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Interdiffusion and reaction between uranium and iron
Journal of Nuclear Materials 424 (2012) 82–88
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Interdiffusion and reaction between uranium and iron K. Huang a, Y. Park a, A. Ewh a, B.H. Sencer b, J.R. Kennedy b, K.R. Coffey a, Y.H. Sohn a,⇑ a b
Advanced Materials Processing and Analysis Center, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, USA Fundamental Fuel Properties Department, Nuclear Fuel and Materials Division, Idaho National Laboratory, Idaho Falls, ID, USA
a r t i c l e
i n f o
Article history: Received 15 November 2011 Accepted 6 February 2012 Available online 18 February 2012
a b s t r a c t Metallic uranium alloy fuels cladded in stainless steel are being examined for fast reactors that operate at high temperature. In this work, solid-to-solid diffusion couples were assembled between pure U and Fe, and annealed at 853 K, 888 K and 923 K where U exists as orthorhombic a, and at 953 K and 973 K where U exists as tetragonal b. The microstructures and concentration profiles developed during annealing were examined by scanning electron microscopy and electron probe microanalysis, respectively. U6Fe and UFe2 intermetallics developed in all diffusion couples, and U6Fe was observed to grow faster than UFe2. The interdiffusion fluxes of U and Fe were calculated to determine the integrated interdiffusion coefficients in U6Fe and UFe2. The extrinsic (KI) and intrinsic growth constants (KII) of U6Fe and UFe2 were also calculated according to Wagner’s formalism. The difference between KI and KII of UFe2 indicate that its growth was impeded by the fast-growing U6Fe phase. However, the thin UFe2 played only a small role on the growth of U6Fe as its KI and KII values were determined to be similar. The allotropic transformation of uranium (orthorhombic a to tetragonal b phase) was observed to influence the growth of U6Fe directly, because the growth rate of U6Fe changed based on variation of activation energy. The change in chemical potential and crystal structure of U due to the allotropic transformation affected the interdiffusion between U and U6Fe. Faster growth of U6Fe is also examined with respect to various factors including crystal structure, phase diagram, and diffusion. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Uranium–zirconium (U–Zr) metallic fuel with stainless steel cladding has been developed for advanced fast reactors because of its high burnup capability and favorable thermal response [1–3]. Under irradiation, the U–Zr fuel can swell and contact the stainless steel cladding because of thermal expansion and the accumulation of fission products, which causes interdiffusion and reaction to form new product phases. This fuel cladding chemical interaction (FCCI) has deleterious effects because it thins the cladding and produces phases with undesirable properties. The FCCIs between U–Zr alloys and stainless steels have been studied extensively [4–10]. In most cases, the interaction zone shows a complex multi-layer structure with various intermetallic compounds. The phase diagram of U– Fe has been well studied by Gordon and Kaufmann [11], Grogan [12] and Chapman and Holcombe [13] and assessed in the literature [14–16] with a good agreement among these studies. The iron– uranium system is comprised of eight solid phases: a (oC4), b (tP30) and c (cI2) uranium; a (cI2), c (cF4) and d (cI2) iron; and two intermetallic compounds UFe2 (cF24) and U6Fe (tI28). The thermodynamic properties of U–Fe, U–Zr and U–Zr–Fe were also
⇑ Corresponding author. Tel.: +1 407 882 1181; fax: +1 407 882 1461. E-mail address: [email protected] (Y.H. Sohn). 0022-3115/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2012.02.004
reported in the literature [16,17]. However, the reactions between pure U and Fe with interdiffusion analysis have never been reported. In this study, U vs. Fe binary diffusion experiments were conducted to help understand the complex FCCI process, and provide quantitative diffusion data from experiments for FCCI modeling. This simple system chosen serves to form the basis for quantitative understanding for the effects of alloying addition (e.g., Zr, Cr and Ni) on the FCCI. Moreover, effects of allotropic transformation in U on the reactions and reactions mechanism between U and Fe have also been investigated based on this binary system. The annealing temperatures were selected in the range of 853–973 K, in order to study the effect of the allotropic transformation of U (from orthorhombic a-U to tetragonal b-U at 940 K) on the diffusional interaction between U and Fe. Scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) were employed to examine the development of intermetallic phases in the interdiffusion zone. Two intermetallic phases, U6Fe and UFe2 were observed, consistent with to the U–Fe equilibrium phase diagram shown in Fig. 1 [14]. The interdiffusion flux, eJ, integrated interdiffusion coefe Int , extrinsic growth constant, KI, and intrinsic growth ficients, D constant, KII, of U6Fe and UFe2 were calculated. The activation ene Int , KI and KII were also determined by the Arrhenius relaergy of D tion. The faster growth kinetics of U6Fe compared to UFe2 is discussed.
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
83
Fig. 1. Equilibrium binary phase diagram of U–Fe system [14].
The interdiffusion flux through the interdiffusion zone can be calculated by:
2. Analytical framework for diffusion Different analytical approaches and diffusion parameters are applied to study diffusion phenomena in binary systems depending on concentration gradients that develop. When a sufficient concentration gradient can be measured in a phase, the Boltzmann–Matano method and/or modified Sauer–Freise method [18] can be used to determine the interdiffusion coefficient as a function of composition. However, it is not appropriate to apply those analyses when the solubility in the intermediate phase is narrow since the error of calculated interdiffusion coefficients may be large due to the small concentration gradient. To extend the above methods to the intermediate phases with negligible compositional ranges, Heumann [19] and Wagner [20] derived phenomenological expressions to determine the average interdiffusion coefficient within a phase under the assumption of linear concentration gradient in the intermediate phase. To that end, e Int [20,21], extrinsic growth integrated interdiffusion coefficients, D constant, KI and intrinsic growth constants, KII [20] can be employed to describe the diffusion process. e Int 2.1. Integrated interdiffusion coefficient, D The integrated interdiffusion coefficient of a specific phase
v ; De Int;ðv Þ is a material constant that is ideally the same in all diffusion couples regardless of experimental boundary conditions [20,22]. Dayananda [21] provided an equation to calculate the e Int;ðv Þ in the range of (x1, x2) in a binary system as: D
e Int ¼ D i
Z
N i ðx2 Þ
e dNi ¼ D
Ni ðx1 Þ
Z
x2
eJ i dx
ð1Þ
þ1
1
ðx x0 ÞdNi ¼ 0
Z
N i
N 1 i
ðx x0 ÞdNi
ð3Þ
where Ni is the mole fraction of component i at the position where the interdiffusion flux is calculated, and N 1 is the mole fraction of i component i at terminal ends. When a phase v, has a very narrow compositional range (i.e., line compound) and is present in the interval from xðv Þ to xðv Þþ , e Int;ðv Þ in the integral rethe integrated interdiffusion coefficient, D i gion, x1 to x2 for the phase v in Eq. (1) can be simplified as:
e Int;ðv Þ ¼ eJ ðv Þ Dxðv Þ where Dxðv Þ ¼ xðv Þþ xðv Þ D i i
ð4Þ
Since there are negligible concentration gradients in the phase
m, the interdiffusion fluxes through the phase m are constant according to Eq. (3). Wagner [20] also gave an alternative means to calculate the integrated interdiffusion coefficients as:
" # ðv Þ N1 ÞðNþ1 Ni Þ ðDxðv Þ Þ2 i i 2t ðNþ1 N1 Þ i i " Z xðv Þ ðv Þ þ1 ðv Þ Ni Ni Dx þ ðNi N1 Þdx 1 i 2t Nþ1 N 1 i i # Z þ1 ðv Þ N i N1 þ1 i ðNi Ni Þdx þ þ1 Ni N1 xðv Þþ i ðv Þ
e Int;ðv Þ ¼ ðNi D i
ð5Þ
This is equivalent to Eq. (4) but does not require the determination of Matano plane.
x1
e is the interdiffusion where Ni is the mole fraction of component i; D coefficient and eJ i is the interdiffusion flux of component i. To obtain eJ i , the Matano plane position x0 can be determined by mass balance [18]:
Z
eJðN Þ ¼ 1 i 2t
ð2Þ
2.2. Extrinsic (KI) and intrinsic (KII) growth constants The growth constant of the phase m may not be a material constant, and can vary in diffusion couples with different terminal ðv Þ ends. Therefore, two kinds of parabolic growth constants, K I and ðv Þ K II were defined by Wagner [20] to describe the diffusion process in a phase v having a negligible concentration gradient. When the
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K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
phase m forms in a diffusion couple with ‘‘pure’’ components as its terminal ends (the first kind diffusion couple according to Wagner’s ðv Þ notation, i.e., N 1 ¼ 0; N þ1 ¼ 1Þ, the extrinsic growth constant, K I i i can be defined as: ðv Þ KI
" # ðDxðv Þ Þ2 ¼ 2t
ð6Þ
N 1 ¼0; N þ1 ¼1 i i Int;ðv Þ
e The integrated interdiffusion coefficient, D and the extrinsic i ðv Þ growth constant K I can be correlated by substituting Eq. (6) into Eq. (5), which yields: e Int; ðv Þ ¼ D i
Z
ðv Þþ
Ni
e i DdN
ðv Þ
Ni
ðv Þ
ðv Þ
ðv Þ
¼ Ni ð1 N i ÞK I " # Z xðv Þ Z þ1 Dxðv Þ ðv Þ ðv Þ þ N i dx þ N i ð1 Ni Þdx ð1 N i Þ 2t xðv Þþ 1
N 1 ¼0; N þ1 ¼1 i i
ð7Þ
Alternatively, phase m can also form in a diffusion couple with its neighboring phases (m 1) and (m + 1) as terminal ends (the second diffusion couple according to Wagner’s notation, ðv 1Þ ðv þ1Þ N 1 ¼ Ni ; N þ1 ¼ Ni ), and the intrinsic parabolic growth i i ðv Þ constant, K II can be expressed using the same equation, however, with different boundary condition, as: ðv Þ K II
" # ðDxðv Þ Þ2 ¼ 2t
ð8Þ ðv 1Þ
N 1 ¼N i i
ðv 1Þ
ðv þ1Þ
; N þ1 ¼N i i
ðv þ1Þ
where N i and N i are the mole fraction of component i in neighboring phases, (m 1) and (m + 1). In this second kind of diffusion couple, the integral terms in Eq. (7) vanish. Thus, one obtains e Int;ðv Þ and intrinsic growth constant K ðv Þ as: the relation between D II i ðv Þ
e Int; ðv Þ ¼ ðNi D i
ðv 1Þ
Ni
ðv þ1Þ ðNi
ðv þ1Þ
ÞðNi
ðv Þ
Ni Þ
ðv 1Þ Ni Þ
ðv Þ ½K II N1 ¼Nðv 1Þ ; Nþ1 ¼Nðv þ1Þ i i i i
ð9Þ
ðv Þ
While K I can vary since the growth of phase v is affected by the ðv Þ growth of other phases in the diffusion zone [20], the K II is considered a ‘‘true’’ growth constant. In this study, the first kind diffusion couple with pure terminal ends (i.e., U and Fe) were employed e Int;ðv Þ and K ðv Þ were readily calculated. The experimentally, so D I i ðv Þ value of K I was also confirmed using Eq. (7). The intrinsic growth ðv Þ e Int;ðv Þ and Eq. (9). constants, K II were also calculated based on D i 3. Experimental procedure All metallographic preparation and assembly of diffusion couples were carried out under an Ar atmosphere inside a glove box to minimize oxidation of the depleted uranium (DU) and iron (Fe). DU rods were cast using high-purity DU via arc melting. They were melted three times to ensure the homogeneity and then drop-cast to form rods with 6.35 mm diameter. Fe rods of 99.99% purity were acquired from a commercial source (AlphaAesar™). The homogeneity in composition, phase constituents and microstructure of DU and Fe were examined by X-ray diffraction (XRD, Rigaku™ DMAX-B), and scanning electron microscopy (SEM, Hitachi™ 3500N) equipped with X-ray energy dispersive spectroscopy (XEDS). Both the U and Fe rods were cut into 3 mm-thick disks. The disk surfaces, which would become the interface of the diffusion couple, were metallographically polished down to 1 lm using diamond paste. Before assembling the diffusion couples, the U disks were immersed momentarily into nitric acid (1:1 volume with distilled water) to remove the
oxide layer on the surface. The prepared surfaces were then placed in contact with each other, and held together by two clamping disks with stainless steel rods to form a jig. Each couple assembly was wrapped with Ta-foil and encapsulated in a quartz capsule that was sealed under vacuum (106 Pa) after repeated vacuum and pure H2 flushing operations. Finally, the couples were annealed in the temperature range from 853 to 973 K using a Lindberg/Blue™ three-zone tube furnace. The diffusion couples examined in this study are listed in Table 1. To study the effect of the allotropic transformation between a-U and b-U, three annealing temperatures (853, 888, 923 K) were selected in a-U temperature range, below the allotropic transformation point at 940 K based on U–Fe equilibrium phase diagram as shown in Fig. 1. Only two annealing temperatures (953 and 973 K) were selected in the b-U temperature range below the U–Fe eutectic temperature around 990 K. After annealing, the diffusion couples were quenched by breaking the quartz capsule in cold water. Each diffusion couple was then mounted in epoxy, cross-sectioned and polished using 1 lm diamond paste for microstructural examination and compositional analysis. For each diffusion couple, SEM (Hitachi™ 3500 N) was first carried out to examine the interdiffusion microstructure. The thickness of U6Fe and UFe2 layers were measured based on backscatter electron (BSE) micrographs from the interdiffusion zone. At least 10 random locations were selected to determine an average and standard deviation of the layer thickness for the U6Fe and UFe2 phases at each annealing temperature. Electron probe microanalysis (EPMA, JEOL™ Superprobe 733) was employed to determine the concentration profile for each couple utilizing a point-to-point scan with a 3–5 lm step size and an accelerating voltage of 20 kV. The pure metals, DU and Fe at the terminal ends of the couple were used as the calibration standards. The measured intensities of the U–Ma and Fe–Ka X-rays were converted to compositions with a ZAF correction. Two independent measurements were carried out for each couple with excellent agreement. The measured compositions of the two intermetallic phases agreed with the stoichiometric ratios of U6Fe and UFe2 very well. Atomic fraction of 0.143 Fe in U6Fe and 0.667 Fe in UFe2 were used for quantitative analysis in this study. 4. Results Typical backscattered electron micrograph and concentration profiles obtained from the U vs. Fe diffusion couple annealed at 923 K for 96 h are presented in Fig. 2. The four phases shown in Fig. 2a are pure U, U6Fe, UFe2 and pure Fe in accordance with the U–Fe equilibrium phase diagram in Fig. 1. The thickness and interface between each phase are uniform and planar, respectively. Because the compositional ranges in all four phases are negligible, the concentration profile does not exhibit any discernable gradient. False gradients appearing at the interfaces are results of the interaction volume of electron beam at the sample interfaces that comprise partially the two neighboring phases. The average thickness, Dxðv Þ and its standard deviation (as the indicated uncertainty) for the U6Fe and UFe2 layers at each temperature are reported in Table 2. Table 1 Temperature and time of anneal for U vs. Fe diffusion couples along with equilibrium allotropic phase of U. Temperature (K)
Time (h)
Allotropic phase of uranium
853 888 923 953 973
240 240 96 96 96
a a a b b
85
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
Fig. 3. Modified concentration profile of Fe in U vs. Fe diffusion couple annealed at 923 K for 96 h.
Fig. 2. (a) Backscattered electron (BSE) micrograph and (b) EPMA concentration profiles obtained from U vs. Fe diffusion couple annealed at 923 K for 96 h.
The U6Fe phase is much thicker than UFe2 in all diffusion couples investigated in this study, although the difference, evaluated by thickness ratio, gets smaller with increasing temperature. Since there are negligible concentration gradients in both U6Fe and UFe2, the interdiffusion flux remains constant within each phase. A modified Fe concentration profile for the U vs. Fe diffusion couple annealed at 923 K for 96 h can be calculated from the average measured thickness and the stoichiometry of U6Fe and UFe2, and is presented in Fig. 3. The corresponding interdiffusion flux of Fe calculated by Eq. (3) is presented in Fig. 4 and reported in Table 3. The interdiffusion flux in the U6Fe phase is higher than that in UFe2, and the ratio between them decreases from 2.1 to 1.67 with an increase in temperature from 853 K to 973 K. The integrated interdiffusion coefficients in U6Fe and UFe2 at each temperature were calculated based on Fe concentration profile using Eqs. (4) and (5). The molar volume variation with compoe Int;ðv Þ by the sition was ignored for this calculation. The calculated D two methods were exactly same since both methods are based on e Int;U6 Fe ; D e Int;UFe2 and Fick’s first law. The calculated magnitude of D their activation energies are reported in Table 4. Fig. 5 shows the e Int;U6 Fe and D e Int;UFe2 , distinguishing temperature dependence of the D the case of a-U and b-U as the terminal phase of the diffusion coue Int;ðv Þ Þ and the reciprocal ple. Linear relationships between Lnð D
Fig. 4. Interdiffusion flux profile of Fe in U vs. Fe diffusion couple annealed at 923 K for 96 h.
e Int;U6 Fe is much larger than absolute temperature are obtained. The D Int;UFe2 e e Int;U6 Fe is D at each temperature, and the activation energy of D e Int;UFe2 in both a-U and b-U correspondingly smaller than that of D temperature ranges. In this study, diffusion couples with pure U and pure Fe as the terminal ends were examined, so the extrinsic growth constants, 2 K IU6 Fe and K UFe were calculated simply using Eq. (6), as reported I e Int;ðv Þ and in Table 5. The integrated interdiffusion coefficient D ðv Þ intrinsic growth constant K II are material constants for the U6Fe and UFe2 phases. Utilizing the correlation given by Eq. (9), the 2 intrinsic growth constants K UII 6 Fe and K UFe were calculated and II are reported in Table 6. ðv Þ ðv Þ The temperature dependence of K I and K II are presented in ðv Þ
ðv Þ
Fig. 6. Again linear relations between LnðK I Þ; LnðK II Þ and the reciprocal absolute temperature were observed within both a-U and b-U temperature ranges. The values of K UI 6 Fe are close to K IIU6 Fe independent of the allotropic phase of U (i.e., a or b) at the terminal end. Accordingly, the activation energy of K IU6 Fe is almost the same 2 was as that of K UII 6 Fe as reported in Tables 5 and 6. However, K UFe I UFe2
2 , and correspondingly, Q K I smaller than K UFe II
Q
UFe2
K II
was higher than
.
Table 2 Thickness of U6Fe and UFe2 in each U vs. Fe diffusion couple. Allotropic phase of U
T (K)
Time (h)
DxðU6 FeÞ (lm)
a-U (orthorhombic)
853 888 923
240 240 96
46.4 ± 0.9 70.1 ± 0.8 64.1 ± 2.5
2.5 ± 0.1 6.0 ± 0.4 7.8 ± 0.6
18.56 11.68 8.22
b-U (tetragonal)
953 973
96 96
78.4 ± 2.0 90.3 ± 2.1
8.4 ± 0.3 12.1 ± 0.5
9.33 7.46
DxðUFe2 Þ (lm)
Ratio DxðU6 FeÞ =DxðUFe2 Þ
86
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
Table 3 Interdiffusion flux of Fe in U6Fe and UFe2. Allotropic phase of U
T (K)
eJ U6 Fe ( 1012 at. frac. m/s)
a-U (orthorhombic)
853 888 923
3.36 5.14 11.90
1.60 2.70 6.92
2.1 1.90 1.72
b-U (tetragonal)
953 973
14.48 16.84
8.10 10.11
1.79 1.67
eJ UFe2 ( 1012 at. frac. m/s)
Ratio eJ U6 Fe =eJ UFe2
Table 4 Integrated interdiffusion coefficients of Fe in U6Fe and UFe2. e Int; D
eInt; QD
e Int; D
eInt; QD
Allotropic phase of U
T (K)
a-U (orthorhombic)
853 888 923
1.56 3.60 7.63
148
0.040 0.162 0.534
243
b-U (tetragonal)
953 973
11.35 15.21
113
0.680 1.22
226
U6 Fe
( 1016 at. frac. m2/s)
U6 Fe
(kJ/mol)
UFe2
( 1016 at. frac. m2/s)
UFe2
(kJ/mol)
e Int;U6 Fe Fig. 5. Temperature dependence of integrated interdiffusion coefficients, D e Int;UFe2 . and D
Fig. 6. Temperature dependence of extrinsic and intrinsic growth constants, 2 2 K UI 6 Fe ; K UFe ; K UII 6 Fe and K UFe . I II
5. Discussion
e Int; UFe2 when U was in the a phase are larger than those when D U was in the b phase, and the difference in the activation energy is more significant for the U6Fe phase than UFe2. This is also true e Int and for both extrinsic and intrinsic growth constants. Both D KII are material constants for a specific phase [20,22], and should obey the Arrhenius relation. However, there is discontinuity of e Int and KII at the allotropic transformation temperature and correD sponding changes in activation energy for a-U and b-U temperature ranges. This indicates that the allotropic transformation of U plays a role on the growth of intermetallic phases, specifically the U6Fe phase. The growth of U6Fe requires: (a) diffusion reactions at U/U6Fe interface; (b) diffusion of U and Fe in the U6Fe; and (c) diffusion reactions at U6Fe/UFe2 interface. In this study, factors (b) and (c) remained unchanged and only the factor (a) may have changed due to the allotropic transformation of U.
ðv Þ
The intrinsic growth constant K II is a characteristic value for a ðv Þ phase v, while the values of K I may be influenced by other phases 2 that exist in the diffusion zone. The fact that K UFe is smaller than I 2 K UFe for the UFe phase indicates that the growth of UFe2 was im2 II peded by the rapid growth of the adjacent U6Fe phase layer. The magnitudes of K UI 6 Fe and K UII 6 Fe are almost the same, and this indicates that the growth of U6Fe was not influenced by the slow e Int;ðv Þ and K ðv Þ are characteristic constants growth of UFe2. Both D II inherent to the diffusion within a phase m, and show the same temperature dependence with the same activation energy as reported in Tables 4 and 6. The allotropic transformation of U had an effect on the growth e Int; U6 Fe and of both U6Fe and UFe2. The activation energies of D
Table 5 Extrinsic growth constant, KI of U6Fe and UFe2 phases. 6 Fe ( 1016 m2 /s) KU I
2 ( 1016 m2/s) K UFe I
Allotropic phase of U
T (K)
a-U (orthorhombic)
853 888 923
12.46 28.44 59.44
146
0.036 0.208 0.880
299
b-U (tetragonal)
953 973
88.93 117.97
109
1.021 2.118
281
U6 Fe
Q KI
(kJ/mol)
UFe2
Q KI
(kJ/mol)
87
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88 Table 6 Intrinsic growth constant, KII of U6Fe and UFe2. 6 Fe ( 1016 m2 /s) KU II
2 ( 1016 m2/s) K UFe II
Allotropic phase of U
T (K)
a-U (orthorhombic)
853 888 923
13.88 32.05 67.91
148
0.196 0.797 2.652
243
b-U (tetragonal)
953 973
101.05 135.40
113
3.342 6.008
226
In the phenomenological description via irreversible thermodynamics, the specific heat of U changes at the allotropic transformation temperature and hence a change in the temperature dependence of the thermodynamic driving force for the reaction may be expected when U transforms between a to b phase. This would only cause the driving force of diffusion/reaction to change. From the mechanism perspective, the allotropic transformation of U causes the crystal structure and binding energy changes, which would affect the rate and distance of atomic motion at the interface. This variation in the growth of U6Fe caused by interfacial changes implies that the growth of U6Fe may not be completely lattice diffusion controlled and interfacial process may be significant. The effect of allotropic transformation on the growth mechanism of U6Fe needs to be further examined based on the growth thickness as a function of time. The variation in the growth of U6Fe, of course, would indirectly affect the growth of UFe2. Therefore, the influence of U allotropic transformation on the growth of U6Fe through changes in the U/ U6Fe interface would also affect the growth of UFe2. Wagner [20] defined the intrinsic growth constant KII without the consideration of the allotropic transformation of the neighboring phases. This study indicates that the allotropic transformation of the neighboring phases can result in variation of KII which is no longer a material constant. Both experimental observation and quantitative analysis demonstrated that U6Fe grew faster than UFe2. Funamizu and Watanabe [23] reviewed several potential factors and summarized that an intermediate phase layer will grow more rapidly if: (a) The diffusion coefficient in the layer is larger. (b) The diffusion coefficient in the adjoining phases is smaller. (c) The homogeneity range of the phase in the phase diagram is wider. (d) The concentration range of the adjoining two-phase areas in the phase diagram is narrower (that means the miscibility gap between the phase and the adjoining phases is smaller). (e) The heat of formation of the phase is higher (that means the thermodynamic stability of a phase is higher and has a greater driving for formation). (f) The crystal structures between the adjoining phases are similar.
U6 Fe
Q K II
(kJ/mol)
UFe2
Q K II
(kJ/mol)
tal structure is dissimilar from both of its neighbors, it would be expected to grow more slowly as per criterion (f). Therefore it is reasonable that the U6Fe phase layer was observed to grow faster than UFe2. 6. Summary e Int , extrinsic growth The integrated interdiffusion coefficient D constant (the first kind according to Wagner’s scheme) KI, and intrinsic growth constant (the second kind according to Wagner’s scheme) KII of U6Fe and UFe2 were calculated in the temperature range from 853 K to 973 K. In each diffusion couple, U6Fe grew faster than UFe2. The thick U6Fe impeded the growth of UFe2, while the UFe2 growth had little influence on the growth of U6Fe. The allotropic transformation of U (orthorhombic a and tetragonal b phase) had an effect on the growth of U6Fe and UFe2. The change in specific heat and/or crystal structure of U due to the allotropic transformation affected the interfacial diffusion reaction between U and U6Fe, and had further influence on the growth of U6Fe and UFe2. The more rapid growth of U6Fe was identified as consistent with the crystal structure, chemical composition, and kinetic properties of the two phases U6Fe and UFe2 with pure U and Fe terminal ends. US department of energy disclaimer This information was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof. Acknowledgments
e Int;U6 Fe is larResults of this study show that the magnitude of D Int;UFe2 e ger than that of D to satisfy criteria (a) and (b). According to the U–Fe phase diagram presented in Fig. 1, both U6Fe and UFe2 are line compounds, but the miscibility gap in concentration of Fe is 14.3% between pure U and U6Fe, and 33.3% between UFe2 and pure Fe, in regards to criterion (d). Also, U6Fe has a lower melting point (about 1273 K) than UFe2 (about 1503 K), consistent with faster interdiffusion but not contra-indicated as the faster growth phase based on criterion (e). U6Fe has a body-centered tetragonal crystal structure [24] that is similar to a-U (orthorhombic) or b-U (tetragonal) structure. However, UFe2 has a complex Laves phase structure (C15 fcc crystal structure, symmetry Fd3m) [25], very different from a-Fe (body center cubic structure). As the UFe2 crys-
This work was supported by the US Department of Energy under DOE-NE Idaho Operations Office Contract DE-AC07-05ID14517. Accordingly, The US Government retains and the publisher, by accepting the article for publication, acknowledges that the US Government retains a nonexclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US Government purposes. Reference [1] G.L. Hofman, L.C. Walters, T.H. Bauer, Prog. Nucl. Energy 31 (1997) 83. [2] W.J. Carmack, D.L. Porter, Y.I. Chang, S.L. Hayes, M.K. Meyer, D.E. Burkes, C.B. Lee, T. Mizuno, F. Delage, J. Somers, J. Nucl. Mater. 392 (2009) 139.
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[3] D. Olander, J. Nucl. Mater. 389 (2009) 1. [4] Hofman GL, Hins AG, Porter DL, Leibowitz L, Wood EL. Chemical interaction of metallic fuel with austenitic and ferritic stainless steel cladding, 1986. [5] D.D. Keiser, M.A. Dayananda, J. Nucl. Mater. 200 (1993) 229. [6] D.D. Keiser, M.C. Petri, J. Nucl. Mater. 240 (1996) 51. [7] T. Ogata, M. Kurata, K. Nakamura, A. Itoh, M. Akabori, J. Nucl. Mater. 250 (1997) 171. [8] K. Nakamura, T. Ogata, M. Kurata, A. Itoh, M. Akabori, J. Nucl. Mater. 275 (1999) 246. [9] T. Ogata, K. Nakamura, M. Kurata, T. Yokoo, M.A. Mignanelli, J. Nucl. Sci. Technol. 37 (2000) 244. [10] K. Nakamura, T. Ogata, M. Kurata, T. Yokoo, M.A. Mignanelli, J. Nucl. Sci. Technol. 38 (2001) 112. [11] P. Gordon, A.R. Kaufmann, Trans. AIME 188 (1950) 182. [12] J.D. Grogan, J. Inst. Met. 77 (1950) 571. [13] L.R. Chapman, C.F. Holcombe Jr., J. Nucl. Mater. 126 (1984) 323. [14] E.A. Brandes, G.B. Brook (Eds.), Smithells Metals Reference Book, 1992.
[15] L. Leibowitz, R.A. Blomquist, J. Nucl. Mater. 184 (1991) 47. [16] S. Chatain, C. Guéneau, D. Labroche, O. Dugne, J. Rogez, J. Phase Equilib. 24 (2003) 122. [17] M. Kurata, T. Ogata, K. Nakamura, T. Ogawa, J. Alloys Compd. 271–273 (1998) 636. [18] H. Mehrer (Ed.), Diffusion in Solid, 2007. [19] T. Heumann, Z. Physik. Chem 201 (1952) 168. [20] C. Wagner, Acta Metall. 17 (1969) 99. [21] M.A. Dayananda, Defect Diffus. Forum 95–98 (1993) 521. [22] V.I. Dybkov (Ed.), Reaction Diffusion and Solid State Chemical Kinetics, 2002. [23] Y. Funamizu, K. Watanabe, Jpn. Inst. Met. 13 (1972) 278. [24] E. Yamamoto, Y. Haga, A. Nakamura, N. Kimura, Y. Inada, H. Sugawara, H. Sato, Y. Nuki, Physica B 230–232 (1997) 394. [25] A.M. Boring, R.C. Albers, G.H. Schadler, A.C. Lawson, P. Weinberger, N.E. Christensen, Phys. Rev. B 36 (1987) 5507.
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Interdiffusion and reaction between uranium and iron K. Huang a, Y. Park a, A. Ewh a, B.H. Sencer b, J.R. Kennedy b, K.R. Coffey a, Y.H. Sohn a,⇑ a b
Advanced Materials Processing and Analysis Center, Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, USA Fundamental Fuel Properties Department, Nuclear Fuel and Materials Division, Idaho National Laboratory, Idaho Falls, ID, USA
a r t i c l e
i n f o
Article history: Received 15 November 2011 Accepted 6 February 2012 Available online 18 February 2012
a b s t r a c t Metallic uranium alloy fuels cladded in stainless steel are being examined for fast reactors that operate at high temperature. In this work, solid-to-solid diffusion couples were assembled between pure U and Fe, and annealed at 853 K, 888 K and 923 K where U exists as orthorhombic a, and at 953 K and 973 K where U exists as tetragonal b. The microstructures and concentration profiles developed during annealing were examined by scanning electron microscopy and electron probe microanalysis, respectively. U6Fe and UFe2 intermetallics developed in all diffusion couples, and U6Fe was observed to grow faster than UFe2. The interdiffusion fluxes of U and Fe were calculated to determine the integrated interdiffusion coefficients in U6Fe and UFe2. The extrinsic (KI) and intrinsic growth constants (KII) of U6Fe and UFe2 were also calculated according to Wagner’s formalism. The difference between KI and KII of UFe2 indicate that its growth was impeded by the fast-growing U6Fe phase. However, the thin UFe2 played only a small role on the growth of U6Fe as its KI and KII values were determined to be similar. The allotropic transformation of uranium (orthorhombic a to tetragonal b phase) was observed to influence the growth of U6Fe directly, because the growth rate of U6Fe changed based on variation of activation energy. The change in chemical potential and crystal structure of U due to the allotropic transformation affected the interdiffusion between U and U6Fe. Faster growth of U6Fe is also examined with respect to various factors including crystal structure, phase diagram, and diffusion. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction Uranium–zirconium (U–Zr) metallic fuel with stainless steel cladding has been developed for advanced fast reactors because of its high burnup capability and favorable thermal response [1–3]. Under irradiation, the U–Zr fuel can swell and contact the stainless steel cladding because of thermal expansion and the accumulation of fission products, which causes interdiffusion and reaction to form new product phases. This fuel cladding chemical interaction (FCCI) has deleterious effects because it thins the cladding and produces phases with undesirable properties. The FCCIs between U–Zr alloys and stainless steels have been studied extensively [4–10]. In most cases, the interaction zone shows a complex multi-layer structure with various intermetallic compounds. The phase diagram of U– Fe has been well studied by Gordon and Kaufmann [11], Grogan [12] and Chapman and Holcombe [13] and assessed in the literature [14–16] with a good agreement among these studies. The iron– uranium system is comprised of eight solid phases: a (oC4), b (tP30) and c (cI2) uranium; a (cI2), c (cF4) and d (cI2) iron; and two intermetallic compounds UFe2 (cF24) and U6Fe (tI28). The thermodynamic properties of U–Fe, U–Zr and U–Zr–Fe were also
⇑ Corresponding author. Tel.: +1 407 882 1181; fax: +1 407 882 1461. E-mail address: [email protected] (Y.H. Sohn). 0022-3115/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jnucmat.2012.02.004
reported in the literature [16,17]. However, the reactions between pure U and Fe with interdiffusion analysis have never been reported. In this study, U vs. Fe binary diffusion experiments were conducted to help understand the complex FCCI process, and provide quantitative diffusion data from experiments for FCCI modeling. This simple system chosen serves to form the basis for quantitative understanding for the effects of alloying addition (e.g., Zr, Cr and Ni) on the FCCI. Moreover, effects of allotropic transformation in U on the reactions and reactions mechanism between U and Fe have also been investigated based on this binary system. The annealing temperatures were selected in the range of 853–973 K, in order to study the effect of the allotropic transformation of U (from orthorhombic a-U to tetragonal b-U at 940 K) on the diffusional interaction between U and Fe. Scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) were employed to examine the development of intermetallic phases in the interdiffusion zone. Two intermetallic phases, U6Fe and UFe2 were observed, consistent with to the U–Fe equilibrium phase diagram shown in Fig. 1 [14]. The interdiffusion flux, eJ, integrated interdiffusion coefe Int , extrinsic growth constant, KI, and intrinsic growth ficients, D constant, KII, of U6Fe and UFe2 were calculated. The activation ene Int , KI and KII were also determined by the Arrhenius relaergy of D tion. The faster growth kinetics of U6Fe compared to UFe2 is discussed.
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
83
Fig. 1. Equilibrium binary phase diagram of U–Fe system [14].
The interdiffusion flux through the interdiffusion zone can be calculated by:
2. Analytical framework for diffusion Different analytical approaches and diffusion parameters are applied to study diffusion phenomena in binary systems depending on concentration gradients that develop. When a sufficient concentration gradient can be measured in a phase, the Boltzmann–Matano method and/or modified Sauer–Freise method [18] can be used to determine the interdiffusion coefficient as a function of composition. However, it is not appropriate to apply those analyses when the solubility in the intermediate phase is narrow since the error of calculated interdiffusion coefficients may be large due to the small concentration gradient. To extend the above methods to the intermediate phases with negligible compositional ranges, Heumann [19] and Wagner [20] derived phenomenological expressions to determine the average interdiffusion coefficient within a phase under the assumption of linear concentration gradient in the intermediate phase. To that end, e Int [20,21], extrinsic growth integrated interdiffusion coefficients, D constant, KI and intrinsic growth constants, KII [20] can be employed to describe the diffusion process. e Int 2.1. Integrated interdiffusion coefficient, D The integrated interdiffusion coefficient of a specific phase
v ; De Int;ðv Þ is a material constant that is ideally the same in all diffusion couples regardless of experimental boundary conditions [20,22]. Dayananda [21] provided an equation to calculate the e Int;ðv Þ in the range of (x1, x2) in a binary system as: D
e Int ¼ D i
Z
N i ðx2 Þ
e dNi ¼ D
Ni ðx1 Þ
Z
x2
eJ i dx
ð1Þ
þ1
1
ðx x0 ÞdNi ¼ 0
Z
N i
N 1 i
ðx x0 ÞdNi
ð3Þ
where Ni is the mole fraction of component i at the position where the interdiffusion flux is calculated, and N 1 is the mole fraction of i component i at terminal ends. When a phase v, has a very narrow compositional range (i.e., line compound) and is present in the interval from xðv Þ to xðv Þþ , e Int;ðv Þ in the integral rethe integrated interdiffusion coefficient, D i gion, x1 to x2 for the phase v in Eq. (1) can be simplified as:
e Int;ðv Þ ¼ eJ ðv Þ Dxðv Þ where Dxðv Þ ¼ xðv Þþ xðv Þ D i i
ð4Þ
Since there are negligible concentration gradients in the phase
m, the interdiffusion fluxes through the phase m are constant according to Eq. (3). Wagner [20] also gave an alternative means to calculate the integrated interdiffusion coefficients as:
" # ðv Þ N1 ÞðNþ1 Ni Þ ðDxðv Þ Þ2 i i 2t ðNþ1 N1 Þ i i " Z xðv Þ ðv Þ þ1 ðv Þ Ni Ni Dx þ ðNi N1 Þdx 1 i 2t Nþ1 N 1 i i # Z þ1 ðv Þ N i N1 þ1 i ðNi Ni Þdx þ þ1 Ni N1 xðv Þþ i ðv Þ
e Int;ðv Þ ¼ ðNi D i
ð5Þ
This is equivalent to Eq. (4) but does not require the determination of Matano plane.
x1
e is the interdiffusion where Ni is the mole fraction of component i; D coefficient and eJ i is the interdiffusion flux of component i. To obtain eJ i , the Matano plane position x0 can be determined by mass balance [18]:
Z
eJðN Þ ¼ 1 i 2t
ð2Þ
2.2. Extrinsic (KI) and intrinsic (KII) growth constants The growth constant of the phase m may not be a material constant, and can vary in diffusion couples with different terminal ðv Þ ends. Therefore, two kinds of parabolic growth constants, K I and ðv Þ K II were defined by Wagner [20] to describe the diffusion process in a phase v having a negligible concentration gradient. When the
84
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
phase m forms in a diffusion couple with ‘‘pure’’ components as its terminal ends (the first kind diffusion couple according to Wagner’s ðv Þ notation, i.e., N 1 ¼ 0; N þ1 ¼ 1Þ, the extrinsic growth constant, K I i i can be defined as: ðv Þ KI
" # ðDxðv Þ Þ2 ¼ 2t
ð6Þ
N 1 ¼0; N þ1 ¼1 i i Int;ðv Þ
e The integrated interdiffusion coefficient, D and the extrinsic i ðv Þ growth constant K I can be correlated by substituting Eq. (6) into Eq. (5), which yields: e Int; ðv Þ ¼ D i
Z
ðv Þþ
Ni
e i DdN
ðv Þ
Ni
ðv Þ
ðv Þ
ðv Þ
¼ Ni ð1 N i ÞK I " # Z xðv Þ Z þ1 Dxðv Þ ðv Þ ðv Þ þ N i dx þ N i ð1 Ni Þdx ð1 N i Þ 2t xðv Þþ 1
N 1 ¼0; N þ1 ¼1 i i
ð7Þ
Alternatively, phase m can also form in a diffusion couple with its neighboring phases (m 1) and (m + 1) as terminal ends (the second diffusion couple according to Wagner’s notation, ðv 1Þ ðv þ1Þ N 1 ¼ Ni ; N þ1 ¼ Ni ), and the intrinsic parabolic growth i i ðv Þ constant, K II can be expressed using the same equation, however, with different boundary condition, as: ðv Þ K II
" # ðDxðv Þ Þ2 ¼ 2t
ð8Þ ðv 1Þ
N 1 ¼N i i
ðv 1Þ
ðv þ1Þ
; N þ1 ¼N i i
ðv þ1Þ
where N i and N i are the mole fraction of component i in neighboring phases, (m 1) and (m + 1). In this second kind of diffusion couple, the integral terms in Eq. (7) vanish. Thus, one obtains e Int;ðv Þ and intrinsic growth constant K ðv Þ as: the relation between D II i ðv Þ
e Int; ðv Þ ¼ ðNi D i
ðv 1Þ
Ni
ðv þ1Þ ðNi
ðv þ1Þ
ÞðNi
ðv Þ
Ni Þ
ðv 1Þ Ni Þ
ðv Þ ½K II N1 ¼Nðv 1Þ ; Nþ1 ¼Nðv þ1Þ i i i i
ð9Þ
ðv Þ
While K I can vary since the growth of phase v is affected by the ðv Þ growth of other phases in the diffusion zone [20], the K II is considered a ‘‘true’’ growth constant. In this study, the first kind diffusion couple with pure terminal ends (i.e., U and Fe) were employed e Int;ðv Þ and K ðv Þ were readily calculated. The experimentally, so D I i ðv Þ value of K I was also confirmed using Eq. (7). The intrinsic growth ðv Þ e Int;ðv Þ and Eq. (9). constants, K II were also calculated based on D i 3. Experimental procedure All metallographic preparation and assembly of diffusion couples were carried out under an Ar atmosphere inside a glove box to minimize oxidation of the depleted uranium (DU) and iron (Fe). DU rods were cast using high-purity DU via arc melting. They were melted three times to ensure the homogeneity and then drop-cast to form rods with 6.35 mm diameter. Fe rods of 99.99% purity were acquired from a commercial source (AlphaAesar™). The homogeneity in composition, phase constituents and microstructure of DU and Fe were examined by X-ray diffraction (XRD, Rigaku™ DMAX-B), and scanning electron microscopy (SEM, Hitachi™ 3500N) equipped with X-ray energy dispersive spectroscopy (XEDS). Both the U and Fe rods were cut into 3 mm-thick disks. The disk surfaces, which would become the interface of the diffusion couple, were metallographically polished down to 1 lm using diamond paste. Before assembling the diffusion couples, the U disks were immersed momentarily into nitric acid (1:1 volume with distilled water) to remove the
oxide layer on the surface. The prepared surfaces were then placed in contact with each other, and held together by two clamping disks with stainless steel rods to form a jig. Each couple assembly was wrapped with Ta-foil and encapsulated in a quartz capsule that was sealed under vacuum (106 Pa) after repeated vacuum and pure H2 flushing operations. Finally, the couples were annealed in the temperature range from 853 to 973 K using a Lindberg/Blue™ three-zone tube furnace. The diffusion couples examined in this study are listed in Table 1. To study the effect of the allotropic transformation between a-U and b-U, three annealing temperatures (853, 888, 923 K) were selected in a-U temperature range, below the allotropic transformation point at 940 K based on U–Fe equilibrium phase diagram as shown in Fig. 1. Only two annealing temperatures (953 and 973 K) were selected in the b-U temperature range below the U–Fe eutectic temperature around 990 K. After annealing, the diffusion couples were quenched by breaking the quartz capsule in cold water. Each diffusion couple was then mounted in epoxy, cross-sectioned and polished using 1 lm diamond paste for microstructural examination and compositional analysis. For each diffusion couple, SEM (Hitachi™ 3500 N) was first carried out to examine the interdiffusion microstructure. The thickness of U6Fe and UFe2 layers were measured based on backscatter electron (BSE) micrographs from the interdiffusion zone. At least 10 random locations were selected to determine an average and standard deviation of the layer thickness for the U6Fe and UFe2 phases at each annealing temperature. Electron probe microanalysis (EPMA, JEOL™ Superprobe 733) was employed to determine the concentration profile for each couple utilizing a point-to-point scan with a 3–5 lm step size and an accelerating voltage of 20 kV. The pure metals, DU and Fe at the terminal ends of the couple were used as the calibration standards. The measured intensities of the U–Ma and Fe–Ka X-rays were converted to compositions with a ZAF correction. Two independent measurements were carried out for each couple with excellent agreement. The measured compositions of the two intermetallic phases agreed with the stoichiometric ratios of U6Fe and UFe2 very well. Atomic fraction of 0.143 Fe in U6Fe and 0.667 Fe in UFe2 were used for quantitative analysis in this study. 4. Results Typical backscattered electron micrograph and concentration profiles obtained from the U vs. Fe diffusion couple annealed at 923 K for 96 h are presented in Fig. 2. The four phases shown in Fig. 2a are pure U, U6Fe, UFe2 and pure Fe in accordance with the U–Fe equilibrium phase diagram in Fig. 1. The thickness and interface between each phase are uniform and planar, respectively. Because the compositional ranges in all four phases are negligible, the concentration profile does not exhibit any discernable gradient. False gradients appearing at the interfaces are results of the interaction volume of electron beam at the sample interfaces that comprise partially the two neighboring phases. The average thickness, Dxðv Þ and its standard deviation (as the indicated uncertainty) for the U6Fe and UFe2 layers at each temperature are reported in Table 2. Table 1 Temperature and time of anneal for U vs. Fe diffusion couples along with equilibrium allotropic phase of U. Temperature (K)
Time (h)
Allotropic phase of uranium
853 888 923 953 973
240 240 96 96 96
a a a b b
85
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
Fig. 3. Modified concentration profile of Fe in U vs. Fe diffusion couple annealed at 923 K for 96 h.
Fig. 2. (a) Backscattered electron (BSE) micrograph and (b) EPMA concentration profiles obtained from U vs. Fe diffusion couple annealed at 923 K for 96 h.
The U6Fe phase is much thicker than UFe2 in all diffusion couples investigated in this study, although the difference, evaluated by thickness ratio, gets smaller with increasing temperature. Since there are negligible concentration gradients in both U6Fe and UFe2, the interdiffusion flux remains constant within each phase. A modified Fe concentration profile for the U vs. Fe diffusion couple annealed at 923 K for 96 h can be calculated from the average measured thickness and the stoichiometry of U6Fe and UFe2, and is presented in Fig. 3. The corresponding interdiffusion flux of Fe calculated by Eq. (3) is presented in Fig. 4 and reported in Table 3. The interdiffusion flux in the U6Fe phase is higher than that in UFe2, and the ratio between them decreases from 2.1 to 1.67 with an increase in temperature from 853 K to 973 K. The integrated interdiffusion coefficients in U6Fe and UFe2 at each temperature were calculated based on Fe concentration profile using Eqs. (4) and (5). The molar volume variation with compoe Int;ðv Þ by the sition was ignored for this calculation. The calculated D two methods were exactly same since both methods are based on e Int;U6 Fe ; D e Int;UFe2 and Fick’s first law. The calculated magnitude of D their activation energies are reported in Table 4. Fig. 5 shows the e Int;U6 Fe and D e Int;UFe2 , distinguishing temperature dependence of the D the case of a-U and b-U as the terminal phase of the diffusion coue Int;ðv Þ Þ and the reciprocal ple. Linear relationships between Lnð D
Fig. 4. Interdiffusion flux profile of Fe in U vs. Fe diffusion couple annealed at 923 K for 96 h.
e Int;U6 Fe is much larger than absolute temperature are obtained. The D Int;UFe2 e e Int;U6 Fe is D at each temperature, and the activation energy of D e Int;UFe2 in both a-U and b-U correspondingly smaller than that of D temperature ranges. In this study, diffusion couples with pure U and pure Fe as the terminal ends were examined, so the extrinsic growth constants, 2 K IU6 Fe and K UFe were calculated simply using Eq. (6), as reported I e Int;ðv Þ and in Table 5. The integrated interdiffusion coefficient D ðv Þ intrinsic growth constant K II are material constants for the U6Fe and UFe2 phases. Utilizing the correlation given by Eq. (9), the 2 intrinsic growth constants K UII 6 Fe and K UFe were calculated and II are reported in Table 6. ðv Þ ðv Þ The temperature dependence of K I and K II are presented in ðv Þ
ðv Þ
Fig. 6. Again linear relations between LnðK I Þ; LnðK II Þ and the reciprocal absolute temperature were observed within both a-U and b-U temperature ranges. The values of K UI 6 Fe are close to K IIU6 Fe independent of the allotropic phase of U (i.e., a or b) at the terminal end. Accordingly, the activation energy of K IU6 Fe is almost the same 2 was as that of K UII 6 Fe as reported in Tables 5 and 6. However, K UFe I UFe2
2 , and correspondingly, Q K I smaller than K UFe II
Q
UFe2
K II
was higher than
.
Table 2 Thickness of U6Fe and UFe2 in each U vs. Fe diffusion couple. Allotropic phase of U
T (K)
Time (h)
DxðU6 FeÞ (lm)
a-U (orthorhombic)
853 888 923
240 240 96
46.4 ± 0.9 70.1 ± 0.8 64.1 ± 2.5
2.5 ± 0.1 6.0 ± 0.4 7.8 ± 0.6
18.56 11.68 8.22
b-U (tetragonal)
953 973
96 96
78.4 ± 2.0 90.3 ± 2.1
8.4 ± 0.3 12.1 ± 0.5
9.33 7.46
DxðUFe2 Þ (lm)
Ratio DxðU6 FeÞ =DxðUFe2 Þ
86
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88
Table 3 Interdiffusion flux of Fe in U6Fe and UFe2. Allotropic phase of U
T (K)
eJ U6 Fe ( 1012 at. frac. m/s)
a-U (orthorhombic)
853 888 923
3.36 5.14 11.90
1.60 2.70 6.92
2.1 1.90 1.72
b-U (tetragonal)
953 973
14.48 16.84
8.10 10.11
1.79 1.67
eJ UFe2 ( 1012 at. frac. m/s)
Ratio eJ U6 Fe =eJ UFe2
Table 4 Integrated interdiffusion coefficients of Fe in U6Fe and UFe2. e Int; D
eInt; QD
e Int; D
eInt; QD
Allotropic phase of U
T (K)
a-U (orthorhombic)
853 888 923
1.56 3.60 7.63
148
0.040 0.162 0.534
243
b-U (tetragonal)
953 973
11.35 15.21
113
0.680 1.22
226
U6 Fe
( 1016 at. frac. m2/s)
U6 Fe
(kJ/mol)
UFe2
( 1016 at. frac. m2/s)
UFe2
(kJ/mol)
e Int;U6 Fe Fig. 5. Temperature dependence of integrated interdiffusion coefficients, D e Int;UFe2 . and D
Fig. 6. Temperature dependence of extrinsic and intrinsic growth constants, 2 2 K UI 6 Fe ; K UFe ; K UII 6 Fe and K UFe . I II
5. Discussion
e Int; UFe2 when U was in the a phase are larger than those when D U was in the b phase, and the difference in the activation energy is more significant for the U6Fe phase than UFe2. This is also true e Int and for both extrinsic and intrinsic growth constants. Both D KII are material constants for a specific phase [20,22], and should obey the Arrhenius relation. However, there is discontinuity of e Int and KII at the allotropic transformation temperature and correD sponding changes in activation energy for a-U and b-U temperature ranges. This indicates that the allotropic transformation of U plays a role on the growth of intermetallic phases, specifically the U6Fe phase. The growth of U6Fe requires: (a) diffusion reactions at U/U6Fe interface; (b) diffusion of U and Fe in the U6Fe; and (c) diffusion reactions at U6Fe/UFe2 interface. In this study, factors (b) and (c) remained unchanged and only the factor (a) may have changed due to the allotropic transformation of U.
ðv Þ
The intrinsic growth constant K II is a characteristic value for a ðv Þ phase v, while the values of K I may be influenced by other phases 2 that exist in the diffusion zone. The fact that K UFe is smaller than I 2 K UFe for the UFe phase indicates that the growth of UFe2 was im2 II peded by the rapid growth of the adjacent U6Fe phase layer. The magnitudes of K UI 6 Fe and K UII 6 Fe are almost the same, and this indicates that the growth of U6Fe was not influenced by the slow e Int;ðv Þ and K ðv Þ are characteristic constants growth of UFe2. Both D II inherent to the diffusion within a phase m, and show the same temperature dependence with the same activation energy as reported in Tables 4 and 6. The allotropic transformation of U had an effect on the growth e Int; U6 Fe and of both U6Fe and UFe2. The activation energies of D
Table 5 Extrinsic growth constant, KI of U6Fe and UFe2 phases. 6 Fe ( 1016 m2 /s) KU I
2 ( 1016 m2/s) K UFe I
Allotropic phase of U
T (K)
a-U (orthorhombic)
853 888 923
12.46 28.44 59.44
146
0.036 0.208 0.880
299
b-U (tetragonal)
953 973
88.93 117.97
109
1.021 2.118
281
U6 Fe
Q KI
(kJ/mol)
UFe2
Q KI
(kJ/mol)
87
K. Huang et al. / Journal of Nuclear Materials 424 (2012) 82–88 Table 6 Intrinsic growth constant, KII of U6Fe and UFe2. 6 Fe ( 1016 m2 /s) KU II
2 ( 1016 m2/s) K UFe II
Allotropic phase of U
T (K)
a-U (orthorhombic)
853 888 923
13.88 32.05 67.91
148
0.196 0.797 2.652
243
b-U (tetragonal)
953 973
101.05 135.40
113
3.342 6.008
226
In the phenomenological description via irreversible thermodynamics, the specific heat of U changes at the allotropic transformation temperature and hence a change in the temperature dependence of the thermodynamic driving force for the reaction may be expected when U transforms between a to b phase. This would only cause the driving force of diffusion/reaction to change. From the mechanism perspective, the allotropic transformation of U causes the crystal structure and binding energy changes, which would affect the rate and distance of atomic motion at the interface. This variation in the growth of U6Fe caused by interfacial changes implies that the growth of U6Fe may not be completely lattice diffusion controlled and interfacial process may be significant. The effect of allotropic transformation on the growth mechanism of U6Fe needs to be further examined based on the growth thickness as a function of time. The variation in the growth of U6Fe, of course, would indirectly affect the growth of UFe2. Therefore, the influence of U allotropic transformation on the growth of U6Fe through changes in the U/ U6Fe interface would also affect the growth of UFe2. Wagner [20] defined the intrinsic growth constant KII without the consideration of the allotropic transformation of the neighboring phases. This study indicates that the allotropic transformation of the neighboring phases can result in variation of KII which is no longer a material constant. Both experimental observation and quantitative analysis demonstrated that U6Fe grew faster than UFe2. Funamizu and Watanabe [23] reviewed several potential factors and summarized that an intermediate phase layer will grow more rapidly if: (a) The diffusion coefficient in the layer is larger. (b) The diffusion coefficient in the adjoining phases is smaller. (c) The homogeneity range of the phase in the phase diagram is wider. (d) The concentration range of the adjoining two-phase areas in the phase diagram is narrower (that means the miscibility gap between the phase and the adjoining phases is smaller). (e) The heat of formation of the phase is higher (that means the thermodynamic stability of a phase is higher and has a greater driving for formation). (f) The crystal structures between the adjoining phases are similar.
U6 Fe
Q K II
(kJ/mol)
UFe2
Q K II
(kJ/mol)
tal structure is dissimilar from both of its neighbors, it would be expected to grow more slowly as per criterion (f). Therefore it is reasonable that the U6Fe phase layer was observed to grow faster than UFe2. 6. Summary e Int , extrinsic growth The integrated interdiffusion coefficient D constant (the first kind according to Wagner’s scheme) KI, and intrinsic growth constant (the second kind according to Wagner’s scheme) KII of U6Fe and UFe2 were calculated in the temperature range from 853 K to 973 K. In each diffusion couple, U6Fe grew faster than UFe2. The thick U6Fe impeded the growth of UFe2, while the UFe2 growth had little influence on the growth of U6Fe. The allotropic transformation of U (orthorhombic a and tetragonal b phase) had an effect on the growth of U6Fe and UFe2. The change in specific heat and/or crystal structure of U due to the allotropic transformation affected the interfacial diffusion reaction between U and U6Fe, and had further influence on the growth of U6Fe and UFe2. The more rapid growth of U6Fe was identified as consistent with the crystal structure, chemical composition, and kinetic properties of the two phases U6Fe and UFe2 with pure U and Fe terminal ends. US department of energy disclaimer This information was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. References herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof. Acknowledgments
e Int;U6 Fe is larResults of this study show that the magnitude of D Int;UFe2 e ger than that of D to satisfy criteria (a) and (b). According to the U–Fe phase diagram presented in Fig. 1, both U6Fe and UFe2 are line compounds, but the miscibility gap in concentration of Fe is 14.3% between pure U and U6Fe, and 33.3% between UFe2 and pure Fe, in regards to criterion (d). Also, U6Fe has a lower melting point (about 1273 K) than UFe2 (about 1503 K), consistent with faster interdiffusion but not contra-indicated as the faster growth phase based on criterion (e). U6Fe has a body-centered tetragonal crystal structure [24] that is similar to a-U (orthorhombic) or b-U (tetragonal) structure. However, UFe2 has a complex Laves phase structure (C15 fcc crystal structure, symmetry Fd3m) [25], very different from a-Fe (body center cubic structure). As the UFe2 crys-
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