overview no. 39 an atomic resolution study of …

,&a mefdf. Vol. 32, No. 8. pp. 1141-1154, 1984 Printed in Great Britain. All rights reserved

OOOt-6160/84 93.00 f0.00 Copyright 0 1984 Pergamon Press Ltd

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 bc- strahlungsinduxierte 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 Ausscheidungs- mechanismus 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 solu- tions, 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 deca- libration 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 fast- neutron irradiated W-25 at.% Re alloys-using trans- mission electron microscopy-and it corresponds to the x phase with the composition WRe,. Williams et

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.

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 atom- probe field-ion microscope (FIM) study of radiation- induced, 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 atom- probe 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 con- ventional analytical electron microscopy techniques.

We demonstrate that significantalterations of the microstructure of this alloy occur as a result of

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 RADIATION-INDUCED PRECIPITATION 1143

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 radiation- induced 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 coun- ter 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 (q4.0 x lo-‘O torr), carbon monoxide (c 2.0 x lo-” torr), and helium (<4.0 x lo-i2 torr); the par- tial pressures were measured employing a Uthe Tech- nology Inc. (UTI) Model 1OOC residual 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

field-evaporated tip was rotated, employing the goni- ometer 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 rate- average number of ions 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 termi- nated, 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 Ap- pendix 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.

1144 HERSCHITZ and SEIDMAN: HOMOGENEOUS RADIATION-INDUCED PRECIPITATION

30D MASS SPECTRUM FOR A NEUTRON- IRRADIATED W-IO AT.% Re ALLOY 1

f

250

Ts ‘45Ki f =O.I5

9 200 Ti ~575.C w

VACUUM s 3 x doTon

b ‘50

,ij/, , , ,I, j: , , , 1 0 20 40 60 60 ‘00

-MASS-TO--CHARGE RATIO-- ---

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 occurring isotopes of Re-‘85Re and “‘Re-can be readily distinguished from one another in the plus- three 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 trans- mutation 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 oc-

tin 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 background pressure was in the range (4.0-6.0) x 1O-‘o Torr.

60 61 62 63 64

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 field- evaporation 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 FOR A NEUTRON-IRRADIATED -

W-IO AT.% Re ALLOY

?

70-

Ill I I 1 I

45 46 47 48 49

MASS-TO-CHARGE 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 PRECIPITATION 1145

Table 1. Comparison of the experimcntai W’+ and Res+ isotopic abundances in a neutron-irradiated W-l0a~% Re alloy with the

handbook values

Number of Experimental* Handbook Isotope atoms detected (“4 (“/,I

‘MW 5 0.24f0.11 0.1 lSlW 494 23.3 f 1.1 26.4 lSlW 393 18.5 f 0.9 14.4 ‘“W 633 29.8 4 1.2 30.1 lSdW 600 28.2 f I .2 28.4

Total W 2125 100 100 ‘“RC 129 40.2 j, 3.5 37. I ‘“RC I92 59.8 f 4.3 62.9

Total Re 321 100 100

‘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 composition in 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 1181 we 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

APPROXIMATE DEPTH SCALE (it

Tl-IR’% A Nk”Tf?O?lRfiADl;Rm

<CR,> .95?16ATX I%,

CUMUL8ZlVE N”h OF W%US Ra6%NTS loGO

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 DEPTH SCALE (&

IO 20 30 40 50 60 I 1 I I I I I 1

r Iso RI INTEGRAL PROFILE Tli UNIRRADIATED W-IO AT. X

g I25

; ID0

!j 75 <h> * 0.4 ?a9 AT $i

z

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 man-

ufacturer.

Table 2. A summary of the results of the measurements of bulk Re composition (cRt) in both neutron-i~diated and unirradiated W-10 at.% Rc alloys

The uncorrected Rc concentration of a

Cumulative Measured Re Presence of Irradiation number of

compositional concentration’ variatiot?

State of local compositionat

temperature W plus Re Cumulative number specimen wc) events of Rc events $$I

changes in the integral protile $t$j

S’eutron 625 1059 158 14.9 f 1.2 Yes Irradiated

26.0 f 3.6

Seutron 625 2866 321 11.2f0.6 Yes Irradiated

29.2 f 2.4

Unirradiatcd - 1263 131 10.4 f 0.9 No -

‘The uncertainty is qua1 to the ratio of the square root of the cumulative number of Rc events to the cumulative number of W plus Re events.

L?his vats corresponds to the local slope in a Re integral profile.

1146 HERSCHITZ and SEIDMAN: HOMOGENEOUS ~DIATION-INDUCED PRECIPITATION

Table 3. A summary of the results on the mesurcments of the composition of different precipitates in a neutron-i~adiated W-10 at.% Re alloy

The uncorrected Re The actual Re Re concentration Cumulative concentration of concentration of outside of the

Irradiation number of Cumulative rhc precipitate’.b the piccipitate’ precipitatea*b tcmpcratun Region W plus Re number of (ckT,l>, (CRV

T (“C) analyzed CVClltS Re events (at.%) (a&) 0

625 PPTI 1738 350 22.1 f 1.2 56. I f 2.9 a.1 f I.1 67.5 PPT2 1463 287 3l.Ok2.1 51.2*2.6 8.1 f 1.1 575 PPr3 919 165 19.1 * 1.7 52.4 f 3. I 12.1 f2.3 625 PPT4a 3882 788 29-6 f 1.2 49.8 f 2.8 11.1 *0.9

‘The uncertainty is equal to the ratio of the square root of the cumulative number of Re events to the cumulative number of W ptus Re

“[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 B of [18].

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 field- evaporation 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.

3.4. Radiation-induced precipitates

Four radiation-induced precipitates were detected and analyzed, whereas no voids were found in the W-lOat.% Re alloy. The density of the radiation- induced precipitates is equal to N 1016 cm-‘; 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.

tained in each run in greater detail; they are sum- marized 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

PPT1

Fig. 7. An FIN micrograph showing PPTl in a fast- neutron 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: HOMOGENEOUS RADIATION-INDUCED PRECIPITATION I147

APPROXIMATE DEPTH SCALE (1)

,~~~!

u 400 800 1200 1600 2000

CUMljLATIVE NUMBER OF W PLUS Re EVENTS

Fig. 8. The Re integral profile from PPTI shown in Fig. 7. The value of <c[:‘)~ is 22. I + 1.2 at.% 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.

APPROXIMATE DEPTH SCALE ifi,

? 600 10 20 30 40 50 60

z RI ,NTECRAL PROFILE FROM PPTZ IN 1 5 w 5oo

t

A NEUTRON- IRRADIATED W-IO AT % RC

B ALLOY T, j 675-C

OBSERVATION i INDICATES THE _ PRECIPITATE IS


Fig. IO. The Re intergral profile from PPT2 shown in Fig. 9. The values of (~g)~ and (c,,) are equal to 31 .O f 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 atom- probe 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

<cK’L the value of (c{{‘)* is equal to

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. 11. Two FIM micrographs showing PPT3 (see WI arrows) before (a) and after (b) the atom-probe anal) Note that this precipitate is no longer present after

completion of the chemical analysis.

hite Isis. the


APPROXIMATE DEPTH SCALE (A,

Re INTEGRAL PROFILE FROM PPT3 IN A NEUTRON-IRRADIATED W-t0 ATY. Re ALLOY

z 160

<C,> = 12.122.3 Al.% R

f

z’ Y 100

F 4 50

2

a 0 200 400 600 800 ICC0


Fig. 12. The Re integral profile from PPT3 shown in Fig. 11. The values of <cl$>,, and (cRc) are equal to 19.1 f 1.7

and 12.1 4 2.3 at.% Re, respectively.

51.2 + 2.6 at.% Re. Equation (A4) was used to esti- mate u,. The Re concentration in a region within a few angstroms of PPT2 is 8.7 f 1.1 at.% Re; this value is in approximate agreement with <c&j.

PPT3 (figs 11 and 12). Figures 1 l(a) and (b)show FIM images of PPT3 before and after the atom-probe analysis; note that it is no longer present in Fig. 1 l(b). It is difficult to determine the exact state of coherency of PPT3; it is one atomic plane thick and D,, is approximately 120A. In this case T, is equal to 575°C. The corresponding integral profile is presented in Fig. 12.f The value of (cj& is equal to 19.1 f 1.7 at.% Re, while the Re concentration within a few angstroms of PPT3 is 12.1 ir 2.3 at.% Re. Equation (A3) was used to correct for the matrix contribution to <cg>,, to obtain (c$)* which is equal to 52.4 f 3.1 at.% Re.

PPT4 (Figs 13 and 14). Finally, Fig. 13 shows an FIM image containing two disc-shaped precipitates (PPT4a and PPT4b) in the field-of-view. The‘atom- probe analysis was performed on the precipitate (PPTa) shown in the top of this figure; it is two atomic planes thick and Dd is sequal to N 60 A. Since the tip failed during probing, PPT4a was only seen prior to the chemical analysis. This precipitate is semicoherent as all the matrix planes are not continuous across its interface. This specimen had been irradiated at I’, = 625°C. The Re integral profile for PPT4a is exhibited in Fig. 14. The values of (cc). 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 radiation- induced 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 integra1 profile changed as the precipitate moved out of the analyzing cylinder during the field evaporation of the specimen. Thus a strong effort was always made to align the plane of the disc-shaped precipitate such that it was parallel to the axis of the analyzing cylinder.

Fig. 13. An FIM micrograph of a fast-neutron irradiated - _ WllOat$ Re alloy with two precipitates-PPT4a and PPT4b-m the field-of-view (se-e black arrow& The orecio- itate shown in the top of the.figure (PPT4a) was cher&aliy

analyzed.

Re alloy is w 50 at.% Re, indicates that the o phase forms in these alloys as a result of a fast-neutron irradiation. Both coherent, semicoherent and possibly an incoherent precipitate of WRe were observed at a number density of w 10’6cm-J.

3.5. On the question of impurity atoms associated with the radiation-induced precipitates

The impurity atoms He, C, N or 0 as well as other impurities have the potential to play a very important rob in the nucleation of voids and radiation-induced precipitates [26]. In addition, to the main W and Re peaks we detected peaks due to ‘HI+, 3Het+ and ‘He’+ in the mass spectra. Figure 15 shows these peaks on the expanded scale 0 to 5 a.m.u.

There are two possible sources of helium detected by the atom-probe FIM:

1. Field-adsorbed helium from the residual helium gas in the ultra-high vacuum system. 2. Helium present inside the specimen.

APPROXIMATE DEPTH SCALE (A, 20 40 60 SO too I I I I I

v) ~OOO- f?k INTEGRAL PROFILE FROM PPT4 IN A

2 r NEUTRON-IRRADIATED W-IO AT% Rc ALLOY

0 1000 2000 3000 4000 5OOo CUMULATIVE NUMBER OF W PLUS Re EVENTS

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

and 1.1 f 0.9 at.% Re, respectively.


‘Ooo r ‘Ii’: ‘He” AND ‘Ha’ SPECTRUM FOR A : NEUTRON-IRRADIATED W-IO AT.% Re ALLOY

r -

5 too e

nHal*

5 :

k -

lH’. 4Hel+

iz m 1Or

s _

I- I , 1

0 I 2 3 4 5 MASS TO CHARGE RATIO

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 radiation- induced precipitation would require the existence of an exceedingly special distribution of dislocations, at a number density which is very high.

APPROXIMATE DEPTH SCALE (A,

3001 20 I 40 60 60 100 1 I 1 I

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


Parameter

Table 4. Relevant point defect snd diffusion data for the W and W(Rc) systems

Notation Value Reference

Prccxponential factor for W self-interstitial atom diiusion By, 0.22 cm* s-r 44,45 Enthalpy change of migration of a W self-interstitial atom 0.085 ev 44.45 Enthalpy change of formation of a monovacancy in W ;;

4: 3.67 f 0.2 eV 48.49

Entropy of formation of a monovacancy in W 2.3 k, 48.49, SO Entbalpy change of migration of a monovacancy in W h”

b 1.78fO.leV 48, SO

Binding cnthalpy of a divacancy in W 0.7 ev 49.51 Binding enthalpy of a W self-interstitial atom to a Re atom hkw >0.8 ev 43 Correlation factor for tracer diffusion by a monovacancy mechanism in a b.c.c.

lattice 0.73 51 Prcmponcntial factor for W selfdiffusion by a monovacancy mechanism $@ O.O6cm’s-’ Derived from traar

self-diffusion and quilibrium vacancy

cont. data Prccxponcntial factor for the traar self-diffusion in W

;f 0.04cm’s-” 52.53

Activation energy for tracer sclfditTusion in W 5.45 CV’ 52.53 Prcexponential factor for Re traar diffusion in W f’s&,is w 275cm2s-‘b 54 Activation energy for Re tracer diiusion in W Qr IW 7.1 eva 54

‘These values correspond to the low temperature regime. bathe Rc tracer diffusion data in W is somewhat “strange” -that is, the pm-exponential factor is anomalously large.

in this alloy. Experimental evidence for homogeneous radiation-induced precipitation has been recently presented by Cauvin and Martin in the case of Al(Zn) alloys [33,34], by Brager et ~1. in the case of a 316 stainless steel [35a], by Mukai and Mitchell for a Ni(Be) alloy [35b], and Kinoshita and Mitchell [35c] and Wahi and Wollenberger [35d] for Cu(Be) alloys. Theoretical treatments of this physical phenomenon have been considered by Cauvin and Martin [36] and Maydet and Russell [37]; the latter authors only considered the possibility of the nucleation of incoherent precipitates, whereas Cauvin and Martin also considered coherent precipitates.

We now describe a possible sequence of plausible events which can result in the homogeneous nucleation of WRe precipitates, in a subsaturated alloy which is subject to irradiation with fast neutrons.

The primary source of radiation damage, in the case of fast neutrons, is the displacement cascade. Each displacement cascade is created by a primary knock-on atom (PRA) with a mean recoil energy of 4 keVt. In the case of pure tungsten it is known from FIM experiments that a displacement cascade, created at 15 K, consists of a vacancy-rich core (H 2 to 30 at.%) surrounded by a distribution of SIAs which is created by the replacement collision sequence mechanism [38,40]. The concentration of SIAS on the periphery of a displacement cascade can

tThis value of 4 KeV is an UDD~C limit to the mean recoil energy of a PKA in EBkI (Dr L. R. Greenwood, Argonne National Laboratory, private communication). This implies the number of vacancies in the mean displacement cascade is -31. This value is obtained from the modified Kinchin-Pease expression (0.8) (4KeV)/2&, where E, is our experimental average displacement threshold energy of 52 eV [38]. The reason for this low mean recoil energy of a PKA is that the fast-neutron spectrum of EBR-II is rather soft [39].

$This calculation employed a total nuclear cross-section for producing primary knock-on atoms of 7.54 x 10b2’ cm*. This value is from ENBF/B-V code (Dr L. R. Green- wood, private communication).

be as high as N 1 at.% [40]. The major differences expected for a displacement cascade created in W-10 at.% Re for the T,s (575, 625 and 675°C) employed are as follows: (1) the point defects (vacancies and SiAs) are both mobile as these T, correspond to Stage III of tungsten [41,42]; (2) each displacement cascade contains-in addition to vacancies, SIAs and tungsten atoms-10 at.% Re atoms; (3) Clustering reactions are taking place among the point defects; and (4) the displacement cascade is continuously dissolving via a self-diffusion mechanism. Since the radiation damage is highly localized in the displacement cascade-the point defect supersaturation in between the displacement cascades is initially negligible-it is probable that the nucleation of a WRe phase precipitate occurs in its vicinity. The absolute efficiency of this nucleation process is low as the 6nal density of radiation-induced WRe precipitates is N lOi6 crnd3, which is significantly less than the number density (nP) of primary km_ck-on atoms

that produce displacement cascades. For a fluence of 4 x 1022 fast neutrons cm-* the value of nP is N 1.8 x 10” cm-‘.$ Thus only one in every approximately 1.8 million primary knock-on events results in a WRe.

The possible point defects in the W-10at.x Re alloy are: (1) a vacancy; (2) a pure tungsten SIA; (3) 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 tracer diffusion data. We now employ these point defect properties to show that plausible first steps in the nucleation of a WRe precipitate involve the migration of tungsten SIAs to Re atoms to form mobile mixed dumbbells, which in turn react to form an immobile di-Re cluster. The di-Re cluster can then grow by the accretion of mixed dumbbells and pure tungsten or rhenium SIAs.

In the temperature range 575-675”C the most mobile defect is the tungsten SIA. At 675°C (all the subsequent calculations refer to this 7’i) the self-


interstitial (&) and monovacancy (D,,) diffusivities,

in pure tungsten, are -7.7 x 10-2 and 2 x lo-“cm* s-l, respectively. Thus, in the same period of time the tungsten SIA moves a root-mean- square 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

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.

(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 alloy- only 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 cascades- is 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 div- ergence 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 solution- the B phase+for the irradiation temperatures employed.

2. Wire specimens of this alloy were irradiated to a fast-neutron fluence of -4 x 1022 cm-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 dis-

placement rate, for the two year irradiation time, of 1.4 x IO-‘dpas-‘.


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 knock- on 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 sink- the 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 Whit- marsh for enthusiastic technical assistance, Dr Alfred Wag- ner (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 em- nlovina the ENBFIB-V code and Dr Georrres Martin Ken- ire h’&des Nuclkaires de Saclay) for usef;l questions and comments on the manuscript.

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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

(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.

(CD* Actual solute composition of a defect. d Volume fraction of the analyzed cylinder oc-

cupied by a defect. Urn The remaining volume fraction of the cylinder

analyzed. The value of v’+ vm must be equal to unity.

0. 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>* = (c%d+ +s> [I - (l/vd)l. 642)

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

(A3)

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.

DISC-SHAPED PRECIPITATE OdIENTATION (b)

DISC-SHAPED PRECIPITATE ORIENTATION (b)

SPHERICAL PRECIPITATE

(A4)

Fig. Al. A schematic illustration which shows the relationship between the cylinder of alloy analyzed and precipitates of different geometrical shapes and orientations.


In the case of a cylinder of alloy containing a spherical precipitate of diameter De Fig. Al(c)-u, is equal to

” _2D:+ (D:- D:)‘P(2D:+ 0:). .f- 3D2[D,,+(D:- D;)ln’ ’ (As)

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

~1. = 2$VaT (B5)

where y is the vacuum-metal surface tension. Therefore 4 is given by

4 =w[exp(g)- 1] (B6)

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

Equation (B8) integrates to

6Y QDr r’(t) = r’(t = 0) - fi,k,Tt.

w

(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 evalu- ated - (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.

overview no. 39 an atomic resolution study of …

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