OOOt-6160/84
93.00f0.00
Copyright 0 1984Pergamon Press Ltd
,&a mefdf. Vol. 32, No. 8. pp. 1141-1154,1984
Printed in Great Britain. All rights reserved
OVERVIEW NO. 39
AN ATOMIC RESOLUTION STUDY OF HOMOGENEOUS
RADIATION-INDUCED
PRECIPITATION
IN A NEUTRON
IRRADIATED
W-1OAT.x Re ALLOY
R. HERSCHITZ~ AND D. N. SEIDMANS
Cornell University, Bard Hall, Department of Materials Science & Engineering, and
The Materials Science Center, Ithaca, NY 14853-0121, U.S.A.
(Receid
28 July 1983; in revisedfirm 2 Janunry 1984)
Abstract-The
phenomenon of radiation-induced precipitation has been investigated in a W-10 at.% Re
alloy using the atom-probe field-ion microscope. This alloy is subsaturated with respect to the solvus line
of the primary solid solution (B phase). The specimens had been irradiated in the Experimental Breeder
Reactor II (EBR-II) to a fast-neutron fluence of -4 x 10” neutrons cm-’ (E > 0.1 MeV) at 575,625 and
675°C. This corresponds to 8.6dpa and an aneroge displacement rate, for the 2 year irradiation time, of
1.4 x IO-‘dpa s-t. The results of the present work show a significant alteration of the microstructure of
this alloy as a result of the fast-neutron irradiation. Precipitates with the composition -WRe were
detectedat a density of 1016cm-3. Coherent, semicoherent and possibly incoherent precipitates of the D
phase have been observed. They were not associated with either linear or planar defects, or with any
impurity atoms; i.e. a true homogeneous radiation-induced precipitation occurs in this alloy. A physical
argument is presented for the nucleation of the WRe precipitates in the vicinity of displacement cascades
produced by primary knock-on atoms. It is suggested that the nucleation of WRe is due to the formation
of tightly-bound mobile mixed dumbbells which react to form an immobile rhenium cluster. A possible
sequence of point-defect reactions is detailed which can lead to a WRe cluster. The growth of this cluster
into a precipitate is most likely driven by the irreuersible vacancy: self-interstitial atom (SIA) annihitation
reaction, as suggested recently by Cauvin and Martin. A mechanism for the suppression of voids, in this
alloy, is presented which is self-consistent with the homogeneous mdiation-induct
precipitation
mechanism.
R&n&-Nous
avons etudi6 la precipitation induite sous irradiation dans un alliage W-lOat?kRe g i’aide
dun microscope a emission d’ions avec sonde atomique. L’alliage est sursature par rapport au solvus de
la solution solide primaire /I. Nous avons irradie les echantillons dans le reacteur surregenerateur
experimental II (EBR-II) avec une fluence de neutrons rapides d’environ -4 x lOuneutrons.cm-*
(E > 0,l MeV) ii 575,625 et 675°C. Ceci correspond a environ 8,6 dpa et a une vitesse de d&placement
moyenne, pour la durCe d’irradiation de deux ans, de I,4 x IO-‘dpavs -I. Notre travail a mis en evidence
une modification notable de la microstructure de l’alliage par suite de I’irradiation aux neutrons rapides.
Nous avons observe aussi dea prtcipitts de composition voisine de WRe et de densiti 10’6cm-3 ainsi que
des pr&cipites de phase c cohtrents, semicohirents et peut-itre incoh&ents. Ces pr&ipids u n’etaient
asso& ni avec des dkfauts lb&&es ou plans, ni avec des atomcs d’impuret&; il se produit ainsi dans
cet atliage une viritable pr&cipitation homogene induite par irradiation. Nous presentons un argument
physique en faveur de la germination des pr&ipitb au voisinage des cascades de dtplacement produites
par les atomes ayant subi des chocs primaires. Nous pensons que la germination de WRe est due a la
formation d’halttres mixtes mobiles rigidement IiCes qui rtagisxnt pour former un amas de rhenium
immobile. Nous presentons en detail une suite possible de reactions entre dtfauts ponctuels qui peut
conduire ii un amas de WRe. La croissance de cet amas en un precipitt est tres probablement conduite
par la reaction d’annihilation irreversible entre lacune et interstitiel, comme l’ont propose recemment
Cauvin et Martin. Nous prCsentons un micanisme pour la suppression des cavitts dans cet alliage,
aut~h~~nt
avec le m&can&me de la p~cipitation homog&re induite sous irradiation.
Zusammenfasaung--Die bestrahlungsinduxierte Ausscheidung in der Legierung W-10 At.-“/, Re Wurde
mittels der Feldionen-Atomprobe untersucht. Diese Legierung ist betiglich der Solvuslinie des primIren
Mischkristalles (B-Phase) iiber&tigt. Die Proben waren im Experimental Breeder Reactor II (EBR-II)
mit -4 x 102.’Neutronen/cm’ (E > 0,l MeV) bei 575, 625 und 675°C bcstrahlt. Diese Dosis entspricht
8,6dpa und einer mitrleren Verlagerungsrate, bei xweijahrigen Bestrahlungsxeit, Von 1,4* lo-‘dpa.s-‘.
Die Ergebnisse dieser Arbeit weisen auf eine bedeutende Anderung inder Mikrostriktur dieser Legierung
durch diese Bestrahlung hin. Auscheidungen mit Zusammensetzung WRe wurden in einer Dichte von
10’6cm-3 gefunden. ICoh&ente, semikohiirente und m@licherweise inkoh~~nte Ausscheidungen der
a-Phase wnrden beobachtet. Diese Ausscheidungen hingen nicht mit linearen oder planaren Defekten oder
tPresent address: R.C.A., Astroelectronics Division, Princeton, NJ 08540, U.S.A.
SPresently on a leave of absence at Hebrew University of Jerusalem, Graduate School of Applied Science, Bergmann Bldg,
Givat Ram Campus, 91904 Jerusalem, Israel.
AM. 32-A
1141
I142
HERSCHITZ
and SEIDMAN:
HOMOGENEOUS
RADIATION-INDUCED’PRECIPITATION
mmit Verunreinigungsatomen
xusammen; daraus folgt, daB in dieser Legierung echte homogene bcstrahlungsinduxierte Ausscheidunguftritt. Fiir die Nukleation von WRe-Ausscheidungen in der NPhe von
Verlagerungskaskaden,
erxeugt durch die ersten RtickstoBatome, wird ein physikalishes Argument
vorgelegt. Es wird vorgeschlagen, daB die Keimbildung von WRe darauf beruht, daB stark gebundene,
bewegliche gemischte hanteln entstehen und dann xu unbeweglichen Rhenium-AnhBufungen reagieren.
Eine MBglichkeit, wie Punktfehler-Reaktionen N einer Wre-Anhlufung Rlhren k&men, wird ausgefiihrt.
Das Wachstum dieser Anhgufung in eine Ausscheidung wirdsehr wahrscheinlich durch eine irreversible
Annihilationsreaktion
zwischen Leerstellen und Zwischengitteratomen bestimmt, die von Cauvin und
Martin kilrxlich vorgeschlagen wurde. Fiir die Unterdriickung von HohlrSiumen in dieser Legierungwird
ein Mechanismus vorgeschlagen, der mit dem bestrahlungsinduxierten
homogenen Ausscheidungsmechanismus vertrgglich ist. -
1. INTRODUCTION
Over the last few years there has been a rapid growth
of interest in the phenomena of radiation-induced (as
opposed to accelerated) segregation and precipitation
[1,2]. Different types of irradiation--electrons,
ions
and neutrons-an
induce significant segregation of
alloying elements either toward or away from grain
boundaries, voids or free surfaces. Radiation can also
cause the heterogeneous
or homogeneous precipitation of a phase in such subsaturated solid solutions, and it can also alter the phase stability of
alloys. Radiation-induced
segregation and precipitation are of paramount technological importance
since they play a crucial role in the nucleation and
growth of voids and have a strong effect on the
physical properties of metals and alloys used in the
fuel ‘cladding and core structure of the fast breeder
reactor, as well as in the materials used in the first
wall of fusion reactors.
The study of W(Re) alloys is of technological
importance, as they are used in thermocouples for the
measurement of temperature in nuclear reactors. As
a result of an exposure to a neutron flux the decalibration of W(Re) thermocouples occurs [3,4]. W-10
at.% Re and W-25 at.% Re alloys are of particular
interest in the study of the radiation-induced
precipitation phenomenon,
as the former alloy is subsaturated with respect to the solvus line of the
primary solid solution (B phase), while the latter alloy
is supersaturated with respect to this solvus line (see
Fig. I)-it is in the B plus u field. Sikka and Moteff
[5] and Williams et al. [6] have identified the crystal
structure of radiation-induced
precipitates in fastneutron irradiated W-25 at.% Re alloys-using
transmission electron microscopy-and
it corresponds to
the x phase with the composition WRe,. Williams et
al. [6] have also investigated fast-neutron irradiated
W-5 at.% Re and W-l 1 at.% Re alloys; however, the
nature of the radiation-induced precipitates could not
be identified in these alloys, for irradiation temperatures below llOO”C, because of their small dimensions.
In this paper we present the results of an atomprobe field-ion microscope (FIM) study of radiationinduced, precipitation
in a neutron-irradiated
W-lO At.% Re alloy and in the following paper [7]
we discuss both radiation-induced
segregation and
precipitation in a W-25 at.% Re alloy. Our atomprobe FIM allows us to determine the chemical
identify of all the elements in the periodic table
[8-l 11.In addition, the atom-probe FIM has a lateral
spatial resolution, for chemistry, of a few angstroms
and a depth resolution which is determined by the
interplanar spacing of the region being analyzed.
Because of the unique capability of the atom-probe
FIM to resolve precipitates on an atomic scale and
also to detect low atomic-number elements (H, He, C,
0), which are believed to play an important role in
the heterogeneous nucleation of voids and precipitates, the atom-probe FIM provides information
which is not presently attainable employing conventional analytical electron microscopy techniques.
We demonstrate that significantalterations
of the
microstructure
of this alloy occur as a result of
tThe identification of the composition -WRe
as the u
phase is nor intended to imply anything about the
crystal structure associated with this composition. as we
are unable to extract detailed crystallographic information on small precipitates. Rather it is a shorthand way
of making the statement that we observed precipitates
with the equiatomic composition.
#The total number of dpa’s was calculated by Dr L. R.
Greenwood (private communication) of the Argonne
National Laboratory based on a displacement threshold
energy of 90 eV. We have modified his value to take into
account our measured value of 53 eV.
W
AT.%
RHENIUM
‘*
Fig. I. The phase diagram for the W(Re) system (Dickinson
and Richardson [30]). Only the temperature regime over
which the phase diagram has been established is exhibited.
HERSCHITZ
and SEIDMAN:
HOMOGENEOUS
fast-neutron irradiation.
Precipitates of the composition -WRe (a phase)t were detected at a number density of +.+lOI cmm3. They were not associated
with either linear or planar defects or with any
impurity atoms; i.e. true homogeneous radiationinduced precipitation occurs in this alloy. Coherent,
semicoherent and incoherent WRe precipitates were
observed.
2. EXPERIM~AL
2. I. Materials and materials preparation
Wire specimens of W(Re) alloys were irradiated to
a fast-neutron fluence of -4 x IO22 neutrons cm-*
(E > 0.1 MeV) at elevated temperatures (575, 625
and 675°C) in Experimental Breeder Reactor II
(EBR-II) at Richland, Washington. This corresponds
to 8.6 dpa for row 7 of EBR 11-S Hence the average
displacement rate for the 2 year irradiation time is
1.4 x lo-’ dpas-‘.
Sharply-pointy
FIM specimens of these alloys
were prepared by an el~~oetching
technique in a
1 N Na0H solution at 4.0 Vat; a stainless-steel counter electrode was employed. Typically, a tip having
the desired radius was obtained by dipping a 5 mm
length of the specimen into the solution and then
elecroetching away a 2 mm length of the specimen. A
good FIM tip has the appearance of a well-sharpened
pencil when examined with an optical microscope at
a magnification of x 400. The initial end-form of the
electroetched tip was rough on an atomic scale. An
atomically smooth end form was obtained by a
combination of d.c. and pulse-field evaporation.
ft
is important to note that the specimen preparation
procedure was not affected by the fast-neutron irradiation.
2.2. Experimental procedure
First, a freshly electroetched specimen was inserted
in the atom-probe. The atom probe was then baked
for 24 hr at N 150°C to obtain a background pressure
in the range of (4.0-6.0) x IO-lo torr. The main residual gases at this pressure were hydrogen
monoxide
(c 2.0 x
(q4.0 x lo-‘O torr), carbon
lo-” torr), and helium (<4.0 x lo-i2 torr); the partial pressures were measured employing a Uthe Technology Inc. (UTI) Model 1OOCresidual gas analyzer.
After cooling the atom-probe to room temperature
the specimens were imaged employing jHe as an
imaging gas. A gauge pressure of -2.0 x IO-‘torr
‘He was typically used and field-evaporation
was
performed at a specimen temperature (T,) of 45 K.
Using the above experimental conditions stable FIM
images of these alloys were obtained. The reason for
using ‘He as an imaging gas, rather than 4He gas, was
to minimize the concentration of ‘He present in the
atom probe and, ihus, to make it possible to identify
‘He atoms which could have had their origin in the
neutron-i~adiated
specimens.
To
analyze
a
specimen
chemically
the
RADIATION-INDUCED
PRECIPITATION
1143
field-evaporated tip was rotated, employing the goniometer stage, in such a way that the probe hole in the
image intensification system was aligned over the
desired precipitate. Following the alignment over a
particular precipitate the atom probe was evacuated
to -4 x 10”Otorr. Next, the atom-probe chemical
analysis was performed . A pulse fraction u) of 0. I5
was used for all the experiments. The quantityfis
the
ratio of the pulse voltage (Y,) to the steady state
voltage (V,,,). A constant pulse frequency of 60 Hz
was employed. The average field-evaporation rateions
average
number
of
evaporated
per
field-evaporation
pulse-was
equal to 0.02 ions
pulse-‘. The field-evaporation rate was monitored
employing an audio ratemeter. After collecting a
number of atoms the atom-probe analysis was terminated, the imaging gas reintroduced and the specimen
reimaged. If the precipitate under consideration was
still present, the system was evacuated again and the
atom-probe analysis was continued until the precipitate had been entirely meld-evaporate.
During the
entire period of imaging, evacuation, and chemical
analysis the value of r, was maintained at 45 K,
Using these experimental conditions we are able to
obtain good agreement between the nominal Re
concentration,
and the Re concentration
was as
determined by the atom-probe technique in unirradiated alloys. These experimental conditions were
used in all of our_analyses.
The basic mode of displaying the data in the
present experiment is in the form of an integral
profile. A Re integral profile is obtained by plotting
the cumulative number of Re events vs the cumulative number of W plus Re events. The average slope
of such a plot corresponds to the auerage Re composition of the volume analyzed, since the cumuiative
number of all the events detected is proportional to
depth. In analyzing a particular precipitate the slope
of the integral profile ((c[:‘)~) is a lower limit to the
acrual Re concentration in the precipitate ((ckt’)*),
as in most cases the dimensions of the analyzed
cylinder are greater than the size of the precipitate.
The superscript ppt stands for precipitate, the subscript u on the bracket means an uncorrected value
and the superscript * implies a corrected value. The
relations~p between (~g>~ and <cg>* for different
possible precipitate mo~hologies is presented in Appendix A.
3. EXPERIMENTAL RESULTS
3.1. Mass spectra
A typical mass spectrum for a neutron-irradiated
W-10 at.% Re specimen, showing the mass-to-charge
range of 0-1OOa.m.u. is exhibited in Fig. 2. Two
major peaks located near 46 and 61 a.m.u. are clearly
visible. And three small peaks due to the residual
gases ‘H, 3He and “He at 1.0, 3.0 and 4.0a.m.u. are
also present.
HERSCHITZ
1144
30D
and SEIDMAN:
MASS
SPECTRUM
IRRADIATED
W-IO
FOR
AT.%
HOMOGENEOUS
A NEUTRONRe ALLOY
RADIATION-INDUCED
PRECIPITATION
1
250
f
9 200
w
b
Ts ‘45Ki
f =O.I5
Ti ~575.C
VACUUM
s 3 x doTon
‘50
,ij/,
0
,
20
,
,I,
40
-MASS-TO--CHARGE
j:
,
,
60
60
RATIO--
,
1
‘00
---
Fig. 2. A typical mass spectrum for a fast-neutron irradiated W-10 at.% Re alloy between 0 and 100 a.m.u. The
spectrum was recorded at T,=45K
with /= 0.15 at
3 x lo-lo torr. Tungsten appears in the plus-three (WJ+)
and plus-four (W‘+) ionization states, while rhenium
appears only in the plus-three (Re’+) ionization state. Note
the presence of small peaks due to ‘HI+, ‘HI+ and ‘HI+.
Figures 3 and 4 show the major peaks on expanded
scales. Tungsten appears in both the plus-three and
plus-four ionization states, while Re appears in only
the plus-three ionization state. Peaks associated with
the five naturally occurring isotopes of W-‘8ow,
“‘W ““W, ‘@W and “‘W-and
the two naturally
be
occurring isotopes of Re-‘85Re and “‘Re-can
readily distinguished from one another in the plusthree ionization state (Fig. 3). Approximately 87% of
all W atoms appear in the plus-three ionization state,
with the remaining 13% appearing in the plus-four
ionization state (Fig. 4).t The same observation was
found to be true in the case of ‘&radiated
W-10at.x
Re alloys. A comparison of the experimental isotopic abundances in a neutron-irradiated
W-10at.x
Re alloy with the handbook values is
given in Table 1. This comparison is of particular
importance as it indicates whether or not a significant
amount of radioactive capture by a particular isotope
had occurred; e.g. whether the reaction “X, + ‘n,+
“+‘Xz + y took place; in this notation X is an
element-W
or Re and Z is the atomic number-74
for W and 75 for Re, A is the mass number of a
particular isotope, ‘q, is a neutron, and 7 is a y-ray
photon.
Compositional
changes due to transmutation
are expected to be minimal for the
tungsten-rhenium
system; see Table 1 in Ref. [6].
The agreement between the experimental isotopic
abundances
and handbook values is reasonably
good. Hence, no significant detectable alteration octin
the case of W-25at.z
Re alloy -95% of all the
tungsten ions detected were in the plus-three ionization
state [7]. In spite of the change in the fraction of ions
field evaporating in the plus-three ionization state with
increasing Re concentration we are able to determine
the composition very accurately [I. For the precipitates
which are even richer in Re than 25at.% we did not
experience any difficulties in distinguishing the rhenium
isotopes from the tungsten isotopes, as long as the
in
the
range
background
pressure
was
(4.0-6.0) x 1O-‘oTorr.
60
61
62
64
63
MASS-TO-CHARGE
RATIO
Fig. 3. The W3+ and Re’+ portion of the spectrum shown
in Fig. 2. Peaks associated with the five naturally occurring
isotopes of W and the two naturally occurring isotopes of
Re are readily distinguished from one another; the successive isotopes are separated by the alternate plain and
cross-hatched regions.
curred in the abundance of a particular isotope as a
result of the fast-neutron
irradiation.
The a.m.u.
ranges for each isotope are indicated in Fig. 3-the
successive isotopes are separated by the alternate
plain and cross-hatched regions.
Note the presence of events in the tail of the “‘Re’+
peak. Two major factors contribute to the events
present in this tail.
(1) Energy deficits associated
with the fieldevaporation process; this phenomenon results in the
exponential decay of each peak [12,13].
(2) Metal hydride and/or metal helide events which
form as a result of the field-induced adsorption of
residual hydrogen and/or helium on the surface of the
FIM tip [14-17.
While energy deficits are inherently present in all
analyses made employing the straight time-of-flight
atom-probe, we found that the number of events
present in the “‘Re’+ tail due to molecular complexes
could be reduced drastically by performing the analyses in ultra-high vacuum. Thus, we employed a
background pressure in the range (4.0-6.0) x lo-”
torr in our experiments.
ao-
W4+
SPECTRUM
W-IO
AT.%
FOR
Re
A NEUTRON-IRRADIATED
-
ALLOY
70?
45
46
Ill
47
MASS-TO-CHARGE
I
I
48
1
I
49
RATIO
Fig. 4. The W4+ portion of the spectrum shown in Fig. 2.
Approximately 13% of all W atoms appear in the plus-four
ionization state.
HERSCHITZ and SEIDMAN:
HOM~ENEOUS
~DIATION-INDUCED
APPROXIMATE
Table 1. Comparison of the experimcntai W’+ and Res+ isotopic
abundances in a neutron-irradiated
W-l0a~% Re alloy with the
handbook values
Isotope
Number of
atoms detected
‘MW
lSlW
lSlW
5
494
393
‘“W
lSdW
Total W
‘“RC
‘“RC
Total Re
633
600
2125
129
I92
321
Experimental*
(“4
0.24f0.11
23.3 f 1.1
18.5 f 0.9
29.8 4 1.2
28.2 f I .2
100
40.2 j, 3.5
59.8 f 4.3
100
DEPTH
Tl-IR’%
Handbook
(“/,I
0.1
26.4
14.4
30.1
28.4
100
37. I
62.9
100
1145
PRECIPITATION
<CR,>
SCALE (it
A Nk”Tf?O?lRfiADl;Rm
.95?16ATX
I%,
loGO
‘The unwtainty is qual to the ratio of the square root of the
number of atoms of a particular isotope to the total number of
atoms detected.
3.2. Meawrements of the bulk compositionin both the
neutron-irradiated and unirradiated W-10 at.% Re
alloys
In this section we describe the measurements of the
bulk composition for both the neutron-irradiated
and
ulrirradiated W-10 at.% Re alloys. No precipitates or
voids were obsgrved in the field-of-view before the
atom-probe analysis was initiated; i.e. a defect-free
region was analyzed. The purpose of these experiments was twofold:
(i) To determine whether the bulk composition of the
alloys was altered as a result of nuclear reactions.
(ii) To determine whether there was a significant
change in the sp$ial distribution of Re in the matrix
as a result of neuin
irradiation.
A summary of the experimental results is given in
Table 2. Figure 5 shows a Re integral profile for a
specimen which had been fast-neutron irradiated at
rj= 625’C. Note the presence of a region in the
integral ’ : prolile
which
has
a
imposition
26.0 & 3.5 at.% Re. This local ~mpositional
variation can nof simply be a random statistical
fluctuation. Using our simple statistical model 1181we
estimated that the probability of the occurrence of
such a local compositional variation in a random
solid solution is equal to ~0.01%. By contrast, Fig.
6 shows a Re integral profile of an unirradiated
W-10 at.% Re alloy. In this case the slope of the
integral profile is uniform indicating that Re atoms
Table
2.
CUMUL8ZlVE
N”h
OF W%US
Fig. 5. The Re integral profile through a fast-neutron
irradiated W-lOat.% Re alloy. Note the presence of a Re
rich region-it is due to the spatial redistribution of Re
atoms as a result of the neutron irradiation and is most
likely due to a precipitate.
are distributed uniformly-the
value of the bulk
concentration (c,,> = 10.4 + 0.9 at.% Re. This value
is in good agreement with the nominal Re concentration supplied by the manufacturer.
Two conclusions can be drawn from the results
presented above. First, spatial redist~bution of Re
atoms occurs as a result of a neutron irradiation. The
presence of a local compositional variation in an
APPROXIMATE
IO
1
I
Iso
r
20
I
RI INTEGRAL
UNIRRADIATED
DEPTH
30
I
S’eutron
Irradiated
Seutron
Irradiated
Unirradiatcd
SCALE
40
I
(&
50
I
60
I 1
PROFILE Tli
W-IO AT. X
g I25
;
ID0
!j
75
<h>
z
* 0.4
?a9 AT
$i
Y=
52)
CUMULATIVE
NUMBER OF W PLUS Re EVENTS
Fig. 6. The Re integral profile through an unirradiated
W-10at.x Re alloy. Note that in this case the profile is
uniform. The value of (CRC)= 10.4 f 0.9 at.%; this value is
in agreement with the nominal value supplied by the manufacturer.
A summary of the results of the measurements of bulk Re composition (cRt) in both neutron-i~diated
Rc alloys
State of
specimen
Ra6%NTS
and unirradiated W-10 at.%
The uncorrected Rc
concentration of a
compositional
variatiot?
Irradiation
temperature
wc)
Cumulative
number of
W plus Re
events
625
1059
158
14.9 f 1.2
Yes
26.0 f 3.6
625
2866
321
11.2f0.6
Yes
29.2 f 2.4
-
1263
131
10.4 f 0.9
No
Measured Re
concentration’
Cumulative number
of Rc events
$$I
‘The uncertainty is qua1 to the ratio of the square root of the cumulative number of
events.
L?his vats corresponds to the local slope in a Re integral profile.
Presence of
local compositionat
changes in the
integral protile
$t$j
-
Rc events to the cumulative number of W plus Re
1146
HERSCHITZ
Table 3.
and SEIDMAN:
HOMOGENEOUS
~DIATION-INDUCED
PRECIPITATION
A summary of the results on the mesurcments of the composition of different precipitates in a neutron-i~adiated W-10 at.% Re
alloy
Irradiation
tcmpcratun
T (“C)
Region
analyzed
625
67.5
575
625
PPTI
PPT2
PPr3
PPT4a
‘The uncertainty is equal to the ratio
Cumulative
number of
W plus Re
CVClltS
Cumulative
number of
Re events
1738
1463
919
3882
350
287
165
788
of the square root
The uncorrected Re
concentration of
rhc precipitate’.b
Re concentration
outside of the
precipitatea*b
(ckT,l>,
(at.%)
The actual Re
concentration of
the piccipitate’
(CRV
(a&)
22.1 f 1.2
3l.Ok2.1
19.1 * 1.7
29-6 f 1.2
56. I f 2.9
51.2*2.6
52.4 f 3. I
49.8 f 2.8
a.1 f I.1
8.1 f 1.1
12.1 f2.3
11.1 *0.9
0
of the cumulative number of Re events to the cumulative number
“[ire vaIucs of <cg). and (cm> are obtained from the Re integral profiles.
‘This value is the average v&e calculated by the two methods described in Appendix
irradiated alloy is, most likely, produced by a
radiation-induced
precipitate. The second conclusion
drawn from the above results is that there is a sharp
transition-in
a distance of less than -5 &in
the
Re distribution to its bulk value (cRe), in the region
leading away from this precipitate.
3.3. Field-ion microscopy
The FIM technique has been used by a number of
authors to study precipitation phenomena [19-243.
The presence of precipitates in an alloy causes
localized image contrast effects in the FIM images.
Since different phases rarely have the same fieldevaporation characteristics, precipitates may appear.
either bright or dark in the micrographs [22].
The voltage on the specimen has to be greater than
the best image voltage (BIV) for unambiguous
identification of the precipitates. The BIV is the
voltage at which the FIN image is typically examined, i.e. it is the value of the voltage which yields the
best overall atomic resolution. At voltages greater
than the BIV the image appears blurred while at
voltages less than the BIV some regions of the image
may not exhibit atomic resolution. The effect of the
BIV on image stability is illustrated for the case of the
W-25 at.% Re alloy in Ref. [7j and the results are
discussed there in greater detail. Even though the
same imaging conditions were used for all of our
specimens the image quality, as will be seen in the
micrographs presented, varied significantly from
specimen-to-specimen.
of W ptus Re
B of [18].
tained in each run in greater detail; they are summarized in Table 3.
PPTI (Figs 7and 8). Figure 7 shows an FIM image
of this alloy containing a precipitate (PPTl) in the
field-of-view. White arrows point to PPTl-it
is one
atomic plane thick and its diameter (D,,) is equal to
-5OA. Note that the lattice planes, even though
bent, are continuous across PPTI indicating that it is
a coherent precipitate.? PPTl was observed only
prior to the atom-probe analysis-the
FIM tip failed
~tastrophically
during its chemical analysis. The
solid black circle is the image of the probe hole. This
specimen had been irradiated at I;:= 625°C. The
corresponding Re integral profile is shown in Fig. 8.
It consists of two distinct regimes. The value of
(c[:~)~ is equal to 22.1 & 1.2 at.% Re, while the
3.4. Radiation-inducedprecipitates
Four radiation-induced
precipitates were detected
and analyzed, whereas no voids were found in the
W-lOat.% Re alloy. The density of the radiationinduced precipitates is equal to N 1016cm-‘; it was
determined following the procedure used by Brenner
and Seidman [25]. We now describe the results ob-
tThe FIM images are extremely useful for determining the
degree of coherency of a precipitate. The degree of
coherency of a precipitate can be determined simply by
counting the number of planes both entering and
emerging from a precipitate. Thus it is possible to
determine the degree of coherency for a disc-shaped
precipitate which is only one atomic plane thick.
PPT1
Fig. 7. An FIN micrograph showing PPTl in a fastneutron irradiated W-lOat.% Re alloy (see white arrows).
Note that the lattice planes, even though bent, are continuous across this precipitate, indicating that PPTI is a
coherent precipitate. The solid black circle is the image of
the probe hole.
HERSCHITZ
and SEIDMAN:
APPROXIMATE
DEPTH
SCALE
HOMOGENEOUS
RADIATION-INDUCED
(1)
?
B
400
CUMljLATIVE
800
NUMBER
1200
OF W PLUS
1600
2000
APPROXIMATE
DEPTH
SCALE
10
30
40
20
RI ,NTECRAL
A NEUTRON-
z
5
w 5oo
,~~~!
u
600
t
ALLOY
CUMULATIVE
I147
PRECIPITATION
ifi,
50
60
PROFILE FROM PPTZ IN
IRRADIATED W-IO AT % RC
T, j 675-C
NUMBER
OBSERVATION
INDICATES THE
PRECIPITATE IS
1
i
_
OF W PLUS Re EVENTS
Re EVENTS
Fig. 8. The Re integral profile from PPTI shown in Fig. 7.
The value of <c[:‘)~ is 22. I + 1.2at.% Re; this value is a
lower limit to the actual Re composition of the precipitate.
The value <c,,) = 8.7 + 1.7at.x Re is in approximate
agreement with the nominal composition of the alloy.
concentration in a region within a few angstroms of
PPTl is equal to 8.7 rf: I.1 at.% Re; the latter value is
in appcoximate_ agreement with (c,,). After correction for the matrix contribution
to (c[?)~, the
value of (cg$‘)* equals 56. I + 2.9 at.% Re. Equation
(A3) was used in calculating the volume fraction
occupied by the defect (rd); in this case a disc-shaped
precipitate.
Fig. 9. Two FIM micrographs showing PPT2 (see white
circle) before (a) and after(b) the atom-probe analysis. Note
that this precipitate is no longer present after the completion
of the chemical analysis.
Fig. IO. The Re intergral profile from PPT2 shown in Fig.
9. The values of (~g)~ and (c,,) are equal to 31.Of 2.1
and 8.7 + 1.1 at.% Re, respectively.
PPT2 (F&V 9 and 10). FIM images exhibiting the
second precipitate (PPTZ) before and after the atomprobe analysis are shown in Fig. 9(a) and 9(b). Note
that PPT2 is no longer present after the completion
of the chemical analysis [Fig. 9(b)]. It is a disc-shaped
semicoherent precipitate. The diameter of its exposed
cross-sectional area is 24 A. This specimen had been
irradiated at Ti = 675°C. The Re integral profile for
PPTZ and in the region leading away from it is
presented in Fig. 10; (c{!r), = 31.0 f 2.1 at.% Re.
After correction for the matrix contribution
to
the value of (c{{‘)* is equal
to
<cK’L
Fig. 11. Two FIM micrographs showing PPT3 (see WIhite
arrows) before (a) and after (b) the atom-probe anal) Isis.
Note that this precipitate is no longer present after the
completion of the chemical analysis.
HERSCHITZ and SEIDMAN:
1148
HOMOGENEOUS
RADIATION-INDUCED
PRECIPITATION
APPROXIMATE DEPTH SCALE (A,
Re INTEGRAL PROFILE FROM PPT3 IN A
NEUTRON-IRRADIATED W-t0 ATY. Re ALLOY
z
<C,>
f
160
z’
Y
100
F
4
50
= 12.122.3 Al.%
R
2
a
0
200
400
600
800
ICC0
CUMULATIVE NUMBER OF W PLUS Re EVENTS
Fig. 12. The Re integral profile from PPT3 shown in Fig.
11. The valuesof <cl$>,, and (cRc) are equal to 19.1f 1.7
and 12.14 2.3at.% Re, respectively.
- _ of a fast-neutron irradiated
51.2 + 2.6 at.% Re. Equation (A4) was used to esti- Fig. 13. An FIM micrograph
WllOat$
Re
alloy
with
two precipitates-PPT4a
and
mate u,. The Re concentration in a region within a
PPT4b-m the field-of-view (se-eblack arrow& The oreciofew angstroms of PPT2 is 8.7 f 1.1 at.% Re; this itate shown in the top of the.figure (PPT4a) was cher&aliy
value is in approximate agreement with <c&j.
analyzed.
PPT3 (figs 11 and 12). Figures 1l(a) and (b)show
FIM images of PPT3 before and after the atom-probe Re alloy is w 50 at.% Re, indicates that the o phase
analysis; note that it is no longer present in Fig. 1l(b). forms in these alloys as a result of a fast-neutron
It is difficult to determine the exact state of coherency irradiation. Both coherent, semicoherent and possof PPT3; it is one atomic plane thick and D,, is ibly an incoherent precipitate of WRe were observed
approximately 120A. In this case T, is equal to at a number density of w 10’6cm-J.
575°C. The corresponding integral profile is 3.5. On the question of impurity atoms associated with
presented in Fig. 12.f The value of (cj& is equal to the radiation-induced precipitates
19.1 f 1.7 at.% Re, while the Re concentration within
The impurity atoms He, C, N or 0 as well as other
a few angstroms of PPT3 is 12.1ir 2.3 at.% Re. impurities have the potential to play a very important
Equation (A3) was used to correct for the matrix rob in the nucleation of voids and radiation-induced
contribution to <cg>,, to obtain (c$)* which is precipitates [26]. In addition, to the main W and Re
equal to 52.4 f 3.1 at.% Re.
peaks we detected peaks due to ‘HI+, 3Het+ and
PPT4 (Figs 13 and 14). Finally, Fig. 13 shows an ‘He’+ in the mass spectra. Figure 15 shows these
FIM image containing two disc-shaped precipitates peaks on the expanded scale 0 to 5 a.m.u.
(PPT4a and PPT4b) in the field-of-view. The‘atomThere are two possible sources of helium detected
probe analysis was performed on the precipitate by the atom-probe FIM:
(PPTa) shown in the top of this figure; it is two
atomic planes thick and Dd is sequal to N 60 A. Since 1. Field-adsorbed helium from the residual helium
the tip failed during probing, PPT4a was only seen gas in the ultra-high vacuum system.
prior to the chemical analysis. This precipitate is 2. Helium present inside the specimen.
semicoherent as all the matrix planes are not conAPPROXIMATE DEPTH SCALE (A,
20
40
60
SO
too
tinuous across its interface. This specimen had been
I
I
I
I
I
irradiated at I’, = 625°C. The Re integral profile for
v) ~OOOf?kINTEGRAL PROFILE FROM PPT4 IN A
NEUTRON-IRRADIATED W-IO AT% Rc ALLOY
PPT4a is exhibited in Fig. 14. The values of (cc).
2
r
and <cR+> are equal to 29.6 + 1.2 and II. 1 f 0.9 at.%
Re, respectively. Correcting for the matrix contribution to <c~~>~,yields <cg)* = 49.8 + 2.8 at.%
Re.
PPT4b is a semicoherent one atomic plane thick
precipitate and D,, is equal to m 30 A.
The fact that the composition of all the radiationinduced precipitates in the subsaturated W-lOat.%
tIf the piane of the disc-shaped precipitate was not parallel
to the axis of the analysis cylinder then the slope of the
0
1000
2000
3000
4000
5OOo
integra1 profile changed as the precipitate moved out of
CUMULATIVE NUMBER OF W PLUS Re EVENTS
the analyzing cylinder during the field evaporation of
the specimen. Thus a strong effort was always made to Fig. 14. The Re integral profile from PPT4a shown in Fig.
13. The values of (cg). and (I+.) are equal to 29.6 f 1.2
align the plane of the disc-shaped precipitate such that
and 1.1 f 0.9 at.% Re, respectively.
it was parallel to the axis of the analyzing cylinder.
HERSCHITZ
and SEIDMAN:
HOMOGENEOUS
APPROXIMATE
‘Ooo r ‘Ii’: ‘He” AND ‘Ha’ SPECTRUM FOR A
: NEUTRON-IRRADIATED W-IO AT.% Re ALLOY
r
-
5
5
too e
:
k
-
iz
m
1Or
s
_
RADIATION-INDUCED
3001
DEPTH
40
1
20I
1149
PRECIPITATION
60
I
SCALE
60
1
(A,
100
I
nHal*
lH’.
4Hel+
II
0
I
,
4
2
3
MASS TO CHARGE RATIO
1
5
Fig. 15. A mass spectrum in the range of O-S a.m.u. Note
the presence of peaks due to ‘HI+, ‘He’+ and ‘He’+.
The imaging gas ‘He was used, rather than the more
commonly employed ‘He gas, to make it easier to
identify ‘He atoms which could have had their origin
within the neutron-irradiated
specimens. Figure 16
shows both the 3He and ‘He integral profiles from
PPTA Each profile consists of two distinct regimes:
(i) A high concentration
surface regime A. This
regime is due to field-adsorbed helium on the surface
of the FIM tip during the initial stages of the
atom-probe analysis.
(ii) A low concentration regime B. In this regime the
electric field was large enough to ionize helium atoms
in the background gas, before they were able to reach
the surface of the tip.
If 4He had been present inside the specimen, then
there should have been a sharp increase in the local
concentration of 4He atoms in regime B.
The profiles shown in Fig. 16 are typical of all four
precipitates analyzed in this alloy, i.e. 3He and “He
events were only detected on the surface of the FIM
specimens. Therefore, we conclude that 4He atoms
were not associated with the radiation-induced
precipitates detected in this alloy. In [7] we present
experimental evidence which indicates that in a supersaturated W-25 at.% Re alloy, ‘He atoms were associated with radiation-induced
precipitates of the x
phase.
All the atom-probe analyses were performed at a
specimen temperature of 45 K. It has been shown by
Amano et al. [27-291 that at this temperature “He is
completely immobile in tungsten and, therefore, the
possibility of helium diffusing to the surface when a
precipitate is uncovered, during the field-evaporation
process, can be ruled out. It is also emphasized
tA
semicoherent or incoherent precipitate implies the
presence of interface dislocations-that
is, structural
defects. However, these structural defects are a result of
the precipitation process and did not exist prior to the
radiation-induced
process. The suggestion that these
interface dislocations existed prior to the radiationinduced precipitation would require the existence of an
exceedingly special distribution of dislocations, at a
number density which is very high.
Fig. 16. The 3He1+ and ‘He’+ integral profiles from PPT4.
These profiles consist of two regimes: (a) is due to field
adsorbed helium on the surface of the tip while in (b) the
field was high enough to ionize helium atoms before they
could reach the surface of the tip.
strongly that no other impurity atoms were found to
be associated with any of the precipitates detected in
this alloy.
4. DISCUSSION
4.1. Determination of the solid solubility limit
The irradiation temperatures for our samples were
below the temperatures which at the W(Re) phase
diagram has been well established [30,31]. To determine the Re solubility limit at the temperatures of
interest we have used the fact that the solvus line is
described by [32]
c:p
= A exp( - h,/kJ)
where the value of b, corresponds to the slope of a
In c:y vs l&T plot, czy is the solubility limit at
each temperature (T), k, is Boltzmann’s constant and
A is an entropic constant. At the lowest irradiation
temperature (575’C) the calculated value of cz is
equal to 16.5 at.% Re. This calculated value of cz is
much greater than the average Re concentration
(10at.x) of this alloy. Which indicates that the
lOat.% Re value is subsaturated with respect to the
solvus line of the primary solid solution (B phase).
4.2. A physical model for the homogeneous nucleation
of WRe precipitates
The fact that the precipitates in the subsaturated
alloy are not associated with either structural defects7
or with any impurity atoms indicates that a true
homogeneous radiation-induced
precipitation occurs
1150
HERSCHITZ
and SEIDMAN:
HOMOGENEOUS RADIATION-INDUCED PRECIPITATION
Table 4. Relevant point defect snd diffusion data for the W and W(Rc) systems
Parameter
Prccxponential factor for W self-interstitial atom diiusion
Enthalpy change of migration of a W self-interstitial atom
Enthalpy change of formation of a monovacancy in W
Entropy of formation of a monovacancy in W
Entbalpy change of migration of a monovacancy in W
Binding cnthalpy of a divacancy in W
Binding enthalpy of a W self-interstitial atom to a Re atom
Correlation factor for tracer diffusion by a monovacancy mechanism in a b.c.c.
lattice
Prcmponcntial factor for W selfdiffusion by a monovacancy mechanism
Prccxponcntial factor
Activation energy for
Prcexponential factor
Activation energy for
for the traar self-diffusion in W
tracer sclfditTusion in W
for Re traar diffusion in W
Re tracer diiusion in W
‘These values correspond to the low temperature regime.
bathe Rc tracer diffusion data in W is somewhat “strange” -that
Notation
Value
Reference
By,
0.22 cm* s-r
0.085 ev
3.67 f 0.2 eV
2.3 k,
1.78fO.leV
0.7 ev
44,45
44.45
48.49
48.49, SO
48, SO
49.51
43
;;
4:
h”
b
hkw
>0.8 ev
$@
;f
f’s&,is w
IW
Qr
is, the pm-exponential
0.73
O.O6cm’s-’
0.04cm’s-”
5.45 CV’
275cm2s-‘b
7.1 eva
factor is anomalously
51
Derived from traar
self-diffusion and
quilibrium vacancy
cont. data
52.53
52.53
54
54
large.
in this alloy. Experimental evidence for homogeneous
be as high as N 1 at.% [40]. The major differences
radiation-induced
precipitation
has been recently
expected for a displacement cascade created in W-10
presented by Cauvin and Martin in the case of
at.% Re for the T,s (575, 625 and 675°C) employed
Al(Zn) alloys [33,34], by Brager et ~1. in the case of are as follows: (1) the point defects (vacancies and
a 316 stainless steel [35a], by Mukai and Mitchell for SiAs) are both mobile as these T, correspond to Stage
a Ni(Be) alloy [35b], and Kinoshita and Mitchell [35c] III of tungsten [41,42]; (2) each displacement cascade
and Wahi and Wollenberger [35d] for Cu(Be) alloys. contains-in
addition to vacancies, SIAs and tungTheoretical treatments of this physical phenomenon
sten atoms-10 at.% Re atoms; (3) Clustering reachave been considered by Cauvin and Martin [36] and
tions are taking place among the point defects; and
Maydet and Russell [37]; the latter authors only
(4) the displacement cascade is continuously
disconsidered the possibility of the nucleation of inco- solving via a self-diffusion mechanism. Since the
herent precipitates, whereas Cauvin and Martin also radiation damage is highly localized in the displaceconsidered coherent precipitates.
ment cascade-the
point defect supersaturation
in
We now describe a possible sequence of plausible between the displacement
cascades is initially
events which can result in the homogeneous nucnegligible-it
is probable that the nucleation of a
leation of WRe precipitates, in a subsaturated alloy
WRe phase precipitate occurs in its vicinity. The
which is subject to irradiation with fast neutrons.
absolute efficiency of this nucleation process is low as
The primary source of radiation damage, in the the 6nal density of radiation-induced
WRe precipcase of fast neutrons, is the displacement cascade.
itates is N lOi6 crnd3, which is significantly less than
Each displacement cascade is created by a primary
the number density (nP) of primary km_ck-on atoms
knock-on atom (PRA) with a mean recoil energy of that produce displacement cascades. For a fluence
4 keVt. In the case of pure tungsten it is known from of 4 x 1022 fast neutrons cm-* the value of nP is
FIM experiments that a displacement cascade, creN 1.8 x 10” cm-‘.$ Thus only one in every approxiated at 15 K, consists of a vacancy-rich core (H 2 to mately 1.8 million primary knock-on events results in
30 at.%) surrounded by a distribution of SIAs which a WRe.
is created by the replacement collision sequence
The possible point defects in the W-10at.x
Re
mechanism
[38,40]. The concentration
of SIAS alloy are: (1) a vacancy; (2) a pure tungsten SIA; (3)
on the periphery of a displacement cascade can
a pure rhenium SIA; and (4) a mixed SIA-i.e.
a
mixed dumbbell consisting of both rhenium and
tungsten atoms. The known properties of these point
defects are listed in Table 4, as well as the relevant
tThis value of 4 KeV is an UDD~C limit to the mean recoil
tracer
diffusion data. We now employ these point
energy of a PKA in EBkI
(Dr L. R. Greenwood,
Argonne National Laboratory, private communication). defect properties to show that plausible first steps
This implies the number of vacancies in the mean in the nucleation of a WRe precipitate involve
displacement cascade is -31. This value is obtained
the migration of tungsten SIAs to Re atoms to form
from the modified Kinchin-Pease
expression (0.8) mobile mixed dumbbells, which in turn react to form
(4KeV)/2&,
where E, is our experimental average
an immobile di-Re cluster. The di-Re cluster can then
displacement threshold energy of 52 eV [38]. The reason
for this low mean recoil energy of a PKA is that the grow by the accretion of mixed dumbbells and pure
fast-neutron spectrum of EBR-II is rather soft [39].
tungsten or rhenium SIAs.
$This calculation employed a total nuclear cross-section for
In the temperature
range 575-675”C the most
producing primary knock-on atoms of 7.54 x 10b2’cm*.
mobile defect is the tungsten SIA. At 675°C (all the
This value is from ENBF/B-V code (Dr L. R. Greensubsequent calculations refer to this 7’i) the selfwood, private communication).
HERSCHITZ and SEIDMAN:
interstitial (&)
HOMOGENEOUS RADIATION-INDUCED PRECIPITATION
(D,,) diffusivities,
x 10-2
and
2 x lo-“cm* s-l, respectively. Thus, in the same
period of time the tungsten SIA moves a root-meansquare diffusion distance which is a factor of 6 x IO’
greater than the root-mean-square distance traversed
by a monovacancy. This implies that during the
nucleation stage we can initially neglect the migration
of monovacancies (see Appendix B).t The tracer
diffusion data for rhenium in tungsten$ shows that
for a 2 year diffusion time the rhenium atoms are
essentially immobile;
DacrnW (675°C) 2 5 x 1O-36
cm* s-i. The concentration of Re atoms is greater
than the concentration of SIAs on the periphery of a
displacement cascade, hence the number of jumps for
a SIA to reach a Re atom (n,) is less than the number
of jumps for one SIA to reach another SIA. For a Re
concentration
(cae) of 10at.z
the value of nj
[(~a~)-‘] is approximately only two jumps, if we take
z z 6. Therefore, the local concentration
of mixed
dumbbells (c,,) rapidly rises. Since c,i is localized near
a displacement_ cascade the number of jumps for
mixed dumbbells to reach one another is probably
less than ten, as c,~can easily reach 1 at.%.
To substantiate the last conclusion we calculate the
number of jumps a mixed dumbbell makes before it
dissociates. We have shown experimentally that a
lolcer limit to the binding enthalpy of a mixed
dumbbell (hb,,) at 390 K is 0.8eV [43]. The time for
a mixed dumbbell to dissociate (Q) is approximately
given by
in
pure
and monovacancy
tungsten,
are
-7.7
where v is the standard frequency factor (lO’*s-‘)
and hd is the dissociation enthalpy (hb,,, + h;); h; is
the migration enthalpy of the pure tungsten SIA
(0.085 eV) [44,45]. Thus, rd is -5 x IO-*s. It is
assumed that the mixed dumbbell can migrate as an
entity with a migration enthalpy which is equal to
11; + #,,_ac [46] and a pre-exponential factor which is
equal to lo-*cm*s-‘.
The above implies that the
mixed dumbbell can migrate a root-mean-square
diffusion distance of 200 A for Q = 5 x lo-* s, which
in turn means that the mixed dumbbell makes N 10’
jumps before dissociating. Thus it is very probable
that two mixed dumbbells react in the vicinity of a
displacement cascade to form a di-Re cluster which
is immobile. The formation of a WRe cluster is
envisaged to occur via the following possible reactions: (a) two mixed dumbbells react to form an
immobile di-Re cluster; (b) the di-Re cluster reacts
with a pure tungsten SIA to form a WRe, cluster; and
tln Appendix B we show that the rate of dissolution of a
displacement cascade is extremely slow. This means that
initially the solute: self-interstitial atom clusters will not
IX “hit” by monovacancies.
ZThe tracer diffusion data for Re in W is somewhat
“strange”, as the preexponential factor is anomalously
large. It would be worthwhile to redo these experiments
using more modem techniques.
1151
(c) the WRe, cluster reacts with a second tungsten
SIA to form W2Re2 (or WRe) cluster. During the
course of the 2 year irradiation the displacement
cascades dissolve slowly (see Appendix B) and they
provide the vacancies which can result in the shrinkage of a cluster. Recent experiments by Averback and
Ehrhart [47] on Ni-1 at.% Si also suggest strongly
that point defect clustering and trapping occurs in
the vicinity of displacement cascades.
The specific details of the growth or shrinkage
of a cluster are difficult to state, but they can be
rationalized in terms of the Cauvin-Martin model for
radiation-induced
metastability [36]. The physical
basis of the Cauvin-Martin
model is that the irreversible vacancy-SIA annihilation reaction drives solute clusters towards a larger solute content and hence
to precipitation; see Fig. 1 in Reference [36] for a
schematic description of how their mechanism works.
4.3. Point defect mechanism for the suppression of
swelling
The addition of 1Oat.x Re to tungsten is known
to suppress the formation of voids in tungsten [5,6].
In addition, we did not observe voids in this alloyonly WRe precipitates-by
field-ion microscopy.
A mechanism for void suppression suggests itself
form the model presented in Section 4.2 for the
homogeneous nucleation of WRe. The latter model
involves point defect clustering and trapping in
the vicinity of displacement cascades. In particular,
the trapping of SIAs by immobile dirhenium clusters
is an essential feature of the homogeneous nucleation
model. This implies that a significant fraction of the
SIAs are strongly trapped and, therefore, recombination with vacancies-which
are emitted from
the nearby slowly-dissolving displacement cascadesis very probable. That is, the recombination of vacancies and SIAs must dominate over the destruction
of these point defects at a biased sink (such as,
dislocations)-this
is a necessary condition for the
suppression of void formation. Hence, the local divergence between the SIA and vacancy fluxes to sinks
can not become large enough to allow for the
sufficient accumulation of vacancies, which is necessary for the nucleation and growth of voids.
5. SUMMARY
1. The atom-probe FIM has been used to study
radiation-induced
precipitation in a W-10 at.% Re
alloy. This alloy is subsaturated with respect to the
solvus line of the primary solid solutionthe B
phase+for the irradiation temperatures employed.
2. Wire specimens of this alloy were irradiated to a fast-neutron fluence of -4 x 1022cm-2
(E > 0.1 MeV) at elevated temperatures (575, 625
and 675°C) in Experimental Breeder Reactor II. nis
fluence corresponds to 8.6 dpa and an average displacement rate, for the two year irradiation time, of
1.4 x IO-‘dpas-‘.
1152
HERSCHITZ
and SEIDMAN:
HOMOGENEOUS
3. Precipitates with the composition WWRe were
detected in this alloy as a result of fast-neutron
bombardment. This result indicates that the -WRe
precipitates are radiation resistant in the temperature
range 575_675”C, in the presence of a fast-neutron
flux, for the composition W-10 at.% Re.
4. Coherent, semicoherent and possibly incoherent
WRe precipitates have been observed. The number
density of precipitates is N lOi cme3.
5. The observed precipitates are disc shaped, one
or two atomic planes thick. Their mean diameter is
N57.L
6. The precipitates were nut associated with either
linear or ptanar defects, or with any impurity atoms;
i.e. a true lromogeneous radiation-induced
precipitation occurs in this alloy.
7. A physical argument is presented for the nucleation of the N WRe precipitates in the vicinity of
displacement cascades produced by primary knockon atoms. It is suggested that the nucleation of the
WRe phase is due to the formation of tightfy-bound
mobile mixed dumbbells which, in turn, react to form
an immobile di-rhenium cluster. A possible sequence
of point-defect reactions is presented which can lead
to a WRe cluster. The growth of this cluster into a
precipitate is most likely driven by the irreversible
vacancy: self-interstitial atom @IA) annihilation reaction as suggested by Cauvin and Martin [36].
8. No voids were detected in this alloy. This
indicates that the addition of Re to W. suppresses
void formation as voids have been detected in pure
tungsten.
9. A plausible mechanism for the suppression of
void swelling, in this alloy, involves the dominance of
vacancy: self-interstitial atom recombination over the
destruction of these point defects at a biased sinkthe dislocation. This is possible, in particular, by the
r~ombination
of vacancies with self-inte~titial
atoms which are trapped in immobile clusters involving self-interstitial
and rhenium atoms. This
strong recombination
process prevents the accumulation of a sufficient number of vacancies for the
nucleation and growth of voids. This mechanism is
consistent with the mechanism for the homogeneous
nucleation of WRe precipitates.
Acknowledgements-This
research was supported by the
U.S. Department of Energy. Additional support was re-
ceived from the National Science Foundation through the
use of the technical facilities of the Materials Science Center
at Cornell University. We wish to thank Mr Robert Whitmarsh for enthusiastic technical assistance, Dr Alfred Wagner (now at Bell Laboratories) for preparing the specime&
for irradiation, Dr Martin Grossbeck (Oak Ridae National
gyrator)
for arranging for the i~~diations~n EBR-II,
Dr Robert S. Averback (Argonne National Laboratory) for
useful discussions, Dr L. R. Greenwood (Argonne National
Laboratory) for kindly performing calculat&s for us emnlovina the ENBFIB-V code and Dr Georrres Martin Kenire h’&des Nuclkaires de Saclay) for usef;l questions and
comments on the manuscript.
RADIATION-INDUCED
PRECIPITATION
REFERENCES
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HERSCHITZ
and SEIDMAN:
HOMOGENEOUS
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D. N. Seidman, Phil. Mug. A 47, 407 (1983).
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Merufl. 19, 1339 (1971); C. Y. Wei and D. N. Seidman,
RADIATION-INDUCED
(CD*
d
Urn
0.
PRECIPITATION
1153
Actual solute composition of a defect.
Volume fraction of the analyzed cylinder occupied by a defect.
The remaining volume fraction of the cylinder
analyzed. The value of v’+ vm must be equal
to unity.
Diameter of the cylinder of alloy analyzed.
An expression for the relationship between (c3), and
(c3* based on conservation of mass is
cc,“>. = <c3’ vd+ (c,) v”.
(Al)
Rearranging this equation and using the fact that
vd+ urn= 1 we obtain the following expression for (c,d)*
xc>*=
+s>[I -
(c%d+
(l/vd)l.
642)
Phil. Mug. A 43, 1319 (1981).
41. K-D. Rasch, R. W. Siegel and H. Schultz, J. nucl.
Muter. 69 & 70, 622 (1978).
42. D. N. Seidman, Scripru merall. 13, 251 (1979).
43. K. L. Wilson, M. I. Baskes and D. N. Seidman, Acru
merall. 28, 89 (1980); C. H. Nielsen, M.S. Thesis,
We now consider ways of calculating v, for defects with
diBerent geometrical shapes.
In the case of a cylinder of alloy containing a disc-shaped
precipitate of thickness r-in the orientation shown in Fig.
Al(a)-v, is given by
Cornell University, Ithaca, New York (1977).
44. R. M. Scanlan, D. L. Styris and D. N. Seidman, Phi/.
(A3)
Mag. 23, 1439 (1971).
45. R. M. Scanlan, D. L. Styris and D. N. Seidman, Phil.
Mug. 13, 1459 (1971).
46. R. A. Johnson and N. Q. Lam, Phys. Rev. B 13, 4364
(1976).
47. R. S. Averback and P. Ehrhart, J. Phys. F, Metal Phys.
(1984). In press.
48. K.-D. Rasch, R. W. Siegel and H. Schultz, J. nucl.
Muter. 69 & 70,622 (1978); K.-D. Rasch, R. W. Siegel
and H. Schultz, Phil. Mug. A 41, 91 (1980).
49. J. Y. Part, H-C. W. Huang. R. W. Siegel and R. W.
Balluffi. Phil. Mug. A 48, 397 (1983).
50. R. W. Siegel, J. &cl. Mater. & & i0, 117 (1978).
51. K. Comnaan and Y. Haven. Trans. Fur&v Sot. 52.
786 (19i6).
52. J. N.‘Mundy, S. J. Rothman. N. Q. Lam, L. J. Nowicki
and H. A. Hoff. J. nucl. Murer. 69 & 70. 526 119781.
53. J. N. Mundy, S: J. Rothman, N. Q. Lam; H. A. Hok
and L. J. Nowicki, Phys. Rev. B IS, 6566 (1978).
54. R. L. Anderlin, J. D. Knight and M-I. Kahn, Trans.
merull. Sot. A.I.M.E. 233, 19 (1965).
55. D. N. Seidman and R. W. Balluffi, Phil. Mag. 13, 649
(1966).
56. k. S.-Ham, J. Phys. Chem. Solidr 6, 335 (1958).
57. C. P. Flvnn. Phvs. Reu. A 133.587 (1964): C. P. Flvnn.
ibid. lg, 241 6964).
’
.
”
* ’
58. E. D. Hondros, in Precipirarion Processes in Solids
Equation (A3) holds when the diameter of the disc-shaped
precipitate is greater than 0. and the height of the cylinder
analyzed.
For a disc-shaped precipitate of diameter D, in the
orientation shown in Fig. Al(b) v, is given by
o, = (DdD,,)2.
(A4)
DISC-SHAPED PRECIPITATE
OdIENTATION (b)
DISC-SHAPED
ORIENTATION
PRECIPITATE
(b)
(edited by K. C. Russell and H. I. Aaronson), pp. I-30.
Metall. Sot. A.I.M.E., Warrendale, PA (1978).
APPENDIX
A
Culcularion o/ rhe ucrual composirion of a precipirare
In most cases the dimensions of the cylinder of alloy
analyzed are greater than the size of the defect under
consideration-precipitate,
void or a grain boundary; voids
and grain boundaries are discussed in Ref. [7]. Therefore the
measured Re concentration had to be corrected for the
matrix contribution, in order to obtain the actual Re
composition of a precipitate. The following quantities are
defined:
cc,>
<CD.
Solute concentration in the matrix of the
alloy.
The average solute concentration of the volume analyzed which contains a defect (precipitate); where the subscript u on the bracket
means an uncorrected value. The value of
(c;d>. is a lower limit to the actual solute
concentration of a defect.
SPHERICAL
PRECIPITATE
Fig. Al. A schematic illustration which shows the relationship between the cylinder of alloy analyzed and precipitates of different geometrical shapes and orientations.
1154
HERSCHITZ
and SEIDMAN:
HOMOGENEOUS
In the case of a cylinder of alloy containing a spherical
precipitate of diameter De
Fig. Al(c)-u,
is equal to
” _2D:+
.f-
(D:- D:)‘P(2D:+ 0:).
(As)
3D2[D,,+(D:D;)ln’
’
0
where D, is the diameter of the cross-section of the precipitate when it is first seen in the field-of-view.
APPENDIX B
Rate of dissohtion of a displacement cascade
The rate of dissolution of a displacement cascade can be
calculated employing a simple diffusion-limited model [55];
this gives the maximum rate of dissolution. We approximate
the displacement cascade by a spherical void of radius r. The
number of vacancies (N,) contained in the void (displacement cascade) is
4zr’
N”=x
where R is the atomic volume. Thus the rate of change r is
WI
The quantity (dN,,/dt) is given by the quasi steady-state
vacancy diffusion flux (4) between the curved surface of the
void and a flat surface (sink) which is at a distance that is
large compared to r. The expression for 4 is [56,571
Q = 4nrD,&
(B3)
where D,, is the monovacancy diffusivity and AC is the
vacancy concentration difference between the void and the
flat surface. The difference AC is given by
AC = c~Jexp&,/&aT)
- 1]
(B4)
where ce is the equilibrium monovacancy concentration at
a flat surface and p,. is the chemical potential of a monovacancy at the surface of the v_oid. The expression for p,,, is
(B5)
~1. = 2$VaT
where y is the vacuum-metal surface tension. Therefore 4
is given by
4 =w[exp(g)-
1]
(B6)
RADIATION-INDUCED
PRECIPITATION
where ct = Ni,,/Q. Thus the dissolution rate is
-($)=f:[exp($)-1]
(B7)
where J,# is the correlation factor for a monovacancy
diffusion mechanism, as the tracer diffusion coefficient (D,)
is equal to f,, D,, Nt,,.
When 2yR/rk,T is less than unity then equation (B7)
becomes
w
Equation (B8) integrates to
6YQDr
r’(t) = r’(t = 0) - fi,k,Tt.
(B9)
For our situation the capillary constant (2yR/k,T) is
approximately 5. lo-’ cm; y 2 2040 erg cm-’ at 675-C (581.
For the displacement cascade sizes of interest (r < 15 A) the
value of 2yQ/rksT is much greater than unity and therefore
we can not use equation (B9).
The differential equation (B7) can also be integrated if one
neglects unity with respect to exp (2yR/rkBT) to obtain
-
6) =t?exp($$).
(BlO)
Equation (BlO) can be integrated, however the solution
involves a series. Therefore, we can not obtain an explicit
expression for r’(t).
Because of this unsatisfactory situation we simply evaluated - (dr/dt) at 675°C. For r = 5. 10 and 15 A, the
respective values of -(dr/dt)
are 2.5 x lo-iq, 8.5 x 10-u
and 10-22cm s-i. These values imply that the cascades are
dissolving very slowly, compared to the time for the clustering reactions involving SIAs and Re atoms. For N, = 3 1
(the number of vacancies in a mean displacement cascade)
the value of r is only 5 A (see Section 4.2). Even for this
small value of r the displacement cascades are dissolving
rather slowly. There is, of course, an acceleration effect with
decreasing r [see equation (BlO)]; therefore displacement
cascades which are smaller than the mean size are dissolving
more rapidly than ones which are larger than the mean size.