Resistometric measurements on molybdenum irradiated with 2.5 MeV electrons

RESISTOMETRIC

MEASUREMENTS WITH M.

DE

ON

2.5 MeV JONGtT

MOLYBDENUM

IRRADIATED

ELECTRONS*

and

H. B. AFMANt

The production and recovery of damage in molybdenum produced by irradiation with 2.5 MeV All damage electrons at N 50°C was studied by observation of the change in electrical resistivity. produced recovered completely in one stage around 195°C and is associated with an activation energy of 1.29 f 0.04 eV. The initial recovery of the isothermal annealing is proportional with Z/t whereas the tail end obeys second-order kinetics. The results are consistent with a model in which the recovery is ascribed to the random migration of interstitials to vacancies leading to their mutual annihilation, whereby the initial recovery involves predominantly the annihilation of interstitials with the vacancy from which they are originally dislodged as theoretically described by Waite. The diffusion constant for the interstitial molybdenum atom is:

D/a2 = 0.9 x 1O1211exp ((-1.29

& O.O4)/kT}

and the capture radius rg for the spontaneous annihilation of interstitials with vacancies: 15 A < v,, .< 36 A. Independent evidence for this large capture radius is obtained from the production rate curve; saturation is observed at large doses giving a maximum concentration of Frenkel pairs of - 8 x lOmA. MESURES

DE

RESISTIVITE

SUR

LE M~LYBDENE DE 2,5 MeV

IRRADIE

AUX

ELECTRONS

Les auteurs ont etudie la production et la restauration des deglts produits dans le molybdene lors de l’irridation aux electrons de 2,5 MeV a -50°C par l’observation des variations de resistiviti: Blectrique. La restauration complete de tous les deglts produits s’effectue en une &ape aux environs de 195°C et s’associe a une Bnergie d’activation de 1,29 k 0,04 eV. La restauration initiale du recuit isotherme est proportionnelle & dt et s’acheve en obeissant a une cinetique du second ordre. Les resuttats sont en accord aveo un modele dans lequel la restauration est attribuee 21la migration au hasard des interstitiels vers les laounes conduisant Q leur annihilation mutuelle, de sorte que la restauration initiale implique principalement l’annihilation des interstitiels avec la lacune de de laquelle ils sont arraches a l’origine comme Waite l’a decrit theoriquement. La constante de diffusion pour l’atome interstitiel de molybdene est:

D/a* = 0,9 x 10l**1exp {(-I,29

& 0,04)/kT}

et le rayon de capture r,, pour l’annihilation spontanee des interstitiels avec les lacunes: 15 A < T,, < 36 A. La courbe de vitesse de production donne une preuve independante de oe grand rayon de capture; la saturation est observee 2t de forte doses dormant une concentration maximum en paires de Frenkel de -8 x 10-s. WIDERSTANDSMESSUNGEN

AN

MOLYBDAN NACH ELEKTRONEN

BESTRAHLUNG

MIT

2,5 MeV

Die Erzeugung und Erholung der Schadigung von Molybdan durch Bestrahlung mit 2,5 MeV Elektronen bei -50°C wurde durch Messung der Anderung des elektrischen Widerstandes untersucht. Die Erholung der gesamten Strahlensohiidigung erfolgt in einer Stufe bei 195% mit einer Aktivierungsenergie von 1,29 & 0,04 eV. Der Anfang der isothermen Erholungskurven verliiuft proportional zu tit, wiihrend der zweite Teil einer Kinetik zweiter Ordnung entspricht. Die Ergebnisse sind konsistent mit dem Modell, welches die Erholung der freien Wanderung von Zwischengitteratomen zu Leerstellen und ihrer gemeinsamen Annihilation zuordnet. Dabei entspricht der Beginn der Erholung hauptsachlich der Annihilation van Zwischengitteratomen an den Leerstellen, von denen sie herriihren, wie theoretisch von Waite behandelt. Der Diffusionskoeffizient des Molybdan-Zwischengitteratoms lautet D/a2 = 0,9

x

lOi”** exp {( -1,29

k 0,04)/kT}

Der Einfangradius TV fur die spontane Rekombination van Zwischengitteratomen und Leerstellen ist 15 A < rg < 36 A. Ein unabhiingiger Hinweis fur diesen gro6en Einfangradius ergibt sich aus der Erzeugungskurve; bei hohen Dosen wird eine Sattigung beobachtet, die einer Konzentration der Frenkel-Paare van -8 x 1O-5 entspricht.

1. INTRODUCTION A

vast

metals,

literature

especially

exists

the f.c.c.

on

our insight is still very confused.(2-s) defects

metals.(l)

concerning the self-interstitial, defects produced by irradiation

to contribute

Nevertheless

defect, a study was made of the anelastic after-effect

one of the major with fast particles,

1

METALLURGICA,

VOL.

15, JANUARY

1967

to a better understanding

in electron-irradiated

molybdenum,

liminary results have been published method

* Received April 26, 1966. t Natuurkundig Laboratorium, Universiteit van Amsterdam, Amsterdam, Netherlands. $ Now at: N. V. Philips, Division of Electronic and Compound Materials (ELCOMA), Eindhoven, Netherlands. ACTA

In an attempt

in damaged

of the after-effect

of this latter of

which

recently.‘@

was adopted

selected 1

for

and the interstitial. reason

that

the

The

here because

this method is very suitable for distinguishing the vacancy

pre-

between

A b.c.c. metal was after-effect

can

be

ACTA

2

exp&ed metals was

to be more

pronounced

than

in f.c.e.

ones.(‘)

chosen

because

the

impurities

METALLURGICA,

in this group

Finally

of

electron irradiation defect

simple.

In these experiments

observed

st,rueture

to

an nft,er-effe&

be brought produced

about

be

produced

at about

110°C which may

by t.he reorientation

by irradiation

is rather

de Jong and Wensink(Q of a defect

and it was argued

basis of the selected experimental

conditions

on the that this

defect is likely to be the interstitial molybdenum In view lacking

of the fact

had

that firstly

about, the behaviour

irradiation

search for the after-effect, started on the recovery electrons

and secondly

in which

after

In cold-worked a distinct

bombardment

the

const’ant.(13)

around

change The

singly activated of annealing

to

resistivity

with

of

2.5 MeV

The results of this

and neutron-irradiated

of t,he electrical

energy,@)

range

with no further

in the

qualitatively

similar

interpretation to

discussion,

but

several

which

should

a

kinet-its is not# well established

of

our

When damage is produced

is complex.

lil~eIy.(14~16) Peacock

to

bhe energy of the incident

electrons

in such

can be chosen

dominantly

collision

and subsequent for

so that the observecl

of these fundamental

electron

irradiation

and Johnson,

very

defects.

rates

and Kinchin

previously bination

the

significant

migration

impurities

of

vacancies

or defect

and Ma&e1 and Brimhall(lsl microscope

studies

to

clusters. that

either

interstitial

Downey

and Eyre,(l’)

concluded

from electron

vacancies

may

migrate

interstitial recovery sten,(lg)

iml)urities

Recently

Each interst,it,ial will be fairly from which it, is dislodged.

to

like carbon

characteristics alt’hongh

do not affect

of neutron-irradiated

on the

other

hand

the

tung-

carbon

may

This

has a great impact on the

be observed(22)

section

rate.

as will become

will be devoted

If dnring

produced

t,o the defect

bombardment

vacancy,

will take place.

an interradius of a

spontaneous

recom-

This process appears to be

st the defect’ concentrations

employed

in

2. EXPERIMENTAL

to

Schultz showed that

the from

our experiments.

interstit’ials, the latter ones being trapped at impurities during bombardment.

It is

t.hat~ initially

from our results.

A separate

and TllomI~son(9) assumed that the recovery involves

pre-

damage

of interstit,iaIs is not independent

Lhat of the vacancies.

apparent

that

recovery may be more directly related

to the properties

annealing

a way

one i~lterst,it,ial-va~an~~~ pair is produced

per primary

but be

Bp

the use of fast electrons,

stitial comes to rest within the capture

seems

on

the nature of the

defects and their spaGal distribution

to

order

The

conclusions

production

second

in

investigators

for tungsten and niobium, which behave very similarly mol_ybdenum,

copper

in met,als by means of

cold-~vorking or i~eutron-irradiations

specific initial distribution

by

groups

be in line with

the latt,ice the order

of

damaged molybdenum.

of length(13) and

is characterized

that

attribute stage III to the free migrat,ion of interstitials,

close to the vacancy

For molybdenum

to

appears

of these stages in copper is still subject

the stored

recovery

up t,o room

denum at 170°C and of copper in stage III.(lo)

resistivity,(9-12)

process.

recovery

The low temperat~lre recovery

distribution

molybdenum

170°C is observed

be

typical

will be presented in this paper.

recovery

increase

upon

simult,aneo~~sly a study was of the electrical

at room temperature.

latter investigation

was

that we

temperature

45°K

1967

so-called stage I. tzl) Also a st’riking analogy has been observed between the recovery behaviour of molyb-

atom.

illformation

of molybdenum

with fast electrons,

no indicat,ion

molybdenum

to

interstitial

low,@) whereas

mas used because then the nature

of the

around

15,

temperature.

molybdenum

solubility

like C, N or 0 is relatively

of

VOL.

The experiment in the electrical

consisted resistance

of determining of molybdenum

irradiation and on annealing.

changes wires on

The meas~lrements were

carried out on mires of 0.1 mm dia. obtained

from

promote the nucleation of interstitial loops in neutron-

N. V. Philips (Eindhoven, Netherlands) with a stated purity of 99.987/,; main metallic impurity: Fe (

irra(~iated

~nol.~bdenum

0.01 T/, (other impurities : C < 0.0040/b ; 0, < 0.007 T$ ;

Nihoul(lo)

and Schultz’lQ

the random

migration

at

room

at,tribute

t~emperat,ure.(ls) the recovery

of interstitials

leading to their mutual annihilation.

to

to vacancies Our results will

be shown to favour this latter mechanisn~ and this interpretation is also supported by our results of the anelastic after-effect.‘6) Investigations on electron-irradiated b.c.c. metals have been report.ed only by Lucasson These authors irradiated subsequent

annealing

molybdenum

75%

and Walker.(zO) at 42°K.

of the damage

On

recovered

no detectible

t’races of N, and H2).

length of this wire was thoroughly a

hairpin,

spot-melded

60

About

15 cm

cleaned, bent into

m&al-glass

through-

connect~ions and en~apsL~lat,ed in Pyrex. The wires were vacuum-annealed (72 X IO-” mm Hg pressure) for 4 hr at! ,~2OOO”C by direct current) heating, and cooled in 8 hr t,o room temperat~ure. The resistance rat20 R ,,,lR,.,V< ranged from 70 to 110. Always two wires were treated simultaneously. Subsequently

the t,mo ends of such a wire were

DE

JONG

IND

AFMAN:

MO IRRADIATED

soldered* on copper tips which were electrically isolated from the rest of the copper specimen holder [Fig. l(a)]. The hairpin protruded about 15 mm out of this holder as shown in the figure. Potential leads were soldered at the specimens near or on the isolated tips. The mounting of the annealed wires did not cause any detectable deformation. This was verified on a separate sample by measuring the resistance ratio and the cha~ngeof resistance upon amrealing at 250°C for one day. After mounting, pairs of specimens were additionally annealed in purified He-gas for 1 hr at 250°C. Subsequently the purest specimen was irradiated and the other kept as dummy. Figure 1(lo) shows a schematic diagram of the set-up used for irradiation. The specimen holder was clamped on a water-cooled plate with a square diaphragm of 10 X 10mm2. This plate was screwed on a watercooled Faraday cup which was continuously flushed with N,-gas during irradiation. Always two specimens were irradiated simul~neo~lsly. The electron accelerator was a van der Graaff generator? (High Voltage Engineering, Amersfoort, Netherlands). In going from the interior of the accelerator to the surface of the samples, the beam passed through two al~~nlinium windows (thickness 0.005 in. and 0.002 in., respectively) and through 2 cm of &-gas of 1 atm. The interior energy E, of our beam was: Ei = 2.5 -& 0.05 MeV. At the point of collision in the samples the electrons will have a lower energy because of losses in the windows and in the sample itself. As a simplification it will be assumed that the damage is all produced with a beam of mono-energetic electrons with an energy equal to the average energy l? of the actual beam at the point half-way through the sample, so that ,7?= E, - (AE),,, where {AE),, is the average energy loss. Following the procedures of Lucasson and Walker,(20) Sosin@s) and Landau,(2P) {AE& = 0.21 MeV, so that l? = 2.3 + 0.05 MeV. To improve the homogeneity of the t’ime-average electron density over the diaphragm, the beam was scanned in one direction over 5 cm with a frequency of 400 c/s and strongly defocussed. Generally the beam current density was 30 + 3 ~A~crnz and was measured with a low resistance micro-ammeter connected directly with the cage. The electron beam caused temperature gradients across the specimen but the tip of the samples never exceeded 50°C. This was continuously controlled on a separately mounted specimen at the tip of which a 0.05 mm constantan * A Ag-Cd-% alloy was used supplied by Johnson and Matthey. This solder forms an excellent joint with molybdenum and does not become superconducting at 4.2% f Installed at the Koninklijke/Shell Laboratories, Amsterdam, Netherlands.

WITH

2.5 MeV

3

ELECTRONS

wire was soldered forming a molybdenum-constantan thermocouple, which was previously calibrated. After irradiation the specimen holder was attached to a thin-walled stainless-steel tube together with its non-irradiated dummy. The whole unit could then be immersed either in liquid He for measuring the electrical resistance, or in an oil-bath for annealing. In the latter case the assembly was enclosed in a thin-walled tube filled with Be-gas to prevent damaging of the specimen and dummy by the stirring oil. For annealing a conventional bath with silicon oil was used. The temperature was kept constant on &O.Z”C with a mercury tllermometer. The measurements of the electrical resistivity were all carried out at 4.2’K. The resistance was measured by a new device which will be described now.$ Using a specimen with parallel dummy, one generally keeps the currents t,hrough both equal and constant, and one measures the voltage across the potential leads of specimen and dummy.(25) We used a device in which the ratio 1, of resistance of specimen R, and that of dummy R, was directly measured: p = %I%

(1)

Figure 2 shows the schematic diagram. The resistances R, and R, are connected to separate electronic current sources supplying the currents i, and i,, respectively. These currents also pass a transductor via n, and nzdturns respectively. id is kept constant electronically and the magnitude of the other one, i,, is now coupled with id by means of a feedback system that compares the magnetic fields produced by i, and i, in the transductor with a magnetic amplifier. This feedback system can be considered as a d.c. transformer@@ for which fi.m,= zdnd. (2) The two currents are only magnetically coupled but not electrically. Therefore one potential lead of specimen and dummy (A and B in Fig. 2) can be inter~onneeted. Between the other set of leads, C and D: a sensitive galvanometer with a variable shunt is placed (Tinsley galvanometer amplifier type 5214). The gaIvanometer will give zero deflection when i,R, = idRd

(3)

apart from thermal e.m.f.‘s which will be neglected for the moment. From (2) and (3) one obtains Equation

%I% = R,IR, (=r)). (4) (3) can be realized by making n, or nd

z The authors are indebted to Prof. Muller for designing the apparatus.

ACTA

FIG. I(a).

adjustable (a)].

METALLURGICA,

VOL.

15,

1967

The specimen holder with mounted specimen.

and thus the ratio of the currents [equation

We used n, = 1000 turns and nd could be varied

provided

the two resistances

For

most

our

pure

are not too far apart.

samples

a change

from 1 to 1000 in steps of one turn by means of three

resistivity

of 5 x lo-l3 Q-cm

ten-position

dials.

In addition

id also passed through

However,

more

a

turn

which

short-circuited

sensitivity

of the galvanometer

separate

potentiometer

was

(Fig. 2) so that a continuous

from 0.01 to 1.00 turns could be made. turns represents resistance

(4)].

a

adjustment The ratio of

the ratio p of specimen

[equation

by

to dummy

p is independent

of the

choice of the current i,. rather

insensitive

We may also note that p is to fluctuations and drift of the

currents because any change in one of them is equally transduced

by the amplifier

to the other, so that if

the two currents are not too far apart, the galvanometer

setting

is not

only to be stabilized

affected.

Therefore

id needed

to 1: 103. With our apparatus p

can be measured with an accuracy of 1: lo5 irrespective of the absolute

resistances

-2 I

H2C

FIG. l(h).

Schematic

of specimen

bilities

caused

severe

limitations

by handling

bath to the other.

in specific

should be detectable. are set by

the specimen

Therefore

the

and the irreproducifrom

one

all our measurements

were accurate to better than lo-l1 G-cm.

The thermal

e.m.f.‘s were eliminated in the usual way by reversing both currents simultaneously. The increment is a direct

of specific

measure

electrical

In our experiments

defects in the metal.

resistivity

of the concentration

Ap

of point

the annealing

is followed by studying the change Ap of the quantity p [equation between

(l)].

Let us now

Ap and Ap.

discuss

the relation

Consider a specimen

of length

and dummy

A-_+ drawing of the irradiation.

set-up

used

for

FIG. 2. Block-diagram of the circuit for measuring ratio of resistances of specimen to dummy.

the

DE

JOKG

AND

AFMAN:

MO IRRADIATED

FIG. 3. The isochronal recovery curve andits temperature derivative. The dashed line represents the line of symmetry. E and diameter d: which is irradiated over a length li. Let p0 be the specific resistivity of the non-irra~ated material and p that of the irradiated one. Then from equation (1) one obtains:

P=

h + 4(P- PO)1

Rd

$mP

Pa)

or if pe is the resistance rat’io before irradiation:

(P-Po~=&&P-Po) d

Thus Ap( =p - pO) is directly proportional with Ap( =p - %). The proport~ionality factor depends on I, and R,. For all irradiations performed E,= 20 mm, but Ed was different for each dummy. Rd was determined before each run by comparison with a standard resistor to an accuracy of ,,tO.Ol”/O. The measured Ap-values could thus be transposed into changes in AP3. EXPERIMENTAL

RESULTS

3.1 lsochronal annealing Figure 3 shows the isochronal recovery of the increment of electrical resistivity Ap of an irradiated specimen up to 250°C. The annealing was performed in ~mperature intervals of S’C and the time for each anneal was 2 hr. After reaching the highest temperature the specimen was additionally annealed for another 14 hr at 250°C resulting in the indicated value Ap(co). It can be seen from the figure that the resistivity induced by irradiation recovered ~~le~e~~. This has been observed very generaby (see also Fig. 4). Figure 3 also shows that Ap( co) has dropped slightly below the value before irradiation, which is also very commonly observed (see also Fig. 4). The recovery takes place in one step as more clearly displayed by

WITH

2.5 MeV

ELECTRONS

5

the derivative curve of the isochronal, also included in the figure. This latter curve has been obtained by plott’ing values of ALAR from pairs of adjacent points against the temperature midway between each pair of point. The rate of recovery is maximal at 195’C at which temperature just about 50% of the total damage was recovered. A corroborating observation is that the derivative curve is very s~metrie; this shown by the dashed line in Fig. 3 which represent,s the line of symmetry. Although both observations are indicative for a second-order recovery process, further experiments to be described under 3.2 will show that the kinetics is more complex. For a pure secolld-order annealing-rate the measured curve in Fig. 3 is calculated to be too high and too narrow by 20%, following the same procedures as of Damask and Dienes(2g) and of Granato and Nilan.(41) 3.2 I~othemal annealing An example of an isothermal amlealing curve is shown in Fig. 4. Again complete recovery is obtained. In case of a second-order annealing process, a plot of l/Ap vs. time should yield a straight line. Figures 5 and 6 show the result. Proper straight lines could only be adjusted to the tail end covering the last 250/b of the recovery. The initial parts of our isothermal recovery curves follow closely a Apcc l/t relationship as displayed in Fig. 7. Neither the whole curve, nor initial or tail end separately could be adjusted satisfactorily to oOher processes of kinetics. 3.3 Activatim energy The activation energy E has been determined in various ways. (1) A specimen was annealed alternately at temperature Tl = 185.2oC and Ts = 195.6’C for short times (Fig. 8). After 70% was recovered the changes were made between Ta and T3 = 203.4’C. The activation energy was determined by Palmer’s met,hod,(27s2s)

4. The isothermal recovery curve at 195.0% A,( co) is the resistivity at t + co obtained from the best fit to second-order kinetics (see Fig. 5).

Fra.

ACTA

6

METALLURGICA,

VOL.

15,

1967

5% INITIAL PART SPEC P

1

J,c 2

TEMPERATURE1950°C

TIME

. - .

(HOURS)-

FIG. 5. Isothermal recovery curves at 195’C plotted as

I/Ap 1’s. t showing second-order kinetics at the tail end. The inset is an enlargement of the initial part and shows an inflexion point.

which is a refined change of slope method.(28~2s) E is then obtained

from the relation

(6) Equation affected

(6) presumes

that the sink density

by the temperature

and [d(Ap)/dt],z ature

changes.

are the rates of annealing

T, and

T,, respectively,

pair of subsequent They

is not

at temperdefect

From the curve

were determined

for each

measuring points Ap(tJ, t, ; Ap(t,),

are now

assumed

to represent

annealing rates midway these points, i.e. at +[Ap(Q

+

Ap(t,)].

of

Figure 9 shows these rates as a function

%A&) + 44t2)l. Th e curves represent the annealing rates at the temperatures T,, T, and T3, respectively. The vertical spacing between the curves gives directly

E using equation (6). We thus calculated E = 1.21 &

kWpWl,I

at identical

states, i.e. for the same value of Ap. in Fig. 8, values of dbpldt

t, ; etc.

FIG. 7. The same curves as in Figs. 5 and 6, but now plotted as Ap versus z/t. This relation is well-obeyed in the initial parts.

the

0.04 eV.

In the range

investigated

or the defect concentration. (2) In another specimen, the annealing temperature was changed from 2OO.l”C to 210.2”C after 85% was isothermally

recovered

(Pig. 10). The annealing rates

at the point of temperature

Apbb 95xl0‘9Rcm TEMPERATlJRE.2092°C

mined by adjusting points

in a plot

change were now deter-

straight

of l/Ap

lines to the measuring

vs. time.

done because this part of the recovery

I

20

t

40

I

I

60

60

l/Ap vs.

t.

This

could

be

curve has been

' ~lOOX 100

TIME (HOURS)FIG. 6. Isothermal recovery curve at 209.2%

the activation

energy seems not to vary with the state of annealing

plotted as

FIG. 8. The change of resistivity Ap vs. time t for an irradiated specimen annealed alternately at three different temperatures.

JONG

DE

AFMAK:

AND

MO IRRADIATED

WITH

2.5

XeV

7

ELECTROSS

I l.6

Fxc. 9. The annealing rate dAp/d~ for each isothermal interval of the annealing curve in Fig. 8, plotted versus the actual increment of resistivity midway this interval.

shown

to obey

second-order.

1.35 & 0.15 eV. very accurate

as is indicated

(3) In Fig.

We thus

Fig. 4 and the isochronal

are not

by the large stated error.

1.1 tjhe isothermal

the temperature-reduced

E =

found

In the tail end such methods annealing

FIG. 11. The curve of Fig. 3, 4 and 8 plotted as the relative change of resistivity versus the temperature reduced time 8 = Ctne-x’krn.

curve

from Fig. 3 are plotted

of on

time-scale

as described to

significant

in Fig.

method

was

slightly

T,.

at temperature increment

time in the n-th annealing ‘For

of resistivity

both

specimens

Ap(0)

was the

recovery is plot,ted here as the fraction which has been annealed

interval

the initial same.

The

of the resistivity

out

A,(o) -

E = 1.30 :I1 0.04 eV

choosing

coincide

excellently

a singly a&ivated

process.

applied

initial

(Fig.

1 summarizes obtained.

Ap(0)

yield

of the activation

an average

value

in the table

the

two

curves range

that the recovery involves The determination

of E

five

different

pairs

They

with one another.

the increments samples The

described

specimens

of resistivity

as a function

accuracy

so-called

of

in this paper, a total were

Ap(O) produced

does not increase curvature

radiation-annealing.{31)

that after bombardment

in these flux Qt.

to be better linearly

is found, indicating It

may

was terminated

be added

the resulting

E(eV)

1

I

50

75

/

100 TIME (HOURS)-

10. The annealing of a specimen at 200.1°C and subsequently at 210.2”C plotted as l/A, vs. time t.

FIG.

125

Other authors Sihoul”o’ Nihou1@0) Peacock and Johnson”‘) Kinchin and Thompson(g)

than

with dose,

TABLE 1. Act,ivation energy for inter&i t,ial molybdenum --

25

with

13 shows

of the tithe-integrated

of @ is estimated negative

irradiated Figure

doses of 2.5 MeV electrons.

Ho/x. but a marked

_.A

of

are the

by other invest~igators.(s-ll,30,

In the investigation of

A,(O)

+L

is

0.07 eV.

Also included

are in good agreement

Also

Palmer’s

Although

the results

They

end.

to which

fit with the other curves

for E = 1.30 f

values reported

or tail

8).

higher, an excellent

I.29 & 0.04 eV.

(8)

over the whole annealing

This indicates

investigated.

at

11 is the curve

3.4 Defect production

AP

v=-Apo* By

Table energies

because

of E from its proper value lead

misfits

included

is obtained t, is the annealing

here, appears to be very sensitive

even small deviations

1.21 1.35 1.30 1.30 1.29

* * * & +

0.04 0.15 0.04 0.07 0.04

1.25 1.23 1.25 1.3

* + & 3

0.04 0.06 0.08 0.1

8

ACTA

METALLURGICA,

VOL.

15,

1907

collisions more than two secondary pairs are created.‘33) These estimates must be regarded as upper limits.(34j It thus becomes clear that in our specimens the damage 31 can be considered to consist of isolated pairs. ,,,/;y / Let us assume now that during bombardment no appreciable diffusion of the defects takes place. Then /’ //’ /( I *i’ after bombardment has been terminated, our speci/ /’ / ./’ mens will contain equal amounts of vacancies and , ,/, / /. . interstitials. The observations (ii) and (iii} then / / / / indicate that the encounter of vacancies with inter/ / stitials leading to their mutual annihilation is the ‘-I ,/ dominating process as proposed in our model. The defect is associated with an activation energy for The resistometrio migration of 1.29 f 0.04 eV. measurements do not yield information about whether FIG. 12. The increment of resistivity Ap (0) vs. the time-integrated flux of electrons Q,. The dots (and full the vacancy or the interstitial migrates. However, line) represent A p(O) for all specimens irradiated. The de Jong and Wensink showedc6) from anelastic afterx - and -t_.-points refer to two specimens for which A p(O) was measured at various times during bombardeffect’ measurements that the interstitial molybdeuum ment. atom has an activation energy for reorientation of A&Of remained stable at the temperature of irradiation. 1.23 & 0.10 eV. The close ~orres~ndence between The defect production curve was reinvestigated on the two activation energies suggests that also in the specimens for which the increment of resistivity was case of the recovery of the electrical resistivity, the measured at various times during bombardment. The interstitial is the migrating defect. results for two runs are incorporated in Fig. 12 as We also have to consider the possibility that during the dashed curves. They all show the same tendency bombar~ent one of the defects, specifically the of a marked negative ourvature. interstitial, diffuses very fast as suggested by Downey and Eyre.(r7) This is even more pertinent because 4. DISCUSSION Lucasson and Walkerc20) observed a marked recovery 4.1 Oen,eraE descr@ion at 45°K (activation energy about 0.13 eV) which may The qualitative and quantitative aspects of our be attributed to the free migration of interstitials as measurements can be accounted for by attributing well. At the bombar~ng temperature of 20°C the the recovery to the free migration of interstitial jump frequency of such interstitials is about 1011per molybdenum atoms towards vacancies resulting in see and thus several reactions may occur of which a In this section the their mutual annihilation. few will be discussed. qualitat,ive arguments which have led to this picture, (a) During bombardment, the interstitials are will be discussed. The most salient points on which trapped at impurities. The 2OO’C recovery may then this conclusion is based are: involve either the diffusion of the vacancies to the (i) The damage to be dealt with is produced by bombardment with fast electrons at room temperature. trapped interstitials, or the release of the interstitials (ii) !l!he damage anneals out completely in one from their traps followed by capturing at the vacancies. recovery step (Figs. 3 and 4). In both cases the requirements (ii) and (iii) can be (iii) The last part of the recovery follows secondfullfilled. On the basis of the resistometric measureorder annealing kinetics (Figs. 5 and 6). ments the diffusion of vacancies to trapped interstitials In eIectron-i~adiation the energy transfers to the cannot be ruled out, but the after-effect measurements lattice are so low that in general only isolated suggestP) that the migrating defect is the interstitial Frenkel-pairs are created. In our case of an incident and not the vacancy. As to the release of interstitials electron energy of 2.3 MeV the maximum energy to from impurity traps, one should expect then a be transferred to a molybdenum atom is 170 eV and broadening of the recovery step and a spectrum of the average one 55 eV.(31) Taking a threshold energy activation energies which is contrary to observation of 37 e’E’ for the creation of a Frenkel pair,@@) one (Figs. 3 and 9). It may also be added that as far as estimates from Snijder’s and Neufeld’s theory(ai~32) interstitial impurities are concerned these seem not that an average of 1.13 pairs are formed per primary to affect the recovery in tungsten upon neutron collision and that in less than 1o/0 of the primary irradiation as reportsed by Schultz.(l@

JONG

DE

(b) During

bombardment

predominantly

The remaining

then

equal

the

annihilated

the interstitials

disappear

etc.

at

vacancies,

concentration

number

it may

dislocation

of vacancies

of interstitials

of 10’ (dislocations

between

etc.)

concentration

from the Ap-

fulfill requirement in addition

(ii).

On subsequent

comparable

As to (iii) one should assume disappear

at defects

of which the concentration

must be

with that

vacancies

of the vacancies;@)

are formed

appearance.

With

estimated

annealing

at 200°C in order to

that these vacancies

like impurities

above

followed

the low

by their rapid

vacancy

0

I

IO

,

20

I

30

40

,

I

1

50

60

70

1

80 TIME(HOURS)--

93

FIG. 13. Annealing curves of two specimens with different initial increment of resistivity plotted as the fractional recovery versus time.

dis-

concentration

!

0

'Ok

or di-

vacancy-vacancy encounters are As to the annihilation at impurities

highly improbable.

53x10-8 Rcrn

an ultimate

orders lower than can be understood should disappear

Ap(d.1

are

This is several

the vacancies

APH-AP Lp=-

For

to lo-*.

values (see also Section 5).

2.5 MeV ELECTROSS

these other sinks

one estimates

of lo-’

WITH

will

which

at other sinks than the vacancies.

an average jump distance vacancy

MO IRRADIATED

AFMAN:

AND

fractional

annealing

rates are the same, even though

their defect concentrations two.

We

may

note

differ by a factor of about

that

this is not

the case for

no tendency has been observed so far for an influence of

specimen X being annealed at a different temperature.

defect

The identical

concentration

nealing.

or purity

on the order of an-

For additional arguments against the vacancy

model the reader is referred to Nihoul’s cold-worked

and neutron-irradiated

(c) Formation

of

bombardment.

interstitial

This process

papers(15) on

b.c.c.-metals. complexes

can be ignored.

For a

are replotted

tail end, initially

of this interstitial

the

of lop5 set, the steady state concen-

so that interstitial-interstitial

is 2 x lo-l4

encounters are negligible.

One may also interpret the observed recovery as to be due to the annealing like C, N or 0. diffusion

Only the activation

impurities

energy for the

of C in MO (1.40 eV(35)) is close to that

determined to explain

out of interstitial

for our process (1.29 * 0.04 eV).

In order

(iii) one should assume diffusion of carbon

rates for III

and V

in terms of the fractional

recovery

If the initial recovery

also involves

(S)].

the annihilation

beam current of 30 ,uA/cm2 and an average life time tration of interstitials during bombardment

annealing

are more clearly shown in Fig. 13 where these curves [equation

during

initial

of interstitials

the result

of Fig.

the interstitials

presence

capturing

of

at vacancies 13 may

v

as in the

indicate

that

do not appear to experience

all vacancies

by the vacancy

produced,

but

that

from which the interstitial

is originally dislodged, prevails.

In electron-irradiated

specimens in which during bombardment

no appreci-

able diffusion takes place, such an annealing behaviour is to be expected because on the average an interstit’ial will be closer to its own vacancy

than to the others.

These conclusions

are substantially

supported

observation

for

A~Kz,/~

that

early

times

by our (Fig. 7).

atoms to vacancies which leads to the same difficulties

Waite showed namely, (22)that for initial predominant

as discussed

the results of the

annihilation

the

the annealing

anelastic

under

(b).

after-effect

consideration

Moreover

show

is produced

cannot be an impurity

that

by irradiation

defect

under

and therefore

interstitial.(‘j)

was found

accuracy

in Fig.

the activation

9 that

within

early times.

experimental

energy was constant throughIn Fig. 11

out the annealing in the range investigated.

with their own vacancy,

rate will follow As annealing

of interstitials

Let us now consider the initial part of the recovery. It

of interstitials

this relationship

proceeds,

the distribution

will become randomized

that of the vacancies,

with respect to

thus approaching

the condition

for second order kinetics as is actually observed. 4.2

Quantitative analysis

Waite(22) treated the problem

the isochronal and isothermal annealing curves, plotted of

freely

migrating

of the recombination

interstitials

with

immobile

on a temperature reduced time-scale 8, were brought into coincidence with the choice of a single activation These results indicate that the whole energy.

with respect to that of the interstitials

annealing process has to be ascribed to the migration of one and t,he same defect. From Fig. 7 one calculates

with which we deal with in our experiment. theory can be applied here only for very

for the specimens

annealing

III

and V, which

at the same temperature

were annealed

of 195”C, that their initial

for

vacancies,

the defect

when the initial distribution

of vacancies is not uniform, His early

times and for very long ones because concentrations

we employed,

at

the average

ACTA

10

distance be

no

between longer

interstitial

the Frenkel

large

METALLURGICA,

pairs will appear

compared

with

the

15,

times.

Waite

grating

interstitial

the annealing

assumed

r0 of a vacancy,

that

comes

P(r)

(1) when

it is immediately

initial separation own vacancy,

a freely

annihilated.

r between the interstitials

are distributed

according

and their

to :

the

width

N is the normalization

FIG. 14. The distribution P(r) of the initial vacancyinterstitial separation according to Waite.l22)

(9)

that an interstitial-vacancy

pair has an initial separation A characterizes

f--i

mi-

radius (2) The

P(r) dr = N~?T&z--(~/“Q)~dr dy is the probability

t

rate for early

within the capture

between of the

constant

1967

to

vacancy-

distances within the pair.*

First let us consider

P(r)

VOL.

r and r + dr.

distribution

and

For very long annealing

times, one finds for the

recovery rate, using Waite’s nomenclature

:

given by

(134 Or,P(Y)& s ro Figure 14 shows equation 1 = 2.

= 1.

(10) c is the concentration

(9) in graphical

For early times the fractional

form for

recovery

p is

then given by:

is the specific

pF

arOzNe-lid’ l/(D/a2)]

D is the difrusion constant given by

D =

Equations

constant.

including

the

Equation

and

(11) holds

for

From

now be evaluated (ro/a)3/(100

(11) (Fig.

range

predicts 7).

q < 0.3. ‘pcc$/t

The

In

bution.

region

as is experimentally

distribution

function

expresses that short vacancy-interstitial far more abundant

this

distances are

than for a homogeneous

This means that the initial

will be faster than for true second

distri-

annealing order.

vs. t plot of the init’ial part of the recovery This figure also shows that the annealing (at t ~2

of similar

curve.

rate passes

concentrations

with which we deal with in these experiments, concentration

l/Ap

hr). This may be related

to the fact that for the high defect may have been produced

rate

This can

be seen in Fig. 5(b) which presents an enlarged

through a minimum

P(Y)

regions

with higher than average defects,‘36,37) leading

to a

higher abundance of large vacancy-interstitial distances as well. This may also explain why our curves obey the qcc\,‘t relation over conditioned for equation (11).

a wider range than

* As will he shown below (Table 2) the average vacancyinterstitial distance within the pairs is F/a N 16, to compare with c-113 - 35.

r,/a

100

our isothermal

within the brackets

be computed

recovery

877 ~

D ~

pRa2

1* t.

W)

(Figs. 5 and 6).

factor which depends

of the interstitial,

1

where

pF)

of pairs, one

kinetics as actually observed for long annealing times

for

observed

of 1 at.:,;

13(a) and (b) typify second order annealing

annealing times such that 4Dt < (h,J2, or with 3, = 2 equation

c = (A~/100

resistivity

_---------_= APK’) AP

and

(12)

of vibration,

configuration

1

(11)

for the interstitial

entropy term ; I? is a geometrical cc is the lattice

dt

a2q,-Z/kT

where y is the frequency

the

of Frenkel pairs at time t. By

and substit’uting

obtains :

r,~== [81/r

on the atomic

integrating

pF)

annealing

in equations

curves:

and from them by elimination,

with 1, as parameter.

Hereby

for each i from equation

proportional

the terms

(11) and (13b) can

=

5 x

with r0p3. For the t,hree different

seen from the table that for the l-values the capture

It can be considered,

radius is quite large, 15 A < r. < 36 8,

but it will be discussed

in the next section that the

A-values substituted here seem to be reasonable.

An independent for

runs

assuming

1OP !&cm/at. y0 pairs, as given by Lucasson

and Walker,c20) also ro/a can be evaluated.

pa7 and

N can

(10) and is

the results are listed in Table 2. Furthermore pF

also

verification

vacancy-interstitial

of this large cross-section

annihilation

above

room

temperature

is namely obtained from a quite different

experiment,

the defect

be analysed

production

in Section

5.

rate (Fig.

The capture

12) to

radius

for

molybdenum compares well with the result of Nihoul on cold-worked niobium (20 A < r. < 43 fi).(15) From the distribution function P(Y) of equation (9) (Fig.

(14)) also the average

vacancy

and its interstitial

be seen from

Table

which may be noted

distance

f between

can be calculated.

2 that

the

It can

f/a N 16 or PN 50 A,

to refer to an average

energy

JON-G

BE

AND

AFMBAX:

&It-r IRR~ADIATED

WITH

2.5 MeV

ELECTRONS

11

2. Compilation of numerical data deduced from the isothermal annealing curves ._~_ . ..-_..__ __--” Defe& ;t _ 1.76 I = 2.25 A=2 production Spt3cimen --~ ___~_~__ (1.06 & 0.5) x 106 (0.56 5 0.3) x 106 (2.3 f 1.1) x 10” III (0.6 & 0.3) x 106 (0.33 i 0.16) x lo6 (1.4 $r: 0.7) x 106 v (0.9 * 0.5) s 108 (1.6 II 0.8) x 10” (3.5 & 2) x 10” s (2.4 f 0.7) x 106 (1.1 & 0.3) x 106 (0.33 rt 0.11) x IO” (1.45 + 0.3) x 106 Average. TABLE

~ZZ-

(r&)3 100 pF (C-em)-1 rob

10.6 & 1

ru

3OA
5.5 5 0.8

1

21A
18.5 & 2

&[a -...

8.2 f

-.

transfer for the primary collision to 55 eV. Comparable distances have been calculated by Erg&soy et &.(345 fop the range of focussed collisions in iron with an energy transfer of 100 eV. The combined etpplication of equations (11) and (1%) to our annealing curves also yield an evaln~tion of J3/a2 and by using E = 1.29 & 0.04 eV of the pre-exponential factor. We thus obtain for 1 = 2 :

15 A < r0 < 20 a -

S&l 24 A < T* .: 30 a

12 & 1.5

where (rsoOis the cross-section for the creation of a stable pair at 300°K with incident electrons of 2.3‘ MeV ; ‘R is the number of lattice sites rvithin the capture volume, so that ‘R.= (%/3) (~~/a)~. Substituting f/N = (hpj100 pf) one finds on integration :

Figure 15 represents the data of the l?roduction curves {Fig. 12) but now plotted according to equation For other values of A, B/c@ was within the uncertainty (14b). A straight line through all points is obtained range assigned above. The pre-exponential factor is by taking (ro/a)3/(lOO pF) = (1.45 & 0.3) x lo6 (!L of the correct order of magnitude for interstitial cm)-l giving P&J = 9 f 1 for pF = 5 S 1fP Q-cm/ diffusion in b.c.c. metaIs.i3s’ For instance if the at.% of pairs. The large capture radii derived here interstitial occupies the oGtahedra1 site and diffuses are in striking agreement with those derived from anly along these sites through the lattice, r = *(38) the recovery experiments and listed in Table 2, thus so that Y = 6 x 1012&lsee-l. presenting strong evidence for the proposed interpreThe results presented here in combination witA tation of these latter experiments (Section 4) and those of the anelastie a.fter-effect@) are not accurate supporting our selection of R N 2. enough as yet to draw any ~onGll~sions about> the The inverse factor atomic ~on~~lr~tio~ of the molybdenum ~~te~t~~,~al.(4z~ u/a” = 0.9 x uP”f

exp I(---1.29 -& ~.~4~~~~J.

5. DEFECT PRODUCTION The defect production does not increase 1inearIy with dose, but tends to saturate (Fig. 121, indicating that radiation annealing takes place. Long range diffusion of the defects produced by irradiation seems to be negligible at the te.mperature of bombardment (see Section 4.1). Therefore this effect may be caused by the spontaneous recombination of the defects during production. If an interstitial comes to rest within the captrme volume of a previously created vacancy, spontaneous recombination will occur. The same fate falls upon a vacancy produced within the capture volume of the interstitial. For this model, the rate of production of Frenkel pairs f per unit of integrated flux cf, within a volume of N lattice &tea is*

* Taking into account clustering of similar defeots,‘g*) higher order terms hsve to be added within the brackets of equation (14).

in equation (14b) corresponds with the maximum increment of resistivity obt&nable upon electron

FIG. 15. The d-egg production curves of Fig. &&ted Esccordingto equation (14b).

12,

12

ACTA

METALLURGICA,

irradiation at 3OO’K (Apmax = (4 & 0.6) x 10-s Gcm) and on substituting pp the maximum pair concentration for molybdenum will be cmax= 8 x 10w5. Prom the slope of the curves in Fig. 15 one calculates that (~,,/a)~ os,,,,= (2.15 & 0.5) x 1O-2ocm2, or with the ro/a value derived above (see also Table 2): 6aoo= (3 .& l.5) X 1O-23cm2. The evaluations above depend sensitively on the choice of pp. It is therefore appropriate to compare these values with other data. Lucasson and Walker(20) determined c and pp from a quite different experiment. These authors studied t,he defect production rate at 42°K as a function of electron energy at very low doses. The maximum energy employed was 1.4 MeV. Extra~olat,iIlg their curves (Figs. 2, 4, 14 of their paper) to 2.3 MeV according to their best fit with the theoretical expressions for the cross-sections given by McKinley and Feshbach(40) results in a,,, = 4.06 x 1O-23 cma. Their cross-section is somewhat larger than ours with oaoo/(r4,s= 0.75 i 0.3. This seems reasonable in view of the different temperatures to which the cross-sections refer. At the higher temperature the capture radius r. will be larger so that a larger fraction of the defects will recombine spontaneously. As a crude approximat’ion this rat,io can be given by: m ~~300/~4.2=

P(r)dv m P(r)&" (15) /l r,(4.2) i r(SOO)

For ~*(4.2)~~= 1 and ~~(3~)~~ as appropriate for 4 = 1.7 and I = 2 given in Table 2, we calculate (r30,,/044.2 = 0.8 and O.O, respectively. This is within the uncertainty range of the experimental data. The consistency of the results of the cross-sections obt,ained by Lucasson and Walker and by us from widely different experiments also strengthens our confidence in the p-value used throughout this paper and taken from Lucasson and Walker’s work.

VOL.

The authors are most grateful to the management of the Koninklijke/Shell Laboratories (Amsterdam, Netherlands) for permission to use the van de Graaf Generator. We want to extend our thanks especially to Dr. R. B. van der Heijden, Dr. H. Nauta and their technical staff, who helped us to set up and carry out the irradiation. Also the critical comments of Prof. de Vries during the course of this investigation are highly appreciated. This work is part of a research program of the Foundation “Fundamenteel Onderzoek der Materiel’ (F.O.M.) and was made possible by

1967

financial support of the organisation “Zuiver Wetenschappelijk Onderzoek” (Z.W.O.). REFERENCES 1. R.

0.

SI~ZXOXS, J. S. KOEHLER

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2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. :;: 18. ;“o: 21. 22. 23. 24. 25. 26. 27. 28.

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Y

->

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