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Interdiffusion of cerium in Fe-base alloys with Ni or Cr
journal of
nuclear
Journal of Nuclear Materials 204 (1993) 165-172 North-Holland
Interdiffusion
~~0~
of cerium in Fe-base alloys with Ni or Cr
P.C. Tortorici and M.A. Dayananda Purdue University, West Lafayette, IN 47907-1289,
USA
Isothermal interdiffusion studies relevant to lanthanide interactions with cladding alloys in the Integral Fast Reactor program were carried out at 425°C by employing solid-solid diffusion couples assembled with disks of Ce and disks of Fe, Ni, and Fe-lO.lNi, and Fe-20.10, binary alloys (com~sition in at%). The diffusion structures and inte~etallic layers which developed in the various couples during the diffusion anneal were metallographically examined and analyzed by SEM-EDS techniques for concentration profiles. Computer programs were developed to construct profiles of concentrations and to evaluate interdiffusion fluxes and effective interdiffusion coefficients for the individual components over selected regions of the diffusion zones of the various couples. Intrinsic diffusion data were calculated at marker planes in the Ni,Ce, and Fe&e phases developed in the Ni vs Ce and Fe vs Ce couples, respectively. The intermetallic phases and diffusion layers observed in the various couples are discussed in the light of phase diagrams and experimental diffusion paths.
1. Introduction The main features underlying the integral fast reactor (IFR) concept which is being developed at Argonne National Laboratory include the use of U-Pu-Zr metallic fuel, liquid sodium cooling, a pool type reactor configuration, and the reprocessing of fuel [l]. The metallic U-Pu-Zr fuel offers high thermal conductivity, ease of fabrication, good irradiation behavior, high burn-up potential, among other benefits. During irradiation, the U-Pu-Zr fuel swells and comes into contact with the stainless steel cladding enclosing the fuel element. Also during the irradiation process, a number of fission products including lanthanides (Ce, La, Pr among others) are generated. The migration of the lanthanides through the fuel towards the fuel/clad interface can result in their chemical interaction with the stainless steel cladding materials. Such interactions can result in the formation of intermetallic phases and low melting eutectics, which adversely affect the structural integrity of the cladding alloy as a result of localized melting. The extent of the interaction between the fuel containing lanthanides and cladding alloys is among the major issues that are currently being investigated in the context of fuel/clad compatibility and assessment of acceptable fuel/cladding combinations. In this study, interdiffusion experiments were carried out at 425°C with soiid-solid diffusion couples assembled with disks ~22-3IiS/93/$06.~
of Ce and disks of Fe, Ni, and Fe-lO.lNi, and Fe20.1Cr binary alloys. The diffusion layers that developed in the various couples are examined for the jdentification of intermetaIli~ phases, analyzed for average effective interdiffusion coefficients for the individual components, and described with the aid of the phase diagrams and diffusion paths.
2. Experimental procedure Ce, Ni and Fe (99.9% pure) were obtained from Rhone-Poulenc Inc, Alpha Products Inc, and Coodfellow Inc., respectively. Binary alloys with compositions of Fe-lO.lNi, and Fe-20.1Cr were fabricated by vacuum induction melting [2]. Charges were melted in alumina crucibles under an argon atmosphere, and drawn up fused silica draw tubes, 10 mm in diameter. AI1 alloys were homogenized at 1150°C for 7 days in an evacuated quartz capsule. Diffusion disks, approximately 5 mm in diameter and S mm thick, were sectioned from Ce, Ni, Fe and various alloys. The disk surfaces were ground through 600 grit Sic paper to ensure parallel faces. The disks were metallographically polished through 1 pm diamond paste in an Aldrich atmosbag with flowing helium (99.9%). This procedure was employed to ensure that the surfaces were free from an oxide layer; the helium environment was especially required for cerium
0 1993 - Elsevier Science Publishers E.V. All rights reserved
P.C. Tortorici, MA. Dayananda / Interdiftiion
166
whose reactivity with air and water based solvents is severe. The polished disks were employed in assembling sandwich couples inside a Kovar steel jig consisting of two end plates and three threaded Kovar steel rods. The couples consisted of a Ce disk sandwiched by selected alloy disks, one on either side. Kovar steel 64Fe-29Ni-17Co at%) was chosen for the jig due to its low coefficient of thermal expansion. The assembled couples were then placed in quartz capsules which were sealed at one end under a constant flow of helium gas. The capsule was then attached to a vacuum system, evacuated and backfilled with hydrogen gas several times. After a final evacuation, the capsule was sealed and annealed in a horizontal Lindberg three-zone tube furnace at 425°C for 4 days. The annealed capsules were quenched in an ice water bath after the diffusion anneal. The couples with the Kovar jigs were removed and cold-mounted in a clear epoxy resin. The mounted couples were sectioned with an Isomet diamond saw to expose surfaces parallel to the diffusion direction. The exposed sections were then mechanically polished on 600 grit Sic paper and through 1 pm diamond paste on a cloth wheel with dehydrated ethyl alcohol used as a lubricant in all steps. The polished sample was immediately transferred to a JEOL 35CF scanning electron microscope (SEMI, equipped with a Tracer Northern Series II energy dispersive X-ray analyzer. The couples were analyzed by point-to-point counting techniques for concentration profiles and phase identification. The intensities of X-ray K, lines for Fe (6.403 keV), Ni (7.477 keV), Cr (5.414 keW, and L, line for Ce (4.839 keV) were collected and stored on floppy disks, then converted into compositions with the aid of pure elemental standards and a ZAF correction program. Secondary electron micrographs were taken to record the diffusion structure and intermetallic layers developed in the various couples.
of Ce in Fe-base alloys
Table 1 Phase layers and their thicknesses in the various couples annealed at 425°C for 4 days Couple
Phases observed a
Layer thickness OLm)
Ni vs Ce
Ni,Ce Ni,Ce, Fe&e (Fe + Ni),Ce (Ni + Fe&e, (Fe + Cr),Ce, Fe&e
10 240 20 IO 10 10 10
Fe vs Ce
Fe-lO.lNi vs Ce Fe-ZO.lCr vs Ce
a The designation of a phase layer is based on the ratio of concentration of Ce to the sum of the concentrations of the other elements present in the phase layer.
sponds to the ratio of the Ce concentration to the sum of all the other elements analyzed in the layer and is not based on any intermetallic structural data. Based on the counting statistics, the uncertainty in the EDS analysis of the major elements Ce, Fe, Ni, and Cr is within +O.S at.%. On the basis of the Ni vs Ce and Fe
(a)
wls 153s* 1400
3. Results (b)
3.1. Difkion
structures
and intemetallic
phases
The phase layers identified in the diffusion structures of the various couples in this study are listed in table 1. The intermetallic designations of the phase layers in table 1 are entirely based on compositional analysis by EDS ignoring the trace impurities such as C, 0, and N. The designation for a phase layer corre-
iw D 100 FE!
Atom Percent Cerium
Ce
Fig. 1. The phase diagrams for the (a> Ni vs Ce and (b) Fe vs Ce binary systems adapted from ref. j3].
167
P.C. Tortorici, MA. Dayananda / Interdiffusion of Ce in Fe-base alloys
vs Ce phase diagrams [3] presented in figs. la and lb, respectively, six possible intermetallic compounds are observed between Ce and Ni, while only two can form between Ce and Fe. Ce and Cr have negligible solubility in each other and form no intermetallic compounds [31. 3.1.1. Binary couples: Ni us Ce and Fe us Ce The diffusion structure and the concentration profile for the Ni vs Ce couple are presented in figs. 2a and 2b, respectively. Two diffusion layers developed in this couple and correspond to Ni,Ce and Ni,Ce, phases of the phase diagram in fig. la. The intermetallit designation of the phases are based on the approximate ratio of Ni concentration to that of Ce. The approximate widths of the Ni,Ce and Ni,Ce, layers are 10 pm and 240 p,m, respectively. The Matano plane for the couple determined on the basis of mass balance is identified at x,, and a marker plane is identified at x, in the Ni,Ce, phase. A secondary electron micrograph and the concentration profile for the Fe vs Ce couple are presented in
Ni$e,
0.8
g
0.7
g
0.6
6
0.5
.g
0.4
2
0.3
5 B 0
0.2
u
(b)
0.1 0 0
5
10
15
20
25
30
35
40
4s
SO
Distance, x (Km)
0.9 0.8
3.1.2. Ternary couples: Fe-l~.lN~ Ce
LE 0.7 E 0.6 gj,
0.9
fig. 3. Only one diffusion layer, approximately 20 p,m wide, develops as can be seen in fig. 3a; the layer corresponds to Fe&e phase on the basis of the phase diagram in fig. lb. The width of the diffusion zone of the Fe vs Ce couple is appreciably smaller than that of Ni vs Ce couple. The interdiffusion of Ni in Ce is much more rapid than that of Fe in Ce. A marker plane is identified in the Fe&e phase in fig. 3b.
1 2 .s u
z 0 ‘G y
Fig. 3. (a) Diffusion structure and (b) concentration profiles for the Fe vs Ce couple annealed at 425°C for 4 days. x0 and x, refer to the locations of the Matano plane and the marker plane, respectively.
Ce
Ni$e
Fe20 1
(b)
0.5
Distance, x (pm)
Fig. 2. (a) Diffusion structure and (b) concentration profiles for the Ni vs Gz couple annealed at 425°C for 4 days. x0 and n, refer to the locations of the Matano. plane and the marker plane, respectxveiy.
us Ce, Fe-20.10
us
In figs. 4a and 4b are presented the diffusion structure and the concentration profiles for the Fe-lO.lNi vs Ce couple. Two diffusion layers observed in the micrograph in fig. 4a correspond to (Fe + Ni),Ce and (Ni + Fe),Ce, phases. The width of the diffusion zone is of the order of 25 pm and is similar to that observed for the Fe vs Ce couple. The diffusion structure and the concentration profiles for the Fe-20.1Cr vs Ce ternary couple are presented in fig. 5. Two diffusion layers corresponding to (Fe + Cr),Ce, and Fe&e phases are observed in the dif~sion zone whose width is appro~mately 20 pm.
P.C. Tortorici, MA. Dayananda / Interdiffusion of Ce in Fe-base alloys
168
The (Fe + Cr),Ce, layer developed in the couple does not correspond to any phase on the binary Fe-Ce diagram. The layer identified as Fe,Ce has negligible amounts of Cr, as can be seen from the Cr concentration profile in fig. 5b. In addition, Cr appears to build up in the (Fe + Cr),Ce, layer. The diffusion paths for all the ternary couples are presented on composition triangles in fig. 6. The paths are S-shaped as required for solid-solid couples. The single phase layers developed in the various couples are identified by the shaded‘areas on the composition triangles. In fig. 6a the dashed line segments, ab, cd and ef of the diffusion path for the Fe-lO.lNi vs Ce couple represent tie lines for two-phase equilibria at the interfaces between Ce and (Ni + Fe),Ce, phases, (Ni + Fe),Ce, and (Fe + Ni),Ce phases, and (Fe + Ni),Ce and Fe-lO.lNi phases, respectively. Similarly, the path segments, ab, cd and ef in fig. 6b correspond to two-phase equilibria at the interfaces between Ce and Fe,Ce phases, Fe&e and (Fe + Cr),Ce, phases and (Fe + Cr),Ce, and Fe-20.1Cr phases, respectively.
\ Fc 2C”
CFe+Cr)(Ce3
-
1 = .o z E ~ E g
0.9
”
0.5
.E t t
0.3
z
0.2
(‘C
0.8 0.7 0.6
(II)
0.4
I
I 0
5
10
15
20
25
30
35
40
4s
jfl
Distance. x (pm) Fig. 5. (a) Diffusion structure and (b) concentration for the Fe-2O.lCr vs Ce couple annealed at 425°C
profiles
for 4 days. x0 refers to the location of the Matano plane.
3.2. Average
I
(Fe+Ni)2Ce
\ Wi+Fe)3Ce7
(b)
effective
interdiffusion
coefficients
On the basis of an analysis by Dayananda [4,5], average effective interdiffusion coefficients and rootmean-square penetration depths can be determined for individual components in binary and multicomponent diffusion couples. This analysis is employed to calculate an effective interdiffusion coefficient for each component over selected ranges of concentrations in the diffusion zones of the diffusion couples investigated in this study. On the basis of Onsager’s formalism [6] of Fick’s law, the interdiffusion flux { of component i in an n-component alloy is expressed by [4]:
(1) where
Fig. 4. (a) Diffusion structure and (b) concentration profiles for the Fe-lO.lNi vs Ce couple annealed at 425°C for 4 days. x0 refers to the location of the Matano plane.
For component i, fii is the main interdiffusion coefficient, and the second term in eq. (2) incorporates cross interdiffusion coefficients, fi$ For an isothermal diffu-
P. C, Tortorici, MA. Daya~a~a
/ I~ter~~~~o~
Ce
169
of Ce in Fe-base alloys
sion couple assembled with two alloys of initial concentrations, C: and CE:, and diffusion annealed for time
t, the interdiffusion fluxes based on a laboratory fixed frame can be determined directly from the concentration profiles on the basis of the relation [7,8]:
(4 where x,, refers to the Matano plane. Upon integration of .( over x from +m to x0, one derives the following relation [4]: Ni
Fe-lO.lNi
Fe
I+-*“&
Ce
dx=
_;
A substitution
j"' c: (X -xo12 dCi of eq. (1) into eq. (4) yields
Icy(x -x0)’ dCi (b)
(5)
’
[cp-c;]
where Cc? refers to the concentration at the Matano plane and gi a is termed the average effective interdiffusion coeffidient for component i to the right of the Matano plane, over the range C+ to Cf. From eq. (5) an effective penetration depth for component i on the right-hand side of the Matano plane can be determined by:
Cr
Fig. 6. Experimental diffusion paths on composition triangles at 425°C for the couple (a) Fe-lO.lNi vs Ce, and (b) Fe-20.10 vs Ce. The phase designations are based on ratios of concentrations.
(6)
5ii$ = @-jg, where
Table 2 Average effective interdiffusion coefficients and root-mean-square for 4 days
xi ,R corresponds
penetration
to tiie root-mean-square
depths for the various couples annealed at 425°C
Diffusion couple assembly Ni vs Ce
Jje” N* *~ Ce,L =
Fe vs Ce
Ljeff Feor&.L
Fe-lO.lNi
vs Ce
B& fi$_
Fe-20.1Cr vs Ce
7.3 x lo- I5
= 2.7x
10-16
= 1.4x 10-16 = 2.6x lo-l6
ii&_ = 2.3 x lo-l6 @ff &J_ = 7.5 x lo-‘6 &&=-&9x10-‘7
$c:L=29x10-‘6 (I .
jjeff N*orCe,R
=
4.9x 10-14
&ff
FeorCe,R=8.4x10-‘7 L)eff Fe,R= 3.4 x lo- I7 r>$,
= 2.9x10-”
value
XN1,L= 70.8
fNi,R = 184.8
x,,, = 13.7 x Fe,L = 9‘4
X,,,
x Fe,R = 4s7
= 7.6
PNj,J_= 13.0
KNi*a= 9.6
@JR = 1.3x lo-= fi&=8.1~10-”
PCe,L= 12.1 x,,, = 22.7
fCeSR= 9.2 RFe,R = 7i5
gteff Cr.R = ---tiff ,,,=7.7x10-‘7
XQL
= ----
%,,
i,,,
=
14.0
= o
P,>, = 7.3
170
P.C. Tortorici, M.A. Dayananda / Interdiffusion of Ce in Fe-base alloys
of
((x-x,)*)“* A similar procedure can be applied to the concentration profile on the left-hand side of the Matano plane for the determination of an average effective interdiffusion coefficient, Di,L, and an effective penetration depth, X1,,_, Effective interdiffusion coefficients and penetration depths for the individual components were evaluated over selected phase layers on either side of the Matano plane for the Ni vs Ce, Fe vs Ce, Fe-lO.lNi vs Ce, and Fe-20.1Cr vs Ce couples and are reported in table 2. 3.3. Intrinsic diffusion in Ni,Ce,
and Fe&e
phases
For the Ni vs Ce and Fe vs Ce binary diffusion couples, marker planes were identified after diffusion in the Ni,Ce, and Fe,Ce phase layers, respectively, as indicated at X, in figs. 2b and 3b. The cumulative intrinsic flux, A,, of component i past a marker plane moving parabolically with time at a constant composition is obtained by integrating the intrinsic flux J, over time t [9]; thus, A,=jorl,
d x = -2tD,-
ac; ax x,
(i =
1, 2),
where D, is the intrinsic diffusion coefficient for component i. A, is determined graphically form appropriate areas under the concentration profiles. For the ratio of cumulative intrinsic fluxes, eq. (7) yields: IA,1
D,
On the basis of eq. (S), the ratio D&D,, of intrinsic diffusion coefficients in the Ni,Ce, phase was determined to be 15, while a value of 4 was obtained for the ratio of D&D,, for the Fe,Ce phase.
4. Discussion 4.1. Phase layer development
As reported in table 1, the phase layers that developed in the binary Ni vs Ce and Fe vs Ce couples include only a few of the various intermetallic phases which can form on the basis of the binary phase diagrams in fig. 1. Among the six possible intermetallic phases between Ni and Ce, only two phases, Ni,Ce
and Ni,Ce,, were observed in the Ni vs Ce couple. The Ni,Ce, phase is expected to form on the Ce side, as there exists some solubility of Ni in Ce. The growth of the Ni,Ce, phase occurs faster towards the Ce side than in the opposite direction towards the Ni side, as can be seen in fig. 2b by the location of the Matano plane. This observation is consistent with the fact that Ni intrinsically diffuses nearly 15 times faster than Ce in the Ni,Ce, phase, as calculated on the basis of eq. (8). The small thickness of the Ni,Ce layer relative to that of Ni,Ce, indicate that the velocities of Ni/Ni,Ce and Ni,Ce/Ni,Ce, interfaces in the direction towards Ni are quite similar. Among the two phases, Fe,,&, and Fe,Ce that can form between Fe and Ce on the basis of the phase diagram in fig. lb, only the Fe,Ce phase was observed as a thin layer in the Fe vs Ce couple. Not all phases based on the phase diagram need to form in a multiphase diffusion couple, as the appearance of a phase in the diffusion zone is influenced by nucleation barriers, incubation time, and interdiffusion behavior in the adjacent phases [lo]. From a comparison of the widths of the diffusion zones for the Ni vs Ce and Fe vs Ce binary couples, it is apparent that the interdiffusion of Ni with Ce is appreciably faster than that of Fe with Ce. The phases, Ni,Ce, and Fe,Ce, formed in the two couples form eutectics with Ce at 477°C and 592°C respectively. In the context of lanthanide interactions with clad alloys, the formation of the Ni,Ce, and Fe,Ce phases can be considered undesirable. The layers of (Fe + Ni),Ce and (Ni + Fe),Ce, intermetallics developed in the ternary Fe-lO.lNi vs Ce couple shown in fig. 4 are comparable to the Fe,Ce and Ni,Ce, phases identified in the binary couples. In the (Fe + Ni),Ce phase, the Ni concentration is about 3 at%, while the concentration of Fe is about 3 at% in the (Ni + Fe&e, phase. Hence, the compositions of these phases are quite close to Fe-Ce and Ni-Ce edges of the composition triangle as indicated on the diffusion path in fig. 6a. The important thing to note is that the presence of 10 at% Ni in the Fe-base terminal alloy of the couple is enough to cause the formation of a layer of Ni,Ce, type phase containing a few at% Fe, although the thickness of the layer is quite limited as indicated in table 1. The ternary Fe-20.1Cr vs Ce couple which developed the layers of (Fe + Cr),Ce, and Fe&e as shown in fig. 5 provides an insight into the effect of Cr addition to Fe on the development of diffusion structure. The Fe,Ce layer has little Cr and is similar to that developed for the Fe vs Ce binary couple. This observation implies that Cr has little solubility in the
P.C. Tortorici,MA. Dayananda / Interdiffusionof Ce in Fe-base alloys
Fe&e phase. On the other hand, the (Fe + Cr),Ce, phase has appreciable Cr, as can be seen in fig. 5b and fig. fib. This is a new ternary phase not reported earlier, and there is no analogous binary Fe&e, phase on the Fe-Ce phase diagram. 4.2. Interdiffusion behauior of the elements in various couples The relative interdiffusion behavior of the individual elements in the various couples can be appreciated from the average effective interdiffusion coefficients reported in table 2. B&T, calculated for the diffusion zone on the right-hand side of the Matano plane for the Ni vs Ce couple in fig. 2b involves essentially the Ni,Ce, phase and is larger than @& calculated for the left-hand-side which includes the Ni,Ce layer. Hence, the interdiffusion coefficient of Ni or Ce for the Ni,Ce, phase is larger than that for the Ni,Ce phase. Similarly, DkT,n for the Fe-lO.lNi vs Ce couple is large and is for the diffusion zone including the (Ni + Fe),Ce, phase, which is the ternary extension of the binary Ni,Ce, phase. Lower values of average effective interdiffusion coefficients are observed specifically for Fe over the diffusion zones involving the Fe,Ce layer in the Fe vs Ce and Fe-20.1Cr vs Ce couples and the (Ni + Fe),Ce, layer in the Fe-lO.lNi vs Ce couple. Fe interdiffusion in the (Ni + Fes)Ce, layer is slower than that in the (Fe + Ni),Ce layer where the interdiffusion behavior of Ni appears comparable to that of Ce. The interdiffusion of Cr in the Fe-20.1Cr vs Ce couple is of special interest. As can be seen in fig. 5b, Cr concentration builds up in the (Fe f Cr),Ce, phase, while negligible Cr appears in the adjacent Fe&e phase. From the Cr concentration profile, the interdiffusion flux, &.,, can be calculated as a function of x on the basis of eq. (3). The calculated .&., is found to be negative and appreciable in magnitude in the (Fe + Cr),Ce, phase; on the other hand jcr is negligibly small in the Fe&e layer. This observation implies that to the left of the (Fe + Cr),Ce,/Fe,Ce interface Cr interdiffuses in the (Fe + Cr),Ce, phase in the direction towards the Fe-2O.lCr alloy, while the Cr flux towards the Ce side on the right-hand side of the interface is negligible. Hence, Cr transfer across the Matano plane is negligible. Cr is considered to exhibit a flux reversal at the (Fe + Cr),Ce,/Fe,Ce interface. Such flux reversals of a component have been reported for multicomponent diffusion couples within single phase layers and at interfaces [ll] and have been
171
discussed by Dayananda in the context of the phenomenon of zero-flux planes and flux reversals 17,8]. A negative effective interdiffusion coefficient L@r for Cr reported in table 2 implies a back-flow and build-up of Cr in the diffusion zone on the left-hand side of the Matano Plane. In the present study, the major emphasis has been placed on the development of phase layers due to interdiffusion between Ce and the elements Fe, Ni and Cr. The presence of trace impurities such as 0 and N would be minimal because of the use of the atmosbag and the He environment employed in the assembly of diffusion couples. The active role of 0 and N in the deveiopment of diffusion structures is considered insignificant in the present study. Systematic assessment of the role of 0 and N on the interdiffusion process between Ce and Fe-based alloys with Ni and Cr would be of interest in the context of exploring .possible barriers that would prevent the development of undesirable low melting eutectic mixtures involving intermetallic layers such as Ni3Ce, and Fe,Ce.
5. Conclusions The following are the main inclusions of this study on interdi~usion of Ce in Ni, Fe, Fe-lO.lNi and Fe2O.lCr alloys carried out at 425°C for 4 days, (11 Only a few of the phases expected on the basis of the binary phase diagrams develop in the Ni vs Ce and Fe vs Ce diffusion couples. A large diffusion zone with layers of Ni,Ce and Ni,Ce, intermetallics is observed in the Ni vs. Ce couple, while a thin layer of Fe,Ce phase forms in the Fe vs Ce couple. (21 The intrinsic diffusion coefficient of Ni is 15 times larger than that of Ce in the Ni,Ce, phase, Fe intrinsically diffuses 4 times as fast as Ce in the Fe&e phase. (31 The addition of 10 at% Ni to Fe is sufficient to form the ternary (Ni + Fe&e, phase analogous to the binary Ni,Ce, phase. (4) The presence of Cr in the Fe-20.1 Cr vs Ce couple results in the formation of a ternary (Fe + Cr),Ce, phase not previously reported. In addition, Cr exhibits the phenomenon of flux reversal at the (Fe + Cr),Ce,/Fe, interface. The back-flow and build-up of Cr in the (Fe + Cr),Ce, layer yields a negative effective interdiffusion coefficient for Cr over the diffusion zone on the ahoy side of the couple. (5) In the context of lanthanide/cladding interactions, the development of a large Ni,Ce, type layer is
172
P.C. Tortorici, M.A. Dayananda / Interdiffusion of Ce in Fe-base alloys
undesirable, as it forms a low melting eutectic with Ce at 477°C. Such phases can be avoided with Fe-base alloys containing little Ni. The Fe-20.1Cr alloy is comparable to pure Fe in the formation of a Fe&e layer which forms a eutectic with Ce at a higher temperature of 592°C.
Acknowledgements The support for this research was provided by the US Department of Energy under contract DE-FG0788ER12814 and by the Argonne National Laboratory under the award No. 800OOMODl and is gratefully acknowledged. This paper is based on a dissertation submitted by P.C. Tortorici to Purdue University in partial fulfillment of the requirements for the M.S. degree in Metallurgical Engineering. Special thanks are given to M.C. Petri at Argonne National Laboratory for assistance with the experimental techniques and sample preparation.
References [l] C.H. Till and Y.I. Chang, Proc. Power Conf. 48 (1986) p. 688. [2] M.A. Dayananda and J.G. Duh, Diffusion and Defect Data 39 (1985) 1. [3] T.B. Massalski (ed), Binary Alloy Phase Diagrams (ASM International, Materials Park, OH 1986). [4] M.A. Dayananda and D.A. Behnke, Scripta Met. 25 (1991) 2187. [5] M.A. Dayananda, in: Ordered Intermetallics-Physical Metallurgy and Mechanical Behavior, eds. C.T. Liu et al. (Kluwer, 1992) p. 465. [6] L. Onsager, Ann. New York Acad. Sci. 46 (19451 241. [7] M.A. Dayananda and C.W. Kim, Metall. Trans. A. 10A (1979) 1333. [8] M.A. Dayananda and C.W. Kim, Metall. Trans. A. 14A (1983) 1851. [9] T. Heumann, Z. Phys. Chem. 201 (1958) 168. [lo] J. Philibert, Atom Movements Diffusion and Mass Transport in Solid &es Edition de Physique, France, 1991) p. 420. [ll] M.A. Dayananda, Mater. Sci. Eng. A121 (1989) 351.
nuclear
Journal of Nuclear Materials 204 (1993) 165-172 North-Holland
Interdiffusion
~~0~
of cerium in Fe-base alloys with Ni or Cr
P.C. Tortorici and M.A. Dayananda Purdue University, West Lafayette, IN 47907-1289,
USA
Isothermal interdiffusion studies relevant to lanthanide interactions with cladding alloys in the Integral Fast Reactor program were carried out at 425°C by employing solid-solid diffusion couples assembled with disks of Ce and disks of Fe, Ni, and Fe-lO.lNi, and Fe-20.10, binary alloys (com~sition in at%). The diffusion structures and inte~etallic layers which developed in the various couples during the diffusion anneal were metallographically examined and analyzed by SEM-EDS techniques for concentration profiles. Computer programs were developed to construct profiles of concentrations and to evaluate interdiffusion fluxes and effective interdiffusion coefficients for the individual components over selected regions of the diffusion zones of the various couples. Intrinsic diffusion data were calculated at marker planes in the Ni,Ce, and Fe&e phases developed in the Ni vs Ce and Fe vs Ce couples, respectively. The intermetallic phases and diffusion layers observed in the various couples are discussed in the light of phase diagrams and experimental diffusion paths.
1. Introduction The main features underlying the integral fast reactor (IFR) concept which is being developed at Argonne National Laboratory include the use of U-Pu-Zr metallic fuel, liquid sodium cooling, a pool type reactor configuration, and the reprocessing of fuel [l]. The metallic U-Pu-Zr fuel offers high thermal conductivity, ease of fabrication, good irradiation behavior, high burn-up potential, among other benefits. During irradiation, the U-Pu-Zr fuel swells and comes into contact with the stainless steel cladding enclosing the fuel element. Also during the irradiation process, a number of fission products including lanthanides (Ce, La, Pr among others) are generated. The migration of the lanthanides through the fuel towards the fuel/clad interface can result in their chemical interaction with the stainless steel cladding materials. Such interactions can result in the formation of intermetallic phases and low melting eutectics, which adversely affect the structural integrity of the cladding alloy as a result of localized melting. The extent of the interaction between the fuel containing lanthanides and cladding alloys is among the major issues that are currently being investigated in the context of fuel/clad compatibility and assessment of acceptable fuel/cladding combinations. In this study, interdiffusion experiments were carried out at 425°C with soiid-solid diffusion couples assembled with disks ~22-3IiS/93/$06.~
of Ce and disks of Fe, Ni, and Fe-lO.lNi, and Fe20.1Cr binary alloys. The diffusion layers that developed in the various couples are examined for the jdentification of intermetaIli~ phases, analyzed for average effective interdiffusion coefficients for the individual components, and described with the aid of the phase diagrams and diffusion paths.
2. Experimental procedure Ce, Ni and Fe (99.9% pure) were obtained from Rhone-Poulenc Inc, Alpha Products Inc, and Coodfellow Inc., respectively. Binary alloys with compositions of Fe-lO.lNi, and Fe-20.1Cr were fabricated by vacuum induction melting [2]. Charges were melted in alumina crucibles under an argon atmosphere, and drawn up fused silica draw tubes, 10 mm in diameter. AI1 alloys were homogenized at 1150°C for 7 days in an evacuated quartz capsule. Diffusion disks, approximately 5 mm in diameter and S mm thick, were sectioned from Ce, Ni, Fe and various alloys. The disk surfaces were ground through 600 grit Sic paper to ensure parallel faces. The disks were metallographically polished through 1 pm diamond paste in an Aldrich atmosbag with flowing helium (99.9%). This procedure was employed to ensure that the surfaces were free from an oxide layer; the helium environment was especially required for cerium
0 1993 - Elsevier Science Publishers E.V. All rights reserved
P.C. Tortorici, MA. Dayananda / Interdiftiion
166
whose reactivity with air and water based solvents is severe. The polished disks were employed in assembling sandwich couples inside a Kovar steel jig consisting of two end plates and three threaded Kovar steel rods. The couples consisted of a Ce disk sandwiched by selected alloy disks, one on either side. Kovar steel 64Fe-29Ni-17Co at%) was chosen for the jig due to its low coefficient of thermal expansion. The assembled couples were then placed in quartz capsules which were sealed at one end under a constant flow of helium gas. The capsule was then attached to a vacuum system, evacuated and backfilled with hydrogen gas several times. After a final evacuation, the capsule was sealed and annealed in a horizontal Lindberg three-zone tube furnace at 425°C for 4 days. The annealed capsules were quenched in an ice water bath after the diffusion anneal. The couples with the Kovar jigs were removed and cold-mounted in a clear epoxy resin. The mounted couples were sectioned with an Isomet diamond saw to expose surfaces parallel to the diffusion direction. The exposed sections were then mechanically polished on 600 grit Sic paper and through 1 pm diamond paste on a cloth wheel with dehydrated ethyl alcohol used as a lubricant in all steps. The polished sample was immediately transferred to a JEOL 35CF scanning electron microscope (SEMI, equipped with a Tracer Northern Series II energy dispersive X-ray analyzer. The couples were analyzed by point-to-point counting techniques for concentration profiles and phase identification. The intensities of X-ray K, lines for Fe (6.403 keV), Ni (7.477 keV), Cr (5.414 keW, and L, line for Ce (4.839 keV) were collected and stored on floppy disks, then converted into compositions with the aid of pure elemental standards and a ZAF correction program. Secondary electron micrographs were taken to record the diffusion structure and intermetallic layers developed in the various couples.
of Ce in Fe-base alloys
Table 1 Phase layers and their thicknesses in the various couples annealed at 425°C for 4 days Couple
Phases observed a
Layer thickness OLm)
Ni vs Ce
Ni,Ce Ni,Ce, Fe&e (Fe + Ni),Ce (Ni + Fe&e, (Fe + Cr),Ce, Fe&e
10 240 20 IO 10 10 10
Fe vs Ce
Fe-lO.lNi vs Ce Fe-ZO.lCr vs Ce
a The designation of a phase layer is based on the ratio of concentration of Ce to the sum of the concentrations of the other elements present in the phase layer.
sponds to the ratio of the Ce concentration to the sum of all the other elements analyzed in the layer and is not based on any intermetallic structural data. Based on the counting statistics, the uncertainty in the EDS analysis of the major elements Ce, Fe, Ni, and Cr is within +O.S at.%. On the basis of the Ni vs Ce and Fe
(a)
wls 153s* 1400
3. Results (b)
3.1. Difkion
structures
and intemetallic
phases
The phase layers identified in the diffusion structures of the various couples in this study are listed in table 1. The intermetallic designations of the phase layers in table 1 are entirely based on compositional analysis by EDS ignoring the trace impurities such as C, 0, and N. The designation for a phase layer corre-
iw D 100 FE!
Atom Percent Cerium
Ce
Fig. 1. The phase diagrams for the (a> Ni vs Ce and (b) Fe vs Ce binary systems adapted from ref. j3].
167
P.C. Tortorici, MA. Dayananda / Interdiffusion of Ce in Fe-base alloys
vs Ce phase diagrams [3] presented in figs. la and lb, respectively, six possible intermetallic compounds are observed between Ce and Ni, while only two can form between Ce and Fe. Ce and Cr have negligible solubility in each other and form no intermetallic compounds [31. 3.1.1. Binary couples: Ni us Ce and Fe us Ce The diffusion structure and the concentration profile for the Ni vs Ce couple are presented in figs. 2a and 2b, respectively. Two diffusion layers developed in this couple and correspond to Ni,Ce and Ni,Ce, phases of the phase diagram in fig. la. The intermetallit designation of the phases are based on the approximate ratio of Ni concentration to that of Ce. The approximate widths of the Ni,Ce and Ni,Ce, layers are 10 pm and 240 p,m, respectively. The Matano plane for the couple determined on the basis of mass balance is identified at x,, and a marker plane is identified at x, in the Ni,Ce, phase. A secondary electron micrograph and the concentration profile for the Fe vs Ce couple are presented in
Ni$e,
0.8
g
0.7
g
0.6
6
0.5
.g
0.4
2
0.3
5 B 0
0.2
u
(b)
0.1 0 0
5
10
15
20
25
30
35
40
4s
SO
Distance, x (Km)
0.9 0.8
3.1.2. Ternary couples: Fe-l~.lN~ Ce
LE 0.7 E 0.6 gj,
0.9
fig. 3. Only one diffusion layer, approximately 20 p,m wide, develops as can be seen in fig. 3a; the layer corresponds to Fe&e phase on the basis of the phase diagram in fig. lb. The width of the diffusion zone of the Fe vs Ce couple is appreciably smaller than that of Ni vs Ce couple. The interdiffusion of Ni in Ce is much more rapid than that of Fe in Ce. A marker plane is identified in the Fe&e phase in fig. 3b.
1 2 .s u
z 0 ‘G y
Fig. 3. (a) Diffusion structure and (b) concentration profiles for the Fe vs Ce couple annealed at 425°C for 4 days. x0 and x, refer to the locations of the Matano plane and the marker plane, respectively.
Ce
Ni$e
Fe20 1
(b)
0.5
Distance, x (pm)
Fig. 2. (a) Diffusion structure and (b) concentration profiles for the Ni vs Gz couple annealed at 425°C for 4 days. x0 and n, refer to the locations of the Matano. plane and the marker plane, respectxveiy.
us Ce, Fe-20.10
us
In figs. 4a and 4b are presented the diffusion structure and the concentration profiles for the Fe-lO.lNi vs Ce couple. Two diffusion layers observed in the micrograph in fig. 4a correspond to (Fe + Ni),Ce and (Ni + Fe),Ce, phases. The width of the diffusion zone is of the order of 25 pm and is similar to that observed for the Fe vs Ce couple. The diffusion structure and the concentration profiles for the Fe-20.1Cr vs Ce ternary couple are presented in fig. 5. Two diffusion layers corresponding to (Fe + Cr),Ce, and Fe&e phases are observed in the dif~sion zone whose width is appro~mately 20 pm.
P.C. Tortorici, MA. Dayananda / Interdiffusion of Ce in Fe-base alloys
168
The (Fe + Cr),Ce, layer developed in the couple does not correspond to any phase on the binary Fe-Ce diagram. The layer identified as Fe,Ce has negligible amounts of Cr, as can be seen from the Cr concentration profile in fig. 5b. In addition, Cr appears to build up in the (Fe + Cr),Ce, layer. The diffusion paths for all the ternary couples are presented on composition triangles in fig. 6. The paths are S-shaped as required for solid-solid couples. The single phase layers developed in the various couples are identified by the shaded‘areas on the composition triangles. In fig. 6a the dashed line segments, ab, cd and ef of the diffusion path for the Fe-lO.lNi vs Ce couple represent tie lines for two-phase equilibria at the interfaces between Ce and (Ni + Fe),Ce, phases, (Ni + Fe),Ce, and (Fe + Ni),Ce phases, and (Fe + Ni),Ce and Fe-lO.lNi phases, respectively. Similarly, the path segments, ab, cd and ef in fig. 6b correspond to two-phase equilibria at the interfaces between Ce and Fe,Ce phases, Fe&e and (Fe + Cr),Ce, phases and (Fe + Cr),Ce, and Fe-20.1Cr phases, respectively.
\ Fc 2C”
CFe+Cr)(Ce3
-
1 = .o z E ~ E g
0.9
”
0.5
.E t t
0.3
z
0.2
(‘C
0.8 0.7 0.6
(II)
0.4
I
I 0
5
10
15
20
25
30
35
40
4s
jfl
Distance. x (pm) Fig. 5. (a) Diffusion structure and (b) concentration for the Fe-2O.lCr vs Ce couple annealed at 425°C
profiles
for 4 days. x0 refers to the location of the Matano plane.
3.2. Average
I
(Fe+Ni)2Ce
\ Wi+Fe)3Ce7
(b)
effective
interdiffusion
coefficients
On the basis of an analysis by Dayananda [4,5], average effective interdiffusion coefficients and rootmean-square penetration depths can be determined for individual components in binary and multicomponent diffusion couples. This analysis is employed to calculate an effective interdiffusion coefficient for each component over selected ranges of concentrations in the diffusion zones of the diffusion couples investigated in this study. On the basis of Onsager’s formalism [6] of Fick’s law, the interdiffusion flux { of component i in an n-component alloy is expressed by [4]:
(1) where
Fig. 4. (a) Diffusion structure and (b) concentration profiles for the Fe-lO.lNi vs Ce couple annealed at 425°C for 4 days. x0 refers to the location of the Matano plane.
For component i, fii is the main interdiffusion coefficient, and the second term in eq. (2) incorporates cross interdiffusion coefficients, fi$ For an isothermal diffu-
P. C, Tortorici, MA. Daya~a~a
/ I~ter~~~~o~
Ce
169
of Ce in Fe-base alloys
sion couple assembled with two alloys of initial concentrations, C: and CE:, and diffusion annealed for time
t, the interdiffusion fluxes based on a laboratory fixed frame can be determined directly from the concentration profiles on the basis of the relation [7,8]:
(4 where x,, refers to the Matano plane. Upon integration of .( over x from +m to x0, one derives the following relation [4]: Ni
Fe-lO.lNi
Fe
I+-*“&
Ce
dx=
_;
A substitution
j"' c: (X -xo12 dCi of eq. (1) into eq. (4) yields
Icy(x -x0)’ dCi (b)
(5)
’
[cp-c;]
where Cc? refers to the concentration at the Matano plane and gi a is termed the average effective interdiffusion coeffidient for component i to the right of the Matano plane, over the range C+ to Cf. From eq. (5) an effective penetration depth for component i on the right-hand side of the Matano plane can be determined by:
Cr
Fig. 6. Experimental diffusion paths on composition triangles at 425°C for the couple (a) Fe-lO.lNi vs Ce, and (b) Fe-20.10 vs Ce. The phase designations are based on ratios of concentrations.
(6)
5ii$ = @-jg, where
Table 2 Average effective interdiffusion coefficients and root-mean-square for 4 days
xi ,R corresponds
penetration
to tiie root-mean-square
depths for the various couples annealed at 425°C
Diffusion couple assembly Ni vs Ce
Jje” N* *~ Ce,L =
Fe vs Ce
Ljeff Feor&.L
Fe-lO.lNi
vs Ce
B& fi$_
Fe-20.1Cr vs Ce
7.3 x lo- I5
= 2.7x
10-16
= 1.4x 10-16 = 2.6x lo-l6
ii&_ = 2.3 x lo-l6 @ff &J_ = 7.5 x lo-‘6 &&=-&9x10-‘7
$c:L=29x10-‘6 (I .
jjeff N*orCe,R
=
4.9x 10-14
&ff
FeorCe,R=8.4x10-‘7 L)eff Fe,R= 3.4 x lo- I7 r>$,
= 2.9x10-”
value
XN1,L= 70.8
fNi,R = 184.8
x,,, = 13.7 x Fe,L = 9‘4
X,,,
x Fe,R = 4s7
= 7.6
PNj,J_= 13.0
KNi*a= 9.6
@JR = 1.3x lo-= fi&=8.1~10-”
PCe,L= 12.1 x,,, = 22.7
fCeSR= 9.2 RFe,R = 7i5
gteff Cr.R = ---tiff ,,,=7.7x10-‘7
XQL
= ----
%,,
i,,,
=
14.0
= o
P,>, = 7.3
170
P.C. Tortorici, M.A. Dayananda / Interdiffusion of Ce in Fe-base alloys
of
((x-x,)*)“* A similar procedure can be applied to the concentration profile on the left-hand side of the Matano plane for the determination of an average effective interdiffusion coefficient, Di,L, and an effective penetration depth, X1,,_, Effective interdiffusion coefficients and penetration depths for the individual components were evaluated over selected phase layers on either side of the Matano plane for the Ni vs Ce, Fe vs Ce, Fe-lO.lNi vs Ce, and Fe-20.1Cr vs Ce couples and are reported in table 2. 3.3. Intrinsic diffusion in Ni,Ce,
and Fe&e
phases
For the Ni vs Ce and Fe vs Ce binary diffusion couples, marker planes were identified after diffusion in the Ni,Ce, and Fe,Ce phase layers, respectively, as indicated at X, in figs. 2b and 3b. The cumulative intrinsic flux, A,, of component i past a marker plane moving parabolically with time at a constant composition is obtained by integrating the intrinsic flux J, over time t [9]; thus, A,=jorl,
d x = -2tD,-
ac; ax x,
(i =
1, 2),
where D, is the intrinsic diffusion coefficient for component i. A, is determined graphically form appropriate areas under the concentration profiles. For the ratio of cumulative intrinsic fluxes, eq. (7) yields: IA,1
D,
On the basis of eq. (S), the ratio D&D,, of intrinsic diffusion coefficients in the Ni,Ce, phase was determined to be 15, while a value of 4 was obtained for the ratio of D&D,, for the Fe,Ce phase.
4. Discussion 4.1. Phase layer development
As reported in table 1, the phase layers that developed in the binary Ni vs Ce and Fe vs Ce couples include only a few of the various intermetallic phases which can form on the basis of the binary phase diagrams in fig. 1. Among the six possible intermetallic phases between Ni and Ce, only two phases, Ni,Ce
and Ni,Ce,, were observed in the Ni vs Ce couple. The Ni,Ce, phase is expected to form on the Ce side, as there exists some solubility of Ni in Ce. The growth of the Ni,Ce, phase occurs faster towards the Ce side than in the opposite direction towards the Ni side, as can be seen in fig. 2b by the location of the Matano plane. This observation is consistent with the fact that Ni intrinsically diffuses nearly 15 times faster than Ce in the Ni,Ce, phase, as calculated on the basis of eq. (8). The small thickness of the Ni,Ce layer relative to that of Ni,Ce, indicate that the velocities of Ni/Ni,Ce and Ni,Ce/Ni,Ce, interfaces in the direction towards Ni are quite similar. Among the two phases, Fe,,&, and Fe,Ce that can form between Fe and Ce on the basis of the phase diagram in fig. lb, only the Fe,Ce phase was observed as a thin layer in the Fe vs Ce couple. Not all phases based on the phase diagram need to form in a multiphase diffusion couple, as the appearance of a phase in the diffusion zone is influenced by nucleation barriers, incubation time, and interdiffusion behavior in the adjacent phases [lo]. From a comparison of the widths of the diffusion zones for the Ni vs Ce and Fe vs Ce binary couples, it is apparent that the interdiffusion of Ni with Ce is appreciably faster than that of Fe with Ce. The phases, Ni,Ce, and Fe,Ce, formed in the two couples form eutectics with Ce at 477°C and 592°C respectively. In the context of lanthanide interactions with clad alloys, the formation of the Ni,Ce, and Fe,Ce phases can be considered undesirable. The layers of (Fe + Ni),Ce and (Ni + Fe),Ce, intermetallics developed in the ternary Fe-lO.lNi vs Ce couple shown in fig. 4 are comparable to the Fe,Ce and Ni,Ce, phases identified in the binary couples. In the (Fe + Ni),Ce phase, the Ni concentration is about 3 at%, while the concentration of Fe is about 3 at% in the (Ni + Fe&e, phase. Hence, the compositions of these phases are quite close to Fe-Ce and Ni-Ce edges of the composition triangle as indicated on the diffusion path in fig. 6a. The important thing to note is that the presence of 10 at% Ni in the Fe-base terminal alloy of the couple is enough to cause the formation of a layer of Ni,Ce, type phase containing a few at% Fe, although the thickness of the layer is quite limited as indicated in table 1. The ternary Fe-20.1Cr vs Ce couple which developed the layers of (Fe + Cr),Ce, and Fe&e as shown in fig. 5 provides an insight into the effect of Cr addition to Fe on the development of diffusion structure. The Fe,Ce layer has little Cr and is similar to that developed for the Fe vs Ce binary couple. This observation implies that Cr has little solubility in the
P.C. Tortorici,MA. Dayananda / Interdiffusionof Ce in Fe-base alloys
Fe&e phase. On the other hand, the (Fe + Cr),Ce, phase has appreciable Cr, as can be seen in fig. 5b and fig. fib. This is a new ternary phase not reported earlier, and there is no analogous binary Fe&e, phase on the Fe-Ce phase diagram. 4.2. Interdiffusion behauior of the elements in various couples The relative interdiffusion behavior of the individual elements in the various couples can be appreciated from the average effective interdiffusion coefficients reported in table 2. B&T, calculated for the diffusion zone on the right-hand side of the Matano plane for the Ni vs Ce couple in fig. 2b involves essentially the Ni,Ce, phase and is larger than @& calculated for the left-hand-side which includes the Ni,Ce layer. Hence, the interdiffusion coefficient of Ni or Ce for the Ni,Ce, phase is larger than that for the Ni,Ce phase. Similarly, DkT,n for the Fe-lO.lNi vs Ce couple is large and is for the diffusion zone including the (Ni + Fe),Ce, phase, which is the ternary extension of the binary Ni,Ce, phase. Lower values of average effective interdiffusion coefficients are observed specifically for Fe over the diffusion zones involving the Fe,Ce layer in the Fe vs Ce and Fe-20.1Cr vs Ce couples and the (Ni + Fe),Ce, layer in the Fe-lO.lNi vs Ce couple. Fe interdiffusion in the (Ni + Fes)Ce, layer is slower than that in the (Fe + Ni),Ce layer where the interdiffusion behavior of Ni appears comparable to that of Ce. The interdiffusion of Cr in the Fe-20.1Cr vs Ce couple is of special interest. As can be seen in fig. 5b, Cr concentration builds up in the (Fe f Cr),Ce, phase, while negligible Cr appears in the adjacent Fe&e phase. From the Cr concentration profile, the interdiffusion flux, &.,, can be calculated as a function of x on the basis of eq. (3). The calculated .&., is found to be negative and appreciable in magnitude in the (Fe + Cr),Ce, phase; on the other hand jcr is negligibly small in the Fe&e layer. This observation implies that to the left of the (Fe + Cr),Ce,/Fe,Ce interface Cr interdiffuses in the (Fe + Cr),Ce, phase in the direction towards the Fe-2O.lCr alloy, while the Cr flux towards the Ce side on the right-hand side of the interface is negligible. Hence, Cr transfer across the Matano plane is negligible. Cr is considered to exhibit a flux reversal at the (Fe + Cr),Ce,/Fe,Ce interface. Such flux reversals of a component have been reported for multicomponent diffusion couples within single phase layers and at interfaces [ll] and have been
171
discussed by Dayananda in the context of the phenomenon of zero-flux planes and flux reversals 17,8]. A negative effective interdiffusion coefficient L@r for Cr reported in table 2 implies a back-flow and build-up of Cr in the diffusion zone on the left-hand side of the Matano Plane. In the present study, the major emphasis has been placed on the development of phase layers due to interdiffusion between Ce and the elements Fe, Ni and Cr. The presence of trace impurities such as 0 and N would be minimal because of the use of the atmosbag and the He environment employed in the assembly of diffusion couples. The active role of 0 and N in the deveiopment of diffusion structures is considered insignificant in the present study. Systematic assessment of the role of 0 and N on the interdiffusion process between Ce and Fe-based alloys with Ni and Cr would be of interest in the context of exploring .possible barriers that would prevent the development of undesirable low melting eutectic mixtures involving intermetallic layers such as Ni3Ce, and Fe,Ce.
5. Conclusions The following are the main inclusions of this study on interdi~usion of Ce in Ni, Fe, Fe-lO.lNi and Fe2O.lCr alloys carried out at 425°C for 4 days, (11 Only a few of the phases expected on the basis of the binary phase diagrams develop in the Ni vs Ce and Fe vs Ce diffusion couples. A large diffusion zone with layers of Ni,Ce and Ni,Ce, intermetallics is observed in the Ni vs. Ce couple, while a thin layer of Fe,Ce phase forms in the Fe vs Ce couple. (21 The intrinsic diffusion coefficient of Ni is 15 times larger than that of Ce in the Ni,Ce, phase, Fe intrinsically diffuses 4 times as fast as Ce in the Fe&e phase. (31 The addition of 10 at% Ni to Fe is sufficient to form the ternary (Ni + Fe&e, phase analogous to the binary Ni,Ce, phase. (4) The presence of Cr in the Fe-20.1 Cr vs Ce couple results in the formation of a ternary (Fe + Cr),Ce, phase not previously reported. In addition, Cr exhibits the phenomenon of flux reversal at the (Fe + Cr),Ce,/Fe, interface. The back-flow and build-up of Cr in the (Fe + Cr),Ce, layer yields a negative effective interdiffusion coefficient for Cr over the diffusion zone on the ahoy side of the couple. (5) In the context of lanthanide/cladding interactions, the development of a large Ni,Ce, type layer is
172
P.C. Tortorici, M.A. Dayananda / Interdiffusion of Ce in Fe-base alloys
undesirable, as it forms a low melting eutectic with Ce at 477°C. Such phases can be avoided with Fe-base alloys containing little Ni. The Fe-20.1Cr alloy is comparable to pure Fe in the formation of a Fe&e layer which forms a eutectic with Ce at a higher temperature of 592°C.
Acknowledgements The support for this research was provided by the US Department of Energy under contract DE-FG0788ER12814 and by the Argonne National Laboratory under the award No. 800OOMODl and is gratefully acknowledged. This paper is based on a dissertation submitted by P.C. Tortorici to Purdue University in partial fulfillment of the requirements for the M.S. degree in Metallurgical Engineering. Special thanks are given to M.C. Petri at Argonne National Laboratory for assistance with the experimental techniques and sample preparation.
References [l] C.H. Till and Y.I. Chang, Proc. Power Conf. 48 (1986) p. 688. [2] M.A. Dayananda and J.G. Duh, Diffusion and Defect Data 39 (1985) 1. [3] T.B. Massalski (ed), Binary Alloy Phase Diagrams (ASM International, Materials Park, OH 1986). [4] M.A. Dayananda and D.A. Behnke, Scripta Met. 25 (1991) 2187. [5] M.A. Dayananda, in: Ordered Intermetallics-Physical Metallurgy and Mechanical Behavior, eds. C.T. Liu et al. (Kluwer, 1992) p. 465. [6] L. Onsager, Ann. New York Acad. Sci. 46 (19451 241. [7] M.A. Dayananda and C.W. Kim, Metall. Trans. A. 10A (1979) 1333. [8] M.A. Dayananda and C.W. Kim, Metall. Trans. A. 14A (1983) 1851. [9] T. Heumann, Z. Phys. Chem. 201 (1958) 168. [lo] J. Philibert, Atom Movements Diffusion and Mass Transport in Solid &es Edition de Physique, France, 1991) p. 420. [ll] M.A. Dayananda, Mater. Sci. Eng. A121 (1989) 351.