Neutron irradiation and defect recovery of tungsten

JOURNAL

OF NUCLEAR

34 (1970)

MATERIALS

260-230.

0 NORTH-HOLLAND

PUBLISHING

CO., AMSTERDAM

NEUTRON IRRADIATIONAND DEFECT RECOVERY OF TUNGSTEN* L. K. General Electric Company,

Received

KEYS

+ and J. MOTEFF

Systems Programs, Cincinnati, Ohio 45215, CTSA

N&ear

16 June

1969, in revised form 9 October

A detailed study of the recovery of defects in tungsten

compris

after fast neutron (E, > 1 MeV) irradiation at about

Trois

70

observes

“C

over

8

fast

neutron

fluence

range

from

entre

8,5X 10’7

domaines aux

1969

n/cm2

principaux

8. I,5 x 1021 njcm2.

de restauration

temperatures

voisines

de

ont eti? 0,15

Tm,

8.5 x 1017 n/cm” to 1.5 x 1021n/cm2 has been completed.

0,22

Three principal recovery regions have been observed

fusion du tungstene en “K. La restauration iL 0,15 T,,,

at about 0.15

T,

about this

0.22 Tm, and 0.31 Tm where T,

0.15 T,,

is the melting

temperature

recovery

involves

with

lower temperatures These

vacancy,

neutron

et une cinetique de ce domaine

of

a mobile

completely

recovery process. The 0.22 T’,

suggested to be due to divacaney basis of its relative magnitude.

restauration,

immobile recovery

migration

The 0.31 T,

de second

de

de 1,7 eV environ

ordre.

de restauration

sont entierement

compatible

self-interstitial,

eat la temperature

Le deplacement

sous l’effet d’un flux plus basses,

est 3trelief 8. la cinetique de second ordre. Ces r&u1 tats

to

is in keeping with second-order are

ob T,

neutronique croissant 8, des temperatures

A shift of fluence,

T,,

implique une energie d’aotivation

The

energy

kinetics.

increasing

results

essentially

in “K.

an activation

1.7 eV and second-order recovery,

kinetics. with

of tungsten

Tm et 0,31

compatibles

par

avec

d&placement

lacunes restant immobiles.

un processus de

des interstitiels,

est supposbe due B une migretion

is

on the recovery

r&son

de son importance

$ 0,31

T,

imphque

les

La restauration & 0,22 T, de bilaeunes,

relative.

en

La restsuration

un processus de premier

ordre

involves a first-order process with an activation energy

aver une Bnergie d’rtotivation de 3,3 eV, en excellent

of 3.3 eV in excellent agreement

accord rtvec d’autre etudes de restauration, f&ant appel 8. des monolacunes. La resistivite residuelle

of monovacancy

recovery.

with other studies

A non-annealing

residual

resistivity remaining after completion of the annealing

subsistsnt

studies

due

has

been

shown

Rhenium

is produced

tungsten

by

the

to

be

from

g-decay

due

the

of

Rhenium

appears

to

rhenium.

transmI~t&tion

appreciably

or greater.

de tungst&ne form&

influence

about 0.27 T,

recoveries

are also

and 0.35 Tm. It is suggested that these

recoveries may be due to the annealing of trivacaneies gonization

also contributing

par

j? d’isotopes

des reactions

du

instables

(n, y),

de

Le rhenium apparait influencer les energies de migration

des

d’tm pourcent atomique

ou plus. De faibles msnifes-

tations

ont 6th aussi observees aux

percent at

etre

differents defauts quand sa concentration est de l’ordre

when its

observed

and defect olusters or loops, respectively,

de faqon appreciable

the

a et& rev&e

p&r la transmutation

tungstene par la d~sint~~&tion neutrons thermiques.

is of the order of one atomic Small

produit

of

isotopes

energies for the various defects

concentration

of

apres recuit prolonge

au rhenium

(n, y) reactions.

unstable

tungsten formed by thermal-neutron migration

to

de restauration

tempemtures

voisines de 0,27 T,

suggere que ces restaurations recuit

with poly-

de

boucles

to the latter.

trilacunes

et

respectivement,

contribuant

eussi

et 0,35 T,.

peuvent

d’amas

de

avec

une

B la formation

11 est

fttre dues au

defauts

on

de

polygonisation

de ces amss

de

defauts. Une etude d&ail& de la r~ta~~tion des defauts a &tBr&lisBe dans le cas du tungst&e apres irradiation par les neutrons

rapides

70 “C sup un intervalle *

(E, >

1 MeV)

Eine

Z%environ

ausfiihrliche

Defekten

de flux de neutrons rapide

Untersuchung

in Wolfram

This paper originated from work sponsored by the Fuels snd Materials

Commission under Contract AT(40-1)2847. t Present address: The Magnvox Company, Indiana

46803,

Govemment

USA. 260

and

der Erholung

von

nach Bestrcthlung bei 70 “C in Branch,

Industry

U.S.

Division,

Atomic

Energy

Fort

Wayne,

NEUTRON einem

schnellen

8,5 x lOr7-15

IRRADIATION

Neutronenfluss wurden

0,22 T, und 0,31 T, (T,=absolute von Wolfram)

beobachtet.

Aktivierungsenergie von

(&, >

I

zweiter

bei

etwa

DEFECT

MeV,

x 1021 njcm2) wurde abgesehlossen.

Haupterhohmgsstufen

ist

AND

Drei

0,15

T,,

Schmelztemporatur

Bei 0,15

T,

betriigt

die

1,7 eV und die Reaktionskinet~

Ordnung.

Bci

Verlagerung

dieser

von

RECOVERY

OF

3,3 oV vor und stimmt

anderen Untersuchungen

sehr gut

Ein

nioht-ausheilbarer

Beendigung

der

Wiirmebehandlung

zuruckfiihren.

Umw~dl~g

Rhenium

von Wolfram

~Volfram~sotope

durch

iiberein mit

zur Erholung iiber einfaehe

Leerstellen. Rhenium

261

TUNGSTEN

Restanteil liisst entsteht

Temperaturen

lichen Einfluss auf die Wanderungsenergien schiedenen

beweglichem Zwischengitteratom,

trationen

stelle und Erholungsprozess bei

0,22

Wanderung

Ts

erfolgt

unbeweglicher Leer-

erkllren.

offensichtlich

von Doppelleerstellen,

auf

Grund &US

der dem

von

z

zu haben,

0,35

Ts

beobachtet.

Erholungsvorgange

vorliegt.

werden such bei 0,27 TB und ~5gliche~eise

durch

Ausheilen

Leerstellen und Leerstellen-Anhiiufmgen

Prozess erster Grdnung mit einer Aktivierungsenergie

wozu bei letzteren

ture and above the temperatures incurred in many reactors (about 70 “C) 10). Therefore, no special cryostat equipment is required to study the recovery of such stages as III and IV. The high strength of tungsten also leads to relatively well separated stages thus minimizing the complications and mixed interpretations which have arisen in face-centered cubic metals from the overlap of important recovery stages (i.e., III and IV in aluminum) 1%).Its low solubility for and relatively low reactivity with interstitial impurities (namely carbon, nitrogen, and oxygen) also minimize the complications arising from these impurities as found in some other

der ver-

wenn es in Konzen-

relativen Betrag schliessen liisst. Bei 0,31 Ts liegt ein

The recovery of defects introduced into metals by fast particle irradiation, cold working, and quenching is of interest to the physicist, the materials scientist and the nuclear engineer. As these defects have pronounced effects on the mechanical properties of materials i-9), a good understanding of the recovery temperature regions and recovery mechanisms for these defects is necessary. We shall describe the results of a comprehensive study of the recovery of irradiation damage introduced by neutrons in tungsten, using the resistivity technique. Tungsten is an excellent metal for studying the recovery of defects in metals, particularly the body-centered cubic metals. Because of its high melting temperature, many of the important recovery stages occur above room tempera-

ther-

scheint einen beacht-

1 Atomprozent

Geringe Erholungen

Die Erholung

wie sich

Defekte

Rhenium

mit

mischen Neutronen.

erfolgt die Kinetik ebenfalls bei zweiter

auf

bei der

durch ,!?-Zerfall instabiler

(n, ~)-Reaktionen

Erholung mit wachsenden Neutronenfliissen zu tieferen Ordnung. Diese Ergebnisse lassen sich vollstandig mit

naoh

sich

erfolgen von

nooh Polygonisation

diese

Dreifach-

oder -Ringen, beitriigt.

body-centered-pubic metals such as niobium 12). Because of its good high temperature properties it also has been of interest to nuclear reactor developers 1). For these reasons, we have carried out the detailed study of the recovery of defects introduced into tungsten by reactor ambient temperature (about 70 “C) neutron irradiations. These studies show that defect recovery in neutron irradiated tungsten can be interpreted according to the Meechan-Sosin-BrinkmanSeeger theory 1s). 2.

Previous

studies

While the recovery of defects introduced into tungsten has not received much attention when compared to the extensive studies carried out on the recovery of defects in face-centeredcubic metals, still a large number of these studies have been undertaken 14-42). These have involved a number of measurement techniques including resistivity 14-34, 39-33), X-ray 25), field_ ion microscopy as-as**I), and internal friction aa-35137~42).These techniques have been used to study the recovery of defects introduced by cold-working 19-25), electron irradiation 36-38~409 43), deuteron irradiation aa-as), fast neutron irradiation 14-16, 26-32, 42 ), thermal neutron irradiation 39), and Wf ion bombardment 41). It has been demonstrated that a number of defect recovery regions occur over the temperature range from 4 to 2173 “K. The principle recovery regions identified to date occur over

262

L.

K.

KEYS

AND

the following temperature limits: 20-60 “K (Stage I) - a multi-component stage I511%33-43) resembling the recovery

of the low temperature

J.

MOTEFF

and

post-irradiation resistivities, fast and thermal neutron fluences, etc., are presented in table 1. All the resistivity rods were of a dia-

defects in copper 44); 100-400 “K (Stage II) a broad recovery region 14-16~33-43) whioh ap-

meter of 0.317 cm and a length of 5.08 to 5.72 cm, They were commercially pure

pears to involve more than one recovery mechanism ; 400-720 “K (Stage III) -a large single recovery region 14-27,as-32941-43) which

(99.98 wt%) and were annealed for one hour at 1900 “C in gettered argon to stabilize the microstructure. The isochronal resistivity mea-

has been interpreted by some researchers 14-16, 2%2s) as due to vacancy recovery, and by otthers 10,17-21, 24, 26, 27, 29-32, 42, 43) as due to seff-

surements were made utilizing a well established technique 1, is). The annealing furnace was stabilized to less than i 0.5 “C during the

720-920 “K-a small interstitial recovery; recovery region of more uncertain origin lo* 17-21$ 29-32 ); and 920-1220 “K (Stage IV) -a large recovery 17-2~ 2%30-32) which can be attributed to vacancy recovery as). These recovery temperature regions are only approximate as some differences exist in comparing the different studies. The Stage III defect has an activation energy for recovery of w 1.7 eV with some studies

isochronal anneals. All the isochronal recovery curves were obtained from a best fit of the recovery data to a cubic spline comput,er program which also generated the recovery spectra. The cubic spline computer program essentially generates a best fit (to within a standard deviation of 0.001 to 0.005) of the normalized data points to a series of cubic equations (y = A + Bx + Cx2 + Dx3), solving for the best values of A, B, C and D for the temperature range over which the data fit that particular cubic relation, within the specified error limits. That is, each complete recovery curve is expressed as a sequence (with increasing of yg = A$ + Btx + C& +- I)& temperature) relations, and associated temperature ranges over which the respective relations hold true. The resulting recovery curves and their derivatives with respect to temperature are generated by a calcomp printer. The isothermal recovery was studied using a pulsed isothermal technique. The anneals were performed at the respective temperatures and the resistivity measurements were made at liquid nitrogen temperatures 29). The annealing time at the respective isothermal temperature was monitored by several Pt, Pt/lOO/b Rh thermocouples in contact with the specimens.

demonstrating a second-order recovery mechanism iO,i7-& 29+3h 3% 43). The Stage IV defect has an activation energy for recovery of m 3.3 eV with some studies demonstrating first-order kinetics as). After complete annealing of neutron-irradiation damage 1%2%31~32) a residual resistivity is observed which has been attributed to the presence of rhenium formed via thermal neutron irradiated (n, y) reactions. 3.

Experimental

technique

Resistivity measurements have been made at 77 “K on some 17 specimens following one hour isochronal anneals at a number of temperatures from 70 to 1900 “C after fast neutron (E, > 1 MeV) irradiation from fluences of 8.5 x 1017 to 1.5 x 1021 n/cm2 at reactor ambient temperature ( RS 70 “C) in a water moderated reactor. The specimens were enclosed in aluminum capsules 8) which were back-filled with helium gas, and sealed. The neutron fluences were obtained from a careful analysis of dosimetry data from nickel-cobalt dosimeters incorporated in each capsule. The pertinent information concerning pre-

4. 4.1.

Experimental ISOCHRONAL

results ANNEALING

STUDIES

The dependence of as-irradiated resistivity increment, ~QO, for the specimens summarized in table 1, on the fast neutron fluence, @, (En 2 1 MeV) is presented in fig. 1. The distinct

-

1.1 x 2.1 x 2.7 x 3.0 x 4.8 x 5.4 x 5.9 x 1.1 x 2.3 x 3.3 x 3.8 x 7.3 x 7.9 x 9.8 x 9.9 x 1.1 x 1.4x 1.5 x 3.9 x

101s 1O’Q 1019 102” 1020 1021 1019

1019

1018 101s 101s 101s 10’8 101s loI* lore 10’9 1019 10’9

8.5 x 101’

F&i I:I& > 1 Mev)

i

6.8 x 2.3 x 2.3 x 3.2 x 4.5 x 7.0 x 2.6 x 4.1 x 9.3 x 1.1 x 1.2 x 2.3 x 3.2 x 4.9 x 3.7 x 7.0 x 5.2 x 3.0 x 2.6 x 2.5 x 0.772 0.771 0.774 0.762 0.776 0.747 0.775 0.732 0.793 0.749 0.767 0.719 0.745 0.721 0.739 0.794 0.720 0.774 0.765

0.769

eo (@cm)

resistivity

-r~n~r~di~ted

101s 1018 10x8 1018 10’8 10’8 lOl@ 10’9 1019 1020 1020 1Om 1020 1020 1oso 1020 1020 10~0 102’ 1019

Thermal

Irradiation conditions a flueme ( /cmZ)

0.236 0.289 0.391 0.501 0.624 0.782 0.717 1.118 1.583 2.531 2.515 3.329 3.974 4.460 4.345 5.963 5.904 5.009 10.872 2.646

APO(@cm)

Total irradiation .i nduced resistivity

0.031 0.046 0.096 0.108 0.205 0.332 0.045 0.369 0.633 0.520 0.279 2.843 0.022

-

-

0.226 0.289 0.391 0.501 0.624 0.782 0.717 1.0870 1.523 2.435 2.407 3.124 3.642 4.015 4.345 5.336 5.384 4.730 8.029 2.624 0.293 0.374 0.507 0.648 0.820 1.007 0.960 1.430 2.103 3.069 3,293 4.074 5.067 5.390 6.027 7,216 6.776 6.694 10.377 3.430

&/eo

307 302 270 320

3.370 3.070 5.287 1.896

1

2.810 i

1.695 2.101 2.300

319 316 313 312

0.211 0.260 0.354 0.441 0.523 0.651 0.604 0.820 1‘187

f

Area

365 359 360 350 352 348 345 333 325

1.15 T,

- --

548 518 500 515

532

541 520 540

556 542 541 539 520 540 550 519 556

0.632 0.569 0.850 0.241

0.531

0.279 0.368 0.481

0.020 0,030 0.036 0.047 0.061 0.082 0.077 0.095 0.149

Ares

(whom)

875 843 874 873

X.102 1.104 1.368 0.482

0.391 0,501 0.722 884 875 877 873

0.103 0.213

Area

--_-

855 853

825 850 892

876 840

E.31 T,

Maximum rate of recovery temperatur0, (“C) and srea under respective recovery peak

as det.ermined from isochronal resistivity studies

&l f$2cm)

j j ’ ! :

tungsten I tesistivit3 inerement fraction

irradiated

Fast neutron induced resistivity increment

in neutron

Residual r resistivity te,(@cm

specific resistivit,y increments

8 The specimens were irradiated at ma&or ambient temperatures (N 70 “C) in a water-moderated reactor. b The residual resistivity de, represents the rem&ning resistivity increment after the one hour anneal at 1900 ‘C. * The maximum rate of recovery temperature refers to the temperature at which the maximum recovery occurs for & specific recovery stage over its respective tem~r&ture interval, lhis stage is related to the melting temperat~e, Tm, as shown.

354 2194 2193 2192 2191 2190 101 355 175 152 104 356 337 358 348 357 2181 2188 218% 35%

Sample no.

Defect recovery stages and important

264

L.

K.

KEYS

ASD

J.

MOTEFF

i I 1 I

I I t I I L I 1 I

P, = as-wradiated resistivity po= unirradiated resistivity

1020 Fast

102’

neutron fluence. nlcm2 (E, > 1 Mevl

fort n.utron

flu.nr.,

0 ---

8.5X10”

E”

k.

1 M.”

n cm-’

a3.3x10’9 n ml-~ 0 ---l.lXlO’~ n rm-? 0 -------- 1.5x10””
0

Fig.

1.

Total radiation induced resistivity increment

of recrystallized tungsten as a function of fast neutron fluence.

curvature in this In-In plot supports pronounced saturation effects (in fact saturation appears to be nearly complete at the highest fluence). While earlier 10) studies appeared to support a region of constant slope in the In-ln plot at the lower fluences, these more detailed studies indicate an appreciable curvature. The general fluence dependence, however, agrees with other lower fluence studies 14). Fig. 2 shows typical recovery curves obtained from these resistivity studies on four specimens spanning the entire fluence range. These curves are similar to those obtained for almost all the specimens given in table 1. The recovery appears to occur in three major stages. The lowest temperature one occurs between 373 “K (100 “C) and 723 “K (450 “C), the next higher temperature one between 723 “K (450 “C) and 923 “K (650 “C), and the third between 923 “K (650 “C) and about 1273 “K (1000 “C). After the 2173 “K (1900 “C) anneal a residual resistivity remains which has been attributed to the formation of rhenium via thermal neutron (n, y) reactions in tungsten followed by B decay 1%2%32). Fig. 3 depicts the dependence of the residual resistivity increment, de,, after the 2173 “K (1900 “C) anneal on the thermal neutron fluence. Fig. 4 shows the rhenium concentration dependence on thermal neutron fluence as obtained by radiochemical analysis of the irradiated resistivity specimens at the

I 200

1 400

I

600

I

I

I

800

1000

1200

*nn*nling

Fig.

2.

I

f*m~~rof~r~.

1400

I

1600

I 1~00

2

IO

‘C

Isochronal resistivity recovery of fast neutron

irradiation

induced

crystallized

tungsten

resistivity as

increment

ES function

of

of

re-

annealing

temperature.

conclusion of the annealing studies 45). A value of 100 ,uQcm per atomic fraction rhenium is obtained from these studies in good agreement with a limited previously reported study 10). The observed rhenium concentrations coincide

NEUTRON

IRRADIATION

AND

DEFECT

RECOVERY

OF

265

TUNCSTEN

Fast n.vtron

ffugnc.,

---

E. z. 1 Mgr

g.5r10t7

n cm-*

33x10”

n cm-*

-.-.--

l.lX10’~

n .m-2

_----_--

1.5x10”

“(m-1

AP,=P-P, wham: P= P,=

0.01 10'9

Fig.

3.

I

I

I111111

Residual

recrystallized

I

I

I111111

I

I

,020 102' Thermal ne"rronfl"e"ce,"icm~

resistivity

tungsten

as

neutron

of a

t.lnp.ratw.

ann*al

neutron-irradiated,

function

of

thermal

fluence.

I 0.1

Fig. analysis of rhenium content

in neutron irradiated tungsten as a function of thermal neutron

ahw highest

1022

400

600

800

Ann*ofing

Radiochemical

ahar 1 hour annmfs

rwistivtty

Illllll

200

Fig. 4.

raistirity

fluence.

with the trend predicted by the calculations of Browning and Miller 46). Subtracting out this residual resistivity increment yields recovery curves typical of most materials, with recovery being complete at the higher temperature 10). Defining der as being equal to (Q-Q*) where er and Q have their previous designations, the recovery spectra may be obtained by plotting d(der)/dT versus the

5.

I

1000

1200

t.mp.ratun,

I

1400

1600

I

I

0.2 0.3 0.4 0.5 Homologous temperature, T/T, Derivative

2

lo

I 0.6

of the isochronal recovery of the

fast neutron radiation of recrystallized

1800

ac

induced resistivity

tungsten

as a function

increment

of annealing

temperature.

annealing temperature. Typical recovery spectra are given in fig. 5. For convenience these recovery spectra are also plotted versus the homologous temperature T/T, where T is the respective annealing temperature and T, “K is the melting temperature of tungsten. The three predominant recovery stages are clearly evident in this plot. Other smaller recovery peaks and shoulders also appear at about

266

L. K. KEYS AND J. MOTEFF

0.27-0.28

T,

and 0.35 T,

in

agreement

with

I

Previously obvious Stage III

from

101s), it has been fig.

recovery

5 and spectra

table

stated 1)

10’9n/crn2

Isotherm

at 333°C

%I %I,

p-

-=

the

Pl

Plllo

- PIII,

4

where p

= resistivity

PIII,

= resisttlwty

peak temperature r

e

., C .z se

reoxery

PI

of stage Ill

= as-irradiated

-I

I

resistkey

0.4

I 0

I 200

100 Annealing

7.

1

after complete

0.5

01

Fig.

I

after respective

annealing time

shifts from about 360 “C (633 OK) at the lowest fast neutron fluence to about 270 “C (543 OK) at the highest fluence. This shift was believed to result from a combination of effects from rhenium as well as the interaction of damage regions resulting from the approach to saturation. The relative importance of these two contributors was not well known, however, subsequent experiments have yielded more detailed information and will be described in a later section in this paper. The scant results appeared to yield a dependence on a semi-log plot of the Stage III peak recovery temperature versus the thermal neutron fluence 10). The present more detailed studies give a similar but better correlation with the fast neutron fluence as demonstrated in fig. 6. While this is strictly an empirical fit, it does allow a simple means of roughly predicting this temperature.

;E ” > 1 Mevl i

(as is

that

1

I

1.1’~

recent results reported on tungsten 47) and molybdenum 47-51). The small size of these peaks hinders their accurate resolution.

Normalized

time, t Imm

isothermal

at 333 “C of recrystallized

3w

)

resistivity

tungsten

fast neutron fluence of 1.1 x 1019 n/cm2 (E, > at about

recovery

irradiated to a 1 MeV)

70 “C.

spectra (figs. 3 and 5, correcting for the rhenium content), the temperatures and resistivity fractions for the beginning and end of the Stage III recovery were found. These resistivity increment fractions, AQ/QO, as previously defined, were utilized to obtain similar values for the isotherm utilizing its post-irradiation resistivity measurement and its resistivity, following completion

of

the

isothermal

study,

after

annealing at 2173 “K. These results were then normalized relative to this recovery region

yieldingA~III/&II~.

Fig. 6. Variation of the Stage III peak recovery temperature as a function of the fast neutron fluence.

4.2.

ISOTHERMALANNEALING STUDIES

Fig. 7 presents the results of an isothermal study at 606 “K for a tungsten specimen irradiated to 1.1 x 1019 n/cm2 (& > 1 MeV). The recovery is normalized to Stage III. From the isochronal recovery annealing curves and

A similar isothermal annealing study has been carried out for the major high temperature recovery region (fig. 8). The isothermal anneals were performed at 870 “C (1143 “K) (the temperature region of the peak in the 0.31 T, recovery stage of fig. 5). Because of the much smaller magnitude for this recovery stage a specimen was selected which had been irradiated to the highest fast neutron fluence of this investigation, namely 1.5 x 10zl n/cm2 (En > 1 MeV). These results were again normalized, for the 0.31 T, recovery region, similarly to

NEUTRON

IRRADIATION

AND

DEFECT

5.

Temperature of anneal= 870°C

AP --

IV

RECOVERY

ACTIVATION ENERGY DETERMINATION MEECHAN-BRINKMAN ANALYSIS

The activation = resistivityin this stageafter respectiveannealingtimes ’

= resistivityafter complete recoveryof this stage

niques

Annealingtime, minutes

Fig. 8. Normalized isothermal resistivity recovery at 870 “C! of recrystallized tungsten irradiated to a fast neutron fluence of 1.5 x 1021n/cm2 (E, > 1 MeV) at about 70 “C.

0

-1

5.2 q>

for determining

the activation

energy

process require either an a priori

knowledge of the reaction order, or else an assumed reaction order. The technique of combining the isothermal and isochronal data, known as the Meechan-Brinkman Method 52), eliminates the reaction order from the equation. If it can be considered that the process occurring in a particular stage is essentially the same over the whole neutron fluence range investigated, then, through the use of normalized data, a single resistivity isotherm for a particular fluence specimen can be combined, by the Meechan-Brinkman technique, with a series of resistivity isochronals over the entire fluence range to yield activation energies. This approach is only considered to be rigorously true for specimens of equal defect concentration.

0

5.2.

-2

5 where -3

PIV

= resistivityin this stageafter respectiveannealingtime

PIV, = resistivityafter complete recoveryof this stege 4vi = resistivityat start of stage -4 100

200 300 Annealingtime, minutes

400

Fig. 9. Dependence of the natural logarithm of the normalized resistivity recovery of recrystallized tung&en, irradiated to a fast neutron fluence of 1.5 x 1021 n/cm2 (E, > 1 MeV) at about 70 “C, on the time.

the

energy for a unique recovery

process can be determined by a combination of isochronal and isothermal data. Most techof a recovery

-

267

Recovery analysis

5.1.

_PIV -pw,

OF TUNGSTEN

lower temperature study. The start of recovery (i.e., ~rv,) was taken at the end of the 0.27 T, recovery. For a first-order process a plot of In (d~rv/derv,) versus the time should yield a straight line as is obtained in fig. 9 5).

STAGE III RECOVERY REGION

In fig. 10 the normalized recovery d~m/d~m, is presented for five specimens. Combining these by the Meechan-Brinkman analysis with the appropriate isotherm (fig. 7) yields fig. 11. The straight lines obtained can be taken as evidence supporting the use of this approach. The four lowest fluence specimens give an average activation energy, from a computer best fit of the data, of 1.66 * 0.05 eV in excellent agreement with previously reported values of about 1.7 eV 1% 1% 17722). The highest fluence specimen, however, shows a somewhat lower energy of about 1.5 eV. This high fluence deviation is believed to represent the influence of rhenium on this recovery process (section 6.2).

0.31 T,

5.3.

STAGE IV RECOVERY REGION

The normalized isochronal recovery of the resistivity for the high temperature peak ( M 0.31 Tm) has been done in a manner similar

268

L.

K.

KEYS

AND

J.

MOTEFF

to the low temperature recovery for the same five irradiated specimens. These norma,lized recoveries

are presented

in fig. 12. Combining

these results in the Meechan-Brinkman with the corresponding leads to straight l/T

isotherm,

manner

fig. 8, again

lines for the In (At) versus

plots in fig. 13. This calculation

yields an

average activation energy from a computer best fit of the data of 3.3 eV.

6.

Discussion

6.1.

DAMAGE PRODUCTION

The curvature of the resistivity increment, on fast neutron fluence, AQO, dependence @ (E, > 1 MeV), given in fig. 1 suggests a fast neutron damage production of the form often

found Fig. 10. Normalized Stage III isochronctl resistivity recovery of neutron-irradiated, recrystallized tungsten as s function of the annealing temperature.

7

at low temperatures, A@&?a cu A (l-

exp (-/I@)),

with A and ,tI being appropriate constants 53). A poor fit to this data was, however, found which was not surprising in view of the relatively high irradiation temperatures. As some success has been found for a dependence of the form 54) A@&‘J m A (l-

6

i.e.,

exp (-@D))+B@

this was also tried, with almost equally poor results. There is, however, recent evidence that in several instances the fluence dependence of damage 55956) may be expressed as

5

.z E z4

Ae~/eo~A1(l-exp(~Bl~))+Az(l~exp(-_1B2~)).

5

The computer

3

of A&p0 damage 2

b-

best fit equation,

fig. 5), is:

AQF/Q~=2.08 [l1 L 1.5

1.6

1.7

1.8

+ 8.10

1.9

rI°K-'l 103

Fig. 11. Meechsn-Brinkman 52) plot of the isothermal resistivity recovery (specimen irrrtdiated to 1.1 x 1019 n/cmz, E, > 1 MeV) and isochronel resistivity recovery (specimens irrrtdieted to 6.9 x lOl*, 1.1 x 1018, 3.3 x 1019, 1.1 x 1020, and 1.5 x 10sl n/cm2, E, > 1 MeV, respectively) of Stage III in neutronirradiated, recrystallized tungsten.

given in terms

(where AQF represents the fast neutron resistivity contribution presented in

[l-

exp (-

1.06 x lO_lW)]

exp (-

6.51 x lo-21@)]

= (A@F/@o)I + (Ae~/eo)z

(1)

where :

@ is the fast neutron

fluence (En > 1MeV).

Plotting eq. (l), and its derivative with respect to fluence, indicates that two different annealing processes (or recoveries) are most

NEUTRON

IRRADIATION

6.9 x lo'*

n/cm2

AND

1.l

(En > 1 MeV)

x 10’9

(En>1

DEFECT

RECOVERY

OF

TUNGSTEN

269

3.3 x 10’9 n/cm2

nlcm2

(En > 1 MeV)

MeV)

1 .o 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 700

800

900

700

800

900

Annealing temperature, ‘C 1.1 x 1020 nlcm2

1.5 x 102’

IEn>

IEn>

1 Me’/)

n/cm2

1 MeV)

0.7

-

0.6

-

0.5

-

0.4

-

0.3

-

PIV,

= resistivity after complete recovery of stage IV.

0.2

-

PIV,

= resistivity at start of stage IV.

0.1

-

700

where

PlV

= resistivity in stage IV after 1 hr anneals at respective temperatures.

800

900

700

800

900

Annealing temperature, ‘C

Fig.

12.

Normalized

Stage IV isochronal resistivity as a function

recovery of neutron-irradiated, of the annealing temperature.

likely occurring during the irradiation and that both apparently completely saturate below 10zl n/cm2 (E, > 1 MeV). In both processes the damage consists of an accumulation and destruction of primary lattice defects during bombardment. While these two processes may relate independently to displacement spike and thermal spike effects 55~57)other processes may contribute to this damage dependence 56958). Treating these two exponential terms as representing equivalent processes (of different magnitude), approximate calculations of the recovery or capture volumes can be made for

recrystadlized tungsten

both from the constants A and @, utilizing the technique of Cooper et a1.59). This approach considers that : A = r/Lana, (2) where r is the resistivity contribution per atom fraction defects, L is the average range of a displaced atom, u is the cross section for defect capture, and no is the density of atoms in the solid ; and that p = ~@‘%_,L~, where Gd is the cross section

(3) for the primary

270

L. K.

5.9 x (En >l

10’8n/cm*

1 1 x

Me’.‘)

,019n/cm*

lEn > 1 MeVj

KEYS

AND

3.3 X 10’9 n/cm* (En > 1 Me”,

J.

MOTEFF

effects

found

an interstitial distance 8.2 8.4 8.6 8.8 9.0 9.2

8.2 8.4 8.6 8.8 9.0 9.2

a’

-c

6 5

-I

8.2 8.4 8.6 8.8 9.0 9.2

10-4 y-1 [

T

Fig. 13. Meechan-Brinkman 52) plot of the isothermal resistivity recovery (specimen irradiated to 1.5 x 1021 n/cm2, E, > 1 MeV) and isochronal resistivity recovery (specimens irradiated to 5.9 x 10’8, 1.1~1019, 3.3~1019, l.l~lO~~, and 1.5~102~ n/cm2, En > 1 MeV, respectively) of Stage IV in neutron irradiated, recrystallized tungsten.

large vacancy

clusters,

may have to be within a short

(i.e., inside the shield region)

annihilated a.2 8.4 8.6 0.8 9.0 9.2

around

reducing the probability of the interstitial-large vacancy clusters recovery mechanism 62). Thus

at a large vacancy

to be

cluster.

This

shielding effect is described in greater detail by Beeler 62). Considering that 1 atomic percent of Frenkel pairs contributes about 20 ,&2cm 16), Lono equals about 645 atomic volumes from Al and 267 atomic volumes from AZ. The Lono from A1 is, as is found for the more completely studied metals [e.g., copper es)], about five times that from @1. The Lono value from A2 is, however, some 24 times that from /Jz. Such a discrepancy leads to considerable doubts with regard to applying these assumptions to the (~QF/QO)Zfluence dependence. As there still is much uncertainty with regard to the expected damage dependence at low and/or high temperatures and fluences, no further analysis will be considered here. 6.2.

STAGE III RECOVERY REGION (M 0.15 Tm)

displacement and v is the average number of atoms displaced per primary atom. Lam has the dimensions [cm] . [cm21 . [atoms/cm31 or atoms. Substituting for appropriate values in with v= 200 for 1 MeV the p equations, neutrons 60), Lana equals about 133 atom volumes for ,!?I and 11 atom volumes for p2. These values are of the order of recovery volumes for high temperature 61) [/?I] and lower (near

induced resistivity increment, AQF upon annealing has been demonstrated to occur between 100 and 450 “C. This result is in good agreement with recovery after cold working l7-1% 2%25), electron irradiation 36-38~40, 429 43), and neutron or other fast. particle 1%14-16926-35339)irradiation studies. Previous studies 29) have demonstrated

0 “K) temperature [82] recovery 62). While such results might fit, a comparison of correlated versus non-correlated defect recombination, it is considered in general that the random recombination of defects in tungsten occurs above 70 “C (the irradiation temperature). These results may fit a model of vacancyinterstitial production and mutual annihilation (#?1) plus a model of cluster formation and point defect, recovery (@z) in which the clusters make only a small (or almost negligible) contribution to the resistivity. Such a small recombination volume for /32 may then result because of the interstitial recovery shielding

that, at least for small amounts of damage (low fast neutron fluences), second-order kinetics are obeyed over a major part of the recovery stage. This is in keeping with the migration of selfinterstitials to an approximately equal number of vacancies over that part of the recovery region. It is felt that any other second-order reaction scheme can be eliminated for this region because of both the magnitude of the Stage III recovery and the requirement of roughly equal concentrations of reactants. The study supporting second-order kinetics over almost the complete fluence range is presented in fig. 14. In a second-order reaction

The recovery

of the fast-neutron-irradiation-

NEUTRON 450

1

I

IRRADIATION

,111,1,

I

,

AND

1

DEFECT

demonstrated

TIllI-

dependence,

p - PI11 APIII/P,=.o

clusters 65) these high significant stitials, at

PO where = unirradiated

PO p1ff,

RECOVERY

resistivity

= resistivity after complete recovery of stage III

by and

OF

the

bend

a high

density

in this region of Stage III. can indeed

in

the of

fluence defect

has been seen for irradiations to fluences, clusters may represent a sink concentration for self-interthe highest fluence, leading to a

possible change or modification

= resinivity after 1 hour anneals at respective temperatures

271

TUNGSTEN

be considered

in reaction-order Such a condition

as a means of ex-

plaining an anomalous reaction order in molybdenum ~67) where it can be considered that the higher homologous irradiation temperature leads to a high ratio of clusters to point defects 47, 4% 50, 67, 68). 0

1

250 1

, I llllll

Stage III resistivity

Fig.

14.

1

I I1111 101

100

10-l

increment

fraction,

Dependence of the Stage

temperature

Ap&p,,

IIIpeak

recovery

on the logarithm of the initial Stage III

defect concentration

for neutron-irradiated,

recrystal-

lized tungsten.

The temperature shift of the Stage III recovery region can for most of the neutron fluences therefore be ascribed to the effects of increased damage on the essentially secondorder region of the recovery process due to the migration of self-interstitials to immobile vacancies. For such a process the temperature shift of the second-order part of the Stage III recovery can be used to obtain a rough value of the activation energy for the migrating defect utilizing the relation 69)

the temperature of the recovery peak depends, to a first approximation, logarithmically on the initial concentration and on the heating rate 64). Our isochronal annealing times were long (one hour) and the temperature intervals, about the same for all, were relatively close together; we

where T refers to the respective temperature and CO the respective initial concentration of Stage III defects.

can therefore consider, for our purposes, that the above relation is independent of the heating rate. The plot of the Stage III peak recovery temperature versus the logarithm of the relative Stage III defect concentration A&Qo, shows a linear relationship over almost the whole fluence region, with the exception of the highest fluence specimen. This last result seems to fit in with the earlier energy analysis which indicated a lower recovery energy for this low temperature stage (fig. 11) for the highest neutron fluence specimen and could reflect the influence of rhenium (although its effect on reaction order might be questioned). This deviation in reaction-order may be a result of the high damage state 2). As the highest fluence specimen represents a high damage state as

It has been considered that the Stage III recovery involves diffusion-controlled kinetics which for low temperatures lead to a I/t time dependence for short to intermediate times, changing to second-order kinetics at the longer times 70). As the isotherm used in the previous Stage III analysis was at a temperature just above the peak in the Stage III recovery spectra for the particular irradiation fluence attained, the essentially second-order kinetics obtained over almost the total isotherm probably is a manifestation of the relatively high annealing temperature. For this portion of the Stage III recovery region eq. (4) gives an average of about 1.7s 0.3 eV for the five specimens in fig. 10, in fair agreement with the previously reported studies.

AT = T, - Tb = (kT,Tb/AH)

In (Cob/CO&),

(4)

272

L.

K.

KEYS

AND

J.

MOTEFF

The effect of rhenium on Stage III as described in an earlier paper 10) could be to lower the migration previously

postulated

energy of recovery.

It was

that it may take as much

as one percent or more rhenium to significantly alter this recovery, as appears to be supported by the current studies. The recovery spectra in the Stage III recovery region for two tungsten specimens irradiated to similar fast neutron fluences but to thermal fluences which differed by a factor of two are presented in fig. 15. The rhenium concentrations were about 0.30 atomic percent for the low thermal neutron fluence specimen and about 0.52 atomic percent for the high thermal fluence specimen. The low rhenium concentration specimen shows about the same temperature of peak recovery (about a 5 “C difference) as the high rhenium concentration specimen. This indicates that in this rhenium concentration Fig.

16.

spectra

Comparison

re-doped) neutron

of

of a low neutron tungsten fluence

the

specimen

(same

Stage

III

recovery

fluence re-irradiated to

rhenium

those content)

of

a

(i.e. high

specimen

and a low neutron fluence specimen.

range (less than one atomic percent) factors of almost two in rhenium concentration have little effect on the recovery temperature. Fig. 16 gives a comparison for a broader rhenium

Fig. 15. Comparison of the Stage spectra of two neutron-irradiated,

III recovery recrystallized

tungsten specimens with about the s&me fast neutron fluences but different thermal

neutron fluenoes.

concentration range. The specimen used for the 1.1 x 1020 n/cm2 (En 2 1 MeV) neutron irradiation was fully annealed for two hours at 1900 “C after the completion of its isochronal study. This sample had accumulated about 0.52 atomic percent rhenium as stated above. It was then re-irradiated to a low neutron fluence, 2.4 x 1018 n/cm2 (E, > 1 MeV) and 1.5 x 10lg n/ems thermal neutrons. The low thermal neutron fluence would contribute a negligible additional amount of rhenium. The recovery of this re-irradiated specimen was compared with that of another specimen irradiated to a low fluence, 2.7 x 101s n/cm2 (En > 1 MeV) and 3.2 x 101s n/cm2 thermal neutron fluence, which had very little rhenium. As can be seen from fig. 16, the re-irradiated specimen lies between

NEUTRON that with a comparable

IRRADIATION

AND DEFECT RECOVERY

rhenium concentration

and that with a nearly comparable

fast neutron

impurities, interstitials

273

OF TUNoSTEN

impurity

defect

complexes,

which have escaped

from

or selfshallow

fluence. The low fast neutron fluence specimen has a peak temperature at 350 “C (623 “K), the highest fast neutron fluence specimen peaks at 307 “C! (580 “K), and the re-irradiated

impurity traps I). It has also been considered that divacancies may contribute to this region 1, 1%20968). This interpretation is somewhat supported by recovery studies on quenched

specimen peaks at 340 “C (613 “K). The impli-

molybdenum

cation is that the fast neutron

in this recovery

damage contri-

71) in which a recovery is observed region.

The divacancy

in the

butes much more than rhenium to the over-all temperature shift, at least for rhenium concen-

body-centered cubic lattice has about the same activation energy for migration 72), 0.66 eV in

trations less than one percent. This indicated influence of the degree of damage on Stage III has also been observed by Schultz 17) in coldworked tungsten. In an earlier study 10) involving a comparison of the resistivity recovery of a cadmium-shielded and a normal non-cadmium-shielded specimen irradiated to the same fast neutron fluence, it was found that Iess damage was present in the shielded specimen. Because the shielding reduced the thermal neutron fluence at the specimen, the rhenium concentration was also reduced. Thus it appeared that the amount of damage may be influenced by the rhenium content. It was also considered that as a result of the capture of thermal neutrons by the shield, the shielded specimen may have experienced a higher irradiation temperature. The studies of the previous two paragraphs support the latter effect. Referring back to table 1, one sees that the specimens 2181 and 2188 have comparable

iron (body-centered cubic) versus 0.68 eV for monovacancies, but would be expected to have quite a different frequency factor for diffusion. Some trivacancies may even contribute to this region as these have been recently predicted by Beeler and Johnson 73) to have about the same diffusional energy as vacancies and divacancies. Some additional support for multiple vacancy migration in this temperature region is found from the studies of Schultz 17). He observed the same activation energy (m 3.3 eV) for recovery in this region as in the 0.31 T, region (i.e., from about 773 “K to about 1173 “K). Although some support exists for vacancy migration in this temperature region 4% 74) we feel previous studies as well as those described in the next section support vacancy migration in Stage IV at about 0.31 T,.

fast neutron fluences and AQF/~Ovalues despite different thermal neutron fluences. The reirradiated 2 18 1 (high rhenium concentration) specimen also shows almost the same AQF/QO value, 0.62, as the comparable fast neutron fluence specimen (with almost no rhenium) 2192, for which AQF/QO=0.64. It thus appears that for these concentrations (less than one atomic percent) rhenium does not significantly influence the production of damage. 6.3.

INTERMEDIATE RECOVERY REGION (w 0.22 Tm)

Much controversy exists over this region in which a number of defects may contribute to the recovery. Some of these are interstitial

6.4.

STAGE IV RECOVERY REGION (m 0.31 Tm)

The recovery in this region, while subject to controversy, can, we feel, be mainly attributed to vacancies in tungsten. Preliminary studies 10) in this laboratory on specimens irradiated to intermediate fast neutron fluences have given first order kinetics and an activation energy of about 3.2 eV for this recovery stage after neutron irradiation. Studies 17) by Schultz in cold-worked tungsten were unable to indicate the reaction order, however, an activation energy of 3.3 eV was found for this process. Subsequent field ion microscope studies of neutron irradiated tungsten by Jeannotte and Galligan 2s) at 1143 “K (0.31 Tm) and 1173 “K of single vacancy migration yielded first-order kinetics with an activation energy of 3.3 eV. From figs. 9 and 13, for most of the fluence

274

L.

range utilized in this investigation,

K.

KEYS

AND

an activation

J.

MOTEFF

energy of about 3.3 eV is obtained with definite first-order kinetics. These results, therefore,

The mechanism of this decrease in shear modulus is purportedly due to the extra (7th) outer electron on rhenium. Tungsten represents a

indicate

metal with the optimum outer electron-to-atom

that the same process is occurring

in

this temperature region for all these experimental conditions, and it is compatible with vacancy migration. Studies

on the

quenching

of vacancies

in

tungsten

provide additional support for the of vacancies at 0.31 T, 75,76). migration Schultz 75) found a vacancy formation energy of 3.3 f 0.1 eV for tungsten. Subsequent studies by Gripshover et a1.76), appear to confirm Schultz’s values. This value combined with the present activation energy value for Stage IV of about 3.3 eV yields a self-diffusion energy of 6.6 eV in excellent agreement with a recent calculation of the self-diffusion energy”) which gave 6.6 eV. For a first-order process the activation energy (AH) may also be related to the position and shape of the recovery spectrum curve (fig. 5) 78) by

AH = 2.4 kT;/AT,,

(5)

with Ta the recovery spectrum peak temperature and AT, the temperature-width at half the recovery spectrum peak height. The result of this calculation over the region of well defined Stage IV recovery spectra (above 5.9 x 10’s to 1.5 x lo21 n/cm2, En > 1 MeV) yields an average activation energy of 3.3 eV f 0.3 eV which agrees quite well with our other values. The Stage III recovery temperature and energy was shown in section 6.2 to be influenced at the high neutron fluence by rhenium. The Stage IV recovery, for a pure lattice weakening effect, also could be expected to exhibit a similar behavior, i.e., temperature decrease, but it does not 10). The nature of the influence of rhenium on the lattice may explain this apparent anomaly. Rhenium directly effects the strength of the group V1.B. metals (at least for concentrations greater than two to three percent). This alteration appears as a decrease in shear modulus 79-31). Such an influence should lower the migration energy for any diffusing defect.

ratio of six. The extra electron due to a substitution of rhenium for tungsten purportedly contributes

to the repulsive

potential

between

the atoms and thus decreases the strength

of

the material. The extra electron, however, may lead to an additional weak trapping of some of the vacancies and thus not only decrease or remove the influence of rhenium on the vacancies via the lattice but lead to a slightly increased recovery energy for them at the high neutron fluence. This explanation is quite speculative and more study is needed to confirm or understand the possible influence of rhenium on Stage IV. This influence of rhenium on the Stage IV recovery, however, would be expected to depend to a large degree on the ratio of defect concentration to rhenium concentration and would be minimized for high values of this ratio. If we compare the AeF/Ae, ratio (calculated from table 1) for the specimens irradiated to 1.5 x 1021 n/cmz, 1.1 x 1020 n/cm2 and 1.1 x 1019 n/cm2 (E, > 1 MeV), we find that the respective ratios increase as 2.8, 9.7 and 33. This explanation is in agreement with a previous study which indicates that Stage IV does shift to lower temperatures for high (25 atomic percent) rhenium concentrations with low defect concentration 82). The consideration that Stages III and IV should show similar temperature shifts as a result of the lattice weakening effects from rhenium inherently involves the assumption that the temperature dependence of the lattice modulus does not change. This consideration may not be true. More studies are needed on the influence of rhenium on the recovery stages. 6.5.

0.35 T,

RECOVERY

REGION

The recovery in the 0.35 T, region appears to be attributable to cluster or defect loop recovery and/or polygonization 1, 83). The density and size of these clusters may relate to the changes in hardness and ultimate tensile strength found

NEUTRON

in tungsten on irradiated

IRRADIATION

AND

DEFECT

in this general region 9~47). Studies molybdenum

83) and cold-worked

molybdenum 49) show good agreement for the activation energy of this recovery, yielding about 3.5 eV and about 3.7 eV respectively. While some researchers 49) have attributed this general recovery region to recrystallization and grain growth, this appears to be too low a temperature

for such phenomena

9).

RECOVERY

These

defect

OF

275

TUNGSTEN

concentration

results,

while

giving good agreement with other studies, appear to cast some doubt on the annealing kinetic studies. These results appear to indicate that quite an excess of vacancies prevails above Stage III and, therefore, also imply that the consideration of equal concentrations of defects may not be too rigorously obeyed. The excellent fit to second-order kinetics over a lengthy time range for the isothermal study is then somewhat

6.6.

DEFECTCONCENTRATION

CONSIDERATIONS

It is of interest to compare the relative concentrations of interstitials and vacancies annihilated in Stage III. A value of 20 @‘2cm per atomic percent Frenkel pairs 16) will be used. This would represent the resistivity change in Stage III for an interstitial-vacancy annihilation recovery process. The concentration of defects recovering in Stage III, obtained from table 1, varies with the fast neutron fluence accordingly; 1.1 x 1018 n/cm2 (En > 1 MeV) 0.015 atomic percent; 1.1 x 10lg n/cm2 (E, > 1 MeV) 0.061 atomic percent; 1.1 x 1020 n/cm2 percent; and (& > 1 MeV) 0.170 atomic 1.5 x 1021 n/cm2 (En > 1 MeV) 0.265 atomic percent. These results agree very well with the field ion microscope study by Attardo et a1.27) for Stage III recovery in tungsten irradiated to 5 x 1019 n/cm2 (En > 1 MeV). A value of about 0.10 atomic percent point defects was found. For Stage IV the assumption is made that vacancies anneal out to traps (dislocations, large loops or clusters, and/or grain boundaries) for which the resistivity contribution is essentially that for vacancies alone. Thus, the resistivity value used is 10 $2cm per atomic values were percent defects. The following obtained: 1.1 x 1019 n/cm2 (E, > 1 MeV) 0.021 atomic percent, 1.1 x lo20 n/cm2 (En > 1 MeV) 0.100 atomic percent; and 1.5 x 1021 n/cm2 (E, > 1 MeV) 0.150 atomic percent. These values also lead to agreement within a factor of two with the excess vacancies found after Stage III annealing in the studies of Attardo et a1.27).

of a surprise although it may be a result of the high annealing temperature used for the isotherm. It may result from a combination of other factors; among these is the influence of defect clusters. If the number of defect clusters becomes sufficiently high at the intermediate to high fast neutron fluences, then the combination of unequal defect concentrations plus the mixed order kinetics arising from clusters as effective interstitial sinks may lead to apparent second-order kinetics. This result would then appear to require the maintenance of a delicate balance between effective interstitial sinks (clusters versus vacancies) and the relative concentration of vacancies and interstitials, a rather strict requirement. In any case, these reaction-order results do agree quite well with those of Schultz 17) and Neely et al.43). As the previously cited studies have indicated that both irradiation temperature and fast neutron fluence can alter defect concentrationsz), i.e., increase defect cluster or loop formation, it would appear that if defect clusters or loops approach a concentration which is significant relative to the excess monovacancy concentration, then these multi-defects could act as major defect traps or sinks for migrating Stage III defects. A recent theoretical analysis@) has indicated that in niobium, which resembles molybdenum as far as the temperatures at which the important defect recovery stages appear s5), the defect loops represent significant sinks for the recovery of the Stage III defects. This result would be in qualitative agreement. with the results for Stage III recovery and defect production cited for molybdenum 64-679 74,83,86). It may also hold true for tungsten at

276

L. K. KEYS

AND

J. MOTEFF

very high fast neutron fluences, i.e., of the order of 1021 n/ems or greater. The recovery in the 0.22 T, region indicates

purities 17), the total resistivity contribution for all these impurities is 0.090@em. This is a negligible value in comparisol~ to t,he magnitude

a magnitude (table 1) slightly smaller (about Q to I) than that for the 0.31 T, region. If

of Stage III found for almost all the fast neutron fluences utilized in this investigation (table I).

it is considered that this region represents divacancy recovery, with a resistivity change twice that for monovaca~cies, a quite

high divacancy

one then obtains

concentration

in the

range of 30-50 percent that of monovacancies. This result is in excellent agreement with the theoretical predictions for divacancy concentration by the cascade damage model used by Beeler 86). A similar result has also recently been found for recovery in this temperature region in neutron irradiated molybdenum 67).

One of the studies only

which

sideration

that

contribute

to the recovery

led to the con-

interstitial

impurit~ies

in the Stage

III

It has been considered by several investigators 1%~88-91) that the Stage III recovery in damaged metals represents the migration or redistribution of redissolved, quenched-in, or dissolved interstitial impurities (carbon, nitrogen, and oxygen). The particular interstitial impurity having a diffusional energy closest to that observed for the Stage III defect in the respective metal is then considered as the defect recovering in Stage III. This interpretation has been supported by studies of recovery of damage

region was a study of the effects of oxygen on the recovery of neutron-irradiated niobium is). This study demonstrated a very good correlation between the magnitude of the Stage III recovery and the oxygen ~oneentration. However, such a correlation may not be as straightforward as it appears. The basic theory ascribing Stage III to selfinterstitials (in a dumbbell configuration) considers that this defect can be generated by conversion from a metastable crowdion 94395) as well as from the normal defect production of a dispersion of self-interstitials and vacancies. This theory has been developed from studies on face-centered cubic metals. From the consideration that interstitial impurities would represent good “deflection sites” for dynamic and/or metastable crowdions, it is not at all surprising that a good correlation exists between the magnitude of Stage III and the oxygen concel~tratio~l in niobium 1s) [or for that matter,

in niobium Is), where oxygen is considered the Stage III recovering defect. More detailed studies by Soo 92) have, however, indicated that both oxygen and intrinsic defects (self-interstitials) migrate in Stage III. Other defect recovery studies on very pure molybdenum 49) and tungsten as) demonstrate that Stage III results from the migration of an intrinsic defect, the self-interstitial. It can be shown for the studies presented here, that the interstitial impurities could make only a very small contribution to the magnitude of Stage III. The total interstitial impurity concentration (carbon, nitrogen, and oxygen) was only about 3.6 x 10-a atomic percent. Taking 2.5 ,t&?cm per atomic percent as a reasonable resistivity value for these im-

for interstitial impurities in some ot,her metals ss-91), in particular, t,hose which display a high solubility for these impurities]. For a very pure metal excess Stage III selfin~rstitials are produced by conversions of crowdions resulting from encounters with other intrinsic defects, crowdions or dumbbells. As this mechanism depends only on the inherent intrinsic defect concentration, a high neutron fluence is necessary to get an appreciable Stage III. As the interstitial impurity concentration is increased in the metal, the fast neutron fluence required to produce a Stage III magnitude comparable to that in the pure metal could therefore decrease, even if the interstitial impurity atoms made no additional contribution to the magnitude of Stage III,

6.7.

GENERAL

IMPURITY

CONCENTRATION

AND

OTHER

DEFECT

CONSIDERATIONS

NEUTRON

their

IRRADIATION

because

of

fluences,

there may be a contribution

deflecting

ability.

AND

For

DEFECT

low

to the

RECOVERY

ness of the 0.31

277

TUNGSTEN

T, recovery in tungsten may

not be true for all body-centered-cubic

magnitude of the Stage III recovery from any dissolved impurity which migrates with almost

or after

the same energy as the Stage III defect. Just as the interstitial impurities (carbon, nitrogen

fluences.

and oxygen)

OF

above

neutron

0.09

T,

irradiation and/or

metals,

at temperatures

higher

fast

neutron

in most metals have migrational

energies similar to each other 8%se), the selfinterstitial in some metals may have a migrational energy close to that of impurity interstitials. It is therefore felt that interstitial impurities may make a contribution to Stage III for low neutron fluences and high impurity concentrations, especially in metals having a high solubility for interstitial impurities. These interstitial impurities in such metals may also trap some defects in this Stage III region 9%97). Such normal lattice defects as dislocations and grain boundaries are inherently present in the purest of polycrystalline metals, although they may be of a low concentration. These may also, as lattice discontinuities, contribute to promoting a larger Stage III, by converting dynamic and metastable crowdions to dumbbell self-interstitials g7-gg). Accordingly, Stage III may be drastically suppressed in ultra-pure metallic single crystals. Such a phenomenon has indeed been observed in neutron irradiated molybdenum 67). This influence of defect and interstitial impurity concentration on the magnitude of Stage III may also result from the interaction of these lattice discontinuities with focusons and channeled atoms 6%100). While it has been considered that excess vacancies migrate in neutron-irradiated tungsten at about 0.31 T,, it appears that some defect cluster annealing can also take place in this recovery region 101). The resistivity results presented in this paper, namely the Stage IV activation energy and its reaction-order, definitely indicate that in 70 “C neutronirradiated tungsten this cluster annealing process makes a negligible resistivity contribution to Stage IV up to a fast neutron fluence of 1.5 x lo21 n/cm’-’ (En > 1 MeV). This unique-

7.

Conclusions

Based upon the analyses and results cited it is felt that the following conclusions can be reached : 1. The recovery of defects in tungsten after neutron irradiation at about 70 “C occurs in three major (w 0.15 T,, e. 0.22 T,, w 0.31 Tm) and two minor (0.27 T, and 0.35 Tm) recovery stages. 2. The low temperature recovery, 0.15 T,, is referred to as Stage III. It involves an activation energy of about 1.7 eV and shows second-order kinetics over a large part of its recovery region. It is ascribed to the migration of self-interstitials to immobile traps, predominantly vacancies. 3. The recovery occurring at about 0.22 T, may be attributed primarily to divacancy migration although other complex defects (or impurities) may also contribute. 4. The 0.27 T, region, while not always well resolved because of its size, has been observed quite often and is speculated to represent trivacancy migration (although it may represent more complex defects such as have been postulated for the 0.22 T, region). 5. Vacancy migration is attributed to the Stage IV (M 0.31 Tm) region because of its excellent agreement, in regards to both reaction order (first-order) and migration energy (3.3 eV), with other studies in which vacancies have been identified. 6. A comparison of the non-annealing residual resistivity component with theory and radiochemical analysis demonstrates that it is definitely due to rhenium. Its contribution to the resistivity of tungsten is 100 yQcm per atom fraction rhenium. For high concentrations ( > one atomic percent) it is

L.

278

considered that rhenium various recovery stages.

K.

KEYS

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J.

MOTEFF

Damage in Solids and Reactor Materials, IAEA, Venice,

7. A shift in the peak recovery temperature of about 100 “C to lower temperatures for Stage III with increasing neutron fluence can be attributed primarily to the influence of increasing defect concentrations, for low rhenium concentrations.

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