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LOW-TEMPERATURE NEUTRON IRRADIATION DAMAGE IN ALUMINUM AND GOLD"
i\/I. L. SWANSON AND G. R. PIERCY Cllcllk Risler iVL~clear Laboratories, Atomic Etzergy of Calzada L i ~ ~ r i t e d , Chalk Riuer, O~ttario
Received .4pril 20, 1964
Fast-neutron irradiation damage a t 1.74' I< and its recovery to 100' I< have been in\;estigatetl in i l l and Au by means of residual electrical resistivity measure- ments. The erfects of impurities, quenched-in vacancies, and dislocations were srudied. I t \\>as fount1 that the damage rate of A1 was ~~nchanged by ilnpurity concentrations of less than 0.5 at . % and quenched-in vacancy concentrations of less than 0.002 a t . Cjo Dislocation concentrations of -2 X 1 0 1 0 / ~ ~ ~ ~ 2 i l l A1 and ,-~10"/cm2 in Au increased thcir danlage rates by 35%and50Y0 respectively. Small amounts of impurity (-0.02 a t . yo) in Au increased its damage rate by l5<:; and suppressed the enhancement caused by deformation. The stage I rcco\.cry of ;\I and Au was only slightly increased by extra dislocations, but was increasecl considerably by quenched-in vacancies. An i m p ~ ~ r i t y concentration of --0.5 at . yo supprcsscd the stage I recovery of i l l , but not that of Au. The results are interpreted in terms of channeling in A1 and collision chains in Au.
ISTRODUC'TION
I11 the present research the effects of defect doping (i.e. the introduction of extra impurities, dislocations, or quenched-in vacancies) on the neutron-irra- diation darnage rate and the subseq~ient low-temperature recovery of A1 and ALI were investigated. Fast-neutron irradiation damage in metals is inhomo- geneous, consisting of small, highly disordered, vacancy-rich zones surrouilded by larger interstitial-rich regions in a relatively damage-free matrix (Seeger 1932; Brinl;man 1954). The size of the interstitial-rich regions depends on the range of the dynamic crowdions and channeled atoms which transport the interstitial atoms away from the depleted zones. In '4u the range of crowdions is of the order of 1000 A (Nelson and Thompson 1DG1; Swanson and Piercy 1963), so that overlap of damaged regions becomes significant a t a very low fission neutron close (at -2 X loll1 n/cm? which is our maximum dose). If the concentration of irradiation-induced defects outside the depleted zones is small compared with controlled amounts of other defects, the effect of the latter on the damage rate and the ltinetics of the recovery processes can be investigated. Consequently, information concerning the dynamics of irradiation damage and the distribution and nature of the irradiation-induced defects can be obtained. Irradiation a t low teinperatures is especially desirable in order to investigate the interstitial-type defects produced by dynamic crowdions. Very few such defect-doping studies have been attempted previously (Blewitt et ad. 1057), and in none has a low dose of relatively thermal-free neutrons been used, which is essential if the effect of small quantities of doped defects is not to be masked b ~ , the irradiation-induced defects. In the experiments to be described here, A1 and ALI (and also Cu, Zn, and Cd) were irradiated
*Issi~ed as A.E.C.L. No. 1992.
Canadian Journal of Pl~ysics. Volume 42 (Allgust. 10G-1)
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1606 CANADIAN JOURNAL O F PI-IYSICS. VOL. 4% 110G4
while immersed in liquid I-Ie I1 in a fission flux of only 5 X 1Os n/cm%ec, and the resulting electrical resistivity changes were measured i n sitlr. The damage rates and stage I recovery were measured as a function of the doped lattice defects.
ESPERIMENTAI , PROCEDURE
1. Cryostat The samples were irradiated in the D-3 external bean1 liquid I-Ie cryostat
(3Iacl;innon and Piercy 1961) of the NRU reactor a t the Chalk River Nuclear Laboratories. A recently modified cryostat is shown in Fig. 1. I t consisted of a cylindrical inner vessel surrounded by a vacuuin-insulated liquid N shield; the whole assembly was easily demountable. The lower 4 feet of the i-foot- loilg cryostat was constructed entirely of 41 to reduce induced radioactivity and gamma heating while ensuring good t l~enna l conductivity. 4 thin-walled (0.015 in.) stainless-steel tube, into which a styrofoam plug was inserted, fornled the upper part of the inner vessel. Because of the danger of explosions in impure irradiated liquid N (Coltman ct al. 1957; Heyne 1962), pure Y2 gas from a cylinder was fed through a heat exchanger ii-nmersed in commercial liquid K, from which it was pumped centrifugally in a closed sj;stein through the annular N vessel.
In order to obtain a maximum neutron flux a t the samples and to minimize shielding, the cryostat was placed a t an angle of 9" to the horizontal in the D-3 experimental hole. This inclined position caused considerable loss of He by convection unless the pressure above the liquid He was reduced; this also had the advantage of producing I-Ie 11, thus providing accurate temperature control b e c a ~ ~ s e of its high thermal conductivity. The I-Ie temperature was controlled to fO.OO1° I< by manual adjustment of the pumping speed. The temperature was measured with a 150-ohm Allen-Bradley carbon resistance thermometer; its calibration, periodically checked by helium vapor pressure measurement, was invariant for irradiations of a t least five days, and only minor changes occurred after cycling to room temperature. The liquid He level was measured by means of 0.001-in. P t wire sensing elements (Wexler and Coral; 1951) which proved effective even for very high He boil-oif rates during filling. The I-Ie losses were 3 I./day with the D-3 gate shut. During irradiation, an additional 3 l./day was lost by gamma heating, which necessi- tated filling of the cryostat every 12 hours.
The neutron beam consisted of a fission neutron flux of 3 X lo8 neutrons/ cm%ec (determined bj7 sulphur threshold detectors), an equal thermal neutron flux, and an ~~ndetermined flux of intermediate energy. The fission flux was uniform within 2% over the samples.
2. Annealing Vessel The sa~nples to be annealed isocl~ronally were mounted in a copper annealing
vessel together with a Pt sensing element, carbon resistance thermometer, copper-constantan thennocouple, and differential thermocouple. The thermo- couple was calibrated with an N.R.C. calibrated Pt resistance thermo~neter.
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SWANSOS AND PIERCY: NEUTRON IRRADIATION DAMXGE
3016-G
LlQUlD NITROGEN TRANSFER TUBES
HlGH VACUUM LINE
TO MECHANICAL VACUUM PUMP
LlQUlD NITROGEN TRANSFER TUBES
COPPER FLANGE
LIQUID HELIUM TRANSFER TUBE
THIN- WALLED
LlQUlD NITROGEN
TUBE TO SAMPLES
HlGH VACUUM
COMPOSITION BUSHING
RADIATION SHIELD
LlQUlD HELIUM
FIG. 1. Schelllatic diagranl ol liquid helium cryostat.
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1608 CANADIAN JOURSAL OF PI-IYSICS. VOL. -12, 1961
The inner can of the annealing vessel was wound noninductively with a 30-011111 constantan heater and was vacuum insulated from the outer can. The samples were annealed by raising the annealing vessel from the liquid I-Ie and passing a current through the heater. After the H e surrounding the samples had boiled off, the desired annealing temperature was reached in 1 to 2 m i n ~ ~ t e s , and it was held constant within 0.2" I< for 10 minutes before the saiuples were quenched into the liquid He. The temperature gradient across the samples during annealing was less than 2" K, and was the sallle for each sample.
3. Resistivity i l~easz~rement T h e electrical resistivity of the samples was measured i n sit11 a t 1.74" I<
by a standard potentio~netric method, using a 1-amp current stabilized to two parts per nlillion, a 0.01-ohm standard resistance immersed in oil, and a sensitive potentiometer. When a Guildline Dauphinee type 9144 potentio- meter was used in an air-conditioned room, changes of 0.01 FI' could be measured accurately in a total voltage of 3000 FV; i.e., the sensitivity was three parts per million. Such sensitivity was necessary if the irradiation damage of impure samples was to be measured, because the fractional error 6/Ap in measurement of the resistivity increment Ap caused by irracliation varies directly as the residual resistivity po:
Ap .v ohm cm/day for i l l . If PO = 2.5 X ohm cm (for approxi- mately 0.3 at.46 impurities), then for a 3-day irradiation 6/Ap = 2.57;, which was approximately the maximum tolerable error. T h e sensitivity of resistivity measurements for high-purity samples was -4 X 10-I.L ohm ~ 1 1 1 , whicll was limitccl mainly by the length of the samples.
Thc resiclual resistivity po of a sample was calculated by conlparing the resistance measurecl a t 1.74" I< (Ro) with tha t measured a t room temperature
ancl using the l;nown value of the resistivity of the pure metal a t room temperature, p.oo ((;erritsen lC)56),
For defect-doped samples a self-consistent correction was applied to paoo, assuining that JIatthiessen's rule applied. This procedure was checlied by measuring pa00 accurately for the impurity-doped ;2l samples, and was found to be correct within the experimental error of 0.5%.
The size effect was important for high-purity samples. Although the meas- ured residual resistivities of some high-purit)~ 0.010-in. samples were approxi- nlately 30% higher than the calculated bull; resistivities (calculation based on Sondheimer 1032), thc effect of size on danlage ra te was always less than 20Jo because the irradiation damage was less than 2y0 of po.
4. Sample Prepamtion The XI and i lu samples to be irradiated were in the form of fine wires or
strips which were wound on inica forms or alumina rods before annealing. The residual resistivities and purities of the various sanlples ~ ~ s e d are shown in Table I . Generally, 0.010-in. wires were used as the starting material, although
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SWAKSON A N D PIERCY: NEUTRON IRRADIATION DAMhGE
TABLE I
Neutron-irradiation datnage rates
Rqsi?u?l reststlvtty
PO R/Iaterial Treatment (10-%hm cm)
Damage-ra te Damage enhancement
rate with respect (10PZ ohm to pure metal cm/(n/cm?)) (%)
99. 999YG Al Annealed 1 .75 4% cleformed 6 .10 8Y0 deforrned 6 .39 127, defor~ned 7.11
99.9907; Al Annealed 1 .60 330" C q ~ ~ e n c h 3 .49
90. 9970 --\I Annealed 3 .76 12% defornled 12 .0
99.9995; Al XI-0.11 Mg Al-0.515; RIg Alcan 1 s XI
( 0 . 3 5 5 Fe + Si)
Annealed Annealetl Annealed
Annealed
90.009$0 ;\u, leatls spot welded
00. 099y0 -4~1, leatls fused
90.000% -411
Annealed 13% dcfortned Annealed 12% deformed Annealcd 750" C slow quench 900° C q~lench 630" C q~lcnch Annealed 125; deformed Annealcd Annenletl
00 11997; ALI ilnnealecl 1 .41 0.76 -09.9SC/l Au Anncalcd 10. 0* 0 . oat -32 -99. 9SyG ~ \ L I 12% deformed 34.0* 1 . 00i -30
99.999C/;, CLI Annealed 2 .58 1 .00 12y0 clcformed 22.4 1 .07 7
99.999C%, Zn A~inealetl 7 .41 6 .50 l2yO defor~lled 18.7 6.78 4 . 4
99.999Ci/o Ccl Annealed 3 .82 7 .10 12% defortned 10.6 7.14 -
"Exhibiter1 resistance ~ni~ i in ia . tBecause of the way these samples were ~ n o u n t e d , their damage rates cannot be acci~rately coml~ased \\.it11
that of the 1,ui.e sample.
some larger diameters were also used to ensure that the results were not altered by the size effect. The grain size of the sainples was 0.01-0.10 mm. The results were independent of the type of electrical coiltact (soldered, fused, or spot welded), the temperature of prior anneal (300"-500" C for .\I and 30O0- 750" C for Hu), and the annealing atinosphere (vacuum or air). Since the attentuatioil of the neutron beam intensity was 15y0 per inch, it was necessary, for accurate damage-rate studies, to mount all sanlples a t equal distances from the cryostat bottom.
The 99.099% HLI was obtained from Sigmund Cohn Corp. and the 99.999yo A1 from United Mineral ancl Cheinical Corp. Their residual resistivities were consistent with the quoted purities. The inajor impurities of the impurity-
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lGl0 CANADIAN JOURNAL OF PIIYSICS. VOL. 42. 10G.i
doped sainples are shown in Table I. The residual resistivity per atomic per- cent 1Ig in XI was 0.5 X ohm cm. The impurity content of the -99.98% Au was estimated to be -0.02 at.yo from the residual resistivity.
The quenched samples were 99.999% pure 0.010-in. wires (except for one pair of 0.020-in. Au wires), which were inounted on mica forms, quenched from low temperatures into ice water froill an argon atmosphere and stored in liquid nitrogen until used. Since the quenched-in resistivity increineilts agreed with the values of other worliers (Bauerle and I<oehler 1057; Bradshaw and Pearson 1937), and since 90% of these increments recovered during a 10-minute anneal a t 150' C, the quenching appareiltly introduced only single vacancies and divacancies rather than clusters.
The deformed sainples were prepared by annealing 0.010-in. wire, rolliilg to 0.003 in. a t rooin temperature, winding the strips on alumina rods, and then storing one set of samples in liquid n' while the other set was again annealed. This treatment gave a 12% reductioil in sample cross-sectional area and resulted in a residual resistivity increment of -2 X lop8 ohm cm for Xu and Cu, but onl) 5 X 10-%hn~ cm for X1. These increments indicated dislocation densities of -~O"/CIII? for CU and Xu, and -2 X 1010/~in2 for A1 (Blewitt et ul. 1953; Basinsky et al. 1963), which are in approxim'tte agreement with densities observed b ) ~ transmission electron microscopy for comparable defor- inations ( B a i l e ~ ~ and EIirsch 1960; Faulliner and EIam 1962). I t should be inentioned that the dis l~c~tt ions in such grossly deforined sainples occur inostly in subgrain boundaries with a subgrain diameter of -2 inicroils (Segall and Partridge 1939). So~ne sainples were rolled to 0.007 in. or 0.005 in., annealed, and tlten rolled to 0.003 in., so as to produce smaller amounts of deformation while ret,zining the same final dimensions.
RESULTS
1. Nelltr.07~ Irra,cl'iat.ion Danzage Rates The damage rates of pure and defect-doped A1 and Au are shown in Table I
and Figs. 2 and 3. An accurate coinparison of damage rates was achieved by irradiating several sa~nples simultai~eously. These are g r o ~ p e d together in Table I. The damage rates of sinlilar samples irradiated separately were generally identical within 2%. Any larger deviations are attributed to changes in the neutron spectrum. The results were:
(a) The damage rates of 99.999% A1 and Au were considerably increased by deformation. The enhancements caused by dislocation concentrations of -2 X 1 0 1 0 / ~ ~ n 2 in A1 and ~lOll /c111~ in Au were respectively 33% and 50%.
(b) The da~nage rate of A1 was not increased by small ainounts of iillpurities or quenched-in vacancies. Annealed sa~nples of A1 - 0.1% &Ig, A1 - 0.5% Mg, and Xlcail 1S A1 exhibited the same damage rates as 00.090% A1 within the experi~neiltal error of 2%.
(c) The clamage rate of Au was increased -15yo by the addition of -0.02 at.% impurities,* and little further increase was produced by deformation.
*Note that this i~ilpure Au exhibited a resistivity minimu~il. A l tho~~gh this minimum was the same for the deformed samples, and probably was not affected by our srnall irradiation doses, it \\~o~+ld, be desirable to investigate further the elkect of impurities for Xu having no resisti\ ity r n ~ n ~ n l u ~ n .
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SWANSON AND PIERCY: NEUTRON IRR.I\DIATION DAMAGE
MATERIAL lo-' ohm cm
0 ANNEALED DEFORMED 9 9 . 9 9 9 % 9 9 . 9 9 9 % A l A1 y;i: / A ANNEALED 9 9 . 9 9 9 % Au A DEFORMED 9 9 . 9 9 9 % Au 18.16
INTEGRATED FISSION NEUTRON FLUX , n /cm2
FIG. 2. Neutr011-irr~diatio1l damage in annealed and deformed 00.000% alu~llinum and gold.
5 x 10." I I I I pol I I I I I MATERIAL l ~ ' o h m cm
0 ANNEALED 9 9 . 9 9 9 % Al 1.59 ANNEALED Al - 0.1 1 % Mg 50.4
s ANNEALED Al - 0.51°/~ Ma 254.3 / o ANNEALED 9 9 . 9 9 9 % Au 1 .32 4 ANNEALED - 9 9 . 9 8 % Au 10.4 r DEFORMED - 9 9 . 9 8 % Au 3 8 . 1 X ANNEALED 9 9 . 5 % A u 1 5 . 0
INTEGRATED FISSION N E U T R O N F L U X , n / crnZ
FIG. 3. Neutron-irradiation damage in impure aluminum and gold.
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CANADI.4N JOURNAL OF PI-IYSICS. VOL. 42. 19C.i
m m . . w m o t-m
N c43 1.
mat- * w 0001 0 Cl1.3W30m- m mu?*. m? w*m ?* t- **=mL-=*m0 *cob0 m e A i m &u? A&& A&A-i-i-iajAaj6GG&&&
m m w 01 3 3 3 3 3 - 01
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SWANSON AND PIERCY: NEUTRON IRRADIATION DAMAGE 1613
(d) The damage rates of pure Cu, Zn, and Cd were increased only slightly by plastic deformation.
The damage rates of some 0.003-in.-diameter Au sanlples were ano~llalously high and showed a saturation effect. Although the size effect was important for these samples, calculations based on Sondheimer's formulas (1962) showed that it could not be responsible for the observed behavior. I t is thought instead that straining of these fine wires was the cause. Consequently, only results for wires of thicliness >0.010 in. will be considered here.
9. Isochro)zal Recovery Curves The isochronal recovery of irradiated A1 and Au is shown in Table I1 and
Figs. 4 and 3. The results were: (a) The stage I (0'-GO0 I<) recovery of A1 and Au was increased by vacancy
doping. X quenched-in vacancy concentration of -2 X 10-5 (Ap,,, = 3.55 x 10-"11m cm) in pure Au increased the fractional recovery below 30" K
Po DAMAGE A p MATERIAL 10'90hm cm lo-'ohm cm
0 ANNEALED 99.999% AI 1.65 0.0450 QUENCHED 99.999% A1 5.36 0 . 0 3 1 1
V DEFORMED 99.999% Al 5.84 0.0356 A DEFORMED 99.999% Al 8.47 0.0435 I
TEMPERATURE ( O K )
FIG. 4. Isochronal recovery of neutron-irradiated aluminum (5-min. intervals)
fro111 0.12 to 0.27 of the total irradiation-induced resistivity increment Ap,
but did not appreciably affect the additional recovery above 30" K (Swanson and Piercy 1963). A corresponding quenched-in vacancy concentration in pure A1 (Ap,,, = 3.76 X ohm cm) did not affect the recovery below 30' K , but increased the recovery by O.lOAp fro111 30' to GO0 K, and by an additional 0.07Ap in the first part of stage I1 (GO0-100" K).
(b) The recovery of 99.999% Al, Cu, and Au below 100" K was slightly enhanced by deformation prior to irradiation. The small enhancement (-0.05 Ap) observed for deformed A1 occurred between 30" and 40" K.
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1614 CANADIAN JOURNAL O F PI-IYSICS. VOL. -42. 19G4
MATERIAL
0 ANNEALED 99.999 % Au 1.31 0.0169 o QUENCHED 99.999% Au 4.56 0.0159
3022 A
> n W
> o 25- U W n
TEMPERATURE ( O K )
FIG. 5. Isochronal rccovery of neutron-irradiated gold (5-~nin. intervals).
(c) Tlic stagc I recovery in A1 was suppressed by thc addition of impurities. The rccovcry below 50" I< was recl~~cecl from 41% for 99.999% A1 to 17% for
- 0.5% 51% This result is siiiiilar to findings by Blewitt et (11. (1957) for neutron-irradiated CLI and Sosin (1963) for electron-irradiatecl 41. In contrast, tlic stage I recovery of ALI was not suppressed b17 0.02-0.5% impurities.
((I) The first part of stage 11 (GO0-100" 1.;) in ALI was considerabl>- enhanced by doping with impurities plus dislocations, but not by impurities, vacancies, or dislocations alone. Comparison with ~ ~ ~ l d o p e c l samples was difficult because they were very easill~ strained by the annealing procedure.
(e) small stage I1 recovery peal; occurred near 85" I< for A1 and was not afiected by prior deformation. 'This recovery stage has also been observed in ~ ~ ~ i i r r a d i a t e d plastically cleformecl samples (Swanson) but does not occur in pure- or impurity-doped A] af ter electron irracliatio~l (Sosill 1063). This stage is attributed to diinterstitial migration, and will be discussed in a forthcoming publication. (Swanson).
DISCUSSION
I. Dnnznge IZates (a) Coinpc~riso7z .iaitl~ Sitlzple l'lzeory T h e measured damage rates of the purest samples are compared with the
simple theory of I<inchin and Pease (1955) in Table 111. A sharp ionization limit of 30 keV was assumecl for Al. Only the lneasured ilssio~l flux of 5.3 x 108 n/cm? sec was considered. Consequently, the absolute calculated clamage rates might be ~~nderestimatecl by as much as 50%, but the relative values for the
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S\VANSOS AND PIERCY: KEUTROS 1RRADI.ATION DAIVI.AGE
TABLE 111
Meas~lred and calculated neutron-irradiation damage rates
Resistivity per atomic percent Damage rates
Threshold energy Frenkel pairs* (lo-?: ohm cm/(n/cm2)) Ed -
Metal (eV) ohm cm) Measured Calculated
"Dier~es: ancl Vineyard (1957). Seeger (19(i9). S i m m o ~ ~ s and Balluffi (1900), Reale (1962). tlucarson aiicl Walker (19LiS). ITlle espectecl damage caused by thermal neutrons has been subtracted (Coltman el 01. 19GS).
different metals (except Al) will be correct according to tlie siinple theory. As is generallj- observed (Billington and Crawford 1 96l), the calculated darnage rates exceed the experimental values by a large factor for face-centered cubic metals.
This discrepancy between experimental and siinple theoretical claillage rates is thought to bc caused largely by spontaneous recovery in damaged regions ("spi1;es") and by energy dissipation in collision sequences. A high-energy primary 1;nocl;-on atom (-60 keV for neutron-irracliated Cu) initiates a cascacle damage process, proclucing a small, highly damaged region because of the relatively short mean free path between atomic collisions (Brinkman 1054; Seegcr 1958). Within this region spontaneous recombination of defects occurs either thermallj~ (Seitz and Koehler 1936) or athermally (Liebfried 1'363; Schilling 1964), and accounts for a large part of the difference between simple theory and experimental results. In addition, the collision chains" and channeled atoms1 which emanate from the depleted zone dissipate muc11 of their energ17 bj- subthreshold collisioi~s (Silsbee 1'357; Gibson ct al . 1'360; Oeil and Robinson 1963; Sigmund 1 '363).
The range and eficiency of defect production of collision chains and chan- neled atoms depend to a large extent on the defect structul-e of the metal lattice. Since our low neutron dose leaves the lattice between depleted zones relatively unclamaged (i.e., the highly disordered regions are widely separated since tlie concentration of primary linock-on atoins is only -10-9, the inter- action of collision chains and channeled atoms with sillall concentratioi~s of doped defects can be investigated. In the following discussion, the effect of doped defects on the threshold energ>, for displacenlent Ed is assumed i~egligible. Spontaneous recovery within the depleted zones is assumed to be relatively unaltered by doped defect concentrations which are small compared with those estimated for the zones (0.2-20%; Schilling 1964; Seeger 1938). Thus, only the effect of doped defects on collision sequences will be considered.
*Collision chains include foc~~sons , crowdions, and replacenlent chains. F o c ~ ~ s o n s ancl cro\\dions are focused collision sequences which respectively do not and do transport matter. Replacenlent chains are de loc~~sed collision sequences which transport matter.
tChannelec1 atoms are high-energy Icnocl<-on atonts (> 1000 eV) \\~hich are prop?gated long distances t h r o ~ ~ g h the open channels between close-paclced rows of atoms (Rob~nson et (21. 19G3; Piercy et al. 19B3).
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1616 CANADIAN JOURKAL OF PI-IYSICS. VOL. 42. 196-4
( b ) Damage Rates of Doped A1 Because of the low ratio of ionic diaineter to interatomic distance in i l l ,
channeling is expected to be more important, and collision chains less import- a n t than in Au. I t is concluded, then, that the enhancement in dainage rate observed for deformed pure A1 (Fig. 2) is caused by dechanneling a t dis- locations, as previously suggested (Swanson et al. 10G2). In support of this view, it has been shown recently (Beeler and Besco) that the calculated damage rate of pure Fe irradiated with fission neutrons is reduced 35% by channeling, so that if channeling were effectively suppressed b y dislocations, a damage-rate enhancement of 54% would result. Soine elementary calcula- tions given in Appendix I1 support this argument in the case of Al, and lead to an average channeled atoll1 range of 3000 A. In view of the low energy of primary knoclt-on atoins in electron-irradiated metals, it is presunled that no channeling occurs and thus that no enhancement in electron damage rate would be caused b y deforination in Al.
Since the neutron damage rate of impurity-doped A1 was the same as that of 09.990y0 A1 (Fig. 3) , it is apparent tha t the substitutional iillpurities present in these sainples (0.35% Fe + Si or <0.5% Mg) do not dechannel atoms. This conclusion is supported by recent ion bombardment experiments (Piercy et ab. to be published) in which channeling effects in Alcan 1s A1 and 99.999y0 A1 were almost identical.
( c ) Damage Rates of Doped il LL In contrast to Al, the ion size of Au is coinparable with the interatomic
distance. This would favor long-range collision chains (Nelson and Thoinpson 1061; Thompson 1063; Seeger 1962) rather than channeling. I t is expected tha t a small fraction of doped defects would alter the propagation of these chains considerably. The %yo enhancement in damage rate observed for deformed pure Xu (Fig. 2) can thus be interpreted in terms of defocusing of collision chains a t the staclting faults between partial dislocations (Leibfried 19GO). By using a simple model, the 50% enhancement is shown in .Appendix I to be compatible with an average collision chain range of 1000-2000 -&.
The observed 1 5 4 0 % enhancement in dainage rate of gold doped with 0.02%-0.5% impurities (Fig. 3) indicates that impurity atoms also defocus collision cllains. Since this enhancement was smaller than that produced by dislocation doping of pure Au, and was not increased further by deforination, it is coilcludecl tha t impurity atoms can "partially" defocus collisioll chains (i.e., the chains focus again so that no extra defects are produced) or "com- pletely" defocus them (i.e., the chains are immediately terminated and thus generally produce extra defects), whereas extended dislocations completely defocus all chains. T h e results indicate tha t the inlpurity cross section for complete defocusing is approximately 17% of tha t for partial defocusing (see Appendix I ) .
T h e dainage rates of Cu, Zn, and Cd were not greatly affected bj- deforina- tion doping (Table I). I t may be concluded tha t the dynamics of irradiation damage in these metals is intermediate between those of Al and X u ; i.e., neither channeled atoms nor collision chains have very long ranges. I t should
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S\VASSON AND PIERCY: XEUTRON IRRADIATION DXMAGE 1617
be noted that the ratios of ionic diameter t o interatomic distance for these metals lie between the extreme cases of A1 and Au.
( a ) Vacancy Doping The enhanced stage I recovery observed for quenched A1 and Xu has been
discussed previously (Swanson and Piercy 1063). A quenched-in vacancy con- centration of -2 X 10-: in Au inore than doubled its recovery below 30" K (from 12% to 27%) (Fig. 5 ) . This enhancement was attributed to the trapping of long-range dynamic crowdions near vacancies, resulting in the formation of extraclose pairs. The range of crowdions was estimated to be -1400 from these results, as is also shown in Appendix I . Since the latter part of stage I was relatively unaffected by the quenched-in vacancies, it was con- cluded tha t randoill migration of iilterstitials or crowdions in this temperature range was not important for neutron-irradiated Au. In XI, however, the observed enhancement of the latter part of stage I by doped vacancies (Fig. 4) was attributed to the annihilation of randomly migrating interstitials or crowd- ions a t the extra vacancies.
( b ) I m p z ~ ~ i t y Doping I t has been found, in agreement with other observers (Sosin 1063), tha t
impurity doping suppressed stage I recovery in Al. Since the damage rate was unchanged by impurity doping, i t must be concluded that this suppression was not a result of dynamic trapping during irradiation, but was caused by trapping of freely migrating interstitials or crowdions during annealing. This conclusion is consistent with the explanation of the A1 quenching results.
The concentration of impurities req~iired for alillost cornplete suppl-ession of stage I (0.5%) is assumed to be approxiinately the saine as the concen- tration of irradiation-induced defects within the depleted zones. Since a much sillaller concentration (-10-9 of quenched-in vacancies increased stage I by O.lOAp, it can be co~lcluded that the17 anniliilated defects which were moving a t some distance from the depleted zones. Thus, a t least 10% of the inter- stitial-type defects produced during neutron irradiation of A1 were outside the highly disordered "spi1;es".
(c ) Dislocation Doping Als was previously observed (Swanson et nl. 1(362), the stage I recover!- of
plastically deformed pure A1 after irradiation was approximately 5glo greater than that of annealed A1 (Fig. 4). The recovery of deformed :lu and Cu showed similar small enl~ancements. This behavior is in marlied contrast to the recovery of electron-irradiated Cu, where a suppression of the latter part of stage I has been reported by i\Ieechan, Sosin, and Brinliman (1960) for cleformecl samples. Their results were explained by assuming that d\,namic crowdiolls were converted to norlnal interstitials a t dislocations, thereby reducing the concentration of "stable" crowdions. Thus, if the interstitials migrated in stage I11 (near 270" I<), whereas crowdions migratecl in the latter part of stage I , a stage I suppression would result. Our apparently contra- dictory results can be interpreted in terms of the high-energy collisioll chains
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1618 CANADIAN JOURNAL O F PEIYSICS. VOL. 42, 1964
produced in Cu and Au by neutron irradiation. As nlentioned previously, high-energy collisioil chains are expected to produce extra Frenlcel pairs when defocused a t dislocations, so tha t more stage I recovery would result. This would not occur after electron irradiation because of the lower energy of the collision chains. The enhancement for deformed A1 is expected because the extra defects produced by dechanneling a t dislocations are inore widely dis- persed than the normal irradiation defects located in depleted zones. Therefore the relative amount of spontaneous recoinbination is reduced. 111 agreement with this interpretation, it was found tha t for all deformed A1 samples a t least '75% of the extra resistivity caused by the deformation anilealed out in stage I.
COKCLUSIOATS
1. The d j namics of neutron irradiation damage varies considerably from metal to metal. Channeling is very important in Al, whereas collision chains are dominant in -%I. Other metals such as Cu, Zn, and Cd appear to be intermediate cases.
2. Collision chains are defocused by substitutional impurity atoms or dis- locations, w l ~ e r e ~ ~ s channeled atoms are defocused only by dislocations.
3. D>.namic crowdioils can be trapped by quenched-in vacancies. 4. The average range of collision chains in neutron-irradiated Au is 1000-
2000 A%. Tllus the interstitial-rich regions are very large and have a defect concentration of only -lo-'.
5 . The average range of channeled atoms in neutron-irradiated XI is -3000 .%.
ti. X iree interstitial-type defect is mobile in stage I in A1 but not in Xu.
XI'I'ESDIS I. CIILCULXTIOS OF COLLISIOS-CH:\IN RL\SGES IK GOLD
1. Ge?zeral I t will be shown that the defocusing of collision chains a t lattice defects
can explain the defect-doping results in Au. Although the effects of doped defects on the displacement production by collision chains is a complicated problem which can perhaps best be solved by computer techniques, some semiquantitative results can be obtained by using a simple model in which the following assumptions are made:
(a) I11 a perfect lattice a chain has a range X which is a function of its initial energy E. In a defect-doped lattice this range is shortened by defocusing a t the various doped defects. (Interaction with irradiation-iilduced defects is neglected for small doses.)
(b) Only collision chains with energy greater than the minimum threshold energy Ed will be considered, since only they transport atoms (Lehmann and Leibfried 1'331; Gibson et al. 1960).
( c ) Impurity atoms can "partially" or "completely" defocus collision chains. The scattering angle for partially defocused chains is small enough tha t the chain will again focus without producing extra defects. The angle for com-
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S~VANSON AND PIERCY: NEUTRON IRRADIATION DA~LIAGE I619
pletely defocused chains is so great that the chain is terminated immediately and extra defects are usually formed.
(d) The energy retained by partially defocused chains is sufficient to produce only one interstitial atom, i.e., their effective range for extra defect production is ended.
( e ) Defocusing of collision chains a t quenched-in vacancies can result in interstitials being deposited near the vacancies, producing extraclose Frenltel pairs. The number of low-energy dynanlic crowdions which are annihilated a t cluenched-in vacancies equals approximately the number of extra defects formed by defocusing of high-energy chains a t vacancies, so that no damage- rate enhancement is observed.
Cf) Extended dislocatio~ls coinpletely defocus all collisio~~ chains. The number of collision chains having initial energy E which are defocused
in a distance dx is
where :V(E, s) is the number of chains having initial energy E which remain a t a distance x.
where u,, u , , and ud are the defocusing cross sections of vacancies, impurity atoms, and dislocations, and n,, nl , and nd are the corresponding defect den- sities. The impurity cross section can be divided into partial and complete defocusing cross sections: (TI = ulp + ulc. Then
lV(E,x)=N(E,O)exp(-unx) f o r x < X , ( 2 )
N(E, m) = 0 for x > X.
The initial energy distribution of chains f (E ) is defined by N(E , 0) = lV0f (E), where No is the initial number of chains produced during an irradiation. (The average range for a chain of given energy E in an imperfect crystal is
(3) X I = [ I - exp (-unX)]/un.
For large unX, X I TV l /un and for small unX, X I -- X.) The number of chains defocused by a particular doped defect in the distance dx is
where U' and n1 refer to the cross section and concentration of the defect. Then the total number of chains having initial energy E which are defocused in the distance X is
if u is independent of the collision chain energy. The total number of defocused chains for all energies is
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1620 ChN.4DI.4N JOURS.4L OF PHYSICS. VOL. 52, 19G4
If all collision chains have the same energy, then
N, = N o (utnt/an) [ l - exp (- unX) 1, (7)
N, IV Noutntx for small unX
and 'V Noutnt/un for large unX
(see Schilling 1964). Thus, X in this equation represents an effective average chain range. If as a first approximation the fraction of collision chains in the interval d E is independent of energy,
and if X(E) = ICE, where K is a constant, then
(8) urnt exp ( - unKE,,,) - exp (- unKE,)
ND=No-- [ l un +- unI~(Emn, - Ed)
If an average X = +X,,,,, is used in equation (7), it is allnost identical with equation (8) for En,,, >> Ed.
Let the number of extra Frenliel defects produced by dND (E, x) defocused chains be d7DE = g(Et)dND, where Et is the chain energy a t x; then the total number of extra Frenkel defects produced by No chains is
where At < X (At IV I i ( E - Ed)), since defocused chains with energy less than Ed cannot produce extra Frenkel pairs.
If the number of Frenliel pairs produced by a defocused collision chain of energy Et is given by the simple theory, g(Et) = Et/2Ed = (X - x)/2KEd. Then if f (E)dE = dE/(Emn, - Ed) and X = K E ,
where P = unK.
2. Vacancy-Doped AZL I t is assumed that the 0.15Ap enhancement in recovery which was observed
below 30" I< in Au containing -2 X 10-5 quenched-in vacancies (Fig. 5) was caused by the defocusing of collision chains a t vacancies, producing extraclose pairs. I t is not known whether trapping of low-energy chains or complete defocusing of high-energy chains is more important. If the ratio of the total number of chains to the total number of stable irradiation-indiiced Frenlcel pairs (or the equivalent) N o / ~ o = 0.75, then 0.2 of these chains inust be defocused a t vacancies.
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S\V.\SSON AND PIERCY: NEUTRON IRRADIATION D.AMAGE
From equation ( i ) ,
ND uvnv - = 0.20 = No
[ l - exp - (u,n, + u,n,) XI. UVG + n~n l
If crl = uv = 1.5 X 10-l4 cn12 (25 atomic areas; i.e., second-nearest neigh- bors of vacancies are displaced enough to defocus collision chains) and n l = $n,, then
This result is sensitive to the values chosen for N o / ~ o and the cross sections. Estimates for Nolrlo vary from 0.2 to 0.75 (Seeger 1958; Schilling 1964). Table IV shows calculated values of X for various values of U, and No/rlo.
TABLE IV
Calculated average collisioll chain ranges in a perfect gold lattice
Damage- rate
Defect, cross enhance- Doped Fraction of sectlon a'n' No - ment X(:f) fro111 defect defect (cm2) (cm-l) 7 o (%I eq. (7)
Vacancies 2 x 1.5 x 10- l~ 1.8 x 10' 0.75 2 X 1 0 - 5 1.5X10-I" 1 . 8 X 1 0 4 0.45 '2x10-5 3 .0X10 -M 3 . 6 X l O L 0.45
Dislocations 3.4 x lo4 1.0 50 %00 7 x 10" 1.0 1050
Impurities 6 X 1.5 X 10-li 5.4 X 1W 1.0 15
3. Dislocation-Doped AIL An average collision-chain range can also be found from the observed 50%
enhancement in damage rate of pure gold which was doped with -10" dis- locations/cm2 (Table I). In this case, some extra defects will be produced by low-energy chains defocusing a t stacking faults, because of the lower value of Ed there (Leibfried 1960). I-Iowever, higher-energy chains are prob- ably more important because their range is greater and because more than one extra Frenkel pair could be produced when they are defocused a t staclcing faults. If there are Cd dislocations per cm', the total dislocation length per cm3 is 2Cd (Schoeck 1962). Let each dislocation be extended b interatomic distances. Then the defocusing probability per cnl is adnd = 2.88 X 10-8Cdb. (The previous factor of 2 is canceled by a factor of 0.5 arising from the two-dimensional nature of the scattering by staclcing faults.) For the dis- location-doped Au, Cd h. 101l/cm' and b h. 12 (Seeger 1955; Suzuki and Barrett 1958; Seeger et al. 1959). Thus adnd = 3.4 X 104/cm.
If No/rlo = 1.0 and each defocused chain produces one extra Frenlcel pair, then ND/No = 0.5 and from equation (7) X = 2300 A, if nl and u1 are the same as before. By using equation (lo), which takes into account ~uultiple Frenlcel pair production, a more reasonable choice of Nolllo = 0.75 leads to the same average range, if Em,, = 400 eV, Ed = 50 eV, and K = lo-' cm/eV.
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1622 C.-1NADI.-\h- JOURNAL O F PHYSICS. VOL. 42, 196.1
4. Inzp~lrity-Doped AIL In order to explain the -15% damage-rate enhancement for -99.98y0
Au and -20% enhancement for deformed -99.98% Au (Table I ) , the impurit>- cross section for complete defocusing, cl,, must be much smaller than that for partial defocusing, G-I,. Since ~ - ~ n , is large, equation (7) becomes N,/lVo = ~ - ' n ' / ~ - n = 0.16 for impurity-doped Au, if iVo/vo = 1.0. Thus, ul, = O . l h l and the impurity cross section for complete defocusing is 17% of that for partial defocusing.
For the ~ 9 9 . 9 8 7 ~ deformed Au,
Putting ulc = 0 . 1 5 ~ ~ and cdnd = 3.4 X 104/c111 as before,
Therefore, if u1 = 1.5 X lO-'.'cm?, n l = 3.6 X 101"cc or G X lo--' fractional concentration of impurities as compared with the value 2 X which was estimatecl from the residual resistivity.
A P P E S D I S 11. DrIWIXGE RATE O F DEFORMED XLUWIIKUNI
I t has been shown by Beeler and Besco that the dissipatioil of energy by cl~annelecl atoms in Fe reduces the neutron-irradiation damage rate by approxi- mately 35CA. In A1 this reduction is expected to be somewl~at higher (Beeler)," perhaps 60%. This energy dissipation will be reduced by shortening the range of channeled atoms, e.g., by introducing dislocations. If the dislocation con- centration is Cd, the number of core dislocation atoms/cc, nCl = 2Cd/D, where D is the interatomic distance. Assuille an effcctive cross section for dechanneling gd = 10-l1 tin? (whic11 is necessarily somewhat arbitrary). Then if the dis- location concentration is 2 X 101n/clll?, the probability of dechanneling U*lZd = 1.-1 x 1O1/~lll.
I f an energy AEo per unit distance is dissipated by a channeled atoin, and a dechanneled atom does not become channeled again, then the total energ)- dissipated by channeled atoms in deformed A1 is Ed,, = NcXIAEo, where N, is the nunlber of cl~anneled atoms and X I is their average range in the deformed lattice (given by equation (3)). If N, is the same for annealed ;ill,t then the ratio of Ed,, to the energy dissipated in annealed A1 is
If the average range of channeled atoms in the perfect lattice T; = 3000 A, Ed,,/Eann = 0.80 and the damage rate is enhanced ~ 3 0 7 ~ by deformation, as observed (Fig. 2).
NOTE ADDED IN PROOF: D. A. Channing of this laboratory has found recently that channeling in Au is affected greatly by temperature, and this might be significant in low-temperature irradiation-damage studies.
*Because of t h e greater number of high-energy primary 1;nocl;-011 a toms in neutron-irra- diatecl Al.
tActually, iV, must b e solnewhat greater in annealed Al, which would increase t h e effect of dislocations on the damage rate.
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SIVXSSON A N D PIERCY: XEUTRON IRRADIATION D:\bI.\GE lG'33
T h e a u t h o r s g ra te fu l ly acl tnowledge helpful c o ~ n ~ n e l l t s by G. 1;. I i i d s o n ,
0. J. C. R u n n a l l s , a n d L. M. H o w e , a n d t h e t echn ica l ass is ta l ice of H. Sc t iu l t z
a n d A. F. Quennevi l le .
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