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Kinetics of radiation-induced segregation in electron-irradiated dilute NiSi and NiGe alloys
82
Journal
of Nuclear
Materials 152 (1988) 82-93 North-Holland, Amsterdam
KINETICS OF RADIATION-INDUCED SEGREGATION IN ELECTRON-IRRADIATED DILUTE NiSi AND Nice ALLOYS A. BARTELS ’ Institut
‘, F. DWORSCHAK
ftir Allgemeine
Metallkunde
2 and M. WEIGERT
und Metallphvsik
’
der R WTH Aachen,
Kopernikusstrasse
14, D-5100
Aachen,
Fed. Rep. Germany 2 Instirut ftir Festkiirperforschung
Received
14 December
Kernforschungsanlage
1987; accepted
27 December
Jiilich, Postfach
1913,
D-5160
Jiilich, Fed. Rep. Germany
1987
The efficiency and the kinetics of the radiation-induced segregation during 3 MeV electron irradiation has been investigated in dilute Nisi and NiGe alloys in the temperature range from 535 K to 735 K. The analysis of the Si and the Ge concentration in solid solution in Ni was performed by damage rate measurements at 86 K in the case of NiSi and 73 K in the case of NiGe. The results indicate a higb efficiency of the radiation-induced Si segregation. Between two and ten Frenkel defects must be produced to transport one Si atom to the sinks, whereas radiation-induced segregation could not be detected in NiGe alloys by this method. The kinetics of the mass transport can be described consistently by the assumption of mobile but thermally unstable Si interstitial complexes. From the evaluation of the experimental data we obtain a value of 0.23 eV for the binding energy of the Si interstitial complex.
1. Introduction The irradiation of alloys with high-energy particles is known to alter the state of solution in numerous alloy systems at a temperature and concentration range where a solid solution is expected to exist [l]. This radiationinduced segregation (RIS) occurs in a temperature range where a pdferential transport of solute atoms via the radiation-induced point defects is possible but where the redistribution of the solute atoms via thermal vacancies is not yet dominant. Normally, undersized solute atoms become enriched at the sinks (e.g. surfaces, grain boundaries, dislocations) for the migrating point defects and oversized solute atoms are depleted near these sinks [2]. Nisi alloys (SV/V- 5.8%) [3] fulfil this rule, whereas NiGe alloys (SV/V = + 14.8%) show a deviation from this rule because they are also enriched at point defect sinks [2,4]. A number of investigations on RIS at NiGe and Nisi have been made by observing the enrichment of the respective solute atoms at special types of sinks. Barbu [4] has found a precipitation of Ni,Ge on dislocation loops and voids in an undersaturated Ni + 6at%Ge alloy after 1 MeV HVEM electron irradiation. Rehn and Okamoto [2] observed the growth of a Ni,Ge surface layer in a Ni + 10 at% Ge alloy by Rutherford
0022-3115/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
backscattering (RBS) during 2 MeV (Y irradiation. The precipitation of y’-Ni,Si at the surface was analyzed by Auger spectroscopy [5] after 3.5 MeV Nit irradiation and by RBS during 2 MeV He+ irradiation [6]. Janghorban and Ardell [7] observed by TEM y’ precipitations at voids, dislocation loops, grain boundaries, stacking faults and twin boundaries after 400 keV proton irradiation. Kesternich et al. [8] have analyzed the Si concentration profile across grain boundaries by energy dispersive X-ray analysis after 7 MeV proton and 28 MeV (Y irradiation. Barbu et al. [9] showed that even a low displacement rate of 5.5 X 10P9 dpa/s during 2 MeV electron irradiation causes a precipitation of y’ in Ni + 4 at% Si. The segregation kinetics has been studied by Averback et al. [lo] during 2 MeV He+ and 2.75 MeV Li+ irradiations using the RBS technique for measuring the growth rate of a Ni,Si surface layer. In the present work the kinetics of RIS in dilute alloys is analyzed during 3 MeV electron irradiation, not by enrichment of solute atoms at a special sink, but by the depletion of the bulk concentration. The 3 MeV electron irradiation produces mainly single Frenkel defects, so that conclusions about the efficiency of RIS can be drawn directly from the experiments because the displacement cross-section needs not be corrected for the reactions of point defects within the cascades, which
B.V.
83
A. Barrels et al. / Kinetics of radiation-induced segregation
are produced by ion or neutron irradiation. The analysis of the Si and Ge concentration in solid solution in Ni is performed by measuring a reciprocal damage rate at a well chosen temperature T,,, in the temperature range of recovery stage II after the segregation irradiation. Bartels et al. [11,12] have shown recently that the Si and Ge concentrations in solid solution can be analyzed by reciprocal damage rates. By systematic variation of the irradiation temperature Tats, electron dose rate ‘p and initial solute atom concentration ct,,, information about the segregation kinetics, the underlying point defect reactions and the transport mechanism can be obtained.
2. Experimental 2. I. Sample material Ni powder with a low carbon content obtained from Johnson-Matthey was melted in a water-cooled Cu crucible in a reducing atmosphere (50% He, 50% Ar). The residual resistivity ratio of this Ni material (RRR = R(293 K)/R(4 K)) varied between 500 and 700. From this pure material Ni + 1 at% Si and Ni + 1 at% Ge base alloys were prepared which were further diluted with pure Ni to obtain the desired solute concentration. The final sample material was analyzed chemically by plasma spectroscopy. The results are listed in table 1. Residual impurities, especially Cu, could be not detected within the limit of sensitivity of plasma spectroscopy. The sample material was cold-rolled to a thickness of 50 pm. After every second rolling step the surface of the
Table 1 Weighted and analyzed concentration atoms
and the residual
Concentration
resistivities
of solute atoms
Weighted
Analyzed
(atppm)
(atppm)
Ni pure 50 Si 100 Si 200 Si 500 Si 50 Ge 100 Ge 200 Ge 500 Ge
54 104 255 480 45 111 246 496
of Si and Ge solute
p,, of the sample PO (nf2 cm)
material
material was cleaned by etching in a mixture of 50% HNO, and 50% HF. Then four-pole resistance samples were punched out from these foils. After cleaning and etching the samples were annealed for 4 h at 800 ’ C in vacuum better than 1O-6 mbar in the presence of a zirconium shield for gettering oxygen. The solute content after the preparation procedure was controlled by residual resistivity measurements. The data given in table 1 increase linearly with the analyzed Si and Ge concentration, respectively, indicating that the solute atoms are in solid solution. The slopes are about 30% higher than those of previous measurements [13]. This difference cannot be caused by residual impurities in our samples because the starting material was very pure (500 < RRR < 700) and residual impurities could not be detected by plasma spectroscopy. A possible explanation for this effect could be clustering effects of Si and Ge because previously more higher concentrated alloys (about 1 at%) have been investigated [13].
2.2. Irradiation
All irradiations were performed at a 3 MeV electron Van de Graaff accelerator. The details of the cryostat and the beam steering system were described by v. Lensa [14]. The maximum beam current density amounted to 930 PA/cm2 corresponding to an electron dose rate ‘p = 5.8 X 10i5/cm2 s. From the electron beam the most homogeneous part passed through an aperture of 1.0 X 1.8 mm2 to irradiate two four-pole resistivity samples (0.6 X 0.15 mm*). The deviation from homogeneity of the beam current density was less than 5%. The sample temperature was obtained by measuring the electrical resistivity at the beginning of each irradiation. All resistivity measurements for the damage rates were performed at 4.2 K by standard four-pole potentiometric methods. The sensitivity of these resistivity measurements was better than lo-” D cm.
2.3. Analysis 11*2 36k4 68k4 131*4 205&4 27*2 56k2 84k2 196+4
and resistivity measurements
reciprocal
of the concentration
damage
of solute
atoms
by
rates
Damage rate measurements in the temperature range of recovery stage II are a well established method to examine the interactions between migrating interstitial atoms and solute atoms in dilute alloys. Considering the competition of the migrating interstitials between trapping at solute atoms and the recombination with immo-
A. Barr& et 01. / Ktnettcs
a4
bile vacancies one obtains the equation [15]:
for the damage
ofradration-induced segregatron
rate dp/d@
3. Experiments
and results
Preliminary
-
=
1
od” ( I - LX, 1 P: with the trapping
Q =
term
+I’~.
(la)
Here I$” is the displacement cross-section for freely migrating interstitials, f,,, is the fraction of Frenkel pairs recombining correlatedly, plF is the resistivity contribution of the Frenkel defects (vacancies and trapped interstitials). r, and r, are the capture radii of spherical capture volumes of solute atom traps and vacancies, respectively, for migrating interstitials, ct is the concentration of solute atoms acting as traps and Ap = p:c, is the radiation-induced residual resistivity increase. Recently Bartels et al. [11,12] have analyzed the reciprocal damage rates in Nisi alloys at 86 K and in NiGe alloys at 73 K by eq. (1). In both cases the reciprocal damage rates do not increase linearly with Ap as suggested by the simple model (eq. (l)), but they show a negative curvature as a function of Ap. This behaviour can be understood quantitatively by an increase of the trapping term Q due to r, growing with the number of interstitials trapped per solute atom. From experiments on well annealed Nisi and NiGe alloys where the solute content c, is known, an unique dependence of the normalized reciprocal damage rates from the ratio cd/c, (cd = c, = Ap/ptF) could be deduced [11,12]. Therefore a reduction of the Si or Ge concentration in solid solution due to RIS should be detectable quantitatively by a decrease of the trapping term Q of the reciprocal damage rate. The preceding segregation irradiation could not only cause RIS, but may also introduce vacancies into the sample. In this case eq. (1) is modified to
damage
3.1. Influence damage
of the pre-irradiation
on
the reciprocal
rate
As shown in section 2.3 already a small concentration of vacancies would falsify the concentration analy-
6070-
1
drn(l -L,>P
work has shown that annealing of radiain Nisi alloys reduces the residual resistivity of the alloys to a value lower than before irradiation, indicating a segregation of Si atoms [ll]. Therefore, one could expect that the residual resistivity of the alloys can be used to analyze the state of segregation. In fig. 1 we have plotted the normalized residual resistivity decrease after a segregation irradiation at T,,, = 535 K. The maximum decrease of the resistivity was about 20%. An analysis of the solute concentration by damage rate measurements following the same segregation irradiation shows a much larger decrease of Q, i.e. the concentration of Si atoms in solution. Thus we must conclude that the residual resistivities cannot fully characterize the state of segregation. Obviously, the segregated Si atoms still contribute partially to the residual resistivity. A similar discrepancy between residual resistivities and trapping terms Q was already observed after RIS experiments in CuBe alloys [16]. Therefore, only reciprocal damage rates will be used to analyze the RIS. tion
i
(2)
with c,” the surplus vacancy concentration. A concentration analysis via reciprocal damage rates is therefore not unambiguous in the presence of large surplus vacancy concentrations. The most obvious effect would be an enhancement of the reciprocal initial damage rates Hence the experimental conditions have (dp,‘d@3&. to be chosen so that there occurs no distortion of the reciprocal damage rates (see section 3.1).
80.
900
Fig. (full ties 255,
5
10
15
20
25
30 0 110’9Crri21
1. Relative decrease of the trapping terms (Q. - Q)/QO) circles) and of the Si contribution to the residual resistivi( p0 - p)/p, (open circles) of Nisi alloys containing 104, and 480 atppm Si as a function of the irradiation dose during the segregation irradiations at TRls = 535 K.
A. Barrels et al. / Kinetics of radiation-induced segregation
85
described by eq. (3). In particular, no systematic deviation of the reciprocal initial damage rate to higher values is observed in the pre-irradiated samples. This means that vacancies or vacancy clusters do not disturb the reciprocal damage rates after the segregation irradiation. 3.2. Segregation
[ 0
,
, , 100
,
,
200
-,-__,_ 300
,
I
400 C, latppml
Fig. 2. Reciprocal initial damage rates of well annealed (+) and pre-irradiated (0, 0) Nisi samples as a function of the analyzed Si concentration in solid solution ct. The circles indicate the reciprocal initial damage rates from the data plotted in figs. 3 and 4. The solid line was calculated according to eq. (3). The dashed lines give the 10% deviation from the calculated line corresponding to the error in dose measurement.
sis by reciprocal damage rates due to an enhanced reciprocal initial damage rate. Therefore, one has to make sure that a surplus concentration of vacancies does not exist after the segregation irradiation. Due to this condition the analysis of the segregation irradiations at temperatures where vacancies are immobile, i.e. below that of recovery stage III (Tn, = 500 K) [ll], is not possible. Besides single vacancies also vacancy clusters could influence the reciprocal damage rates. In order to assess the effect of the pre-irradiation on the initial damage rate and hence on the evaluation of c,, all reciprocal initial damage rates of NiSi alloys measured at 86 K after the pre-irradiation are plotted in fig. 2 as a function of the analyzed Si concentration. The reciprocal initial damage rates depend on the Si concentration via the factor f,,, (see eq. (l)), which is a function of the Si concentration cr [17]:
f corr = texp(
-(
rP - rv)(4~r,c,)l’*).
(3)
Here rP is the average displacement distance. The solid line in fig. 2 was calculated according to eq. (3) using the parameters r, = 3.5 a, (ac = lattice constant), r /rv = 1.5, rt = 1.05 rv and udrn ptF = 1.68 x 1O-26 s2 cm’, as obtained from the analysis of recovery and damage rate data [18]. Within an error bar of 10% - corresponding to the error in the measurement of the initial damage rates - the reciprocal initial damage rates can be
experiments
on NiSi alloys
Ni + 104 atppm Si, Ni + 255 atppm Si and Ni + 480 atppm Si alloys were pre-irradiated with 3 MeV electrons at 535 K, 630 K, 735 K to different doses. The standard electron dose rate + amounted to QI= 1.2 x 1015/cm2 s (A 1.6 x lOma dpa/s). At 535 K an additional series of pre-irradiations with an increased dose rate q = 5.8 x 10’5/cm2 s (A 7.5 x lo-* dpa/s) was performed. After annealing for lh at 523 K damage rates were measured at 86 K to determine the Si concentration in solid solution. For an example in fig. 3 the reciprocal damage rates measured in Ni + 480 atppm Si samples after the preirradiation at Tars = 535 K with the standard dose rate are plotted as a function of the radiation-induced resistivity increase with the dose of the pre-irradiation as a parameter. The reciprocal damage rates in fig. 3 are normalized to the respective reciprocal initial damage rates (dp/d@),,‘,, which are summarized in fig. 2. With increasing dose of the pre-irradiation the slope of the normalized reciprocal damage rates increases, corresponding to a decreasing trapping term Q due to a decrease of the concentration of Si atoms in solid solution. The quantitative evaluation of the remaining Si concentration c, acting as traps for the interstitials during the analysis irradiation at 86 K is performed by scaling the Ap axis of fig. 3 with the respective trap concentration. It has been shown before that the damage rate data of well annealed Nisi alloys, when plotted as normalized reciprocal damage rate against the ratio cd/c1 (c,, = A p/p:), follow one curve independent,,of the concentration of Si [ll]. Thus the Si concentration in solid solution of a pre-irradiated sample can be determined by fitting the damage rate data to this master curve. The fitted damage rate data of fig. 3 are shown in fig. 4. The solid line in fig. 4 represents the master curve obtained from well annealed dilute Nisi alloys [ll]. The resulting Si concentrations as a function of pre-irradiation dose are plotted in figs. 5-7. For each series of experiments a systematic decrease of the Si concentration is found as a function of the dose. The error of the evaluation of c, can be estimated to be + 3% of the analyzed trap concentration. However,_ the
A. Barrels et al. / K/netics ofrudirrtion-lnducedsegregatton
86
TE,-= 535K C,,=480atppm
0 110'9cm~2] 8.0
+'
14
13
\
1.2
doses Qc from experiments with different initial SI concentrations c,,, are nearly equal at the same temperature, corresponding to parallel lines in a semi-logarithmic plot (see fig. 5). the initial segregation rate BY comparing with the production rate of freely migrat(dc,/d@),,, ing Frenkel defects (dc,/d@ = udm(l -f,,,,)) we can define a measure for the efficiency of the Si segregation (dc,/dc,). With a production cross-section of u,“(l f,,,, ) = 13 x 10 II4 cm2 [11,18] we obtain at 535 K a maximum efficiency of segregation of dc,/dc, = 0.71 for the Ni + 480 atppm Si sample, which means only 1.4 Frenkel defects are necessary to segregate one Si atom. With decreasing initial Si concentration the segregation is less effective. The temperature dependence is shown in figs. 6 and 7. In Ni + 104 Si atppm samples as well as in Ni + 255 atppm Si samples a decrease of the efficiency is found
11
1.0
I
0
20
40
60
1
80
100
Ap InRcml Fig. 3. Normalized reciprocal damage Ni+480 atppm Si after pre-irradiations
rates at Tir, = 86 K of at Tars = 535 K. The pre-irradiation doses are given in units of 10’9/cm2 as parame ters.
data points in figs. 5-7 scatter partly by a larger amount. This must be attributed to the error in dose measurement (+ 10%) and to the fact that for each data point a new sample had to be used. Therefore, inevitable influences like different residual impurities in the samples, small fluctuation of the initial Si concentration and different sink densities will increase the error of the analyzed Si concentration. The trap concentrations do not decrease linearly with the dose as found in earlier investigations on CuBe [16], but the decrease can be described quite well by an exponential behavior: c, = c,~ exp( - @/Gc). Therefore, in figs. 5-7 the analyzed Si concentrations c, are plotted semi-logarithmically against the dose @. The lines in figs. 5-7 are obtained from fitting linear regressions to the data. The results of the fits, the characteristic dose @= and initial segregation rate are listed in table 2. The characteristic (dc,/d@)o-+,,,
.N-
I
g lb-
,” 13-
12T,,,=535K C tO
0
02
0.4
06
=480atppm
J 08
10 cjIc,
Fig. 4. Example for the evaluation of the Si concentration in solid solution c,. The data of fig. 3 are plotted versus the ratio cd/c,. The defect concentration cd is given by cd = Ap/p: (p’, = 7.1 x 10m4 Q cm). The trap concentration c, is varied so that the data fit to the master curve (solid line), obtained from experiments on well annealed NiSi alloys.
A. Bartels et al. / Kinetics
of radiation-induced segregation
87
/
\I
80 30
t
20’ 0
’
Y i
-b
(L
< 2
6
4
8
60’ 0
IO
2
4
8
6
IO
cp il0”cm~l
Fig. 5. Semi-logarithmic plot of the Si concentration in solid solution (c,) as a function of the pre-irradiation dose @ at T RIS -- 535 K for two different electron dose rates ‘p (open symbols: cp=1.2X 1015 cm* s, full symbols: cp= 5.8~ 1015/ cm* s, crs = 480 atppm (Cl),255 atppm (o), 104 atppm (0)).
with increasing temperature. The closed symbols in fig. 5 show segregation experiments under an enhanced electron flux density. Within the scattering of the data no i&l uence of the dose rate can be detected by increasing the dose rate by a factor of 5. This result is a typical feature of the case of predominant sink absorption, whereas in the case of predominant recombination of defects a dependence on the square root of the dose rate ‘p is expected [19]. For two samples (Ni + 104 atppm Si and Ni + 255 atppm Si) a concentration analysis was performed after a dose up to 3 X 1020/cm2 at Tnts = 535 K. The results of these experiments are induded in fig. 1. An evaluation of the respective reciprocal damage rates yields 17
Fig. 6. ~~-loga~th~c plot of the Si concentration insolid solution (c,) versus dose @ of Nisi samples with c,e .= 255 atppm for three different pre-irradiation temperatures Fk,s.
atppm and 25 atppm of residual Si concentration. These two samples with about 90% of Si segregated toQ$sinks were annealed at 735 K for 4 h and analyzed again by damage rate measurements at 86 K to test the thermal stability of the Si segregation. The measurement yielded the same residual Si concentrations indicating that a resolution by thermal vacancies can be neglected at this temperature. After a further annealing at a higher temperature (4 h, 773 K), however, the subsequent analysis irradiation yielded an increase of the Si concentration (53 atppm Si for the Ni + 104 atppm Si and 57 atppm Si for the Ni + 255 atppm Si sample). Obviously an annealing at 773 K causes a thermal back diffusion of the segregated Si atoms. 3.3. Segregation
ex~~rirne~t~
on N&e
aIioy.9
In fig. 8 the normalized reciprocal damage rates of two NiGe alloys measured at 73 K are plotted as a
Table 2 Results of the segregation experiments obtained by linear regressions of the data in figs. 5-7. Tais = pr~i~adiation temperature, cr,, = fitted initial Si concentration, @== characteristic dose (c( = ctOexp( Q/Q?)), dc, /d@ 14,_ o = initial segregation rate, d cd /de, = number of Frenkel defects to segregate one Si atom, dc,/dc,, = efficiency of RIS Si cont. (atppm)
TRIS (R)
CCC! (atppm)
@C (10’P/cm2)
dc,/d@l,-, (barn)
dc,/dc,
Efficiency dc,/dc,,
104 104 104
535 630 735
104.4 104.0 103.5
5.65 8.64 11.6
1.8 1.2 1.0
7.2 10.8 13.6
0.138 0.093 0.073
255 255 255
535 630 136
249.0 258.0 259.9
6.70 8.46 11.9
4.1 3.0 2.2
3.1 4.3 5.9
0.322 0.233 0.169
480
535
479.7
5.27
9.1
1.4
0.714
A. Bartels et al. / Kinetm
ofradmtron-induced
segreptmn
trapping term, which lies just outside the error limits for Ni + 111 atppm Ge. Under the assumption that this effect is real, the RIS causes a decrease of the Ge concentration by 6 atppm, from which we can estimate an upper limit for the segregation rate in NiGe dc,/d@ < 0.05 barn. From a comparison with the cross-section for the production of freely migrating Frenkel pairs uz (1 - f,,,) = 13 barn [11,18] we obtain that more than 260 Frenkel pairs are necessary to segregate one Ge atom.
20/-ll 0
2
i
6
8 10 0 110’9cmZ1
7. Semi-logarithmic plot of the Si concentration in solid solution (c,) versus dose @ of Nisi samples with c,,, = 104 atppm for three different pre-irradiation temperatures Ta,s.
function of Ap. The reciprocal damage rates before and after the pre-irradiation to the maximum dose of 1.2 x 10” cm-* at 530 K show a small decrease of the
0
I
0 q
o q +.
Ni IllatppmGe N1496atppmGe well annealed pre-Irradiated to 12*1020cfli*
1.4-
1.3-
1.2-
I 0
20
40
60
80
A0 [nRcml Fig. 8. Normalized reciprocal damage rates of well annealed and preirradiated NiGe samples.
4. Discussion The most obvious result of the segregation experiments described in section 3 is the high efficiency of the RIS in Nisi alloys. The data listed in table 2 show that at 535 K between two and ten defects must be produced to transport one Si atom to the sinks. On the other hand RIS in NiGe alloys could not be detected with our method. From the sensitivity of this method it can be estimated that RIS must be at least two orders of magnitude less effective in NiGe than in Nisi at 535 K. Obviously different transport mechanisms have to be considered for RIS in these alloys. For the segregation in Nisi we follow the conceptions developed for RIS in CuBe. Since Si is an undersized atom in the Ni matrix (SV/V= - 5.8% [3]) the formation of Si interstitial complexes in the form of mixed dumb-bells seems possible [20]. This mixed dumb-bell interstitial can transport the Si atoms by two different mechanisms: the “looping” mechanism [21] and the “caging and rotation” mechanism [20]. Hence, whenever the efficiency of solute transport is high one tends to describe this transport by the interstitial mechanism. Reviews of the geometry of interstitial-solute complexes and the transport mechanisms are given by Robrock [22] and Wiedersich et al. [23]. According to calculations of Dederichs et al. [20] the ratio of the migration energy to the dissociation energy of the mixed dumb-bell depends strongly on the value of the volume size misfit of the solute atom. Mixed dumb-bells formed with solute atoms with a large volume size misfit are expected to be more stable than those formed with solutes with a small misfit. Due to this theoretical model, segregation experiments with CuBe (SV/V= -26.4%) have been interpreted by stable migrating mixed dumb-bells [6]. In the case of Nisi (61//V- 5.8%) the calculations predict considerable smaller dissociation energies, so that the existence of a stable migrating mixed dumb-bell is questionable. We
89
A. Bartels et al. / Kinetics o~radiat~o~-inducedsegregation will examine here how a dissociation of the Si interstitial complexes will affect the segregation kinetics. Two different morphologies of solute segregation have been discussed in the literature [l], a homogeneous segregation all over the material and an inhomogeneous segregation at the point defect sinks (dislocations, grain boundaries, surfaces). TEM investigations of irradiated Nisi alloys with a Si concentration below 6 at% exhibit only inhomogeneous segregation or precipitation at sinks [24]. Only Janghorban and Ardell [7] have found a homogeneous Si precipitation at Si concentrations above 6 at%. Thus we can assume that in the present experiments on dilute Nisi alloys the Si atoms will segregate at point defect sinks only. As we observe the Si depletion of the bulk material we cannot distinguished between the efficiency of the different point defect sinks. Hence, in the following model calculations the sum of all point defect sinks will be considered by the product of a uniformly distributed sink concentration c, and the reaction radius rs. In an earlier investigation on radiation-induced segregation in CuBe alloys Bartels et al. [16] were able to describe the segregation kinetics by a rate equation model on the basis of a Be transport via Be interstiti~ complexes. They considered the production of vacancies and self-interstitials, the formation of migrating solute atom interstitial complexes which are formed by trapping of the self-interstitials at the solute atoms, the recombination of self-interstitials and complexes with vacancies and the ~ni~lation of all ~grating defects at point defect sinks. The absorption of complexes by the sinks causes an enrichment of the solute atom concentration at these sinks and thus reduces the bulk concentration of solute atoms. This model predicts a linear decrease of the solute concentration in the bulk with increasing dose, no dependence of the segregation rate from the initial solute concentration and an increasing efficiency of segregation with increasing temperature up to the saturation value of dc,/dcd = 1. At a first glance this model cannot explain the results of the Nisi experiments. If we allow for a thermal dissociation of the solute interstitial complexes into self-interstitials and immobile solute atoms as discussed before and expand the model accordingly, the Nisi results can be described consistently. The following set of rate equations describes the defect reactions mentioned above:
E, = K, - K;,c;c, - KCvc,c, - Kvsc,c,, (4)
the the and the
Ki,=4n(Di+DV)rV, K,,=47r(D,+
D,)r:,
Ki, = 4aDirC are the reaction constants interstitials and complexes formation of complexes;
for the recombination of with vacancies and for the
K,, = 4rD,r,, are the reaction constants for the sink annihilation the three defect types (X = v, i, c);
of
D, = D,, exp( - E;/kT) are the diffusion (x = v, i, c); r-1 = r-1 0
exd
coefficients
of the three defect
types
-~&,/~~)
is the inverse lifetime of the complexes; r,, r:, r,, ri,, rv,, rC. are the reaction radii for recombination of interstitials and complexes with vacancies, trapping of interstitials at solute atoms, sink absorption of interstitials, vacancies and complexes; Ki,,,, is the dissociation energy of the complexes; ~
‘c, ,
f, = K,,c,c; - K,,c,c, - r - ‘c, , C,= -K CSccs E.
Ei = K, - Kivc,ci - K;,c,q - Ki,c,ci + T- ‘c,,
C, = K,,c,c; - Kcvc,c, - K,,c,c, - r- ‘c,.
The decrease of concentration of solute atoms in bulk due to segregation is given by 6, = - Kcscscc. The parameters in eqs. (4) are: ci, c,, cc, c, are concentrations of interstitials, vacancies, complexes solute atoms, respectively, in the bulk; K, = a+ is production rate for freely migrating Frenkel pairs;
(5)
For the solution of eq. (5) we assume stationary conditions for the interstitial and complex concentrations (2, = C, = 0), which are justified on the condition that the time for diffusion of the slowest defect to the sinks
90
A. Burt&
is negligibly small compared Then we obtain
with the irradiation
time. + NI + 104atppm l NI+ 255atppm m NI+ 480atppm
with @ = r+~tand after substitution we obtain: dc L= d@
et al. / Kinetrcs of radratron-induced segregatron
of the rate constants
a l+A+B’
(6)
with A=‘”
_J
I
1.3
r. c
14
15
17
18 1000/T 1K-'I
rtct
Fig. 9. Arrhenius plot of the characteristic doses QC evaluated
and
from the linear regression
Expression A in eq. (6) is much smaller than one, since the sink absorption strength is small compared with the trapping efficiency ( rlscs < rtc,). The pre-exponential factor of B is predominantly determined by (r,c,)-’ and therefore is always large compared with one. For a further discussion the value of the exponential factor must be considered. In the case of a stable solute interstitial complex, (E& - Ek) is so large that B becomes negligibly small and the segregation efficiency dc,/dcd = 1. Only if (E& - Ez) is sufficiently small so that B > 1 is it possible to approximate eq. (6) by: !!!L_ - -const d@
16
ct exp{ (E&
- Ek)/kT}.
(7)
The above mode1 can describe the exponential dependence of the solute segregation from the irradiation dose CD found in the NiSi experiments (figs. 5-7). Moreover, the decrease of the segregation rate with increasing temperatures can be understood within this model and is given by the difference (E,& - Eh). In fig. 9 the values of the characteristic doses CD=(see table 2) are shown in an Arrhenius plot. The slope yields (E&, - Ez) = (0.14 f 0.02) eV. In order to evaluate the general case, when the dominant sink absorption is not valid, a numerical integration of eqs. (4) was performed using the GEAR package [25]. Only the following parameters are known: the migration energy of the vacancy EG = 1.04 eV [26], the migration energy of the Ni self-interstitial E,!,, = 0.15 eV (271, the cross-section for the production of freely migrating Frenkel pairs u = 13 X 10-24/cm2 [11,18] and the difference between the dissociation and migration energies of the complexes (.I?&, - Ek) = 0.14 eV (see
lines in figs. 5-7.
fig. 9). If the interpretation of the recovery in stage IIa at 105 K in NiSi is correct, we can estimate by scaling Ek with the peak temperature: Es = 0.24 eV and hence EC d,sn= 0.38 eV. Plausible values were assumed for: rv = ~0’= 5 x ri = r: = 3a,, with a, the lattice parameter, s-1, 70-i=5x10’3 s-1. 10’4 s-1 ) v,c=v;=5x10’3 The sink strengths were estimated so that for the lowest irradiation temperature 530 K and for the highest dose rate of 5.8 X 10”/cm2 s the case of dominant sink absorption is achieved: rs’cs = r,‘c, = rscc, = 2 x IO-“U;~. From the numerical solution of eqs. (4) the efficiency of segregation dc,/dcd (= dc,/o d@) was evaluated. Since the efficiency depends on the instantaneous solute concentration c, (see eq. (6)) the initial efficiency was used for a comparison with the (dc,/dcd),+, experimental data *. In fig. 10 these initial efficiencies at a dose rate of 1.2 x 10”/cm2 s are plotted as a function of the reciprocal temperature. The solid lines represent the efficiencies calculated with the parameters given above, the dashed line gives the efficiency when the complexes are stable, i.e. when E& > Ek. At high temperatures (T> 500 K) all defect concentrations are limited by the absorption at point defect sinks, i.e. the case of dominant sink absorption. If the complexes were stable then a constant efficiency dc,/dc, = 1 is expected. Because of the thermal dissociation of the complexes the efficiency is reduced and above 500 K the efficiency decreases with the temperature. The decrease of the efficiencies can be described quite well by an Arrhenius plot with (E& - Ek) as activation energy, according to eq. (7). At temperatures
* It should be remarked that the initial efficiency must be determined when the system achieves stationary conditions.
A. Barrels et al. / Kinetics of radiation-induced
I’ 0°2
a
14
j
16
I
18
1
c
20
22
”
/
24
”
1
2.6 28 1000/T [I?1
Fig. 10. Initial efficiency of the Si segregation (dc,/dcd),, 0 as a function of the reciprocal temperature for different initial Si concentrations ctO. The solid to eqs. (4) with (E.& - E&) = calculated for stable complexes points are taken from the initial 7.
lines are calculated according 0.14 eV. The dashed line is ((E&, - E&) + co). The data part of the lines in figs. 6 and
below 500 K the efficiencies decrease with decreasing temperature, because then higher vacancy equilibrium concentrations can be generated, so that the recombination rate exceeds the absorption rate at sinks. As can be seen in fig. 10 the measured initial efficiencies for Ni + 104 atppm Si and Ni + 255 atppm Si can be described very well by this model. Unfortunately the theoretical curves cannot be compared with experimental data at temperatures below 500 K because vacancies, which are produced in the pre-irradiation, are immobile below recovery stage III, i.e. 500 K. As has been discussed in section 3.1, small vacancy concentrations can already falsify damage rate measurements (see section 3.1). In addition, the calculated temperature dependence of the efficiency for a very high Si concentration (2000 atppm) is shown in fig. 10. This curve demonstrates that the efficiencies approach the efficiency curve for stable complexes when the Si concentration is increased. For high solute concentrations an evaluation of activation energies becomes meaningless. At high solute concentrations the probability for an interstitial to become trapped after the dissociation of a complex is so high that practically no single interstitials react with sinks. This is probably the reason, why investigations on Nisi alloys containing several percent Si cannot detect the thermal decay of Si interstitial complexes [lo].
segregation
91
An important result of the complete numerical solution is that a decrease of the efficiency with increasing temperature can be found only in the temperature range where the defect reactions are governed by sink annihilation. In the case of dominant recombination the efficiency increases with the temperature in spite of the thermal dissociation of the complexes. This result is a further confirmation for dominant sink annihilation during the present irradiation experiments. The results of this work and those on RIS in CuBe show the different segregation kinetics depending on the volume size misfit. In the case of CuBe with a large negative volume size misfit of SV/V= - 26% a rather stable Be interstitial complex must be assumed to interpret the segregation experiments. Bartels et al. [16] have estimated that (E&, - Ez) > 0.42 eV. In the case of Nisi with a smaller but still negative size misfit of S V/ V = - 5.8% the evaluation of experimental data gave (E&, - Ek) = 0.14 eV. In case of NiGe with a positive volume size misfit (6V/V= + 14.8%) the very low efficiency of RIS does not give an indication for a transport via interstitial complexes. This is in accordance with resistivity recovery data which yield a main recovery peak at 115K and which was interpreted by the dissociation of Ge interstitial complexes [12]. Below 115K no peak was observed which could be assigned to the migration of the complex. On the other hand, an enrichment of Ge at point defect sinks was observed [2,4] after irradiation to very high doses. Consequently RIS in NiGe must be caused by other transport mechanisms (i.e. inverse Kirkendall effect or migrating vacancy complexes) which have a low efficiency of RIS. For comparison with theory we have to obtain further data on the binding or the migrating energy of the complex. Bartels et al. [ll] conclude that the recovery stage at 105 K is caused by the migration of the Si interstitial complex. By scaling the migration energy with the peak temperature we obtain Ek = 0.24 eV. The binding energy Ei of the complex is given by Ei = (E&, - Ek) + E& - EL. With E,!,, = 0.15 eV [27] we then obtain EE = 0.23 eV. This value agrees exceptionally well with Eg = 0.25 eV calculated according to Dederichs et al. [20] if the ratio r,,/R, of the potential shift r. divided by the equilibrium ratio of Ni is multiplied by a factor of about six to obtain the volume size misfit [28]. For Nisi also other migrating energies of the complex have been proposed depending on the type of experiment. Averback and Ehrhart [29] conclude that Ek = E,!,,, Okamoto et al. [30] conclude that Ek = 0.6 eV (however, this interpretation has been altered recently [22]). Binding energies calculated with these val-
ues of Ek are either 0.14 eV or 0.53 eV. Both values differ by a factor of about two from the predictions of Dederichs et al. [20]. All binding energies discussed so far are much lower than the value Et = 0.90 eV calculated by Gupta [31]. The migrating energy of the complex by the caging rotation mechanism is calculated according to Dederichs et al. to be Ez = 5Ek = 0.75 eV in the case of Nisi. This value is considerably higher than the measured value E,“1= 0.24 eV. Whereas the RIS in CuBe could be described well by the migrating of a mixed dumb-bell due to a rotation and caging mechanism, other transport mechanisms (e.g. looping) should be taken into account to interpret the small migration energy of the complex in Nisi.
[27] the migration energy of the Ni self-interstitial, we obtain E’ = 0.23 eV. (10) This value ii in good agreement with theoretical calculations [20.28].
Acknowledgements This work was supported by schungsgemeinschaft. The authors edge the experimental assistance of de Graaff laboratory, Aachen during ations. We thank Prof. K. Lticke support.
the Deutsche Forgratefully acknowlthe staff of the Van the electron irradifor his continuous
References 5. Conclusions work we have determined the kinetics of RIS in dilute Nisi and NiGe alloys during 3 MeV electron irradiation. The Si and Ge concentration in solid solution in Ni was obtained by damage rate measurements at a well chosen temperature in the temperature range of recovery stage II after the segregation irradiation. From these results we can conclude: (1) RIS is very efficient in Nisi alloys. At 535 K between two and ten Frenkel defects must be produced to segregate one Si atom. (2) With decreasing initial Si concentration the segregation becomes less effective. (3) The efficiency decreases with increasing temperature. (4) No influence of the dose rate on RIS could be detected. (5) RIS is very inefficient in NiGe alloys. At 530 K at least 260 Frenkel defects must be produced to segregate one Ge atom. (6) A theoretical model which describes the kinetics of RIS in Nisi by mobile but thermally unstable Si interstitial complexes is presented. (7) Fitting the data to this model we obtain for the difference between dissociation and migration energy of the Si interstitial complex (E& - Ek) = (0.14 * 0.02) eV. that the recovery stage at 105 K is (8) Assuming caused by the migration of the Si interstitial complex [ll] and scaling the migration energy with this temperature we obtain Ek = 0.24 eV and hence E& = 0.38 eV. (9) The binding energy EE of the complex is given by EE = (E,& - Ek) + Ek - E,!,,. With Em = 0.15 eV
[l] G. Margin, R. Cauvin and A. Barbu, in: Phase Transfor-
In the present
[2]
[3] [4]
[5] [6] [7] [S] [9] [lo] [ll] [12] [13]
[14] [15] [16] [17]
mations during Irradiation, Ed. F.V. Nolfi (Applied Science Publishers, London, 1983) p. 47. L.E. Rehn and P.R. Okamoto, in: Phase Transformations during irradiation, Ed. F.V. Nolfi (Applied Science Publishers, London, 1983) p. 247. H.W. King, J. Mater. Sci. 1 (1966) 79. A. Barbu, in: Comportment Sous Irradiation des Materiaux Metalliques et des Coeurs des Reacteurs Rapides, Eds. J. Poirier and J.M. Dupouy (Commissariat a I’Energie Atomique, Gif-Sur-Yvette, 1979) p. 69. L.E. Rehn, P.R. Okamoto, D.I. Potter and W. Wiedersich, J. Nucl. Mater. 74 (1978) 242. P.R. Okamoto, L.E. Rehn and R.S. Averback, J. Nucl. Mater. 108 & 109 (1982) 319. K. Janghorban and A.J. Ardell, J. Nucl. Mater. 85 & 86 (1979) 719. W. Kestemich, N.H. Packan and H. Schroeder, in: Proc. XIth Int. Congr. on Electron Microscopy, Kyoto (1986). A. Barbu, G. Martin and A. Chamberod, J. Appl. Phys. 51 (1980) 6192. R.S. Averback, L.E. Rehn, W. Wagner, H. Wiedersich and P.R. Okamoto, Phys. Rev. B28 (1983) 3100. A. Bartels, F. Dworschak and M. Weigert, J. Nucl. Mater. 137 (1986) 130. A. Bartels, F. Dworschak and M. Weigert, J. Nucl. Mater. 149 (1987) 160. Landolt-Bornstein, New Series III/lSa, Eds. K.H. Hellwege and K.L. Olsen (Springer-Verlag, Berlin, Heidelberg, New York, 1982). W.V. Lensa, Berichte der Kernforschungsanlage Jiilich, Jtil-1426 (1977). A. Kraut, F. Dworschak and H. Wollenberger, Phys. Status Solidi B44 (1971) 805. A. Bartels, F. Dworschak, H.-P. Meurer, C. Abromeit and H. Wollenberger, J. Nucl. Mater. 83 (1979) 24. K. Schroeder and W. Heidrich, Phys. Lett. 34A (1973) 315.
A. Bariels et al. / Kinetics of radiation-induced [18] M. Weigert,
Thesis RWTH
Aachen
(1987).
[19] R. Sizmann, J. Nucl. Mater. 69 & 70 (1978) 386. 1201 P.H. Dederichs, C. Lehmann, H.R. Schober, A. Scholz and R. Zeller, J. Nucl. Mater. 69 & 70 (1978) 176. [21] R.A. Johnson and N.Q. Lam, Phys. Rev. B13 (1976) 4364. (221 K.-H. Robrock, Mater. Sci. Forum 15-18 (1987) 537. [23] H. Wiedersich and N.Q. Lam, in: Phase Transformations during Irradiation, Ed. F.V. Nolfi (Applied Science Publishers, London, 1983) p. 1. [24] A.J. Ardell and J. Janghorban, in: Phase Transformations during Irradiation, Ed. F.V. Nolfi (Applied Science PubIishers, London, 1983) p. 291. (251 A. Hindmarsch, Lawrence Livermore Lab. Rep. UCID30001 (1974).
segregation
93
[26] SK. Khanna and K. Sonnenberg, Radiat. Eff. 59 (1981) 91. [27] J. Knoll, U. Dedek and W. Schilling, J. Phys. F4 (1974) 1095. [28] P.H. Dederichs, private communication. [29] R.S. Averback, and P. Ehrhart, J. Phys. F14 (1984) 1347. [30] P.R. Okamoto, L.E. Rehn, R.S., Averback, K.-H. Robrock and H. Wiedersich, in: Proc. Yamada Conf. V, Eds. J.I. Takamura, M. Doyama and M. Kiritani (University of Tokyo Press, 1982) p. 946. [31] R.P. Gupta, Phys. Rev. B22 (1980) 5900.
Journal
of Nuclear
Materials 152 (1988) 82-93 North-Holland, Amsterdam
KINETICS OF RADIATION-INDUCED SEGREGATION IN ELECTRON-IRRADIATED DILUTE NiSi AND Nice ALLOYS A. BARTELS ’ Institut
‘, F. DWORSCHAK
ftir Allgemeine
Metallkunde
2 and M. WEIGERT
und Metallphvsik
’
der R WTH Aachen,
Kopernikusstrasse
14, D-5100
Aachen,
Fed. Rep. Germany 2 Instirut ftir Festkiirperforschung
Received
14 December
Kernforschungsanlage
1987; accepted
27 December
Jiilich, Postfach
1913,
D-5160
Jiilich, Fed. Rep. Germany
1987
The efficiency and the kinetics of the radiation-induced segregation during 3 MeV electron irradiation has been investigated in dilute Nisi and NiGe alloys in the temperature range from 535 K to 735 K. The analysis of the Si and the Ge concentration in solid solution in Ni was performed by damage rate measurements at 86 K in the case of NiSi and 73 K in the case of NiGe. The results indicate a higb efficiency of the radiation-induced Si segregation. Between two and ten Frenkel defects must be produced to transport one Si atom to the sinks, whereas radiation-induced segregation could not be detected in NiGe alloys by this method. The kinetics of the mass transport can be described consistently by the assumption of mobile but thermally unstable Si interstitial complexes. From the evaluation of the experimental data we obtain a value of 0.23 eV for the binding energy of the Si interstitial complex.
1. Introduction The irradiation of alloys with high-energy particles is known to alter the state of solution in numerous alloy systems at a temperature and concentration range where a solid solution is expected to exist [l]. This radiationinduced segregation (RIS) occurs in a temperature range where a pdferential transport of solute atoms via the radiation-induced point defects is possible but where the redistribution of the solute atoms via thermal vacancies is not yet dominant. Normally, undersized solute atoms become enriched at the sinks (e.g. surfaces, grain boundaries, dislocations) for the migrating point defects and oversized solute atoms are depleted near these sinks [2]. Nisi alloys (SV/V- 5.8%) [3] fulfil this rule, whereas NiGe alloys (SV/V = + 14.8%) show a deviation from this rule because they are also enriched at point defect sinks [2,4]. A number of investigations on RIS at NiGe and Nisi have been made by observing the enrichment of the respective solute atoms at special types of sinks. Barbu [4] has found a precipitation of Ni,Ge on dislocation loops and voids in an undersaturated Ni + 6at%Ge alloy after 1 MeV HVEM electron irradiation. Rehn and Okamoto [2] observed the growth of a Ni,Ge surface layer in a Ni + 10 at% Ge alloy by Rutherford
0022-3115/88/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
backscattering (RBS) during 2 MeV (Y irradiation. The precipitation of y’-Ni,Si at the surface was analyzed by Auger spectroscopy [5] after 3.5 MeV Nit irradiation and by RBS during 2 MeV He+ irradiation [6]. Janghorban and Ardell [7] observed by TEM y’ precipitations at voids, dislocation loops, grain boundaries, stacking faults and twin boundaries after 400 keV proton irradiation. Kesternich et al. [8] have analyzed the Si concentration profile across grain boundaries by energy dispersive X-ray analysis after 7 MeV proton and 28 MeV (Y irradiation. Barbu et al. [9] showed that even a low displacement rate of 5.5 X 10P9 dpa/s during 2 MeV electron irradiation causes a precipitation of y’ in Ni + 4 at% Si. The segregation kinetics has been studied by Averback et al. [lo] during 2 MeV He+ and 2.75 MeV Li+ irradiations using the RBS technique for measuring the growth rate of a Ni,Si surface layer. In the present work the kinetics of RIS in dilute alloys is analyzed during 3 MeV electron irradiation, not by enrichment of solute atoms at a special sink, but by the depletion of the bulk concentration. The 3 MeV electron irradiation produces mainly single Frenkel defects, so that conclusions about the efficiency of RIS can be drawn directly from the experiments because the displacement cross-section needs not be corrected for the reactions of point defects within the cascades, which
B.V.
83
A. Barrels et al. / Kinetics of radiation-induced segregation
are produced by ion or neutron irradiation. The analysis of the Si and Ge concentration in solid solution in Ni is performed by measuring a reciprocal damage rate at a well chosen temperature T,,, in the temperature range of recovery stage II after the segregation irradiation. Bartels et al. [11,12] have shown recently that the Si and Ge concentrations in solid solution can be analyzed by reciprocal damage rates. By systematic variation of the irradiation temperature Tats, electron dose rate ‘p and initial solute atom concentration ct,,, information about the segregation kinetics, the underlying point defect reactions and the transport mechanism can be obtained.
2. Experimental 2. I. Sample material Ni powder with a low carbon content obtained from Johnson-Matthey was melted in a water-cooled Cu crucible in a reducing atmosphere (50% He, 50% Ar). The residual resistivity ratio of this Ni material (RRR = R(293 K)/R(4 K)) varied between 500 and 700. From this pure material Ni + 1 at% Si and Ni + 1 at% Ge base alloys were prepared which were further diluted with pure Ni to obtain the desired solute concentration. The final sample material was analyzed chemically by plasma spectroscopy. The results are listed in table 1. Residual impurities, especially Cu, could be not detected within the limit of sensitivity of plasma spectroscopy. The sample material was cold-rolled to a thickness of 50 pm. After every second rolling step the surface of the
Table 1 Weighted and analyzed concentration atoms
and the residual
Concentration
resistivities
of solute atoms
Weighted
Analyzed
(atppm)
(atppm)
Ni pure 50 Si 100 Si 200 Si 500 Si 50 Ge 100 Ge 200 Ge 500 Ge
54 104 255 480 45 111 246 496
of Si and Ge solute
p,, of the sample PO (nf2 cm)
material
material was cleaned by etching in a mixture of 50% HNO, and 50% HF. Then four-pole resistance samples were punched out from these foils. After cleaning and etching the samples were annealed for 4 h at 800 ’ C in vacuum better than 1O-6 mbar in the presence of a zirconium shield for gettering oxygen. The solute content after the preparation procedure was controlled by residual resistivity measurements. The data given in table 1 increase linearly with the analyzed Si and Ge concentration, respectively, indicating that the solute atoms are in solid solution. The slopes are about 30% higher than those of previous measurements [13]. This difference cannot be caused by residual impurities in our samples because the starting material was very pure (500 < RRR < 700) and residual impurities could not be detected by plasma spectroscopy. A possible explanation for this effect could be clustering effects of Si and Ge because previously more higher concentrated alloys (about 1 at%) have been investigated [13].
2.2. Irradiation
All irradiations were performed at a 3 MeV electron Van de Graaff accelerator. The details of the cryostat and the beam steering system were described by v. Lensa [14]. The maximum beam current density amounted to 930 PA/cm2 corresponding to an electron dose rate ‘p = 5.8 X 10i5/cm2 s. From the electron beam the most homogeneous part passed through an aperture of 1.0 X 1.8 mm2 to irradiate two four-pole resistivity samples (0.6 X 0.15 mm*). The deviation from homogeneity of the beam current density was less than 5%. The sample temperature was obtained by measuring the electrical resistivity at the beginning of each irradiation. All resistivity measurements for the damage rates were performed at 4.2 K by standard four-pole potentiometric methods. The sensitivity of these resistivity measurements was better than lo-” D cm.
2.3. Analysis 11*2 36k4 68k4 131*4 205&4 27*2 56k2 84k2 196+4
and resistivity measurements
reciprocal
of the concentration
damage
of solute
atoms
by
rates
Damage rate measurements in the temperature range of recovery stage II are a well established method to examine the interactions between migrating interstitial atoms and solute atoms in dilute alloys. Considering the competition of the migrating interstitials between trapping at solute atoms and the recombination with immo-
A. Barr& et 01. / Ktnettcs
a4
bile vacancies one obtains the equation [15]:
for the damage
ofradration-induced segregatron
rate dp/d@
3. Experiments
and results
Preliminary
-
=
1
od” ( I - LX, 1 P: with the trapping
Q =
term
+I’~.
(la)
Here I$” is the displacement cross-section for freely migrating interstitials, f,,, is the fraction of Frenkel pairs recombining correlatedly, plF is the resistivity contribution of the Frenkel defects (vacancies and trapped interstitials). r, and r, are the capture radii of spherical capture volumes of solute atom traps and vacancies, respectively, for migrating interstitials, ct is the concentration of solute atoms acting as traps and Ap = p:c, is the radiation-induced residual resistivity increase. Recently Bartels et al. [11,12] have analyzed the reciprocal damage rates in Nisi alloys at 86 K and in NiGe alloys at 73 K by eq. (1). In both cases the reciprocal damage rates do not increase linearly with Ap as suggested by the simple model (eq. (l)), but they show a negative curvature as a function of Ap. This behaviour can be understood quantitatively by an increase of the trapping term Q due to r, growing with the number of interstitials trapped per solute atom. From experiments on well annealed Nisi and NiGe alloys where the solute content c, is known, an unique dependence of the normalized reciprocal damage rates from the ratio cd/c, (cd = c, = Ap/ptF) could be deduced [11,12]. Therefore a reduction of the Si or Ge concentration in solid solution due to RIS should be detectable quantitatively by a decrease of the trapping term Q of the reciprocal damage rate. The preceding segregation irradiation could not only cause RIS, but may also introduce vacancies into the sample. In this case eq. (1) is modified to
damage
3.1. Influence damage
of the pre-irradiation
on
the reciprocal
rate
As shown in section 2.3 already a small concentration of vacancies would falsify the concentration analy-
6070-
1
drn(l -L,>P
work has shown that annealing of radiain Nisi alloys reduces the residual resistivity of the alloys to a value lower than before irradiation, indicating a segregation of Si atoms [ll]. Therefore, one could expect that the residual resistivity of the alloys can be used to analyze the state of segregation. In fig. 1 we have plotted the normalized residual resistivity decrease after a segregation irradiation at T,,, = 535 K. The maximum decrease of the resistivity was about 20%. An analysis of the solute concentration by damage rate measurements following the same segregation irradiation shows a much larger decrease of Q, i.e. the concentration of Si atoms in solution. Thus we must conclude that the residual resistivities cannot fully characterize the state of segregation. Obviously, the segregated Si atoms still contribute partially to the residual resistivity. A similar discrepancy between residual resistivities and trapping terms Q was already observed after RIS experiments in CuBe alloys [16]. Therefore, only reciprocal damage rates will be used to analyze the RIS. tion
i
(2)
with c,” the surplus vacancy concentration. A concentration analysis via reciprocal damage rates is therefore not unambiguous in the presence of large surplus vacancy concentrations. The most obvious effect would be an enhancement of the reciprocal initial damage rates Hence the experimental conditions have (dp,‘d@3&. to be chosen so that there occurs no distortion of the reciprocal damage rates (see section 3.1).
80.
900
Fig. (full ties 255,
5
10
15
20
25
30 0 110’9Crri21
1. Relative decrease of the trapping terms (Q. - Q)/QO) circles) and of the Si contribution to the residual resistivi( p0 - p)/p, (open circles) of Nisi alloys containing 104, and 480 atppm Si as a function of the irradiation dose during the segregation irradiations at TRls = 535 K.
A. Barrels et al. / Kinetics of radiation-induced segregation
85
described by eq. (3). In particular, no systematic deviation of the reciprocal initial damage rate to higher values is observed in the pre-irradiated samples. This means that vacancies or vacancy clusters do not disturb the reciprocal damage rates after the segregation irradiation. 3.2. Segregation
[ 0
,
, , 100
,
,
200
-,-__,_ 300
,
I
400 C, latppml
Fig. 2. Reciprocal initial damage rates of well annealed (+) and pre-irradiated (0, 0) Nisi samples as a function of the analyzed Si concentration in solid solution ct. The circles indicate the reciprocal initial damage rates from the data plotted in figs. 3 and 4. The solid line was calculated according to eq. (3). The dashed lines give the 10% deviation from the calculated line corresponding to the error in dose measurement.
sis by reciprocal damage rates due to an enhanced reciprocal initial damage rate. Therefore, one has to make sure that a surplus concentration of vacancies does not exist after the segregation irradiation. Due to this condition the analysis of the segregation irradiations at temperatures where vacancies are immobile, i.e. below that of recovery stage III (Tn, = 500 K) [ll], is not possible. Besides single vacancies also vacancy clusters could influence the reciprocal damage rates. In order to assess the effect of the pre-irradiation on the initial damage rate and hence on the evaluation of c,, all reciprocal initial damage rates of NiSi alloys measured at 86 K after the pre-irradiation are plotted in fig. 2 as a function of the analyzed Si concentration. The reciprocal initial damage rates depend on the Si concentration via the factor f,,, (see eq. (l)), which is a function of the Si concentration cr [17]:
f corr = texp(
-(
rP - rv)(4~r,c,)l’*).
(3)
Here rP is the average displacement distance. The solid line in fig. 2 was calculated according to eq. (3) using the parameters r, = 3.5 a, (ac = lattice constant), r /rv = 1.5, rt = 1.05 rv and udrn ptF = 1.68 x 1O-26 s2 cm’, as obtained from the analysis of recovery and damage rate data [18]. Within an error bar of 10% - corresponding to the error in the measurement of the initial damage rates - the reciprocal initial damage rates can be
experiments
on NiSi alloys
Ni + 104 atppm Si, Ni + 255 atppm Si and Ni + 480 atppm Si alloys were pre-irradiated with 3 MeV electrons at 535 K, 630 K, 735 K to different doses. The standard electron dose rate + amounted to QI= 1.2 x 1015/cm2 s (A 1.6 x lOma dpa/s). At 535 K an additional series of pre-irradiations with an increased dose rate q = 5.8 x 10’5/cm2 s (A 7.5 x lo-* dpa/s) was performed. After annealing for lh at 523 K damage rates were measured at 86 K to determine the Si concentration in solid solution. For an example in fig. 3 the reciprocal damage rates measured in Ni + 480 atppm Si samples after the preirradiation at Tars = 535 K with the standard dose rate are plotted as a function of the radiation-induced resistivity increase with the dose of the pre-irradiation as a parameter. The reciprocal damage rates in fig. 3 are normalized to the respective reciprocal initial damage rates (dp/d@),,‘,, which are summarized in fig. 2. With increasing dose of the pre-irradiation the slope of the normalized reciprocal damage rates increases, corresponding to a decreasing trapping term Q due to a decrease of the concentration of Si atoms in solid solution. The quantitative evaluation of the remaining Si concentration c, acting as traps for the interstitials during the analysis irradiation at 86 K is performed by scaling the Ap axis of fig. 3 with the respective trap concentration. It has been shown before that the damage rate data of well annealed Nisi alloys, when plotted as normalized reciprocal damage rate against the ratio cd/c1 (c,, = A p/p:), follow one curve independent,,of the concentration of Si [ll]. Thus the Si concentration in solid solution of a pre-irradiated sample can be determined by fitting the damage rate data to this master curve. The fitted damage rate data of fig. 3 are shown in fig. 4. The solid line in fig. 4 represents the master curve obtained from well annealed dilute Nisi alloys [ll]. The resulting Si concentrations as a function of pre-irradiation dose are plotted in figs. 5-7. For each series of experiments a systematic decrease of the Si concentration is found as a function of the dose. The error of the evaluation of c, can be estimated to be + 3% of the analyzed trap concentration. However,_ the
A. Barrels et al. / K/netics ofrudirrtion-lnducedsegregatton
86
TE,-= 535K C,,=480atppm
0 110'9cm~2] 8.0
+'
14
13
\
1.2
doses Qc from experiments with different initial SI concentrations c,,, are nearly equal at the same temperature, corresponding to parallel lines in a semi-logarithmic plot (see fig. 5). the initial segregation rate BY comparing with the production rate of freely migrat(dc,/d@),,, ing Frenkel defects (dc,/d@ = udm(l -f,,,,)) we can define a measure for the efficiency of the Si segregation (dc,/dc,). With a production cross-section of u,“(l f,,,, ) = 13 x 10 II4 cm2 [11,18] we obtain at 535 K a maximum efficiency of segregation of dc,/dc, = 0.71 for the Ni + 480 atppm Si sample, which means only 1.4 Frenkel defects are necessary to segregate one Si atom. With decreasing initial Si concentration the segregation is less effective. The temperature dependence is shown in figs. 6 and 7. In Ni + 104 Si atppm samples as well as in Ni + 255 atppm Si samples a decrease of the efficiency is found
11
1.0
I
0
20
40
60
1
80
100
Ap InRcml Fig. 3. Normalized reciprocal damage Ni+480 atppm Si after pre-irradiations
rates at Tir, = 86 K of at Tars = 535 K. The pre-irradiation doses are given in units of 10’9/cm2 as parame ters.
data points in figs. 5-7 scatter partly by a larger amount. This must be attributed to the error in dose measurement (+ 10%) and to the fact that for each data point a new sample had to be used. Therefore, inevitable influences like different residual impurities in the samples, small fluctuation of the initial Si concentration and different sink densities will increase the error of the analyzed Si concentration. The trap concentrations do not decrease linearly with the dose as found in earlier investigations on CuBe [16], but the decrease can be described quite well by an exponential behavior: c, = c,~ exp( - @/Gc). Therefore, in figs. 5-7 the analyzed Si concentrations c, are plotted semi-logarithmically against the dose @. The lines in figs. 5-7 are obtained from fitting linear regressions to the data. The results of the fits, the characteristic dose @= and initial segregation rate are listed in table 2. The characteristic (dc,/d@)o-+,,,
.N-
I
g lb-
,” 13-
12T,,,=535K C tO
0
02
0.4
06
=480atppm
J 08
10 cjIc,
Fig. 4. Example for the evaluation of the Si concentration in solid solution c,. The data of fig. 3 are plotted versus the ratio cd/c,. The defect concentration cd is given by cd = Ap/p: (p’, = 7.1 x 10m4 Q cm). The trap concentration c, is varied so that the data fit to the master curve (solid line), obtained from experiments on well annealed NiSi alloys.
A. Bartels et al. / Kinetics
of radiation-induced segregation
87
/
\I
80 30
t
20’ 0
’
Y i
-b
(L
< 2
6
4
8
60’ 0
IO
2
4
8
6
IO
cp il0”cm~l
Fig. 5. Semi-logarithmic plot of the Si concentration in solid solution (c,) as a function of the pre-irradiation dose @ at T RIS -- 535 K for two different electron dose rates ‘p (open symbols: cp=1.2X 1015 cm* s, full symbols: cp= 5.8~ 1015/ cm* s, crs = 480 atppm (Cl),255 atppm (o), 104 atppm (0)).
with increasing temperature. The closed symbols in fig. 5 show segregation experiments under an enhanced electron flux density. Within the scattering of the data no i&l uence of the dose rate can be detected by increasing the dose rate by a factor of 5. This result is a typical feature of the case of predominant sink absorption, whereas in the case of predominant recombination of defects a dependence on the square root of the dose rate ‘p is expected [19]. For two samples (Ni + 104 atppm Si and Ni + 255 atppm Si) a concentration analysis was performed after a dose up to 3 X 1020/cm2 at Tnts = 535 K. The results of these experiments are induded in fig. 1. An evaluation of the respective reciprocal damage rates yields 17
Fig. 6. ~~-loga~th~c plot of the Si concentration insolid solution (c,) versus dose @ of Nisi samples with c,e .= 255 atppm for three different pre-irradiation temperatures Fk,s.
atppm and 25 atppm of residual Si concentration. These two samples with about 90% of Si segregated toQ$sinks were annealed at 735 K for 4 h and analyzed again by damage rate measurements at 86 K to test the thermal stability of the Si segregation. The measurement yielded the same residual Si concentrations indicating that a resolution by thermal vacancies can be neglected at this temperature. After a further annealing at a higher temperature (4 h, 773 K), however, the subsequent analysis irradiation yielded an increase of the Si concentration (53 atppm Si for the Ni + 104 atppm Si and 57 atppm Si for the Ni + 255 atppm Si sample). Obviously an annealing at 773 K causes a thermal back diffusion of the segregated Si atoms. 3.3. Segregation
ex~~rirne~t~
on N&e
aIioy.9
In fig. 8 the normalized reciprocal damage rates of two NiGe alloys measured at 73 K are plotted as a
Table 2 Results of the segregation experiments obtained by linear regressions of the data in figs. 5-7. Tais = pr~i~adiation temperature, cr,, = fitted initial Si concentration, @== characteristic dose (c( = ctOexp( Q/Q?)), dc, /d@ 14,_ o = initial segregation rate, d cd /de, = number of Frenkel defects to segregate one Si atom, dc,/dc,, = efficiency of RIS Si cont. (atppm)
TRIS (R)
CCC! (atppm)
@C (10’P/cm2)
dc,/d@l,-, (barn)
dc,/dc,
Efficiency dc,/dc,,
104 104 104
535 630 735
104.4 104.0 103.5
5.65 8.64 11.6
1.8 1.2 1.0
7.2 10.8 13.6
0.138 0.093 0.073
255 255 255
535 630 136
249.0 258.0 259.9
6.70 8.46 11.9
4.1 3.0 2.2
3.1 4.3 5.9
0.322 0.233 0.169
480
535
479.7
5.27
9.1
1.4
0.714
A. Bartels et al. / Kinetm
ofradmtron-induced
segreptmn
trapping term, which lies just outside the error limits for Ni + 111 atppm Ge. Under the assumption that this effect is real, the RIS causes a decrease of the Ge concentration by 6 atppm, from which we can estimate an upper limit for the segregation rate in NiGe dc,/d@ < 0.05 barn. From a comparison with the cross-section for the production of freely migrating Frenkel pairs uz (1 - f,,,) = 13 barn [11,18] we obtain that more than 260 Frenkel pairs are necessary to segregate one Ge atom.
20/-ll 0
2
i
6
8 10 0 110’9cmZ1
7. Semi-logarithmic plot of the Si concentration in solid solution (c,) versus dose @ of Nisi samples with c,,, = 104 atppm for three different pre-irradiation temperatures Ta,s.
function of Ap. The reciprocal damage rates before and after the pre-irradiation to the maximum dose of 1.2 x 10” cm-* at 530 K show a small decrease of the
0
I
0 q
o q +.
Ni IllatppmGe N1496atppmGe well annealed pre-Irradiated to 12*1020cfli*
1.4-
1.3-
1.2-
I 0
20
40
60
80
A0 [nRcml Fig. 8. Normalized reciprocal damage rates of well annealed and preirradiated NiGe samples.
4. Discussion The most obvious result of the segregation experiments described in section 3 is the high efficiency of the RIS in Nisi alloys. The data listed in table 2 show that at 535 K between two and ten defects must be produced to transport one Si atom to the sinks. On the other hand RIS in NiGe alloys could not be detected with our method. From the sensitivity of this method it can be estimated that RIS must be at least two orders of magnitude less effective in NiGe than in Nisi at 535 K. Obviously different transport mechanisms have to be considered for RIS in these alloys. For the segregation in Nisi we follow the conceptions developed for RIS in CuBe. Since Si is an undersized atom in the Ni matrix (SV/V= - 5.8% [3]) the formation of Si interstitial complexes in the form of mixed dumb-bells seems possible [20]. This mixed dumb-bell interstitial can transport the Si atoms by two different mechanisms: the “looping” mechanism [21] and the “caging and rotation” mechanism [20]. Hence, whenever the efficiency of solute transport is high one tends to describe this transport by the interstitial mechanism. Reviews of the geometry of interstitial-solute complexes and the transport mechanisms are given by Robrock [22] and Wiedersich et al. [23]. According to calculations of Dederichs et al. [20] the ratio of the migration energy to the dissociation energy of the mixed dumb-bell depends strongly on the value of the volume size misfit of the solute atom. Mixed dumb-bells formed with solute atoms with a large volume size misfit are expected to be more stable than those formed with solutes with a small misfit. Due to this theoretical model, segregation experiments with CuBe (SV/V= -26.4%) have been interpreted by stable migrating mixed dumb-bells [6]. In the case of Nisi (61//V- 5.8%) the calculations predict considerable smaller dissociation energies, so that the existence of a stable migrating mixed dumb-bell is questionable. We
89
A. Bartels et al. / Kinetics o~radiat~o~-inducedsegregation will examine here how a dissociation of the Si interstitial complexes will affect the segregation kinetics. Two different morphologies of solute segregation have been discussed in the literature [l], a homogeneous segregation all over the material and an inhomogeneous segregation at the point defect sinks (dislocations, grain boundaries, surfaces). TEM investigations of irradiated Nisi alloys with a Si concentration below 6 at% exhibit only inhomogeneous segregation or precipitation at sinks [24]. Only Janghorban and Ardell [7] have found a homogeneous Si precipitation at Si concentrations above 6 at%. Thus we can assume that in the present experiments on dilute Nisi alloys the Si atoms will segregate at point defect sinks only. As we observe the Si depletion of the bulk material we cannot distinguished between the efficiency of the different point defect sinks. Hence, in the following model calculations the sum of all point defect sinks will be considered by the product of a uniformly distributed sink concentration c, and the reaction radius rs. In an earlier investigation on radiation-induced segregation in CuBe alloys Bartels et al. [16] were able to describe the segregation kinetics by a rate equation model on the basis of a Be transport via Be interstiti~ complexes. They considered the production of vacancies and self-interstitials, the formation of migrating solute atom interstitial complexes which are formed by trapping of the self-interstitials at the solute atoms, the recombination of self-interstitials and complexes with vacancies and the ~ni~lation of all ~grating defects at point defect sinks. The absorption of complexes by the sinks causes an enrichment of the solute atom concentration at these sinks and thus reduces the bulk concentration of solute atoms. This model predicts a linear decrease of the solute concentration in the bulk with increasing dose, no dependence of the segregation rate from the initial solute concentration and an increasing efficiency of segregation with increasing temperature up to the saturation value of dc,/dcd = 1. At a first glance this model cannot explain the results of the Nisi experiments. If we allow for a thermal dissociation of the solute interstitial complexes into self-interstitials and immobile solute atoms as discussed before and expand the model accordingly, the Nisi results can be described consistently. The following set of rate equations describes the defect reactions mentioned above:
E, = K, - K;,c;c, - KCvc,c, - Kvsc,c,, (4)
the the and the
Ki,=4n(Di+DV)rV, K,,=47r(D,+
D,)r:,
Ki, = 4aDirC are the reaction constants interstitials and complexes formation of complexes;
for the recombination of with vacancies and for the
K,, = 4rD,r,, are the reaction constants for the sink annihilation the three defect types (X = v, i, c);
of
D, = D,, exp( - E;/kT) are the diffusion (x = v, i, c); r-1 = r-1 0
exd
coefficients
of the three defect
types
-~&,/~~)
is the inverse lifetime of the complexes; r,, r:, r,, ri,, rv,, rC. are the reaction radii for recombination of interstitials and complexes with vacancies, trapping of interstitials at solute atoms, sink absorption of interstitials, vacancies and complexes; Ki,,,, is the dissociation energy of the complexes; ~
‘c, ,
f, = K,,c,c; - K,,c,c, - r - ‘c, , C,= -K CSccs E.
Ei = K, - Kivc,ci - K;,c,q - Ki,c,ci + T- ‘c,,
C, = K,,c,c; - Kcvc,c, - K,,c,c, - r- ‘c,.
The decrease of concentration of solute atoms in bulk due to segregation is given by 6, = - Kcscscc. The parameters in eqs. (4) are: ci, c,, cc, c, are concentrations of interstitials, vacancies, complexes solute atoms, respectively, in the bulk; K, = a+ is production rate for freely migrating Frenkel pairs;
(5)
For the solution of eq. (5) we assume stationary conditions for the interstitial and complex concentrations (2, = C, = 0), which are justified on the condition that the time for diffusion of the slowest defect to the sinks
90
A. Burt&
is negligibly small compared Then we obtain
with the irradiation
time. + NI + 104atppm l NI+ 255atppm m NI+ 480atppm
with @ = r+~tand after substitution we obtain: dc L= d@
et al. / Kinetrcs of radratron-induced segregatron
of the rate constants
a l+A+B’
(6)
with A=‘”
_J
I
1.3
r. c
14
15
17
18 1000/T 1K-'I
rtct
Fig. 9. Arrhenius plot of the characteristic doses QC evaluated
and
from the linear regression
Expression A in eq. (6) is much smaller than one, since the sink absorption strength is small compared with the trapping efficiency ( rlscs < rtc,). The pre-exponential factor of B is predominantly determined by (r,c,)-’ and therefore is always large compared with one. For a further discussion the value of the exponential factor must be considered. In the case of a stable solute interstitial complex, (E& - Ek) is so large that B becomes negligibly small and the segregation efficiency dc,/dcd = 1. Only if (E& - Ez) is sufficiently small so that B > 1 is it possible to approximate eq. (6) by: !!!L_ - -const d@
16
ct exp{ (E&
- Ek)/kT}.
(7)
The above mode1 can describe the exponential dependence of the solute segregation from the irradiation dose CD found in the NiSi experiments (figs. 5-7). Moreover, the decrease of the segregation rate with increasing temperatures can be understood within this model and is given by the difference (E,& - Eh). In fig. 9 the values of the characteristic doses CD=(see table 2) are shown in an Arrhenius plot. The slope yields (E&, - Ez) = (0.14 f 0.02) eV. In order to evaluate the general case, when the dominant sink absorption is not valid, a numerical integration of eqs. (4) was performed using the GEAR package [25]. Only the following parameters are known: the migration energy of the vacancy EG = 1.04 eV [26], the migration energy of the Ni self-interstitial E,!,, = 0.15 eV (271, the cross-section for the production of freely migrating Frenkel pairs u = 13 X 10-24/cm2 [11,18] and the difference between the dissociation and migration energies of the complexes (.I?&, - Ek) = 0.14 eV (see
lines in figs. 5-7.
fig. 9). If the interpretation of the recovery in stage IIa at 105 K in NiSi is correct, we can estimate by scaling Ek with the peak temperature: Es = 0.24 eV and hence EC d,sn= 0.38 eV. Plausible values were assumed for: rv = ~0’= 5 x ri = r: = 3a,, with a, the lattice parameter, s-1, 70-i=5x10’3 s-1. 10’4 s-1 ) v,c=v;=5x10’3 The sink strengths were estimated so that for the lowest irradiation temperature 530 K and for the highest dose rate of 5.8 X 10”/cm2 s the case of dominant sink absorption is achieved: rs’cs = r,‘c, = rscc, = 2 x IO-“U;~. From the numerical solution of eqs. (4) the efficiency of segregation dc,/dcd (= dc,/o d@) was evaluated. Since the efficiency depends on the instantaneous solute concentration c, (see eq. (6)) the initial efficiency was used for a comparison with the (dc,/dcd),+, experimental data *. In fig. 10 these initial efficiencies at a dose rate of 1.2 x 10”/cm2 s are plotted as a function of the reciprocal temperature. The solid lines represent the efficiencies calculated with the parameters given above, the dashed line gives the efficiency when the complexes are stable, i.e. when E& > Ek. At high temperatures (T> 500 K) all defect concentrations are limited by the absorption at point defect sinks, i.e. the case of dominant sink absorption. If the complexes were stable then a constant efficiency dc,/dc, = 1 is expected. Because of the thermal dissociation of the complexes the efficiency is reduced and above 500 K the efficiency decreases with the temperature. The decrease of the efficiencies can be described quite well by an Arrhenius plot with (E& - Ek) as activation energy, according to eq. (7). At temperatures
* It should be remarked that the initial efficiency must be determined when the system achieves stationary conditions.
A. Barrels et al. / Kinetics of radiation-induced
I’ 0°2
a
14
j
16
I
18
1
c
20
22
”
/
24
”
1
2.6 28 1000/T [I?1
Fig. 10. Initial efficiency of the Si segregation (dc,/dcd),, 0 as a function of the reciprocal temperature for different initial Si concentrations ctO. The solid to eqs. (4) with (E.& - E&) = calculated for stable complexes points are taken from the initial 7.
lines are calculated according 0.14 eV. The dashed line is ((E&, - E&) + co). The data part of the lines in figs. 6 and
below 500 K the efficiencies decrease with decreasing temperature, because then higher vacancy equilibrium concentrations can be generated, so that the recombination rate exceeds the absorption rate at sinks. As can be seen in fig. 10 the measured initial efficiencies for Ni + 104 atppm Si and Ni + 255 atppm Si can be described very well by this model. Unfortunately the theoretical curves cannot be compared with experimental data at temperatures below 500 K because vacancies, which are produced in the pre-irradiation, are immobile below recovery stage III, i.e. 500 K. As has been discussed in section 3.1, small vacancy concentrations can already falsify damage rate measurements (see section 3.1). In addition, the calculated temperature dependence of the efficiency for a very high Si concentration (2000 atppm) is shown in fig. 10. This curve demonstrates that the efficiencies approach the efficiency curve for stable complexes when the Si concentration is increased. For high solute concentrations an evaluation of activation energies becomes meaningless. At high solute concentrations the probability for an interstitial to become trapped after the dissociation of a complex is so high that practically no single interstitials react with sinks. This is probably the reason, why investigations on Nisi alloys containing several percent Si cannot detect the thermal decay of Si interstitial complexes [lo].
segregation
91
An important result of the complete numerical solution is that a decrease of the efficiency with increasing temperature can be found only in the temperature range where the defect reactions are governed by sink annihilation. In the case of dominant recombination the efficiency increases with the temperature in spite of the thermal dissociation of the complexes. This result is a further confirmation for dominant sink annihilation during the present irradiation experiments. The results of this work and those on RIS in CuBe show the different segregation kinetics depending on the volume size misfit. In the case of CuBe with a large negative volume size misfit of SV/V= - 26% a rather stable Be interstitial complex must be assumed to interpret the segregation experiments. Bartels et al. [16] have estimated that (E&, - Ez) > 0.42 eV. In the case of Nisi with a smaller but still negative size misfit of S V/ V = - 5.8% the evaluation of experimental data gave (E&, - Ek) = 0.14 eV. In case of NiGe with a positive volume size misfit (6V/V= + 14.8%) the very low efficiency of RIS does not give an indication for a transport via interstitial complexes. This is in accordance with resistivity recovery data which yield a main recovery peak at 115K and which was interpreted by the dissociation of Ge interstitial complexes [12]. Below 115K no peak was observed which could be assigned to the migration of the complex. On the other hand, an enrichment of Ge at point defect sinks was observed [2,4] after irradiation to very high doses. Consequently RIS in NiGe must be caused by other transport mechanisms (i.e. inverse Kirkendall effect or migrating vacancy complexes) which have a low efficiency of RIS. For comparison with theory we have to obtain further data on the binding or the migrating energy of the complex. Bartels et al. [ll] conclude that the recovery stage at 105 K is caused by the migration of the Si interstitial complex. By scaling the migration energy with the peak temperature we obtain Ek = 0.24 eV. The binding energy Ei of the complex is given by Ei = (E&, - Ek) + E& - EL. With E,!,, = 0.15 eV [27] we then obtain EE = 0.23 eV. This value agrees exceptionally well with Eg = 0.25 eV calculated according to Dederichs et al. [20] if the ratio r,,/R, of the potential shift r. divided by the equilibrium ratio of Ni is multiplied by a factor of about six to obtain the volume size misfit [28]. For Nisi also other migrating energies of the complex have been proposed depending on the type of experiment. Averback and Ehrhart [29] conclude that Ek = E,!,,, Okamoto et al. [30] conclude that Ek = 0.6 eV (however, this interpretation has been altered recently [22]). Binding energies calculated with these val-
ues of Ek are either 0.14 eV or 0.53 eV. Both values differ by a factor of about two from the predictions of Dederichs et al. [20]. All binding energies discussed so far are much lower than the value Et = 0.90 eV calculated by Gupta [31]. The migrating energy of the complex by the caging rotation mechanism is calculated according to Dederichs et al. to be Ez = 5Ek = 0.75 eV in the case of Nisi. This value is considerably higher than the measured value E,“1= 0.24 eV. Whereas the RIS in CuBe could be described well by the migrating of a mixed dumb-bell due to a rotation and caging mechanism, other transport mechanisms (e.g. looping) should be taken into account to interpret the small migration energy of the complex in Nisi.
[27] the migration energy of the Ni self-interstitial, we obtain E’ = 0.23 eV. (10) This value ii in good agreement with theoretical calculations [20.28].
Acknowledgements This work was supported by schungsgemeinschaft. The authors edge the experimental assistance of de Graaff laboratory, Aachen during ations. We thank Prof. K. Lticke support.
the Deutsche Forgratefully acknowlthe staff of the Van the electron irradifor his continuous
References 5. Conclusions work we have determined the kinetics of RIS in dilute Nisi and NiGe alloys during 3 MeV electron irradiation. The Si and Ge concentration in solid solution in Ni was obtained by damage rate measurements at a well chosen temperature in the temperature range of recovery stage II after the segregation irradiation. From these results we can conclude: (1) RIS is very efficient in Nisi alloys. At 535 K between two and ten Frenkel defects must be produced to segregate one Si atom. (2) With decreasing initial Si concentration the segregation becomes less effective. (3) The efficiency decreases with increasing temperature. (4) No influence of the dose rate on RIS could be detected. (5) RIS is very inefficient in NiGe alloys. At 530 K at least 260 Frenkel defects must be produced to segregate one Ge atom. (6) A theoretical model which describes the kinetics of RIS in Nisi by mobile but thermally unstable Si interstitial complexes is presented. (7) Fitting the data to this model we obtain for the difference between dissociation and migration energy of the Si interstitial complex (E& - Ek) = (0.14 * 0.02) eV. that the recovery stage at 105 K is (8) Assuming caused by the migration of the Si interstitial complex [ll] and scaling the migration energy with this temperature we obtain Ek = 0.24 eV and hence E& = 0.38 eV. (9) The binding energy EE of the complex is given by EE = (E,& - Ek) + Ek - E,!,,. With Em = 0.15 eV
[l] G. Margin, R. Cauvin and A. Barbu, in: Phase Transfor-
In the present
[2]
[3] [4]
[5] [6] [7] [S] [9] [lo] [ll] [12] [13]
[14] [15] [16] [17]
mations during Irradiation, Ed. F.V. Nolfi (Applied Science Publishers, London, 1983) p. 47. L.E. Rehn and P.R. Okamoto, in: Phase Transformations during irradiation, Ed. F.V. Nolfi (Applied Science Publishers, London, 1983) p. 247. H.W. King, J. Mater. Sci. 1 (1966) 79. A. Barbu, in: Comportment Sous Irradiation des Materiaux Metalliques et des Coeurs des Reacteurs Rapides, Eds. J. Poirier and J.M. Dupouy (Commissariat a I’Energie Atomique, Gif-Sur-Yvette, 1979) p. 69. L.E. Rehn, P.R. Okamoto, D.I. Potter and W. Wiedersich, J. Nucl. Mater. 74 (1978) 242. P.R. Okamoto, L.E. Rehn and R.S. Averback, J. Nucl. Mater. 108 & 109 (1982) 319. K. Janghorban and A.J. Ardell, J. Nucl. Mater. 85 & 86 (1979) 719. W. Kestemich, N.H. Packan and H. Schroeder, in: Proc. XIth Int. Congr. on Electron Microscopy, Kyoto (1986). A. Barbu, G. Martin and A. Chamberod, J. Appl. Phys. 51 (1980) 6192. R.S. Averback, L.E. Rehn, W. Wagner, H. Wiedersich and P.R. Okamoto, Phys. Rev. B28 (1983) 3100. A. Bartels, F. Dworschak and M. Weigert, J. Nucl. Mater. 137 (1986) 130. A. Bartels, F. Dworschak and M. Weigert, J. Nucl. Mater. 149 (1987) 160. Landolt-Bornstein, New Series III/lSa, Eds. K.H. Hellwege and K.L. Olsen (Springer-Verlag, Berlin, Heidelberg, New York, 1982). W.V. Lensa, Berichte der Kernforschungsanlage Jiilich, Jtil-1426 (1977). A. Kraut, F. Dworschak and H. Wollenberger, Phys. Status Solidi B44 (1971) 805. A. Bartels, F. Dworschak, H.-P. Meurer, C. Abromeit and H. Wollenberger, J. Nucl. Mater. 83 (1979) 24. K. Schroeder and W. Heidrich, Phys. Lett. 34A (1973) 315.
A. Bariels et al. / Kinetics of radiation-induced [18] M. Weigert,
Thesis RWTH
Aachen
(1987).
[19] R. Sizmann, J. Nucl. Mater. 69 & 70 (1978) 386. 1201 P.H. Dederichs, C. Lehmann, H.R. Schober, A. Scholz and R. Zeller, J. Nucl. Mater. 69 & 70 (1978) 176. [21] R.A. Johnson and N.Q. Lam, Phys. Rev. B13 (1976) 4364. (221 K.-H. Robrock, Mater. Sci. Forum 15-18 (1987) 537. [23] H. Wiedersich and N.Q. Lam, in: Phase Transformations during Irradiation, Ed. F.V. Nolfi (Applied Science Publishers, London, 1983) p. 1. [24] A.J. Ardell and J. Janghorban, in: Phase Transformations during Irradiation, Ed. F.V. Nolfi (Applied Science PubIishers, London, 1983) p. 291. (251 A. Hindmarsch, Lawrence Livermore Lab. Rep. UCID30001 (1974).
segregation
93
[26] SK. Khanna and K. Sonnenberg, Radiat. Eff. 59 (1981) 91. [27] J. Knoll, U. Dedek and W. Schilling, J. Phys. F4 (1974) 1095. [28] P.H. Dederichs, private communication. [29] R.S. Averback, and P. Ehrhart, J. Phys. F14 (1984) 1347. [30] P.R. Okamoto, L.E. Rehn, R.S., Averback, K.-H. Robrock and H. Wiedersich, in: Proc. Yamada Conf. V, Eds. J.I. Takamura, M. Doyama and M. Kiritani (University of Tokyo Press, 1982) p. 946. [31] R.P. Gupta, Phys. Rev. B22 (1980) 5900.