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The influence of radiation-induced segregation on precipitate stability in austenitic steels
journal of nuclear mall!rials
Journal of Nuclear Materials 207 (1993) 303-312 North-Holland
The influence of radiation-induced segregation on precipitate stability in austenitic steels V.A. Pechenkin
and G.A. Epov
institute of Physics and Power Engineering, Obninsk 249020, Russian Federation
Received 2 July 1992; accepted 20 July 1993
The influence of radiation-induced segregation of major components and silicon in austenitic steels on the stability of M,,C,, y’ and G phases under irradiation is theoretically studied. The low temperature boundary TL of MZJC, carbide stability and the high temperature boundary Tu of y’ and G silicides stability are estimated by comparing the steady-state chromium and silicon concentrations at point defect sinks with corresponding solubility limits for these precipitates. It is shown that both T, and T, are decreased with increasing sink density and decreasing point defect generation rate. The value of T, drops with increasing carbon content while the value of TH does with decreasing silicon concentration.
1. Introduction
Understanding and controlling phase evolution has practical benefits in the design of more radiation-resistant advanced austenitic stainless steels for fast breeder reactor and magnetic fusion reactor applications. Phase composition of complex alloys is greatly changed under high-energy particle irradiation. The acceleration of formation and growth of stable phases, the appearance of nonequilibrium (radiation-induced) precipitates and the dissolution of thermally stable phases have been observed in austenitic steels [1,2]. The composition of the precipitates formed frequently also appear to be modified by irradiation in comparison with that observed after normal thermal aging [3]. In particular, neutron irradiation retards the formation of M,,C, carbides [4] in austenitic steels, while these precipitates form easily at grain boundaries during annealing in a wide range of temperatures [5]. M.,,C, precipitates have been detected in AISI 316 during EBR-2 irradiation at temperatures above 550600°C only [4]. Pedraza and Maziasz [4] have pointed out, that there is a correlation between M,,C, precipitation and radiation-induced segregation (RIS) decreasing. Chromium and iron depletion at point defect sinks has been observed in model Fe-Cr-Ni alloys and technological steels. This phenomenon has been theoretically investigated in the framework of RIS theory [6]. It was shown that chromium content at grain 0022-3115/93/$06.00
boundaries drops significantly with temperature decreasing. Therefore the lowest temperature of chromium-rich M,sC, precipitate stability under irradiation may be related to the decrease of Cr concentration. Nickel- and silicon-rich y’ and G precipitates do not form in austenitic steels during thermal aging but they were observed after neutron irradiation at 400600°C. These precipitates are often adjacent to pointdefect sinks [2]. Studies indicated that a sufficiently high silicon concentration at point defect sinks should be reached for y’ precipitation in dilute Si-Ni alloys [7,8]. This Si enrichment is caused by RIS of silicon via an interstitial mechanism [9]. As it was shown by Williams and Titchmarch [lo], during annealing G phase forms in an alloy similar to the type FV548 steel for major components but with = 6 wt% Si. Therefore the existence of the highest temperature for the growth of y’ and G phases in irradiated austenitic steels may be related to a low silicon concentration near point defect sinks due to some suppression of RIS at high temperatures. In this paper a method to estimate the influence of RIS on temperature regions of stability of secondary phase precipitates is developed. The theoretical model for segregation in Fe-Cr-Ni alloys proposed in ref. [ll] is modified to account for the segregation of silicon. The lowest temperature of chromium-rich M& carbide stability and the highest temperature of
0 1993 - Elsevier Science Publishers B.V. All rights reserved
%A. Pechenkin, G.A. Epor’ / The influence of RIS on precipitate stability
304
silicon-rich y’ and G phases stability depending on irradiation conditions and alloy mirostructure are estimated.
2. Model description Irradiation can variously influence the temperature boundaries of precipitate existence in alloys as it was shown in the introduction. However, RIS may be a unified reason of such influence if these precipitates are associated with point defect sinks or precipitates are sinks themselves (incoherent precipitates). The instability of a certain precipitate occurs at temperatures when the concentration of the “crucial” component which is set due to RIS near sinks proved to be lower than corresponding solubility limit for this precipitate. This approach will be used below to determine the temperature boundaries of stability for the two types of precipitates most influenced by irradiation in austenitic stainless steels: radiation-retarded M,,C, and radiation-induced y’ and G phases. 2.1. M,,C,
precipitates
The formation of M&, precipitates at grain boundaries in austenitic stainless steels during thermal aging has been the subject of many investigations in the last two decades [5,12,13]. A considerable interest to this phenomenon is explained by strong correlation between precipitation and corrosion resistance of alloys. The main problem of theoretical treatment of this process is the evaluation of chromium concentration C& in thermodynamic equilibrium with M,,C, carbide, because these grain boundary precipitates-may grow only if the chromium concentration in alloy is higher than C&. A thermodynamic model of M,,C, carbide formation in Types AISI 304 and 316 stainless steels has been developed by Bruemmer [5]. Chromium carbides Cr,,C, were considered as the model precipitates since chromium is the primary component of carbides in these steels. According to ref. [5]:
cg = K,-d'23yCrl(yCCC)-6/23, where C, is the carbon concentration (in atomic units), ycr and yc are the activity coefficients of chromium and carbon, respectively, and K,, is the equilibrium constant [5]: K,, = exp( - AG/RT),
ture range 400-850°C (for more details, see below section 3). The absence of M,,C, carbides on grain boundaries in austenitic stainless steels under irradiation at temperatures below 500-600°C may be caused by RIS. RIS leads to nickel enrichment and chromium depletion at point defect sinks. The depletion is more pronounced at lower irradiation temperatures, where the steadystate chromium concentration at sinks C& can be lower than the thermal equilibrium concentration C&. Since the chemical composition of M,,C, in steels under irradiation is similar to that under thermal aging [14], one can assume that the thermodynamic model of M,,C, carbide evolution and the estimate of C& derived in ref. [5] are also valid in the case of irradiation. Let us evaluate C$i. Approximate analytical expressions for steady-state component profiles near point defect sinks in ternary substitutional alloy A-B-C caused by RIS have been derived in ref. [II]. These formulae are in a satisfactory agreement with computer calculations and experimental data available on the major element radiation-induced segregation in concentrated Fe-Cr-Ni alloys obtained in refs. [15,16]. A-component profile has the following form: F’/‘IC
CA =
A0
1 - CA,, - C,, + F”F’(CA,, + F”‘-““C,,,)
’ (3)
F = C,(r)/(C,>,
where d: are the partial diffusivities ((u = Cr, Ni, Fe) of alloy components via vacancy (k = v) and interstitial (k = i) mechanisms, Cue are the alloy component concentrations in unirradiated alloy, dt = dfj, exp(-E,k,/kT) (E,k, is the cY-component migration energy), D,, are the point defect diffusion coefficients in unirradiated material (DkO = dk,,(C,,d&/dE, + CNid$/dE, + C,,) for Fe-Cr-Ni alloy). C,(r) is the vacancy concentration profile near a given sink [ll] and (C,) is the bulk average value of vacancy concentration:
(2)
AG is the free energy of carbide formation and T is the temperature. This model is valid over the tempera-
(c.);o.5(~~+[~~-~)+c.,;
(4)
KA. Pechenkin, G.A. Epou / The influence of RIS on precipitate stabiliiy
where K is the point defect generation rate, pa is the vacancy-interstitial recombination coefficient and ps is the point defect sink strength. The thermal equilibrium vacancy concentration can be expressed as C C, exp(-E,‘/kTl (ET is the vacancy formation?;ergy). It should be pointed out that for grain boundary one can obtain: (C,)/C,(O) = (C,)/C, = s, where s is the vacancy supersaturation in material under irradiation. Let indexes A, B and C denote Cr, Ni and Fe components, respectively, then C,(O) = C$:. Comparing C& and C& at various irradiation temperatures with the use of eqs. (3) and (1) it is easy to find the characteristic temperature TL above which C& < C& and, consequently, the growth of M,,C, carbides is possible at grain boundaries. 2.2. y ’ precipitates Gamma prime is a radiation-induced precipitate that does not form in technological steels during thermal aging. It forms in austenitic stainless steels during irradiation at temperature range from 400 to 550°C. These precipitates are usually attached to dislocations and dislocation loops [2,15]. For y’ precipitates to grow, local Ni and Si concentrations should likely be higher than corresponding solubility limits of these components for y’ phase. Thus, a theoretical description of Si and Ni concentration profiles near point defect sinks is necessary to determine the temperature range of y’ precipitation. Let us consider a simple model of Si and Ni concentration behaviour in irradiated Fe-Cr-Ni-Si alloys, where Si is a solute. It should be noted that silicon content in austenitic steels does not exceed several percents. Nickel enrichment at point defect sinks can be explained by a vacancy segregation mechanism [16181. Radiation-induced silicon segregation near sinks and the growth of y’ phase have been extensively studied in dilute Si-Ni alloys [7,19,20]. The available experimental data can be satisfactorily explained on the basis of interstitial segregation mechanism of Si. The binding and migration energies of Si-Ni mixed dumbbells were estimated in this case [8]. In contrast to nickel and silicon, chromium and iron are always depleted at point defect sinks in irradiated austenitic steels [16,17]. Using this information one can simplify the problem if to consider a hypothetical ternary alloy A-B-C, where A corresponds to Si, B to Ni and C to the sum of Cr and Fe. Further we shall investigate the case of
305
high temperatures when interstitial atoms of different types are in thermal equilibrium [21]:
Cf c=
Cc #$c,+ca+ccY
(5)
where .$= exp(Ei/kT), Ei is the binding energy of mixed dumbbells AB and AC types (AA dumbbells are neglected due to low silicon content in alloy). This energy is required for the transformation of AB and AC dumbbells to those of BB, BC and CC. Since Si atom size is much smaller than that of major components in Fe-Cr-Ni-Si alloys, the binding energy of mixed dumbbells with Si only is taken into account in eq. (5). Interstitial atoms may be considered in thermal equilibrium if two conditions are fulfilled: 1) interstitial atoms of BB, BC and CC types have a chance to meet A atom during their free path. This condition is justified when the distances between vacancies and sinks are larger than that between A atoms. This holds for CA > 0.1 at% of interest, 2) mixed dumbbells of AB and AC types have a chance to be destroyed, i.e. to transform to interstitials of BB, BC and CC types (the reverse conversion) during their free path time 7,. This condition is fulfilled if the average time of the conversion TV is less than T,. Note, that l/r,
= Z,( C, + C,) exp( -E,b/kT)d&/a2,
l/Till =44(P,+PR(Cv)),
the geometrical factor Z, accounts for possible ways of the conversion (it is of the order of coordination number), a is the lattice constant. As a result one can evaluate the temperature T,,, above which the thermal equilibrium may be set: T,, =
E,b+E&k In
-UC,
E; + Cc>
’
(6)
a’(p, + CL&) where Ek c is the interstitial migration energy of B or C component. To is equal to 420 K at ps = 1013-1016 me2 and diffusion parameters adopted in this paper (see section 31. For simplicity we do not consider a nonideality of solid solution and correlation effects that allows us to derive alloy component profiles in an analytical form.
306
V.A. Pechenkin, G.A. Eporj / The influence of RIS on precipitate stability
In this case the equations for component and point defect fluxes near sinks take the following form: d,,C,
JA = -
+
i + CA d,,VC, i JB=
-
i
d&v+
C,;(r)
5dAi (1+ -
[l-
l]Cyi
i vc,4
tdAi 1+[5-l]c,vc’
d,i 1+~5_llcA
(6 - l)d,i + I+ [t _ l]C,
(7)
1’
ci
vc, 1
‘icBvcA
(8) J, = -D,VC,
+ C,( d,, - d,,)VC,
+ C,(d,v J, = _ vd,i I
- d,,)VC,,
+ (d,i -d,i)C~
C,,,d&)/(C,,,,
concentration
(9) + (ifdAi -d,i)C~
1 + Et - llcA
c,
1. (10)
It is accounted in eqs. (7)-(10) that CA + C, + Cc = 1. In the case of binary alloy this system is identical to that suggested by Bakai and Turkin [8] for y’ phase in Si-Ni alloys. Their model is successful in evaluation of the shift of y’ phase equilibrium curve in dilute Si-Ni alloys under irradiation. The model proposed (eqs. (7)-(10)) may have reasonably wide areas of application, because it describes RIS arising due to migration of impurity-interstitial atom complexes (mixed dumbbells) and due to inverse Kirkendall effect. It is suitable for the study of buildup of undersized impurities (for example, Si or P types) near point defect sinks in irradiated austenitic stainless steels, in this case concurrent accumulation of nickel near sinks is accounted for. For usual level of silicon content in austenitic steels and with the binding energy Ej estimated in ref. [9], it is proved that [C, I 1. So we can take 1 + (5 - DC, = 1 in eqs. (7-10). Using the steady-state conditions JA = JB = 0 and Ji = J, these equations may be transformed to the set of equations for AC, and AC, of ref. [ll] (eq. (10)) if to replace the value of dAi by .$d,,. Employing the results of ref. [ll] it is easy to derive Si and Ni profiles near sinks. Si profile C,(r) has the form of eq. (3) where db = td&, the effective partial diffusion coefficient d$ = (C,,,,dk, +
+ CCr,,)), (k = i, v). The profile of Ni
is:
= CNi,OICsi(r)/Cs,,o]F(P~l)‘El.
(11)
Due to RIS both Si and Ni concentrations may exceed the solubility limits of these elements for y’ phase in stainless steel. This may lead to continuous growth of y’ precipitates. But the question arises: is the concentration of nickel or silicon crucial for the growth of y’ precipitates in steels? Experimental data (see section 3) indicate that this crucial element seems to be silicon. In particular, with increasing Si content in steel the temperature range of y’ precipitate formation is significantly expanded. This fact allows us to assume that the growth of y’ phase is possible at temperatures T < Tu when the local silicon concentration at point defect sinks Cc exceeds the thermal equilibrium silicon concentration C&(T). A thermodynamic model of y’ precipitate formation in steels has not yet been developed and the value of C& is unknown. Below (see section 3.3) we tried to construct some approximation of it on the base of data available about y’ phase in binary Si-Ni alloys and to estimate the highest temperature of y’ phase stability TH.
3. Comparison
of the theory with experimental
data
3.1. Diffusion parameters
For vacancy migration mechanism of Fe, Cr and Ni in steels we use the parameters of Norris et al. [17]. A satisfactory agreement was reached in ref. [17] between calculated profiles of these components near grain boundaries and experimentally measured ones in 20/25/Nb steel after annealing and irradiation using the following constants: d& = d& = d& = 1.16 X 1O-5 m’/s, E&, = 1.3 eV, E&, = 1.2578 eV, EAim = 1.3784 eV, Ej = 1.6 eV, c0 =‘exp(l), pn = 8 X 10” m-‘, and taking the cascade efficiency of point defect creation as 0.1. It should be noted, that both this set of parameters and that from the work of Perks and Murphy [16] lead to similar component profiles near point defect sinks in irradiated Fe-Cr-Ni alloys. This may stem from their common origin from high temperature experimental data by Rothman et al. [22]. Experimental data on diffusion parameters of Si in steels and on interstitial component diffusivities in Fe-Cr-Ni alloys are lacking now. To estimate these diffusion characteristics we shall use both the experi-
bCA.Pechenkin, G.A. Epou / The inj7uence of RIS on precipitate stability
mental data on y’ phase formation in Si-Ni alloys and on segregation profiles of Si and Ni near grain boundaries in PCA [23]. For alloy component profile calculation the partial diffusion coefficient ratios are necessary. These ratios can be expressed in terms of migration energy differences for various components. Besides, for Si migration the value of E = E& + Eki,, - E&, is important. This value was estimated by Bartels et al. [9] for dilute Si-Ni alloy: E = 0.14 eV (binding energy of Si-Ni mixed dumbbells Et Ni z 0.23 eV). The influence of silicon RIS on y’ phase evolution in dilute Si-Ni alloys has been theoretically studied by Bakai et al. [20]. They have estimated the high temperature boundary for y’ phase growth using the value of E from ref. [9] and Eki,, = 0.15 eV. The agreement between theory and experiment was obtained in ref. [20] with the suggestion of low vacancy formation energy E,’ = 1.4 eV in Si-Ni alloy as compared with usually adopted value of 1.6-1.7eV in pure nickel. The use of such low formation energy for dilute Ni-Si alloy seems to be questionable, because Si atom is undersized in nickel and the binding energy of Si atommonovacancy is likely small. An alternative possibility for the improvement of theoretical predictions is connected with higher silicon diffusivity via a vacancy mechanism than that of nickel in Si-Ni alloys [24]. Our calculations show that the best agreement between experimental data presented in refs. [25-271 and the theory in the case of highest temperature T, for y’ phase growth in Si-Ni alloys is achieved at E,V = 1.6 eV and d,‘,/dci = exp(0.12 eV/kT).
307
Table 1 Alloy composition (wt%) Elements
Fe Ni Cr MO C Si
Alloys PCA
304
316
FV548
Balance 16.2 14.0 2.3 0.05 0.4
Balance 8.75 18.5 0.2 0.06 _
Balance 10.9 17.4 2.17 0.05 0.5
Balance 11.8 16.5 1.44 0.11 0.4
The segregation profiles of major components and silicon near point defect sinks in Si-doped “pure” Fe-Cr-Ni alloys have not been experimentally investigated in detail. Such profiles were studied in technological steels only. Their interpretation proved to be too complicated because of the influence of other impurities and precipitates adjacent to the sinks (this problem has been discussed in ref. [12]). Kenic et al. [23] have measured silicon and major component profiles near grain boundaries in PCA irradiated at 420°C in FFTF. Experimental data and results of our calculations (using the model described in section 2) are shown in fig. 1. The point defect generation rate was taken as K = 10e6 dpa/s and the cascade efficiency as 0.1. The alloy compositions are given in table 1, where the concentrations of only those components of alloys are indicated, which were used in calculation or in their interpretation. The dotted line corresponds to parameters E z 0.14 eV and d&/d& = exp(0.12 eV/
PCA 42ooc
0
-25
,o-150 ( 1
0 r
I
I
1
7
1
r(
cc5
DISTANCE FROM GRAIN BOUNDARY (nm) DISTANCE F$M GR;N BO::DARY2&m) Fig. 1. Comparison of experimental 1231composition prof lies (Ni - solid circles, Si - circles) across a grain boundary of PCA neutron irradiated to 9 dpa at 420°C with profiles, calculated by eqs. (3) and (11).
308
%A. Pechenkin, G.A.
Epou
/
The influence of RIS on precipitate stability
kT). Interstitial partial diffusivities of alloy components (Fe, Cr, Ni) were taken to be identical. It is seen from fig. 1 that the theory predicts too large Ni concentration near the-grain boundary. The agreement of theory with experiment can be improved if to suggest that mixed nickel dumbbells migrate slower than Fe and Cr ones. The result of calculation with dki/di = exp( - 0.05 eV/kT), where d& is the partial interstitial diffusivity of Fe and Cr is shown by the solid line in fig. 1. This value will be used below to calculate precipitate stability in steels. It should be noted, that the assumption of slower Ni migration (as the chemical element with maximum size misfit [28]) as compared with Fe and Cr migration is in a qualitative agreement with the results of Murphy [29]. It was shown that the migration of mixed dumbbells can be significantly retarded due to slow rotation of these dumbbells in a concentrated substitutional alloy [29]. 3.2. The lowest temperature of M&,-precipitate
stability
under irradiation
/
‘/
%
E -_-_-
FV 548
ol”,,‘~‘,,I,-““‘,,““““‘l”““‘,‘I Fig. 2. Temperature concentrations C&
In yc=
-1.845 +5100/T+
C,(11.92 - 6330/T)
- CNi(2.2 - 7600/T) + C&(24.4 - 38400/T) - C$(96.8
- 84800/T),
550
600 TEMPERATURE
650 (“C)
- 700
dependence of equilibrium chromium and steady-state concentrations C&v at grain boundaries.
(12)
where T is the temperature in K, Cm is the bulk nickel concentration and C,*, is the effective chromium concentration: C& = co, + 0.35c,,, (Cc, and C,, are the bulk concentrations MO, respectively) ycr = 10.55 - 94.84T, + 282.9T; - 242.8T;,
As it was discussed in section 2, the growth of M,,C, carbides is possible at temperatures, wherein the steady state chromium concentration C’& at grain boundaries exceeds the equilibrium one C& The latter can be calculated from eq. (l), if values of yCr, yc and AG are known. The free energy of Cr& carbide formation in Types AISI 304 and 316 steels has been deduced by Bruemmer [5] as AG = 98 280-9.2T (cal/mol). The composition of M,,C, carbides in 304 steel is very similar to that of Cr,,C, ones but they contain some amount of iron. The constitution of car-
500
bides in 316 steel is more complex, normally (Cr,,Fe,Mo,Ni)C, [14]. The deviation of M,sC, composition from that of Cr,,C, and the influence of other carbide formers (for example MO, Ti, Nb) can be accounted for in activity coefficients y. Bruemmer [5] suggested the following activity coefficients for these steels:
(13) of Cr and (14)
where TP = T/2000 for steel without molybdenum and T, = (T - 30)/2000 for steel with molybdenum. This model is valid over the temperature range 400-850°C (see for details ref. [5]). The calculated temperature dependencies of equilibrium chromium concentration C& (eq. (1)) and steady-state one Cg; (eq. (3)) for steels AISI 304, 316 and FV548 are shown in fig. 2. It is seen that C$ is increased slowly but the magnitude of CE; is increased rapidly with temperature increasing. This behavior of C& is connected with the significant drop of vacancy supersaturation (see eqs. (3) and (4)). To calculate Cz: the following parameters were used: ps = 1014 m-‘, K = 1O-6 sP ‘. The composition of steels is shown in the table. The parameters of Norris et al. [17] for the vacancy mechanism of diffusion, and for interstitial one d,&/d&, = exp( - 0.05 eV/kT), db,/d& = 1 were taken. As it is seen from fig. 2, the characteristic temperature T,, above which M,,C, carbides can grow on grain boundaries in AISI 304, 316 and FV548 steels irradiated with fast neutrons is close to 550°C. It should be pointed out that irradiation conditions and the microstructure of materials may be significantly varied. For example, the point defect generation rate K depends on the reactor power and on the location in reactor core. The total sink strength depends on the preliminary treatment of a material (especially on the extent of cold work), irradiation dose, neutron spectrum, secondary phase precipitation. The carbon content in steels may be different also. The sensitivity of
VIA. Pechenkin, G.A. Epol: / The influence of RIS on precipitate stability 650 L 600
\\\
j.
450 j iA
-1
--_ -.
;
C1=0.06 wt wC c2=0.01 wt SC Kl=lO -6 dpa/s K2=10 -’ dpa/s
400: 10 IS
,""T
Cl,Kl
‘_.._
"""I 13 s1,o,cDEiwIT:"(m2)
_>
. Cl,K2
"""'I 10 I8
Fig. 3. The dependence of low temperature stability limit of M,,C, precipitates CT,) on sink density (p,).
TL to these parameters is shown in fig. 3. The composition of 304 steel is used for calculations because the value of TL is not sensitive to small variation of Ni and Cr contents. It is seen from fig. 3 that T, drops significantly with increasing sink density and/or with decreasing point defect generation rate. This behavior is connected with the decrease of vacancy supersaturation. Besides, the temperature T, is decreased with increasing carbon content due to the decrease of C,$ Experimentally, a great deal of work has been carried out to study the behavior of various precipitates under irradiation in austenitic stainless steels (see e.g. refs. [1,2]), but only in few works M,C, carbides were investigated in detail because of very high temperature of M,,C, formation in irradiated steels. The estimates of T,_ found above are in a satisfactory agreement with experimental data available. Cold worked (CW) type 316 steel has been examined in ref. [4] after EBR-2 irradiation. The formation of M,,C, precipitates on grain boundaries was observed at T > 600°C (pd = 1014 m-‘) in Ti-stabilized 316 steel. M&Z, precipitates in nonstabilized solution-treated steel (P,, = 2 x lOi m-‘) have not been detected in the temperature range investigated (500 to 630°C). 15Ni/15Cr Ti-stabilized steel (CW) irradiated in RAPSODIA at 400-600°C has been studied in ref. [30]. M,C, precipitates on grain boundaries were observed at temperatures higher than 560°C. These precipitates were not detected in the steel samples with lower carbon content. Titanium stabilized commercial 16Cr-15Ni-3Mo steel (20% CW) has been microscopically investigated
309
after irradiation in BN-600 over the temperature range 350-600°C [31]. It was found, that M,,X, carbides are formed on grain boundaries at temperatures above 500°C. Specimens of Nb-stabilized FV548 steel after DFR irradiation at 380-730°C have been examined in ref. [14]. Unfortunately, only summary data concerning M,,C, formation on grain boundaries and in grain bulk have been presented. It was shown, that these carbides are formed at temperatures above 550°C in the annealed steel and above 475°C in CW samples. The very high sink density both in CW (pd = 4 X 1014 me2) and annealed (pd = 2 X 1014 rne2> specimens at T g 500°C should be noted. The authors of ref. [14] pointed out that the contribution of finely dispersed NbC carbides into the total sink density can exceed that of dislocations. It should also be noted that the carbon content in FV548 is higher than that in AISI 304 and 316 steels. The estimates of T, derived above are valid for M,,C, carbides on grain boundaries. Similar estimates can be derived for the precipitates adjacent to other sinks. The influence of RIS on the growth of M,,C, precipitates in the interior of grains depends on the coherency of precipitates with matrix [32]. The absence of bulk M,,C, in the grain interior at low irradiation temperatures can be explained by the precipitate incoherency with matrix. The summary of data concerning the microstructure of 316 steel with different cold work levels after irradiation in several reactors indicate that M,,C, precipitates form at temperatures T > 500°C [33]. Bulk M,,C, precipitates in DFR-irradiated FV548 steel were observed at T > 475°C and in 316 steel at T > 425°C [3]. It was pointed out however, that precipitates of the form of bicrystals M,,C,-M,C, M,sC,Laves, M,,C,-n are often observed in type 316 stainless steel. 3.3. The highest temperature of y ’ phase stability A thermodynamic model of y’ precipitate formation in steels has not yet been developed and the value of C$ is unknown. With experimental data [17] on silicon profiles near grain boundaries containing these precipitates it is possible to obtain an upper estimate of C$ only. y’ phase growth both under and without irradiation has been thoroughly investigated in binary Si-Ni alloys where the composition of this phase is Ni,Si. In this case the equilibrium Si concentration depends on the temperature as follows [34]: C&&T)
= 0.283 exp( - 0.077 eV/kT).
(15)
310
V.A. Pechenkin, G.A. Epor / The influence of RIS on precipitate stability
The chemical composition of y’ precipitates in austenitic stainless steels is more complex than that in Si-Ni alloys. Indeed, y’ phase in steels contains significant amounts of Fe, Cr, Mn, MO [2]. Relative Si and Ni contents in y’ precipitates are lower in steels than those in pure Si-Ni alloys. So one can expect that in steels the thermally equilibrium concentration of silicon near y’ precipitates is lower than that predicted by eq. (1.5): C&(T)=6C&(Ni)(T), where 6 I 1 is the parameter, which must depend on alloy composition. A rough approximation C&(7’) may be improved if the thermodynamic model of y’ precipitates in steels will be developed. The profile of silicon is considerably altered at distances of the order of several lattice parameters near a sink as RIS calculations have shown (see fig. 11. So for the growth and especially for the nucleation of y’ precipitates the silicon concentration not only at sink boundary, but in the whole region of the thickness d near sink boundary should be higher than C&(T) Therefore the highest temperature T, of y’ stability in austenitic stainless steels can be estimated from the following equation: (16) where 0 5 d I a, a is the lattice constant. The model developed can also be used for the analyses of G phase stability as it will be shown in section 3.4. The highest temperature Tn of y’ precipitates stability was calculated by eq. (16) using the following diffusion parameters: E z 0.14 eV, d&/d& = exp(0.12 eV/kT), dki/d& = exp( -0.05 eV/kT), dh,/d& = 1. The results of T, calculation at K = lop6 dpa/s for AISI 316 versus the point defect sink density are shown in fig. 4. This temperature depends strongly upon the silicon content Csi, the ratio 6 of Si solubility limits for y’ phase in steel and that in nickel, the thickness d defined above and the sink density ps. It is seen from fig. 4 that at ps = lOi me2 the predicted magnitude of TH is 500-550°C for austenitic stainless steels with 0.5-l wt% Si. This estimation is in an agreement with available experimental data [2]. y’ phase forms in type 316 or Ti-modified steels during FBR irradiation at 400-550°C [2]: But y’ can form at 600°C and above in type 316 steel with > 2 wt% Si. y’ forms in D9 alloy (Csi = 2 wt%) more abundantly than in stainless steels with lower silicon content. -y’ phase in 20% CW AISI 316 is formed at temperatures lower than 500°C as Itoh et al. [33] pointed out. Yang [35] has presented the same results for EBR-2 irradiated AISI 316 and AISI 316(Ti).
600 J
550i
-._
*.
..’
2 at.% Si ‘-.
400 :
3
The dependence of high temperature stability limit of y’ and G phase precipitates (T,) on sink density (p,).
Fig. 4.
The microstructure of 20% CW titanium stabilized commercial 16Cr-15Ni-3Mo steel irradiated in BN-600 reactor was studied by Dmitriev et al. [31]. y’ formation was detected at 425 and 490°C. The increase of He/dpa ratio results in a destabilization of -y’ phase as it was pointed out in ref. [2]. It is likely due to the total sink strength increase as a result of helium bubble formation. 3.4. Comparison of y ’ and G phase stability It is interesting to analyze y’ phase behavior in Ti-doped steels. y’ forms at several dpa but dissolves after 20 dpa in neutron irradiated CW N-lot AISI 316 and PCA as Maziasz [2] pointed out. At higher doses M,C and G phases formation begins. G phase precipitates appear abundantly in Nb or Ti-doped Fe-Cr-Ni alloys, but y’ phase was not observed in Nb-stabilized steels. G phase is a complex silicide M6Ni,,Si, (M can be Ti, Nb, Mn, Cr) compound. This phase is enriched in Si and Ni similar to y’ phase. But relative Si content in G phase is lower than that in y’ phase. G phase precipitates are often associated with voids and grain boundaries. During annealing G phase forms in an alloy with the same major component concentrations as in FV548 steel but with higher Si content (Csi = 6 wt%) as it was shown by Williams and Titchmarch [lo]. This experiment proves the critical influence of silicon on G phase formation and growth. From the above consideration one can assume that y’ and G phases are competitive radiation-induced precipitates. It is quite probably that the formation energy of y’ phase is lower in Ti-doped steels and that
VIA. Pechenkin, G.A. Epov / The influence of RIS on precipitate stability
of G phase is lower in Nb-doped ones. Correspondingly, the silicon solubility limit C& is likely lower for G phase. So y’ phase must precipitate first in Ti-stabilized steels. The increase of sink density and/or silicon matrix depletion due to %-rich precipitates growth can reduce silicon concentration near sinks below y’ phase solubility limit. This would result in y’ precipitate dissolution and G phase formation, since the silicon solubility limit is lower for G phase. Subsequent growth of G phase precipitates can be supported by silicon dissolved from y’ phase. So the model developed in section 3 can be used for the estimation of the highest temperature of radiation-induced G phase stability. In this case we can adopt that the magnitude of S in eq. (16) for G phase is lower than that for y’. It means that the temperature range of G phase precipitate stability is expected to be similar to that for y’, but the value of TH for G phase must be higher than that for y’ (see fig. 41. This consideration is in agreement with experimental data. G phase precipitates are formed in temperature range 400-650°C under fast neutron irradiation in Ti and/or Nb-stabilized austenitic stainless steels as Maziasz [2] pointed out. The same temperature range was found for AISI 316(Ti) in ref. [35]. According to Williams et al. [14], G phase precipitates in DFR irradiated FV.548 steel are formed up to 600°C. G phase formation is retarded with increasing sink density. These precipitates form more easily in annealed samples than in cold worked ones [2]. The increase of He/dpa ratio results in the retardation of G phase formation also. In particular, G phase has been observed in AISI 316(Ti) and PCA irradiated in EBR-2 (0.5 appm He/dpa) but has not been detected in these alloys after HFIR irradiation (70 appm He/dpa). This phase has been observed in annealed samples of PCA, but was not observed in cold worked ones after FFTF irradiation [2]. It should be pointed out, that the formation and growth of another siliconrich precipitates (especially M,C carbides) may significantly affect the evolution of y’ and G phases [lo]. No y’ and G phase precipitates were observed in irradiated austenitic steels at temperatures below 400°C except for the y’ formation in neutron irradiated 316 steel at 270°C (see work by Cawthorne and Brown [37]). The absence of these phases in steels under low temperature irradiation can be explained by two reasons. The first one is too large characteristic dose @a which is necessary to reach steady state component profiles at low temperatures, because the alloy component diffusivities are small. The results of computer calculations of the set of diffusion equations for point defect and component concentrations near a
311
grain boundary indicate that @s is very large at temperatures below 200-250°C only [16]. The second reason is the destruction of small precipitates by collision cascades. The effect of the displacement cascades on y’ formation in dilute Si-Ni alloys has been analyzed in ref. [19]. The lowest temperature of precipitate growth is shown to shift to approximately 400°C due to this effect.
5. Summary 1. The instability of chromium-rich M&Z, carbides at low temperatures in irradiated austenitic steels is explained by Cr depletion at grain boundaries as a result of radiation-induced segregation. The lowest temperature T,_ of M,,C, stability is equal to 550600°C depending on the material microstructure and irradiation conditions. 2. The high temperature boundary T, of siliconrich -y’ and G phase stability is due to the reduction of silicon concentration near point defect sinks at high irradiation temperatures and equals 500-600°C. 3. Both temperatures T,_ and TH are decreased with increasing sink density and decreasing point defect generation rate. T,_ drops with increasing carbon content while TH does with decreasing silicon concentration.
Acknowledgement
The authors would like to thank Prof. Konobeev for useful discussions of the work.
Yu.V.
References
111K.C. Russell, Prog. Mater. Sci. 28 (1984) 229. [2] P.J. Maziasz, J. Nucl. Mater. 169 (1989) 95. 131T.M. Williams, Effects of irradiation on Materials: 11th Conf., ASTM-STP 782 (American Society for Testing and Materials, Philadelphia, 1982) p. 166. 141D.F. Pedraza and P.J. Maziasz, Radiation induced Changes in Microstructure: 13th Int. Symp. (Part l), ASTM-STP 955 (American Society for Testing and Materials, 1987) p. 161. [51 S.M. Bruemmer, Corrosion 46 (1990) 698. 161C.A. English, S.M. Murphy and J.M. Perks, J. Chem. Sot. Faraday Trans. 86 (1990) 1263. 171L.E. Rehn, P.R. Okamoto and R.S. Averback, J. Nucl. Mater. 80 (1979) 172.
312
VA. Pechenkin, G.A. Epoc: / The influence of RIS on precipitate stability
[S] AS. Bakai and A.A. Turkin, J. Nucl. Mater. 152 (1988)
331. [9] A. Bartels, F. Dworschak and M. Weigert, J. Nucl. Mater. 152 (1988). 82. [lo] T.M. Williams and J.M. Titchmarsh, J. Nucl. Mater. 98 (19811 223. [ll] V.A. Pechenkin and G.A. Epov, J. Nucl. Mater. 186 (1992) 269. [12] E.L. Hall and C.L. Briant, Metall. Trans. A 15 (1983) 793. [13] SM. Bruemmer and L.A. Charlot, Scripta Metall. 20 (1986) 1019. [14] T.M. Williams, J.M. Titchmarsh and D.R. ArkelI, J. Nucl. Mater. 107 (1982) 222. [15] R.M. Boothby and T.M. Williams, J. Nucl. Mater. 152 (1988) 123. [16] J.M. Perks and SM. Murphy, Proc. Conf. on Materials for Nuclear Reactor Core Applications, Bristol, October 1987, vol. 1 (BNES, London, 1987) p. 165. [17] D.I.R. Norris, C. Baker and J.M. Titchmarsh, in ref. [16] p. 277. [18] S. Dumbill and T.M. Williams, in ref. [16] p. 119. [19] P.R. Okamoto, L.E. Rehn and R.S. Averback, J. Nucl. Mater. 108&109 (19821 319. [20] A.S. Bakai, A.V. Buz and A.A. Turkin, Met. Fiz. 13 (19911 68. [21] H. Wiedersich, P.R. Okamoto and N.Q. Lam, J. Nucl. Mater. 83 (1979) 98.
[22] S.J. Rothman, L.J. Nowicki and G.E. Murch, J. Phys. F 10 (1989) 383. [23] E.A. Kenik, T. Inazumi and G.E.C. Bell, J. Nucl. Mater. 183 (1991) 145. [24] D. Treheux, A. Heurtel and P. Guiraldenq, Acta Metall. 24 (1976) 503. [25] P.R. Okamoto and L.E. Rehn, J. Nucl. Mater. 83 (1979) [26] 2. Janghorban and A.J. Ardell, J. Nucl. Mater. 85&86 (1979) 719. [27] A. Barbu, G. Martin and A. Chamberod. J. Appl. Phys. 61 (1980) 6192. [28] C. Dimitrov and 0. Dimitrov, J. Nucl. Mater. 152 (1988) 21. [29] S.M. Murphy, J. Nucl. Mater. 182 (1991) 73. [30] D. Gilbon et al., in ref. [16] p. 307. [31] V.D. Dmitriev et al., Proc. Int. Conf. on Radiation Materials Science, Alushta, USSR, May 22-25, 1990, vol. 3, p. 54. [32] A.S. Bakai and A.A. Turkin, Fiz. Met. Metalloved. 3 (1991) 67. [33] M. Itoh, Sh. Onose and Sh. Yuhara, in ref. [4] p. 114. [34] P.K. Rastogi and A.J. Ardell, Acta Metall. 17 (1969) 595. [35] W.J.S. Yang, in ref. [4] p. 628. [36] P.J. Maziasz, J. Nucl. Mater. 122&123 (1984) 472. [37] C. Cawthorne and C. Brown, J. Nucl. Mater. 66 (1977) 201.
Journal of Nuclear Materials 207 (1993) 303-312 North-Holland
The influence of radiation-induced segregation on precipitate stability in austenitic steels V.A. Pechenkin
and G.A. Epov
institute of Physics and Power Engineering, Obninsk 249020, Russian Federation
Received 2 July 1992; accepted 20 July 1993
The influence of radiation-induced segregation of major components and silicon in austenitic steels on the stability of M,,C,, y’ and G phases under irradiation is theoretically studied. The low temperature boundary TL of MZJC, carbide stability and the high temperature boundary Tu of y’ and G silicides stability are estimated by comparing the steady-state chromium and silicon concentrations at point defect sinks with corresponding solubility limits for these precipitates. It is shown that both T, and T, are decreased with increasing sink density and decreasing point defect generation rate. The value of T, drops with increasing carbon content while the value of TH does with decreasing silicon concentration.
1. Introduction
Understanding and controlling phase evolution has practical benefits in the design of more radiation-resistant advanced austenitic stainless steels for fast breeder reactor and magnetic fusion reactor applications. Phase composition of complex alloys is greatly changed under high-energy particle irradiation. The acceleration of formation and growth of stable phases, the appearance of nonequilibrium (radiation-induced) precipitates and the dissolution of thermally stable phases have been observed in austenitic steels [1,2]. The composition of the precipitates formed frequently also appear to be modified by irradiation in comparison with that observed after normal thermal aging [3]. In particular, neutron irradiation retards the formation of M,,C, carbides [4] in austenitic steels, while these precipitates form easily at grain boundaries during annealing in a wide range of temperatures [5]. M.,,C, precipitates have been detected in AISI 316 during EBR-2 irradiation at temperatures above 550600°C only [4]. Pedraza and Maziasz [4] have pointed out, that there is a correlation between M,,C, precipitation and radiation-induced segregation (RIS) decreasing. Chromium and iron depletion at point defect sinks has been observed in model Fe-Cr-Ni alloys and technological steels. This phenomenon has been theoretically investigated in the framework of RIS theory [6]. It was shown that chromium content at grain 0022-3115/93/$06.00
boundaries drops significantly with temperature decreasing. Therefore the lowest temperature of chromium-rich M,sC, precipitate stability under irradiation may be related to the decrease of Cr concentration. Nickel- and silicon-rich y’ and G precipitates do not form in austenitic steels during thermal aging but they were observed after neutron irradiation at 400600°C. These precipitates are often adjacent to pointdefect sinks [2]. Studies indicated that a sufficiently high silicon concentration at point defect sinks should be reached for y’ precipitation in dilute Si-Ni alloys [7,8]. This Si enrichment is caused by RIS of silicon via an interstitial mechanism [9]. As it was shown by Williams and Titchmarch [lo], during annealing G phase forms in an alloy similar to the type FV548 steel for major components but with = 6 wt% Si. Therefore the existence of the highest temperature for the growth of y’ and G phases in irradiated austenitic steels may be related to a low silicon concentration near point defect sinks due to some suppression of RIS at high temperatures. In this paper a method to estimate the influence of RIS on temperature regions of stability of secondary phase precipitates is developed. The theoretical model for segregation in Fe-Cr-Ni alloys proposed in ref. [ll] is modified to account for the segregation of silicon. The lowest temperature of chromium-rich M& carbide stability and the highest temperature of
0 1993 - Elsevier Science Publishers B.V. All rights reserved
%A. Pechenkin, G.A. Epor’ / The influence of RIS on precipitate stability
304
silicon-rich y’ and G phases stability depending on irradiation conditions and alloy mirostructure are estimated.
2. Model description Irradiation can variously influence the temperature boundaries of precipitate existence in alloys as it was shown in the introduction. However, RIS may be a unified reason of such influence if these precipitates are associated with point defect sinks or precipitates are sinks themselves (incoherent precipitates). The instability of a certain precipitate occurs at temperatures when the concentration of the “crucial” component which is set due to RIS near sinks proved to be lower than corresponding solubility limit for this precipitate. This approach will be used below to determine the temperature boundaries of stability for the two types of precipitates most influenced by irradiation in austenitic stainless steels: radiation-retarded M,,C, and radiation-induced y’ and G phases. 2.1. M,,C,
precipitates
The formation of M&, precipitates at grain boundaries in austenitic stainless steels during thermal aging has been the subject of many investigations in the last two decades [5,12,13]. A considerable interest to this phenomenon is explained by strong correlation between precipitation and corrosion resistance of alloys. The main problem of theoretical treatment of this process is the evaluation of chromium concentration C& in thermodynamic equilibrium with M,,C, carbide, because these grain boundary precipitates-may grow only if the chromium concentration in alloy is higher than C&. A thermodynamic model of M,,C, carbide formation in Types AISI 304 and 316 stainless steels has been developed by Bruemmer [5]. Chromium carbides Cr,,C, were considered as the model precipitates since chromium is the primary component of carbides in these steels. According to ref. [5]:
cg = K,-d'23yCrl(yCCC)-6/23, where C, is the carbon concentration (in atomic units), ycr and yc are the activity coefficients of chromium and carbon, respectively, and K,, is the equilibrium constant [5]: K,, = exp( - AG/RT),
ture range 400-850°C (for more details, see below section 3). The absence of M,,C, carbides on grain boundaries in austenitic stainless steels under irradiation at temperatures below 500-600°C may be caused by RIS. RIS leads to nickel enrichment and chromium depletion at point defect sinks. The depletion is more pronounced at lower irradiation temperatures, where the steadystate chromium concentration at sinks C& can be lower than the thermal equilibrium concentration C&. Since the chemical composition of M,,C, in steels under irradiation is similar to that under thermal aging [14], one can assume that the thermodynamic model of M,,C, carbide evolution and the estimate of C& derived in ref. [5] are also valid in the case of irradiation. Let us evaluate C$i. Approximate analytical expressions for steady-state component profiles near point defect sinks in ternary substitutional alloy A-B-C caused by RIS have been derived in ref. [II]. These formulae are in a satisfactory agreement with computer calculations and experimental data available on the major element radiation-induced segregation in concentrated Fe-Cr-Ni alloys obtained in refs. [15,16]. A-component profile has the following form: F’/‘IC
CA =
A0
1 - CA,, - C,, + F”F’(CA,, + F”‘-““C,,,)
’ (3)
F = C,(r)/(C,>,
where d: are the partial diffusivities ((u = Cr, Ni, Fe) of alloy components via vacancy (k = v) and interstitial (k = i) mechanisms, Cue are the alloy component concentrations in unirradiated alloy, dt = dfj, exp(-E,k,/kT) (E,k, is the cY-component migration energy), D,, are the point defect diffusion coefficients in unirradiated material (DkO = dk,,(C,,d&/dE, + CNid$/dE, + C,,) for Fe-Cr-Ni alloy). C,(r) is the vacancy concentration profile near a given sink [ll] and (C,) is the bulk average value of vacancy concentration:
(2)
AG is the free energy of carbide formation and T is the temperature. This model is valid over the tempera-
(c.);o.5(~~+[~~-~)+c.,;
(4)
KA. Pechenkin, G.A. Epou / The influence of RIS on precipitate stabiliiy
where K is the point defect generation rate, pa is the vacancy-interstitial recombination coefficient and ps is the point defect sink strength. The thermal equilibrium vacancy concentration can be expressed as C C, exp(-E,‘/kTl (ET is the vacancy formation?;ergy). It should be pointed out that for grain boundary one can obtain: (C,)/C,(O) = (C,)/C, = s, where s is the vacancy supersaturation in material under irradiation. Let indexes A, B and C denote Cr, Ni and Fe components, respectively, then C,(O) = C$:. Comparing C& and C& at various irradiation temperatures with the use of eqs. (3) and (1) it is easy to find the characteristic temperature TL above which C& < C& and, consequently, the growth of M,,C, carbides is possible at grain boundaries. 2.2. y ’ precipitates Gamma prime is a radiation-induced precipitate that does not form in technological steels during thermal aging. It forms in austenitic stainless steels during irradiation at temperature range from 400 to 550°C. These precipitates are usually attached to dislocations and dislocation loops [2,15]. For y’ precipitates to grow, local Ni and Si concentrations should likely be higher than corresponding solubility limits of these components for y’ phase. Thus, a theoretical description of Si and Ni concentration profiles near point defect sinks is necessary to determine the temperature range of y’ precipitation. Let us consider a simple model of Si and Ni concentration behaviour in irradiated Fe-Cr-Ni-Si alloys, where Si is a solute. It should be noted that silicon content in austenitic steels does not exceed several percents. Nickel enrichment at point defect sinks can be explained by a vacancy segregation mechanism [16181. Radiation-induced silicon segregation near sinks and the growth of y’ phase have been extensively studied in dilute Si-Ni alloys [7,19,20]. The available experimental data can be satisfactorily explained on the basis of interstitial segregation mechanism of Si. The binding and migration energies of Si-Ni mixed dumbbells were estimated in this case [8]. In contrast to nickel and silicon, chromium and iron are always depleted at point defect sinks in irradiated austenitic steels [16,17]. Using this information one can simplify the problem if to consider a hypothetical ternary alloy A-B-C, where A corresponds to Si, B to Ni and C to the sum of Cr and Fe. Further we shall investigate the case of
305
high temperatures when interstitial atoms of different types are in thermal equilibrium [21]:
Cf c=
Cc #$c,+ca+ccY
(5)
where .$= exp(Ei/kT), Ei is the binding energy of mixed dumbbells AB and AC types (AA dumbbells are neglected due to low silicon content in alloy). This energy is required for the transformation of AB and AC dumbbells to those of BB, BC and CC. Since Si atom size is much smaller than that of major components in Fe-Cr-Ni-Si alloys, the binding energy of mixed dumbbells with Si only is taken into account in eq. (5). Interstitial atoms may be considered in thermal equilibrium if two conditions are fulfilled: 1) interstitial atoms of BB, BC and CC types have a chance to meet A atom during their free path. This condition is justified when the distances between vacancies and sinks are larger than that between A atoms. This holds for CA > 0.1 at% of interest, 2) mixed dumbbells of AB and AC types have a chance to be destroyed, i.e. to transform to interstitials of BB, BC and CC types (the reverse conversion) during their free path time 7,. This condition is fulfilled if the average time of the conversion TV is less than T,. Note, that l/r,
= Z,( C, + C,) exp( -E,b/kT)d&/a2,
l/Till =44(P,+PR(Cv)),
the geometrical factor Z, accounts for possible ways of the conversion (it is of the order of coordination number), a is the lattice constant. As a result one can evaluate the temperature T,,, above which the thermal equilibrium may be set: T,, =
E,b+E&k In
-UC,
E; + Cc>
’
(6)
a’(p, + CL&) where Ek c is the interstitial migration energy of B or C component. To is equal to 420 K at ps = 1013-1016 me2 and diffusion parameters adopted in this paper (see section 31. For simplicity we do not consider a nonideality of solid solution and correlation effects that allows us to derive alloy component profiles in an analytical form.
306
V.A. Pechenkin, G.A. Eporj / The influence of RIS on precipitate stability
In this case the equations for component and point defect fluxes near sinks take the following form: d,,C,
JA = -
+
i + CA d,,VC, i JB=
-
i
d&v+
C,;(r)
5dAi (1+ -
[l-
l]Cyi
i vc,4
tdAi 1+[5-l]c,vc’
d,i 1+~5_llcA
(6 - l)d,i + I+ [t _ l]C,
(7)
1’
ci
vc, 1
‘icBvcA
(8) J, = -D,VC,
+ C,( d,, - d,,)VC,
+ C,(d,v J, = _ vd,i I
- d,,)VC,,
+ (d,i -d,i)C~
C,,,d&)/(C,,,,
concentration
(9) + (ifdAi -d,i)C~
1 + Et - llcA
c,
1. (10)
It is accounted in eqs. (7)-(10) that CA + C, + Cc = 1. In the case of binary alloy this system is identical to that suggested by Bakai and Turkin [8] for y’ phase in Si-Ni alloys. Their model is successful in evaluation of the shift of y’ phase equilibrium curve in dilute Si-Ni alloys under irradiation. The model proposed (eqs. (7)-(10)) may have reasonably wide areas of application, because it describes RIS arising due to migration of impurity-interstitial atom complexes (mixed dumbbells) and due to inverse Kirkendall effect. It is suitable for the study of buildup of undersized impurities (for example, Si or P types) near point defect sinks in irradiated austenitic stainless steels, in this case concurrent accumulation of nickel near sinks is accounted for. For usual level of silicon content in austenitic steels and with the binding energy Ej estimated in ref. [9], it is proved that [C, I 1. So we can take 1 + (5 - DC, = 1 in eqs. (7-10). Using the steady-state conditions JA = JB = 0 and Ji = J, these equations may be transformed to the set of equations for AC, and AC, of ref. [ll] (eq. (10)) if to replace the value of dAi by .$d,,. Employing the results of ref. [ll] it is easy to derive Si and Ni profiles near sinks. Si profile C,(r) has the form of eq. (3) where db = td&, the effective partial diffusion coefficient d$ = (C,,,,dk, +
+ CCr,,)), (k = i, v). The profile of Ni
is:
= CNi,OICsi(r)/Cs,,o]F(P~l)‘El.
(11)
Due to RIS both Si and Ni concentrations may exceed the solubility limits of these elements for y’ phase in stainless steel. This may lead to continuous growth of y’ precipitates. But the question arises: is the concentration of nickel or silicon crucial for the growth of y’ precipitates in steels? Experimental data (see section 3) indicate that this crucial element seems to be silicon. In particular, with increasing Si content in steel the temperature range of y’ precipitate formation is significantly expanded. This fact allows us to assume that the growth of y’ phase is possible at temperatures T < Tu when the local silicon concentration at point defect sinks Cc exceeds the thermal equilibrium silicon concentration C&(T). A thermodynamic model of y’ precipitate formation in steels has not yet been developed and the value of C& is unknown. Below (see section 3.3) we tried to construct some approximation of it on the base of data available about y’ phase in binary Si-Ni alloys and to estimate the highest temperature of y’ phase stability TH.
3. Comparison
of the theory with experimental
data
3.1. Diffusion parameters
For vacancy migration mechanism of Fe, Cr and Ni in steels we use the parameters of Norris et al. [17]. A satisfactory agreement was reached in ref. [17] between calculated profiles of these components near grain boundaries and experimentally measured ones in 20/25/Nb steel after annealing and irradiation using the following constants: d& = d& = d& = 1.16 X 1O-5 m’/s, E&, = 1.3 eV, E&, = 1.2578 eV, EAim = 1.3784 eV, Ej = 1.6 eV, c0 =‘exp(l), pn = 8 X 10” m-‘, and taking the cascade efficiency of point defect creation as 0.1. It should be noted, that both this set of parameters and that from the work of Perks and Murphy [16] lead to similar component profiles near point defect sinks in irradiated Fe-Cr-Ni alloys. This may stem from their common origin from high temperature experimental data by Rothman et al. [22]. Experimental data on diffusion parameters of Si in steels and on interstitial component diffusivities in Fe-Cr-Ni alloys are lacking now. To estimate these diffusion characteristics we shall use both the experi-
bCA.Pechenkin, G.A. Epou / The inj7uence of RIS on precipitate stability
mental data on y’ phase formation in Si-Ni alloys and on segregation profiles of Si and Ni near grain boundaries in PCA [23]. For alloy component profile calculation the partial diffusion coefficient ratios are necessary. These ratios can be expressed in terms of migration energy differences for various components. Besides, for Si migration the value of E = E& + Eki,, - E&, is important. This value was estimated by Bartels et al. [9] for dilute Si-Ni alloy: E = 0.14 eV (binding energy of Si-Ni mixed dumbbells Et Ni z 0.23 eV). The influence of silicon RIS on y’ phase evolution in dilute Si-Ni alloys has been theoretically studied by Bakai et al. [20]. They have estimated the high temperature boundary for y’ phase growth using the value of E from ref. [9] and Eki,, = 0.15 eV. The agreement between theory and experiment was obtained in ref. [20] with the suggestion of low vacancy formation energy E,’ = 1.4 eV in Si-Ni alloy as compared with usually adopted value of 1.6-1.7eV in pure nickel. The use of such low formation energy for dilute Ni-Si alloy seems to be questionable, because Si atom is undersized in nickel and the binding energy of Si atommonovacancy is likely small. An alternative possibility for the improvement of theoretical predictions is connected with higher silicon diffusivity via a vacancy mechanism than that of nickel in Si-Ni alloys [24]. Our calculations show that the best agreement between experimental data presented in refs. [25-271 and the theory in the case of highest temperature T, for y’ phase growth in Si-Ni alloys is achieved at E,V = 1.6 eV and d,‘,/dci = exp(0.12 eV/kT).
307
Table 1 Alloy composition (wt%) Elements
Fe Ni Cr MO C Si
Alloys PCA
304
316
FV548
Balance 16.2 14.0 2.3 0.05 0.4
Balance 8.75 18.5 0.2 0.06 _
Balance 10.9 17.4 2.17 0.05 0.5
Balance 11.8 16.5 1.44 0.11 0.4
The segregation profiles of major components and silicon near point defect sinks in Si-doped “pure” Fe-Cr-Ni alloys have not been experimentally investigated in detail. Such profiles were studied in technological steels only. Their interpretation proved to be too complicated because of the influence of other impurities and precipitates adjacent to the sinks (this problem has been discussed in ref. [12]). Kenic et al. [23] have measured silicon and major component profiles near grain boundaries in PCA irradiated at 420°C in FFTF. Experimental data and results of our calculations (using the model described in section 2) are shown in fig. 1. The point defect generation rate was taken as K = 10e6 dpa/s and the cascade efficiency as 0.1. The alloy compositions are given in table 1, where the concentrations of only those components of alloys are indicated, which were used in calculation or in their interpretation. The dotted line corresponds to parameters E z 0.14 eV and d&/d& = exp(0.12 eV/
PCA 42ooc
0
-25
,o-150 ( 1
0 r
I
I
1
7
1
r(
cc5
DISTANCE FROM GRAIN BOUNDARY (nm) DISTANCE F$M GR;N BO::DARY2&m) Fig. 1. Comparison of experimental 1231composition prof lies (Ni - solid circles, Si - circles) across a grain boundary of PCA neutron irradiated to 9 dpa at 420°C with profiles, calculated by eqs. (3) and (11).
308
%A. Pechenkin, G.A.
Epou
/
The influence of RIS on precipitate stability
kT). Interstitial partial diffusivities of alloy components (Fe, Cr, Ni) were taken to be identical. It is seen from fig. 1 that the theory predicts too large Ni concentration near the-grain boundary. The agreement of theory with experiment can be improved if to suggest that mixed nickel dumbbells migrate slower than Fe and Cr ones. The result of calculation with dki/di = exp( - 0.05 eV/kT), where d& is the partial interstitial diffusivity of Fe and Cr is shown by the solid line in fig. 1. This value will be used below to calculate precipitate stability in steels. It should be noted, that the assumption of slower Ni migration (as the chemical element with maximum size misfit [28]) as compared with Fe and Cr migration is in a qualitative agreement with the results of Murphy [29]. It was shown that the migration of mixed dumbbells can be significantly retarded due to slow rotation of these dumbbells in a concentrated substitutional alloy [29]. 3.2. The lowest temperature of M&,-precipitate
stability
under irradiation
/
‘/
%
E -_-_-
FV 548
ol”,,‘~‘,,I,-““‘,,““““‘l”““‘,‘I Fig. 2. Temperature concentrations C&
In yc=
-1.845 +5100/T+
C,(11.92 - 6330/T)
- CNi(2.2 - 7600/T) + C&(24.4 - 38400/T) - C$(96.8
- 84800/T),
550
600 TEMPERATURE
650 (“C)
- 700
dependence of equilibrium chromium and steady-state concentrations C&v at grain boundaries.
(12)
where T is the temperature in K, Cm is the bulk nickel concentration and C,*, is the effective chromium concentration: C& = co, + 0.35c,,, (Cc, and C,, are the bulk concentrations MO, respectively) ycr = 10.55 - 94.84T, + 282.9T; - 242.8T;,
As it was discussed in section 2, the growth of M,,C, carbides is possible at temperatures, wherein the steady state chromium concentration C’& at grain boundaries exceeds the equilibrium one C& The latter can be calculated from eq. (l), if values of yCr, yc and AG are known. The free energy of Cr& carbide formation in Types AISI 304 and 316 steels has been deduced by Bruemmer [5] as AG = 98 280-9.2T (cal/mol). The composition of M,,C, carbides in 304 steel is very similar to that of Cr,,C, ones but they contain some amount of iron. The constitution of car-
500
bides in 316 steel is more complex, normally (Cr,,Fe,Mo,Ni)C, [14]. The deviation of M,sC, composition from that of Cr,,C, and the influence of other carbide formers (for example MO, Ti, Nb) can be accounted for in activity coefficients y. Bruemmer [5] suggested the following activity coefficients for these steels:
(13) of Cr and (14)
where TP = T/2000 for steel without molybdenum and T, = (T - 30)/2000 for steel with molybdenum. This model is valid over the temperature range 400-850°C (see for details ref. [5]). The calculated temperature dependencies of equilibrium chromium concentration C& (eq. (1)) and steady-state one Cg; (eq. (3)) for steels AISI 304, 316 and FV548 are shown in fig. 2. It is seen that C$ is increased slowly but the magnitude of CE; is increased rapidly with temperature increasing. This behavior of C& is connected with the significant drop of vacancy supersaturation (see eqs. (3) and (4)). To calculate Cz: the following parameters were used: ps = 1014 m-‘, K = 1O-6 sP ‘. The composition of steels is shown in the table. The parameters of Norris et al. [17] for the vacancy mechanism of diffusion, and for interstitial one d,&/d&, = exp( - 0.05 eV/kT), db,/d& = 1 were taken. As it is seen from fig. 2, the characteristic temperature T,, above which M,,C, carbides can grow on grain boundaries in AISI 304, 316 and FV548 steels irradiated with fast neutrons is close to 550°C. It should be pointed out that irradiation conditions and the microstructure of materials may be significantly varied. For example, the point defect generation rate K depends on the reactor power and on the location in reactor core. The total sink strength depends on the preliminary treatment of a material (especially on the extent of cold work), irradiation dose, neutron spectrum, secondary phase precipitation. The carbon content in steels may be different also. The sensitivity of
VIA. Pechenkin, G.A. Epol: / The influence of RIS on precipitate stability 650 L 600
\\\
j.
450 j iA
-1
--_ -.
;
C1=0.06 wt wC c2=0.01 wt SC Kl=lO -6 dpa/s K2=10 -’ dpa/s
400: 10 IS
,""T
Cl,Kl
‘_.._
"""I 13 s1,o,cDEiwIT:"(m2)
_>
. Cl,K2
"""'I 10 I8
Fig. 3. The dependence of low temperature stability limit of M,,C, precipitates CT,) on sink density (p,).
TL to these parameters is shown in fig. 3. The composition of 304 steel is used for calculations because the value of TL is not sensitive to small variation of Ni and Cr contents. It is seen from fig. 3 that T, drops significantly with increasing sink density and/or with decreasing point defect generation rate. This behavior is connected with the decrease of vacancy supersaturation. Besides, the temperature T, is decreased with increasing carbon content due to the decrease of C,$ Experimentally, a great deal of work has been carried out to study the behavior of various precipitates under irradiation in austenitic stainless steels (see e.g. refs. [1,2]), but only in few works M,C, carbides were investigated in detail because of very high temperature of M,,C, formation in irradiated steels. The estimates of T,_ found above are in a satisfactory agreement with experimental data available. Cold worked (CW) type 316 steel has been examined in ref. [4] after EBR-2 irradiation. The formation of M,,C, precipitates on grain boundaries was observed at T > 600°C (pd = 1014 m-‘) in Ti-stabilized 316 steel. M&Z, precipitates in nonstabilized solution-treated steel (P,, = 2 x lOi m-‘) have not been detected in the temperature range investigated (500 to 630°C). 15Ni/15Cr Ti-stabilized steel (CW) irradiated in RAPSODIA at 400-600°C has been studied in ref. [30]. M,C, precipitates on grain boundaries were observed at temperatures higher than 560°C. These precipitates were not detected in the steel samples with lower carbon content. Titanium stabilized commercial 16Cr-15Ni-3Mo steel (20% CW) has been microscopically investigated
309
after irradiation in BN-600 over the temperature range 350-600°C [31]. It was found, that M,,X, carbides are formed on grain boundaries at temperatures above 500°C. Specimens of Nb-stabilized FV548 steel after DFR irradiation at 380-730°C have been examined in ref. [14]. Unfortunately, only summary data concerning M,,C, formation on grain boundaries and in grain bulk have been presented. It was shown, that these carbides are formed at temperatures above 550°C in the annealed steel and above 475°C in CW samples. The very high sink density both in CW (pd = 4 X 1014 me2) and annealed (pd = 2 X 1014 rne2> specimens at T g 500°C should be noted. The authors of ref. [14] pointed out that the contribution of finely dispersed NbC carbides into the total sink density can exceed that of dislocations. It should also be noted that the carbon content in FV548 is higher than that in AISI 304 and 316 steels. The estimates of T, derived above are valid for M,,C, carbides on grain boundaries. Similar estimates can be derived for the precipitates adjacent to other sinks. The influence of RIS on the growth of M,,C, precipitates in the interior of grains depends on the coherency of precipitates with matrix [32]. The absence of bulk M,,C, in the grain interior at low irradiation temperatures can be explained by the precipitate incoherency with matrix. The summary of data concerning the microstructure of 316 steel with different cold work levels after irradiation in several reactors indicate that M,,C, precipitates form at temperatures T > 500°C [33]. Bulk M,,C, precipitates in DFR-irradiated FV548 steel were observed at T > 475°C and in 316 steel at T > 425°C [3]. It was pointed out however, that precipitates of the form of bicrystals M,,C,-M,C, M,sC,Laves, M,,C,-n are often observed in type 316 stainless steel. 3.3. The highest temperature of y ’ phase stability A thermodynamic model of y’ precipitate formation in steels has not yet been developed and the value of C$ is unknown. With experimental data [17] on silicon profiles near grain boundaries containing these precipitates it is possible to obtain an upper estimate of C$ only. y’ phase growth both under and without irradiation has been thoroughly investigated in binary Si-Ni alloys where the composition of this phase is Ni,Si. In this case the equilibrium Si concentration depends on the temperature as follows [34]: C&&T)
= 0.283 exp( - 0.077 eV/kT).
(15)
310
V.A. Pechenkin, G.A. Epor / The influence of RIS on precipitate stability
The chemical composition of y’ precipitates in austenitic stainless steels is more complex than that in Si-Ni alloys. Indeed, y’ phase in steels contains significant amounts of Fe, Cr, Mn, MO [2]. Relative Si and Ni contents in y’ precipitates are lower in steels than those in pure Si-Ni alloys. So one can expect that in steels the thermally equilibrium concentration of silicon near y’ precipitates is lower than that predicted by eq. (1.5): C&(T)=6C&(Ni)(T), where 6 I 1 is the parameter, which must depend on alloy composition. A rough approximation C&(7’) may be improved if the thermodynamic model of y’ precipitates in steels will be developed. The profile of silicon is considerably altered at distances of the order of several lattice parameters near a sink as RIS calculations have shown (see fig. 11. So for the growth and especially for the nucleation of y’ precipitates the silicon concentration not only at sink boundary, but in the whole region of the thickness d near sink boundary should be higher than C&(T) Therefore the highest temperature T, of y’ stability in austenitic stainless steels can be estimated from the following equation: (16) where 0 5 d I a, a is the lattice constant. The model developed can also be used for the analyses of G phase stability as it will be shown in section 3.4. The highest temperature Tn of y’ precipitates stability was calculated by eq. (16) using the following diffusion parameters: E z 0.14 eV, d&/d& = exp(0.12 eV/kT), dki/d& = exp( -0.05 eV/kT), dh,/d& = 1. The results of T, calculation at K = lop6 dpa/s for AISI 316 versus the point defect sink density are shown in fig. 4. This temperature depends strongly upon the silicon content Csi, the ratio 6 of Si solubility limits for y’ phase in steel and that in nickel, the thickness d defined above and the sink density ps. It is seen from fig. 4 that at ps = lOi me2 the predicted magnitude of TH is 500-550°C for austenitic stainless steels with 0.5-l wt% Si. This estimation is in an agreement with available experimental data [2]. y’ phase forms in type 316 or Ti-modified steels during FBR irradiation at 400-550°C [2]: But y’ can form at 600°C and above in type 316 steel with > 2 wt% Si. y’ forms in D9 alloy (Csi = 2 wt%) more abundantly than in stainless steels with lower silicon content. -y’ phase in 20% CW AISI 316 is formed at temperatures lower than 500°C as Itoh et al. [33] pointed out. Yang [35] has presented the same results for EBR-2 irradiated AISI 316 and AISI 316(Ti).
600 J
550i
-._
*.
..’
2 at.% Si ‘-.
400 :
3
The dependence of high temperature stability limit of y’ and G phase precipitates (T,) on sink density (p,).
Fig. 4.
The microstructure of 20% CW titanium stabilized commercial 16Cr-15Ni-3Mo steel irradiated in BN-600 reactor was studied by Dmitriev et al. [31]. y’ formation was detected at 425 and 490°C. The increase of He/dpa ratio results in a destabilization of -y’ phase as it was pointed out in ref. [2]. It is likely due to the total sink strength increase as a result of helium bubble formation. 3.4. Comparison of y ’ and G phase stability It is interesting to analyze y’ phase behavior in Ti-doped steels. y’ forms at several dpa but dissolves after 20 dpa in neutron irradiated CW N-lot AISI 316 and PCA as Maziasz [2] pointed out. At higher doses M,C and G phases formation begins. G phase precipitates appear abundantly in Nb or Ti-doped Fe-Cr-Ni alloys, but y’ phase was not observed in Nb-stabilized steels. G phase is a complex silicide M6Ni,,Si, (M can be Ti, Nb, Mn, Cr) compound. This phase is enriched in Si and Ni similar to y’ phase. But relative Si content in G phase is lower than that in y’ phase. G phase precipitates are often associated with voids and grain boundaries. During annealing G phase forms in an alloy with the same major component concentrations as in FV548 steel but with higher Si content (Csi = 6 wt%) as it was shown by Williams and Titchmarch [lo]. This experiment proves the critical influence of silicon on G phase formation and growth. From the above consideration one can assume that y’ and G phases are competitive radiation-induced precipitates. It is quite probably that the formation energy of y’ phase is lower in Ti-doped steels and that
VIA. Pechenkin, G.A. Epov / The influence of RIS on precipitate stability
of G phase is lower in Nb-doped ones. Correspondingly, the silicon solubility limit C& is likely lower for G phase. So y’ phase must precipitate first in Ti-stabilized steels. The increase of sink density and/or silicon matrix depletion due to %-rich precipitates growth can reduce silicon concentration near sinks below y’ phase solubility limit. This would result in y’ precipitate dissolution and G phase formation, since the silicon solubility limit is lower for G phase. Subsequent growth of G phase precipitates can be supported by silicon dissolved from y’ phase. So the model developed in section 3 can be used for the estimation of the highest temperature of radiation-induced G phase stability. In this case we can adopt that the magnitude of S in eq. (16) for G phase is lower than that for y’. It means that the temperature range of G phase precipitate stability is expected to be similar to that for y’, but the value of TH for G phase must be higher than that for y’ (see fig. 41. This consideration is in agreement with experimental data. G phase precipitates are formed in temperature range 400-650°C under fast neutron irradiation in Ti and/or Nb-stabilized austenitic stainless steels as Maziasz [2] pointed out. The same temperature range was found for AISI 316(Ti) in ref. [35]. According to Williams et al. [14], G phase precipitates in DFR irradiated FV.548 steel are formed up to 600°C. G phase formation is retarded with increasing sink density. These precipitates form more easily in annealed samples than in cold worked ones [2]. The increase of He/dpa ratio results in the retardation of G phase formation also. In particular, G phase has been observed in AISI 316(Ti) and PCA irradiated in EBR-2 (0.5 appm He/dpa) but has not been detected in these alloys after HFIR irradiation (70 appm He/dpa). This phase has been observed in annealed samples of PCA, but was not observed in cold worked ones after FFTF irradiation [2]. It should be pointed out, that the formation and growth of another siliconrich precipitates (especially M,C carbides) may significantly affect the evolution of y’ and G phases [lo]. No y’ and G phase precipitates were observed in irradiated austenitic steels at temperatures below 400°C except for the y’ formation in neutron irradiated 316 steel at 270°C (see work by Cawthorne and Brown [37]). The absence of these phases in steels under low temperature irradiation can be explained by two reasons. The first one is too large characteristic dose @a which is necessary to reach steady state component profiles at low temperatures, because the alloy component diffusivities are small. The results of computer calculations of the set of diffusion equations for point defect and component concentrations near a
311
grain boundary indicate that @s is very large at temperatures below 200-250°C only [16]. The second reason is the destruction of small precipitates by collision cascades. The effect of the displacement cascades on y’ formation in dilute Si-Ni alloys has been analyzed in ref. [19]. The lowest temperature of precipitate growth is shown to shift to approximately 400°C due to this effect.
5. Summary 1. The instability of chromium-rich M&Z, carbides at low temperatures in irradiated austenitic steels is explained by Cr depletion at grain boundaries as a result of radiation-induced segregation. The lowest temperature T,_ of M,,C, stability is equal to 550600°C depending on the material microstructure and irradiation conditions. 2. The high temperature boundary T, of siliconrich -y’ and G phase stability is due to the reduction of silicon concentration near point defect sinks at high irradiation temperatures and equals 500-600°C. 3. Both temperatures T,_ and TH are decreased with increasing sink density and decreasing point defect generation rate. T,_ drops with increasing carbon content while TH does with decreasing silicon concentration.
Acknowledgement
The authors would like to thank Prof. Konobeev for useful discussions of the work.
Yu.V.
References
111K.C. Russell, Prog. Mater. Sci. 28 (1984) 229. [2] P.J. Maziasz, J. Nucl. Mater. 169 (1989) 95. 131T.M. Williams, Effects of irradiation on Materials: 11th Conf., ASTM-STP 782 (American Society for Testing and Materials, Philadelphia, 1982) p. 166. 141D.F. Pedraza and P.J. Maziasz, Radiation induced Changes in Microstructure: 13th Int. Symp. (Part l), ASTM-STP 955 (American Society for Testing and Materials, 1987) p. 161. [51 S.M. Bruemmer, Corrosion 46 (1990) 698. 161C.A. English, S.M. Murphy and J.M. Perks, J. Chem. Sot. Faraday Trans. 86 (1990) 1263. 171L.E. Rehn, P.R. Okamoto and R.S. Averback, J. Nucl. Mater. 80 (1979) 172.
312
VA. Pechenkin, G.A. Epoc: / The influence of RIS on precipitate stability
[S] AS. Bakai and A.A. Turkin, J. Nucl. Mater. 152 (1988)
331. [9] A. Bartels, F. Dworschak and M. Weigert, J. Nucl. Mater. 152 (1988). 82. [lo] T.M. Williams and J.M. Titchmarsh, J. Nucl. Mater. 98 (19811 223. [ll] V.A. Pechenkin and G.A. Epov, J. Nucl. Mater. 186 (1992) 269. [12] E.L. Hall and C.L. Briant, Metall. Trans. A 15 (1983) 793. [13] SM. Bruemmer and L.A. Charlot, Scripta Metall. 20 (1986) 1019. [14] T.M. Williams, J.M. Titchmarsh and D.R. ArkelI, J. Nucl. Mater. 107 (1982) 222. [15] R.M. Boothby and T.M. Williams, J. Nucl. Mater. 152 (1988) 123. [16] J.M. Perks and SM. Murphy, Proc. Conf. on Materials for Nuclear Reactor Core Applications, Bristol, October 1987, vol. 1 (BNES, London, 1987) p. 165. [17] D.I.R. Norris, C. Baker and J.M. Titchmarsh, in ref. [16] p. 277. [18] S. Dumbill and T.M. Williams, in ref. [16] p. 119. [19] P.R. Okamoto, L.E. Rehn and R.S. Averback, J. Nucl. Mater. 108&109 (19821 319. [20] A.S. Bakai, A.V. Buz and A.A. Turkin, Met. Fiz. 13 (19911 68. [21] H. Wiedersich, P.R. Okamoto and N.Q. Lam, J. Nucl. Mater. 83 (1979) 98.
[22] S.J. Rothman, L.J. Nowicki and G.E. Murch, J. Phys. F 10 (1989) 383. [23] E.A. Kenik, T. Inazumi and G.E.C. Bell, J. Nucl. Mater. 183 (1991) 145. [24] D. Treheux, A. Heurtel and P. Guiraldenq, Acta Metall. 24 (1976) 503. [25] P.R. Okamoto and L.E. Rehn, J. Nucl. Mater. 83 (1979) [26] 2. Janghorban and A.J. Ardell, J. Nucl. Mater. 85&86 (1979) 719. [27] A. Barbu, G. Martin and A. Chamberod. J. Appl. Phys. 61 (1980) 6192. [28] C. Dimitrov and 0. Dimitrov, J. Nucl. Mater. 152 (1988) 21. [29] S.M. Murphy, J. Nucl. Mater. 182 (1991) 73. [30] D. Gilbon et al., in ref. [16] p. 307. [31] V.D. Dmitriev et al., Proc. Int. Conf. on Radiation Materials Science, Alushta, USSR, May 22-25, 1990, vol. 3, p. 54. [32] A.S. Bakai and A.A. Turkin, Fiz. Met. Metalloved. 3 (1991) 67. [33] M. Itoh, Sh. Onose and Sh. Yuhara, in ref. [4] p. 114. [34] P.K. Rastogi and A.J. Ardell, Acta Metall. 17 (1969) 595. [35] W.J.S. Yang, in ref. [4] p. 628. [36] P.J. Maziasz, J. Nucl. Mater. 122&123 (1984) 472. [37] C. Cawthorne and C. Brown, J. Nucl. Mater. 66 (1977) 201.