovery of hardness increase in neutron irradiated MRC nickel-2 hr anneals at each temperature.

and (2) a ‘?ectangular”

by Harkness et nl. tQ)which fits the Guinier and Porod diameters

29

110

.D is the particle diameter, and D, and n are constants determined N(D)

Ni

is

2??s i(h) = j$$ P

scattering

OF

BEHAVIOR

2

at 975”C,

it was

above

900°C.

215 p wide,

a 2 hr

and after

a

hr anneal at 105O”C, the denuded zone had extended

completely across the grains. This inhomogeneous dissolution

of voids

requires

the data to be reported in two different ways : (1) a density pertaining to the center of each grain, and (2) a density which would be measured as an average

ACTA

METALLURGICA,

VOL.

19,

1971

FIG. 2. Typical void densities in MRC nickel after 2 hr anneals at various temperatures. Photomicrographs are of regions within the grains away from any denuded zones. (a) As irradiated, (b) 800°C, (c) 9OO’C Land (d) 975°C. TABLE 2. Gummary of postirr~di&tion annetaiing data on tr&~m~ssion electron microscopy of voids in irredi&ed __ Annealing temperature * (“Cl

Grain boundary denuded zone widths (,u)

As Irr. 650 800 900 975 1050 1150

0.1-0.2 0.1-I .o 0.3-3.0 2.0-3.0 215 $15 Entire grain

Void density

x

10’4/cc

Within grein

Overall

1.8 + 0.4 1.6 * 0.3 1.9 & 0.4 1.7 f 0.4 2.0 & 0.4
1.8 * 0.4 1.5 * 0.3 1.5 & 0.3 1.4 + 0.3 0.4 f 0.1
* Different sa,mple used for each anneal.

Void size (A) 400 430 410 410 360

* 30 l 30 f 30 & 30 rt 30 _ _

nickel .._~

Volume change (%) Within grain 0.64 0.62 0.56 0.61 0.47

* & f & * _ _

0.14 0.13 0.12 0.13 0.10

Overall 0.64 0.59 0.45 0.44 0.10

-& 0.14 $-r:0.13 & 0.10 $I 0.10 IJ,:0.02 _. -

OF

VOIDS

IS

NEUTRON-IRRADIATED

Ni

31

It was found that the volume increase after irradiation was 0.64 per cent and that most of the overall volume increase was

was removed

a considerable

by annealing difference

at 975°C.

between

There

the

micro-

scopically

measured

volume increase within the grains

and that

corrected

for denuding

975°C

anneals.

closely

Since

correspond

the

during the 900 and

corrected

to immersion

values

density

should

data,

it is

obvious that one might be misled about the annealing behavior

of voids in the higher

if TEM

studies were not conducted.

The

overall

picture

in the

present

study

surface

of each

of

temperature

void

annealing

is one in which

grain

region

becomes

revealed

the

denuded

outside

of voids,

while inside, the grains retain much the same characteristics of the as-irradiated annealing

should

be

sample.

postirradiation

high-temperature

measurements

of irradiated

A particularly samples

that

observation

During

3. Typical denuded zones in MRC nickel after 2 hr anneals at various temperatures. (a) As irradiated, (b) 65O”C, (c) 800°C and (d) 900°C.

1For example, the void density “smear” density. the center of the grains was relatively constant

these

the

postirradiation

to 0.4 x 1014/cm3 after

value

of

the anneal

tially no voids were observed

but cavities

on the grain boundaries after

annealing

at

at

Essen-

after the 1050°C anneal.

void size remained

@ z G I I

1o13

I

relatively

constant

I

at 400 A during anneals up to 9OO”C, but a slight drop to 360 A occurred Both the maximum

during

the 975°C

and minimum

anneal

observed

(Fig.

5).

diameters

lower the maximum observed diameter. The average volume change as calculated

from the

void size and density data is shown in Fig. 6. The effect of including the grain boundary denuding is the overall volume

change.

I I I I II , <1012

0 VOID DENSITY IN CENTER OFGRAINS ---

are plotted in .Fig. 5, and it is apparent that annealing tends to raise the minimum observed diameter and

also shown and is labeled

of the un-

1050-1150%.

in

Figure 4 shows the data for both cases. The average

were

Fig. 7. Similar cavities

I

1.8 x 10r4/cm3

at 975’C.

high-temperature

1o14

1.6-2.0 x 101”/cm3 up to 975”C, while the overall void density (including the denuded zone) dropped from

controls

was made in

at 1050 and 1150°C

all voids had disappeared,

irradiated

property

nickel.

significant

were not present

interpreting

mechanical

found on the grain boundaries,

FIG.

when

had been annealed

and were void-free. anneals,

This mode of void

considered

12 10

OVERALLVOID DENSITY (INCLUDINGDENUDED ZONE)

I 0

ml

I

I

400

600

I ml

I t I , t 1000

TEMPERATURE,'C FIG. 4.

Void density in neutron irradiated various 2 hr vacuum anneals.

nickel aftor

ACTA

METALLURGICA,

VOL.

19,

19il

.---___,__--4.,

‘Y “b MAXIMUM

/

I

I

I

,

1

400

600

800

1000

1200

1400

ANNEALING TEMPERATURE'C FIU. 5. Effect of annealing temperature on the void diameters observed with transmission electron microscopy techniques.

Careful x-e-examination of the irradiated samples, which were annealed at lower temperatures, revealed that these grain boundaries were normal and contained no cavities whatsoever. The observed cavities have several features common to bubbles : they are generally spherical instead of polyhedral, and they enlarge during a~ealing-from 200 A after the 1050°C anneal to 500 A after the 1150°C anneal. While it is difficult to obtain an accurate count of the cavities, there were approximately 5 x lo8 bubbles/cm* of grain boundary after the 1150°C anneal, If these cavities are filled with gas to balance the surface tension forces, then the number of gas atoms required to stabilize these cavities is ~1 ppm. This is not far from the 3 ppm of helium atoms which would be produced by this irradiation for an (n, a) erosssection of 0.95 mb.(i4)

FIG. 7. Typica. grain boundaries in nickel which has been annealed for 2 hr at 1050’%. Note cavities on boundary in (b). (a) Unirradiated control, (b) irradiated to 3 x 102’ n/cm2 (>O.l MeV).

(0) hall

angle scattering

(XAX)

Figure 8 displays the average void diameters determined by four SAS techniques and compares them to the average diameter determined by TEM studies. It is apparent that the method of Roess and Shull(*) and that of Pored(5) give sizes which are in particularly good agreement with the average diameters obtained by TEM. The average of the

0 0.4 -

_ 1 1 I 0

200

I 400

,

I M)o

,

1 , 800

IRRADIATIDN / ~~PERA~RE!

\I.,

1000

0

//

\ \ \ \ \ \

0.2 0

GUINIER

CI AVG.RECT. DIST.

1

1W

1200

TEMPERATURE,'C FIG. 6. Volume change associated with voids in nickel after various 2 hr vacuum anneals.

0

ml

A pi

I

I

400

MM

P~AKOFh~XWEUi~

ROESSAND SHUtl

POROD TEM

I

I

I

800

lC0.l

1200

ANNEALING TEMPERATURE%

FIG. 8. Comparison of average void diameters in irradiated nickel obtained by small angle scattering and transmission electron microscopy (TEAM) techniques.

KULCINSKI

rectangular the

distribution

best

agreement

particularly and Porod void lo-20

of Roess

with

gratifying

the

that

BEHAVIOR

and

TEM

the

Shull

Roess

from

As expected,

below

drop in

the Guinier diameter was always by TEM

obtained from the method by Harkness@) were consistently 20 per cent

the

observed

are not shown.

diameters,

The important

the SAS results substantiate average

void

~400

up

A

diameter to

the

and

is

relatively of

constant

complete

the void size frequency

distribution

TEM

derived

to

that

determined

from

SAS

a Maxwellian

distribution

to the distribution

by TEM techniques.

to 100 per cent.

quite acceptable

considering

The agreement after

the

from

and rectangular determined

The agreement

the completely

between higher

is

different are

the SAS and TEM

temperature

anneals

obtain void Figure

it was found

a qualitative, density

after

that one can utilize SAS to

if not quantitative, various

treatments. tend to over-

void density

but more importantly,

the annealing

idea of the

annealing

10 shows that SAS techniques

estimate the TEM-observed of ~2,

1.0

2 B

0.4

!

by a factor

the general

shape of

curve is similar to that determined

by

I

I

_I

1200

1000

1400

FIG. 10. Void densities, determined by small angle scattering (SAS) and transmission electron microscopy (TEM) techniques. 4.

It

DISCUSSION

between TEM

(a) Comparison

and SAS results

is felt that, the present

least for nickel-the certain

extent)

work

shows

that-at

void size distribution

void

SAS techniques.

density

While

and (to a

can be determined

SAS techniques

by

will never

replace the need for good TEM studies, SAX measurements offer certain advantages. to characterize

considerably

First of all, the time

a sample

through

SAS is

less than that required to properly

a highly radioactive of the magnetic

thin

Ni sample, take proper pictures

material,

and perform

the tedious

task of measuring

the size of several hundred voids in order to obtain an average size. Another advantage of the SAS technique voids

(-loll)

the void

is that it averages over many

as compared treated

rapidly

size distributions measure

to the several

by TEM studies.

hundred

The fact that

can be obtained

Roess and Shull(s) method ISA8RECTANGULAR \

I

I

800

6QO

ANNEALING TEMP.,%

customarily

TEM.

I

I

400

required

was also quite good. Finally,

g

studies.

manner in which the TEM and SAS distributions distribution

x

at

The areas under all three curves

were normalized

derived.

33

2

z

annealing in matching

Figure 9 shows both compared

Ni

consequently

success was also obtained

studies

f

the TEM result that the

point

NEUTRON-IRRADIATED

point of Fig. 8 is that

(between 975 and 1050°C.) Considerable

IN

is

The diameters

described

VOIDS

Shull

the 975°C

per cent higher than that determined

studies.

It

and

420 to 360 A after

OF

shows

results.

results reflect the TEM-observed

diameter

anneal.

ASNEALING

et al.:

by the

(Fig. 9) also allows one to

how the range of void

sizes varies

with annealing treatment. A

disadvantage

components

of

scattering.

of

However,

micrographs

SAS

damage

are

is that

might

other

unknown

contribute

to

only a few transmission

required

to

settle

this

question.

In the case of Ni, there were no other visible ponents

of damage

significantly

that

could

alter the results.

scatter

the

photo-

X-rays

comand

Other areas in which

SAS is lacking are the determination of the morphology of the voids and detection of inhomogeneous void 200

400

6OO

VOID DIAMETER,A

FIG. 9. Comparison of TEM determined void size distribution with that determined by the Rows and Shull method. Sample: high-purity nickel irradiated to 3 x 10el n/cm2 (E > 0.1 MeV) at 45O’C. 3

distributions Therefore, in nickel

such

after

most efficiently TEM

as

denuded

grain

it is felt that an in-depth

studies,

various

thermal

accomplished the former

boundaries.

study

treatments

by combining

for void

of voids can be SAS and

size and density

ACTA

34

determinations details

and

the

latter

for

and as an independent

measurements

at this point

(0.64 & 0.14

per

cent)

that the volume

observed

in the as-irradiated

by

TEM

Ni of this study

agrees quite well with the immersion

density

minations

a 0.7 per cent

volume

19,

1971

has investigated

of Holmes,(15) who reported change

for

Ni-270

irradiated

deter-

in the

and also found irradiation hardness

damage, number

It is reasonable

to assume

that

the increase

is due mainly to the production are no other such

major

as defect

hardness

increase

of voids, since there

components

clusters, in

in

irradiation

of visible

prismatic

metals

can

damage

loops, be

etc.

The

qualitatively

linked to the ease with which dislocations

can move

within

assumptions hardness ment

the

strength, Ao,, caused by the presence of voids average diameter d, density N and spacing L, is AoU = 2 pub/L,

of

ships for hardness

(4)

elements

hardness

and alloys

can be expressed

the

number

(HI’)

relationfor several

temperature.

to the

This relationship

as

where u, is in kg/mm*. 2.8 to 3.3.

that C == ~3

that

between

microhardness

equation

data

Nunes

(5)

Tabor found that C varies and Larsonos) also found

and that it was independent

perature over the range -196°C

of tem-

to +2OO”C for several

TABLE 3. Hardness

void

to resort to the tedious

counting

1.8 1.6 1.9 1.4 2.0

450 650 800 900 975 1050

0.4 0.3 0.4 0.3 0.4 0.01 _

1150 Void t Equation

(6)

C =

3.

may be

void

measured

of minutes,

may be confidently

by

techniques

SAS

typically

measurements

(Fig.

numbers consuming

in less then 3 hr).

can be made in a matter

will

(6).

It is not suggested

eliminate

the

necessity

which

will in turn

allow

It must be quickly

a method

may only be applicable

the more

pointed

should not be applied to alloys steels without extreme caution.

400 & 30 430 9 30 410 410 * 30 + 30 360 & 30 _ -

0.37 0.38 0.36 0.38 0.37

* & & f + -

Call?. t 0.08 0.08 0.08 0.08 0.08

28 27 29 27 28

5 f * * f 0 0

6 6 7 6 6

TEM time-

on selective

out that such

to pure metals and such

as stainless

increase due to voids in irradiated nickel

(&

that this for

quantitative

TEM work to be concentrated

samples.

(d)

and

8) (i.e.

and it is then a simple manner to solve

for N in equation approach

in TEM

diameter

results can be obtained Microhardness

of voids

(k/m~~2)

1014*

and

another

The present work has shown that

Ii/Cd x

(“C)

(6)

density

HV Temperature

values

suggests

studies, but it should provide reasonably

HV = Co,, from

agreement

the average

proportional

after

by which the average

rapidly

stress/strain

is directly

flow stress at room

close

observed

photomicrographs.

changes in metals and has shown

that the Vickers

The the

method

b = Burgers vector of the dislocation, L = (Na)p. has analyzed

observed

due to the fact that

measured in a large number of samples without having

where p = shear modulus,

Taboro7)

and

between

The disagree-

Such an difficulty would result in lower observed

hardness values.

in yield

increase.

the large denuded

properties.

yield increase

is well

anneal.

irradiation

on

expected

error and the error in the

calculated

(15 ,u) present

effect

the

actually agreement

zone

on

that

The

(6) observed

some hardness indents overlapped experimental

found

to that

(6).

after the 975% anneal is probably

treatments

of

of

increase

made concerning the relationship

similar to theoretical

has

nickel

and yield strength

between

of

Vickers

to the presence

the hardness

the experimental

the lattice

the

in

expression:

3 compares

through

Coulomb(16)

increase

can be related

if C = 3 in equation

hardness of nickel after a high temperature

If C is independent an

AHV = 2C,ub(Nd)1’2. Table

hardening

then

voids by the following

in the irradiated (b) Irradiation

Paine(nn

and yield stress of nickel

C = 2.8-3.4.

same

capsule as the foils for this study.

alloy.

the effects of cold work and irradia-

tion on both the hardness

noting

measurements

VOL.

steels, Cu, Fe, Ti and an aluminum

microstructural

check on the density

.

It is worth change

METALLURGICA,

Obs. 28 24 25 30 16

* & k + i 0 0

3 3 3 3 3

(c) Annealing There

ANNEALING

et aZ.:

KULCINSKI

BEHAVIOR

are two

rather

unexpected

results

studied : (1) the relatively high temperature of the average ments.

all voids,

void

Because

stantiated

in the

of the voids in the nickel samples

to remove

(~1000’C)

of

these

results

treat-

were

sub-

by results from three separate techniques,

microhardness

measurements,

TEM

is little doubt

on the validity

of these observations.

They

are, however,

by Brimhall

contrary

(>O.l

and SAS, there

to the data

and Mastel,(2c) who found

voids in Ni irradiated

with increasing

A clue to the unusual behavior

sinks, one would

The

word

the case of partially cavities

annealing

expect

= T[exp

D, = self-diffusion

voids,

which

are in mechanical

contain

in Cu and

the shrinkage

vacancies,

restraints.

equi-

These investigators

(g)

-

I] ,

spacing

E,(l)

= the special

in the direction

F,

(7)

interaction

energy

between a vacancy and a void distance 1, usually taken as 3a/2,

at the

= the

attractive

mechanical

the cavity

force

to

shrink

3nkT

‘12Y-4r’ r

coefficient (including structure

tending

and is equal to

7rs

n = the number of gas atoms in the cavity. Bullough

and Perrin’25) considered

irradiation tion

constant,

annealing

depends

t = time. (7) assumes that whenever

a vacancy

on the rate

from one void it is absorbed

sink and that the average

is dr

by a vacancy

void size should decrease

temperature.

The

model

used

(7) is based on the assumption

at which

at = ii

between

selves and that the emitted the

from the equilibrium

vacancy

vacancy value (C,“).

the voids

to

them-

does not signifi-

concentration However,

(C,)

when the

3rd 4m3 1 -E,

1+

that

concentra-

vacancies

& exp

( kT

equation

1

-1 f

(9)

1

[ Comparing

can

For P = 0 they found

2YQ __-__ D, I exp ( rkT

the spacing between the void and sinks is much smaller spacing

the case of post-

where the vacancy

diffuse away from the cavity.

change

and bubbles,

where P = external pressure,

k = Boltzmann’s

than the average

between

and thermodynamic

where a = the interatomic

rate

T = temperature,

increasing

cavities.

distinguish

found that the shrinkage rate of a cavity is given by

temperature.

of voids

y = surface energy,

derive equation

and Perrin,(25)

gasflled

of the jump,

factor),

cantly

to

only

librium with external

Q = atomic volume,

with

is used

which

where r = radius,

removed

of the voids can be

found in a recent analysis by Bullough

to be

Equation.

does not lit either of the

above situations.

that all the

A1(s1-23) suggest that for an isolated void with nearby

--drldt

this pattern

35

Ni

reported

at 800°C and that the average

Past studies of the annealing vacancy

NEUTRON-IRRADIATED

to a fluence of 1 x 10zo n/cm2

MeV) disappeared

size increased

IN

who treated

and (2) the constancy

size during the annealing

both

VOIDS

temperature;

behavior of L~O~G!S

annealing behavior required

OF

1 (9) with equation

(7), one finds

that there are two forces tending

to slow down the

shrinkage

of the gas atoms

rate:

in the cavity,

(1) the pressure and

(2) the attraction

between

the

spacing bet ween the voids is much less than between

vacancy

the voids

that for small r and large n the term exp [(By/&T) (3n/4rrrs)]Q can be less than 1 and it is possible for small cavities to grow. For large r, cavities would

some

and sinks, it is reasonable

voids

will capture

other voids.

Such a situation

neutron-irradiated

metals

to expect

the vacancies

Unfortunately, stant average

that by

can exist in heavily

and is thought

reason why previous authors have found voids grow at the expense of smaller This latter situation void size average

emitted

to be the that larger voids.@0,s4)

would result in an increasing with increasing temperature.

the results of this study show a convoid size uith increasing annealing

and the cavity.

Furthermore,

one can see

always be expected to shrink. Such behavior would result in a relatively constant average size and would tend to increase the thermal stability of the cavities. These observations are entirely consistent with the data presented

in Fig. 5.

to hypothesize that gas cavities in nickel.

It is therefore atoms

reasonable

are stabilizing

the

36

ACTA

METALLURGICA,

Rather conclusive evidence for the presence of gas in the irradiated samples is offered by the microstructure shown in Fig. 7. Since the amount of gas measured experimentally is consistent with that which could be produced by the (w, 0~)reaction in Ni, it is very likely that the gas is helium. It is therefore concluded that the “voids” present in the irradiated Ni of this study are not true voids in the sense that they contain only vacancies, but in fact are partially gas-filled. This conclusion would also explain the difference in annealing behavior between the nickel used in this study and that used by Brimhall and Mastel.(20) The present samples contain ~30 times more neutronically produced helium, whioh would tend to increase the temperature stability of the oavities. It should be pointed out that the present work does not necessarily support the h~othesis that voids are nucleated by gas atoms. It is not possible at this time to determine whether the gas atoms entered the void after it formed or if they indeed nucleated the void. ACKNOWLEDGMENTS

The authors wish to thank Mr. T. J. Larson and Mr. J. M. Leahy for their assistance in gathering the hardness and X-ray data. The provision of the irradiation space by J. J. Holmes is also greatly appreeia~ted. The authors also wish to acknowledge the helpful comments and criticisms of Dr. T. K. Bierlein, Dr. J. L. Straalsund and Dr. 5. L. Brimhall.

VOL.

19,

1971

REFERENCES 1. J. J. HOLMES, ABS Trans. 12, 701 (1969). 2. I. ‘I’. CLA~~DSOX,J. J. HOLMES, J. L. STR~~LSUNDand H. R. BRAOER.in Radiation Da?naoe in Rea&or Materials. Vol. II, p. 165: IAEA (1969). ” 3. C. CAWTHORNE and P. J. FULTON,Nature 218,575 (1967). 4. A. GUINXERand G. FOURNET, &n&E Anale Scarred of X-Raye, pp. 24-26, 126-127. &. Wiley (1955). - 5. A. GUINIER and G. FOURWET,SmaEEAngle Scattering of X-Rays, pp. 78-80. J. Wiley (1955). 6. L. C. ROESSa;ndC. G. SHULL,J. a&. P&s. lSt 295 (1947). 7. V. GEROLD, in Small Angle X-Rag Scatterzng, p. 265, edited by H. BRUMBEROER.Gordon and Breach (1967). 8. L. C. ROESSand C. G. SHULL,J. appl. Phys. 18,308 (1947). 9. S. D. HARKNESS, R. W. GOULD and J. J. WREN, Phil. Mag. 19,115 (1969). 10. A. GUINIER and G. FOURNET,Small Angle Scattering of X-Rays, p. 133. J. Wiley (1955). 11. A. GUINIER and G. FOURNET,Small Angle Scattering of X.Raye, F. 38. J. Wiley (1955). 12. A. GUINIER and G. FOURNET,Small Angle Scattering of X-Rays, p. 6. J. Wiley (1955). 13. J. L;. BRINKALL and B. MASTEL, J. mcL Mater. 29, 123 (1969). 14. W. N. MCELROY,H. FARRARand C. H. KNOX, AiVS !&ans. to be published. 15. J. J. HOLMES, ANS Trans. 12, 117 (1969). 16. P. COULOMB, Acta Het. 7, 556 (1959). 17. D. TABOR, The Hardness of Metals, Oxford University Press (1951). Also see Proc. R. SW. A149,247(1948). 18. J. NUNESand F. R. LARSON,J. Inst. Metals 91,114 (1962). 19. S. I-I. PAINE, W. F. MURPHY and W. W. HACKETT, ANL-6102 (1960). 20. J. L. BRIMHALLand B. MASTEL, J. nucl. Mater. 53, 189 (1969). 21. T. E. VOL~Nand R. W. BALLUFFI,Phys. Status Solidi 25, 163 (1968). 22. K. H. WESTIIIACOTT, R. E. SSIALLMAN and P. S. DODSON, Metal Sci. J. 2, 177 (1968). 23. H. G. BOVVDEN and R. W. BALLUFFI,Phil. Mug. 19,lOOl (1969). 24. J. L. STRAALSDNL), J. Metals, N.Y. 44A (1969). 25. R. Buzr,ouo~ and R. C!. PERRIB, in Rad~at~~~ ~arnage~~ Reactor Materiak, Vol. II p, 233. IAEA (1969).