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Diffusion of tritium in intermetallic compound β-LiAl: Relation to the defect structure
Solid State Ionics 177 (2007) 3507 – 3512 www.elsevier.com/locate/ssi
Diffusion of tritium in intermetallic compound β-LiAl: Relation to the defect structure Hiroyuki Sugai ⁎ Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan Received 23 June 2006; received in revised form 3 October 2006; accepted 11 October 2006
Abstract The diffusion coefficients (1.0 × 10− 12–4.0 × 10− 11 m2 s− 1) and its activation energy (103.7 ± 9.5 kJ/mol) for tritium in intermetallic compound β-LiAl are determined at temperatures from 699 to 886 K. Though the present result for the diffusion coefficient is almost the same as that reported earlier, the activation energy turns out nearly twice of that (64.9 ± 3.8 kJ/mol) reported earlier. On the basis of the crystal structure and defect structure, the large activation energy of this study suggests that tritium diffuses interstitially and is impeded by an attractive interaction with lithium atoms in lithium sublattices. © 2006 Elsevier B.V. All rights reserved. Keywords: Intermetallic compound; Lithium aluminide; Tritium; Diffusion; Activation energy; Defect structure; Lithium sublattice; Fusion reactor
1. Introduction Aluminum alloy with 12.7% of Li in atomic concentration has been used for the tritium production in the Japan Atomic Energy Research Institute (JAERI), with the aim of providing fuel tritium (T) of a nuclear fusion reactor research [1–3] and tritium specimens of basic research such as the muon-catalyzed fusion experiments [4,5]. The alloy was selected because of its high heat conductivity and of low induced radioactivity. It is composed of α- and β-phase as shown in a phase diagram of Al–Li system [6,7]. The crystal structure of α-phase is f.c.c., which is the same structure as that of aluminum. The crystal structure of β-phase (β-LiAl) is NaTl-type, which is composed of two interpenetrating diamond sublattices such that each atom has eight nearest neighbors: four like and four unlike atoms [8], as shown in Fig. 1. The intermetallic compound β-LiAl has been studied as an electrode material for secondary batteries [6,7] and as a blanket material for nuclear fusion reactors [9], because of its high diffusivity of Li. The characteristic defect structure [10] of the compound consists of two types of defects at room temperature, i.e., vacancies in the lithium sublattice (VLi) and lithium antistructure ⁎ Tel.: +81 29 282 5466; fax: +81 29 282 6716. E-mail address: [email protected]. 0167-2738/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2006.10.012
atoms in the aluminum sublattice (LiAl) as shown in Fig. 1. The VLi concentration [VLi] decreases from 3.5 to 0.2 at.% with increasing Li content CLi over the range 48–56 at.%, while the LiAl concentration [LiAl] increases from 0 to 5.4 at.% with increasing CLi [10]. Moreover, a defect complex (VLi–LiAl) composed of VLi and LiAl has been suggested by lithium diffusion studies [11–13]; VLi and LiAl exist in the nearest neighbor sites by the attractive interaction due to the atomic size effect [11] as shown in Fig. 1. The NMR studies [11,12] indicated that the selfdiffusion coefficients of Li are around 10− 8 m2 s− 1 at room temperature and 3 × 10− 8 m2 s− 1 at 485 K, and the Li diffusion data above 485 K is not presented until now; the tracer-diffusion measurements of Li using short-lived radioactive nuclear beams of 8Li are in progress [14]. In the circumstances, we determined the complex concentration as a function of CLi by the electrical resistivity measurements and showed that the diffusion behavior of tritium in β-LiAl closely correlates with that of lithium [15]. Tritium, a radioactive isotope of hydrogen, decays through β− emission with a half-life of 12.33 y [16] and is used as a tracer to examine the hydrogen behavior. Although the diffusion coefficient in β-LiAl is reported in a few studies [17–19], the relation between the diffusion mechanism of hydrogen isotopes and the defect structure has not been clarified at all. Increasing resistivity [15] with CLi over 48–54 at.% is closely correlated with the increase of [LiAl], because the lithium atom
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Chemical purity of lithium (95.5 % in Lithium-6 isotopic purity) metal and aluminum metal were 99.9 % and 99.999 %, respectively. Reflection and transmission Laue X-ray analysis showed that the crystal was a polycrystal. The content of lithium determined by the lattice parameter measurements [15] was 49.5 ± 0.5 at.%. 2.2. Neutron irradiation
Fig. 1. Crystal Structure of NaTl type (Ref. [8]) containing defects (Ref. [15]).
on the vacant aluminum site, i.e., LiAl (valence-2) is much more effective as a scatterer for carriers than VLi (valence-1) according to Linde's rule [20,21]. The rule means that the residual resistivity of metal containing charged impurities is proportional to the square of the valence difference between the impurity atom and the matrix atom. Indeed, we demonstrated that the carrier scattering for VLi–LiAl complex is stronger than the sum of the carrier scattering for VLi and LiAl defects that exist separately in β-LiAl [15]. The idea was also confirmed in βLiGa [22]. The results of band calculation [23–25] support the valence features in β-LiAl; the Li–Al bonds are ionically polarized covalent, the Al–Al bonds are metallic-like and the Li–Li bonds are nonbonding. Since the electronegativity difference between H (electronegativity CEN = 2.9) and Li (CEN = 1.0) is larger than that between H (CEN = 2.9) and Al (CEN = 1.5) [26], the ionic interaction between H and Li is stronger than that between H and Al. Considering the electronegativity and the valence features in β-LiAl mentioned in the former paragraph, the tritium diffusion of β-LiAl should be influenced by the ionic interaction between tritium and lithium atom. Furthermore, for the attractive interaction the Li–T bonds are important as mentioned in Section 3.6. As a matter of fact, Hayashi et al. [17] reported that the valence state of tritium in neutron-irradiated βLiAl was T−; the ionic feature of tritium was attributed to the presence of the interstitial tritium ion localized around lithium ion in β-LiAl crystal. We also reported that most of tritium existed in the T− state in Al-12.7 at.% Li alloy [3]. In this study, tritium was incorporated into the well characterized β-LiAl crystal through 6Li(n,α)T reaction and the activation energy of tritium diffusion was determined by a radiometric method in the temperature range from 699 to 886 K. Moreover, We will discuss the diffusion mechanism of tritium in the intermetallic compound β-LiAl and consider its relation to the defect structure. 2. Experimental 2.1. Materials The crystal of intermetallic β-LiAl was grown by the Tammam-stöer method starting from a mixture of lithium and aluminum metals in the same way reported previously [18].
The samples for irradiation were cut in a rectangular parallelepiped by a diamond saw, and the dimension was 5 mm × 5 mm × 1.5 mm. The samples were sealed in quartz ampules under vacuum and then irradiated for 120 min at temperatures below 480 K in the JRR-4 reactor of JAERI. The thermal neutron flux was 5.5 × 1013 cm− 2 s−1. The fast neutron flux was 1.3 × 1013 cm− 2 s−1. 2.3. Apparatus and procedure In the measurement of the tritium release rate, the amount of tritium released from the crystals was observed as a function of heating time under neon gas flow (60 cm3/min) at each temperature. The released tritiated species was introduced into a specially designed ion chamber through a cold trap cooled with liquid nitrogen, and the radioactivity of gaseous species (expressed by HT) was continuously measured. The ion chamber system used neon carrier gas for the convenience of other experiments [2,3], and the kind of inert carrier gas is not essential in this study. The radioactivity of aqueous species (expressed by HTO) collected in the cold trap was measured by a liquid scintillation counter. Details of the apparatus are described in the previous paper [2]. 3. Results and discussion 3.1. Irradiation effects The dose induced by 6Li(n,α)T reaction in β-LiAl was estimated to be 1.5 × 10− 2 dpa (displacement per atom) by the NRT (modified Kinchin–Pease) model [27]. The number of nuclear reaction was calculated using the neutron energy spectrum of the JRR-4 [28] and the neutron cross-section libraries ENDF/B-IV [29,30]. The damage energy used in the NRT model was calculated by the extended EDEP-1 code [31]. The recoil events for the energetic tritium and helium-4 atoms are 73 and 121 per reaction. In the EDEP-1 calculation, the mean mass number of 6Li and 27Al was used as a mass of the irradiated material. The exact calculation of dose for the cascade in two components was not done at present, but the above approximations are enough for order estimation [32]. On the other hand, the dose induced by the knock-on of fast neutrons was estimated to be 1.5 × 10− 4 dpa using the method mentioned above. Therefore, as mentioned in the previous study [15], the dominant irradiation effects on β-LiAl are due to the 6Li(n,α)T reaction induced by thermal neutrons. In the stoichiometric β-LiAl of this study, the concentration of native Li-vacancy attained to 1.4 at.% (5 × 1020 cm− 3) and the concentration of helium-4 produced
H. Sugai / Solid State Ionics 177 (2007) 3507–3512
Fig. 2. Isothermal tritium release curves of β-LiAl. The solid lines are the release curves calculated to determine the diffusion coefficients for each temperature.
by the 6Li(n,α)T reaction was less than 1019 cm− 3 [15]. The amount of helium-3 decayed from tritium was also negligible, because the experiment was conducted in one or two months after neutron irradiation. Although the irradiation effects mainly originate from vacancies and helium produced by the 6Li(n, α)T reaction, we assume that the irradiation effects on the tritium release behavior are not dominant, but the large amount of native Li-vacancy are dominant. 3.2. Determination of tritium diffusion coefficients In the tritiated species released above the melting point of βLiAl (968 K) [33], the other gaseous tritiated species except HT was negligible. The percentage of aqueous tritium (HTO) collected in the cold trap was less than 2% for the total tritium released from β-LiAl. The origin of HTO was ascribed to the presence of oxygen [18] that existed in the oxide layer on the surface of β-LiAl. The typical tritium release-rate of gaseous tritiated species are shown as a function of heating time in Fig. 2. The tritium release curves were analyzed on the basis of the diffusion-controlled kinetics. The kinetics assumed that the original concentration of tritium was uniform in the crystal and the tritium was continuously removed from the rectangular parallelepiped of side length a, b and c. For this condition, owing to the solution of Fick's equation for the diffusion coefficient D, the fraction of tritium released up to the time t is written as [34] f ¼ 1−RaRbRc
ð1 1Þ
Ra ¼
raising the heating temperatures. The surface of β-LiAl crystal is active to react with oxygen and nitrogen; oxides and nitrides might be formed on the surface of crystals heated in the neon carrier gas which contained trace amounts of oxygen and nitrogen, in spite of purification before use. The oxides and nitrides on the surface lead to depression of tritium release, because the tritium release rates of oxides [35] and nitrides [36] are smaller than that of β-LiAl. Since the surface reaction of βLiAl with oxygen and nitrogen was accelerated with increasing the temperature, the start of depression of tritium release becomes earlier with increasing the temperature, i.e., 6000 s for 699 K, 1250 s for 752 K and 600 s for 886 K. Though the experimental results are not shown for all the heating time of 104 s in Fig. 2, the depressed tritium release-rate at 699 K was 0.239 for the calculated value of 0.265 in 104 s. Thus, it is reasonable to derive the diffusion coefficient from the curve fitting at the early stage of heating time, where contribution of the oxides and nitrides to the tritium diffusion in β-LiAl crystals is negligibly small. The diffusion coefficients determined from the experimental tritium release-curves are listed in Table 1. 3.3. Arrhenius plot of tritium diffusion coefficients The Arrhenius plot of the diffusion coefficients determined in Section 3.2 are shown in Fig. 3, with those of β-LiAl, Al-4.4 at. % Li alloy and pure-Al reported by Hayashi et al. [17]. The temperature T (K) dependence of diffusion coefficient in β-LiAl is expressed as D ¼ ð7:78F1:19Þ 10−5
nX ¼l
2 2
2 2
½8=ð2n þ 1Þ k exp½−ð2n þ 1Þ k Dt=a ; 2
ð1 2Þ
n¼1
where Σb and Σc are the corresponding expression of Eq. (1–2) substituted by b and c. The calculated curves for 699, 752 and 886 K are shown with the experimental data in Fig. 2. The diffusion coefficient at each temperature was derived by the curve fitting for the experimental data. As shown in Fig. 2, the fitted regions moved to the early stage of heating time with
ð2Þ
exp½−ð103:7F9:5ÞðkJ=molÞ=RT m2 s−1
in temperatures from 699 to 886 K, where R is the gas constant (J/mol·K). The probable errors of pre-exponential factor and activation energy are the standard deviation derived from the least-squares method. As shown in Fig. 3, though the present result for the diffusion coefficient is almost the same as that reported by Hayashi et al. [17] at temperatures above 700 K, the present result for the activation energy turns out nearly twice of that (64.9 ± 3.8 kJ/mol). The discrepancy comes from the reason mentioned below. Since the defect structure above 700 K is different from that below 700 K as discussed in Section 3.5, the tritium diffusion above 700 K is different from that below 700 K. Table 1 Temperature dependence of tritium diffusion coefficient D in β-LiAl Temperature, T/K
with
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699 722 747 752 776 799 822 824 849 873 886
D/m2 s− 1 − 12
1.00 × 10 1.70 × 10− 12 4.50 × 10− 12 7.00 × 10− 12 1.50 × 10− 11 1.50 × 10− 11 2.00 × 10− 11 1.75 × 10− 11 4.00 × 10− 11 4.00 × 10− 11 4.00 × 10− 11
log D/m2 s− 1 −12.00 − 11.77 − 11.35 − 11.16 −10.80 −10.80 −10.70 −10.75 −10.40 −10.40 −10.40
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Li alloy and β-LiAl at temperatures above 700 K. We consider that the dominant origin of the tritium diffusion as follows. For a migrating tritium in Al-4.48 at.% Li alloy the possibility to meet a Li atom is less than 1 in the nearest neighbor of the tritium, because Li-atom number is 0.6 per the f.c.c. unit cell of the alloy. On the other hand, a migrating tritium in β-LiAl has the attractive interaction with some Li-atoms of the nearest neighbor at the same time as supposed in Fig. 1. Thus, the tritium diffusion coefficients in Al–Li system become smaller owing to the increase of trapping sites number and the activation energy in Al–Li system becomes larger owing to the attractive interaction with some Li-atoms around the nearest neighbor of tritium with increasing CLi as shown in Fig. 3. As shown in Fig. 3, Hayashi et al. [17] obtained the value of ELiAl (64.9 ± 3.8 kJ/mol), which is smaller than EAl–Li (72.4 ± 7.5 kJ/mol). Since the fact conflicts with the tritium diffusion feature discussed in the former paragraph, the value of ELiAl (64.9 ± 3.8 kJ/mol) is not adequate. 3.5. Defect structure of β-LiAl Fig. 3. Arrhenius plot of diffusion coefficients D for tritium in β-LiAl, Al-4.4 at. % Li alloy and pure-Al (this work and Ref. [17]).
Thus, the tritium diffusion above 700 K has to be analyzed individually from that below 700 K. However, Hayashi et al. [17] continuously analyzed the tritium diffusion above and below 700 K and did not considered the defect structure of βLiAl. Furthermore, the activation energy obtained in this study is supported by the features of tritium diffusion in Al–Li system, but the activation energy by Hayashi et al. [17] conflicts with the features of tritium diffusion as discussed in Section 3.4. We believe that the diffusion coefficients and the activation energy obtained in this study have a good reliability, because CLi of β-LiAl crystals was controlled in 49.5 ± 0.5 at.% and the leastsquares methods used the enough number of data to determine the activation energy as shown in Fig. 3. On the other hand, CLi of β-LiAl crystals used by the earlier study [17] is unknown, although the intermetallic compound crystallizes in β-phase with CLi over 48–56 at.%. 3.4. Tritium diffusion in Al–Li system The activation energy of tritium diffusion in neutronirradiated β-LiAl (ELiAl = 103.7 ± 9.5 kJ/mol) in this study was larger than that in neutron-irradiated Al-4.4 at.% Li (EAl–Li = 72.4 ± 7.5 kJ/mol) [17] and that in Al (EAl = 53.4 ± 2.2 kJ/mol) [17], i.e., ELiAl N EAl–Li N EAl. Considering the results of pure-Al, Al-4.4 at.% Li alloy and β-LiAl as shown in Fig. 3, the increase of lithium concentration reduces the diffusion coefficients and raises the activation energy except the case of β-LiAl in the previous study [17]. Nakashima et al. [37] also reported that with increasing the lithium concentration in Al-0.08 at.% Li, Al-1.04 at.% Li and Al4.48 at.% Li alloy the diffusion coefficients decrease and the activation energy increases. Thus, the increase of lithium concentration not only increase the number of trapping sites but also raises the activation energy for escape from a trap in Al–
As shown in Fig. 1, the crystal structure of β-LiAl is composed of both the lithium and the aluminum sublattices, and contains two types of defects (VLi and LiAl) at room temperature. However, a neutron diffraction study [7] revealed that the crystal structure composed of the Li and Al sublattices is not changed but Li antisite atoms (LiAl) and Al antisite atoms (AlLi) are created by the exchange between Li atoms in the Li sublattice (LiLi) and Al atoms in the Al sublattice (AlAl) at temperatures above 700 K. That is, two kinds of antisite defects (LiAl and AlLi) of 10 at.% [7] are newly created for β-LiAl of 48 at.% Li and the increase of disorder in the atom arrangement of β-LiAl is induced at elevated temperatures above 700 K. The difference between the defects structure in β-LiAl above 700 K and that below 700 K suggests that the tritium diffusivity above 700 K is different from that below 700 K as discussed in the second paragraph of Section 3.6. 3.6. Diffusion mechanism There are two kinds of typical diffusion mechanisms in solids; one is an interstitial mechanism and the other is a vacancy mechanism [38]. The diffusivity of interstitial atoms is larger than that of substitutional atoms which obey the vacancy mechanism. The activation energy of interstitial atom diffusion is smaller than that of substitutional atoms. For a typical example of the interstitial mechanism, the diffusion coefficient of hydrogen in metals (e.g., V, Fe, Ni, Cu, Nb, Pd, Ta) is in the range from 10− 7 to 10− 8 m2 s− 1 around 800 K and the activation energy of hydrogen diffusion in the metals is from 4 to 40 kJ/mol [39,40]. The activation energy of hydrogen diffusion in aluminum is from 40 to 60 kJ/mol [41,42]. On the other hand, the activation energy of vacancy diffusion (self-diffusion) is 124 kJ/mol in Al and from 110 to 550 kJ/mol in the other metals mentioned above [39]. The activation energy of tritium ELiAl was 103.7 ± 9.5 kJ/mol as determined in Section 3.2. Although the activation energy is comparable with that of vacancy
H. Sugai / Solid State Ionics 177 (2007) 3507–3512
diffusion, we conclude that tritium in β-LiAl diffuses owing to the interstitial mechanism, because there is a repulsive interaction between tritium (valence-1) and VLi (valence-1). The dominant origin of the large activation energy ELiAl in the interstitial mechanism is attributed to the impeded diffusion due to the strong attractive interaction between tritium (valence-1) and LiLi (valence + 1) in β-LiAl. In view of chemical bond, the strong attractive interaction is due to the Li–T bonds. The above valence and bond features are the same as the metal hydrides like LiH and NaH [43]. Analogically, we consider that the Li–T bonds of β-LiAl play the similar role in the tritium diffusion as the O–H bonds of the perovskite-type oxide play the important role in the proton conduction [44,45]. However, the details of tritium diffusion mechanism in β-LiAl are not clear yet. As mentioned in Section 3.5, AlLi (valence + 2) and LiAl (valence-2) are created by the exchange between LiLi and AlAl at temperatures above 700 K; the interaction between tritium (valence-1) and the latter two atoms below 700 K is different from that between tritium and the former two atoms above 700 K. The above attractive and repulsive interactions possibly cause the different tritium diffusivity in β-LiAl above and below 700 K. Since the tritium release curve in β-LiAl heated at a constant rate has each peak at temperatures above and below 700 K [15,19], it was also made sure that the feature of tritium diffusion in β-LiAl at temperatures above 700 K is different from that below 700 K. 4. Conclusion Compared with the activation energy (53.4 ± 2.2 kJ/mol) [17] of tritium diffused interstitially in Al, the large activation energy (103.7 ± 9.5 kJ/mol) of that in intermetallic β-LiAl was determined at temperatures from 699 to 886 K. We conclude that tritium diffuses interstitially in β-LiAl and the large activation energy in the impeded diffusion of tritium is due to the attractive interaction with lithium atoms at the lithium sublattices. The present result in β-LiAl with the previous study [17] showed the systematics that the increase of lithium concentration in Al– Li system decreases the diffusion coefficient and increases the activation energy above 700 K, but the tritium diffusivity in β-LiAl below 700 K is not established yet. Thus, in future, we are going to examine that below 700 K. Acknowledgements I am grateful to Dr T. Hayashi of JAERI for his pioneer work of tritium diffusion in Al–Li system and helpful discussion. I would like to thank Messrs. M. Kato and K. Kurosawa of JAERI for the technical supports. I acknowledge Drs M. Tanase and M. Nishi of JAERI, Profs M. Yahagi of Aomori Univ., H. Hamanaka and K. Kuriyama of Hosei Univ., and S. Sawamura of Hokkaido Univ. for their valuable suggestions. References [1] M. Tanase, M. Kato, K. Kurosawa, S. Motoishi, S. Okane, H. Sugai, M. Fujie, K. Onoma, H. Yamabayashi, J. Nucl. Sci. Technol. 25 (1988) 198.
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Diffusion of tritium in intermetallic compound β-LiAl: Relation to the defect structure Hiroyuki Sugai ⁎ Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan Received 23 June 2006; received in revised form 3 October 2006; accepted 11 October 2006
Abstract The diffusion coefficients (1.0 × 10− 12–4.0 × 10− 11 m2 s− 1) and its activation energy (103.7 ± 9.5 kJ/mol) for tritium in intermetallic compound β-LiAl are determined at temperatures from 699 to 886 K. Though the present result for the diffusion coefficient is almost the same as that reported earlier, the activation energy turns out nearly twice of that (64.9 ± 3.8 kJ/mol) reported earlier. On the basis of the crystal structure and defect structure, the large activation energy of this study suggests that tritium diffuses interstitially and is impeded by an attractive interaction with lithium atoms in lithium sublattices. © 2006 Elsevier B.V. All rights reserved. Keywords: Intermetallic compound; Lithium aluminide; Tritium; Diffusion; Activation energy; Defect structure; Lithium sublattice; Fusion reactor
1. Introduction Aluminum alloy with 12.7% of Li in atomic concentration has been used for the tritium production in the Japan Atomic Energy Research Institute (JAERI), with the aim of providing fuel tritium (T) of a nuclear fusion reactor research [1–3] and tritium specimens of basic research such as the muon-catalyzed fusion experiments [4,5]. The alloy was selected because of its high heat conductivity and of low induced radioactivity. It is composed of α- and β-phase as shown in a phase diagram of Al–Li system [6,7]. The crystal structure of α-phase is f.c.c., which is the same structure as that of aluminum. The crystal structure of β-phase (β-LiAl) is NaTl-type, which is composed of two interpenetrating diamond sublattices such that each atom has eight nearest neighbors: four like and four unlike atoms [8], as shown in Fig. 1. The intermetallic compound β-LiAl has been studied as an electrode material for secondary batteries [6,7] and as a blanket material for nuclear fusion reactors [9], because of its high diffusivity of Li. The characteristic defect structure [10] of the compound consists of two types of defects at room temperature, i.e., vacancies in the lithium sublattice (VLi) and lithium antistructure ⁎ Tel.: +81 29 282 5466; fax: +81 29 282 6716. E-mail address: [email protected]. 0167-2738/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ssi.2006.10.012
atoms in the aluminum sublattice (LiAl) as shown in Fig. 1. The VLi concentration [VLi] decreases from 3.5 to 0.2 at.% with increasing Li content CLi over the range 48–56 at.%, while the LiAl concentration [LiAl] increases from 0 to 5.4 at.% with increasing CLi [10]. Moreover, a defect complex (VLi–LiAl) composed of VLi and LiAl has been suggested by lithium diffusion studies [11–13]; VLi and LiAl exist in the nearest neighbor sites by the attractive interaction due to the atomic size effect [11] as shown in Fig. 1. The NMR studies [11,12] indicated that the selfdiffusion coefficients of Li are around 10− 8 m2 s− 1 at room temperature and 3 × 10− 8 m2 s− 1 at 485 K, and the Li diffusion data above 485 K is not presented until now; the tracer-diffusion measurements of Li using short-lived radioactive nuclear beams of 8Li are in progress [14]. In the circumstances, we determined the complex concentration as a function of CLi by the electrical resistivity measurements and showed that the diffusion behavior of tritium in β-LiAl closely correlates with that of lithium [15]. Tritium, a radioactive isotope of hydrogen, decays through β− emission with a half-life of 12.33 y [16] and is used as a tracer to examine the hydrogen behavior. Although the diffusion coefficient in β-LiAl is reported in a few studies [17–19], the relation between the diffusion mechanism of hydrogen isotopes and the defect structure has not been clarified at all. Increasing resistivity [15] with CLi over 48–54 at.% is closely correlated with the increase of [LiAl], because the lithium atom
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Chemical purity of lithium (95.5 % in Lithium-6 isotopic purity) metal and aluminum metal were 99.9 % and 99.999 %, respectively. Reflection and transmission Laue X-ray analysis showed that the crystal was a polycrystal. The content of lithium determined by the lattice parameter measurements [15] was 49.5 ± 0.5 at.%. 2.2. Neutron irradiation
Fig. 1. Crystal Structure of NaTl type (Ref. [8]) containing defects (Ref. [15]).
on the vacant aluminum site, i.e., LiAl (valence-2) is much more effective as a scatterer for carriers than VLi (valence-1) according to Linde's rule [20,21]. The rule means that the residual resistivity of metal containing charged impurities is proportional to the square of the valence difference between the impurity atom and the matrix atom. Indeed, we demonstrated that the carrier scattering for VLi–LiAl complex is stronger than the sum of the carrier scattering for VLi and LiAl defects that exist separately in β-LiAl [15]. The idea was also confirmed in βLiGa [22]. The results of band calculation [23–25] support the valence features in β-LiAl; the Li–Al bonds are ionically polarized covalent, the Al–Al bonds are metallic-like and the Li–Li bonds are nonbonding. Since the electronegativity difference between H (electronegativity CEN = 2.9) and Li (CEN = 1.0) is larger than that between H (CEN = 2.9) and Al (CEN = 1.5) [26], the ionic interaction between H and Li is stronger than that between H and Al. Considering the electronegativity and the valence features in β-LiAl mentioned in the former paragraph, the tritium diffusion of β-LiAl should be influenced by the ionic interaction between tritium and lithium atom. Furthermore, for the attractive interaction the Li–T bonds are important as mentioned in Section 3.6. As a matter of fact, Hayashi et al. [17] reported that the valence state of tritium in neutron-irradiated βLiAl was T−; the ionic feature of tritium was attributed to the presence of the interstitial tritium ion localized around lithium ion in β-LiAl crystal. We also reported that most of tritium existed in the T− state in Al-12.7 at.% Li alloy [3]. In this study, tritium was incorporated into the well characterized β-LiAl crystal through 6Li(n,α)T reaction and the activation energy of tritium diffusion was determined by a radiometric method in the temperature range from 699 to 886 K. Moreover, We will discuss the diffusion mechanism of tritium in the intermetallic compound β-LiAl and consider its relation to the defect structure. 2. Experimental 2.1. Materials The crystal of intermetallic β-LiAl was grown by the Tammam-stöer method starting from a mixture of lithium and aluminum metals in the same way reported previously [18].
The samples for irradiation were cut in a rectangular parallelepiped by a diamond saw, and the dimension was 5 mm × 5 mm × 1.5 mm. The samples were sealed in quartz ampules under vacuum and then irradiated for 120 min at temperatures below 480 K in the JRR-4 reactor of JAERI. The thermal neutron flux was 5.5 × 1013 cm− 2 s−1. The fast neutron flux was 1.3 × 1013 cm− 2 s−1. 2.3. Apparatus and procedure In the measurement of the tritium release rate, the amount of tritium released from the crystals was observed as a function of heating time under neon gas flow (60 cm3/min) at each temperature. The released tritiated species was introduced into a specially designed ion chamber through a cold trap cooled with liquid nitrogen, and the radioactivity of gaseous species (expressed by HT) was continuously measured. The ion chamber system used neon carrier gas for the convenience of other experiments [2,3], and the kind of inert carrier gas is not essential in this study. The radioactivity of aqueous species (expressed by HTO) collected in the cold trap was measured by a liquid scintillation counter. Details of the apparatus are described in the previous paper [2]. 3. Results and discussion 3.1. Irradiation effects The dose induced by 6Li(n,α)T reaction in β-LiAl was estimated to be 1.5 × 10− 2 dpa (displacement per atom) by the NRT (modified Kinchin–Pease) model [27]. The number of nuclear reaction was calculated using the neutron energy spectrum of the JRR-4 [28] and the neutron cross-section libraries ENDF/B-IV [29,30]. The damage energy used in the NRT model was calculated by the extended EDEP-1 code [31]. The recoil events for the energetic tritium and helium-4 atoms are 73 and 121 per reaction. In the EDEP-1 calculation, the mean mass number of 6Li and 27Al was used as a mass of the irradiated material. The exact calculation of dose for the cascade in two components was not done at present, but the above approximations are enough for order estimation [32]. On the other hand, the dose induced by the knock-on of fast neutrons was estimated to be 1.5 × 10− 4 dpa using the method mentioned above. Therefore, as mentioned in the previous study [15], the dominant irradiation effects on β-LiAl are due to the 6Li(n,α)T reaction induced by thermal neutrons. In the stoichiometric β-LiAl of this study, the concentration of native Li-vacancy attained to 1.4 at.% (5 × 1020 cm− 3) and the concentration of helium-4 produced
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Fig. 2. Isothermal tritium release curves of β-LiAl. The solid lines are the release curves calculated to determine the diffusion coefficients for each temperature.
by the 6Li(n,α)T reaction was less than 1019 cm− 3 [15]. The amount of helium-3 decayed from tritium was also negligible, because the experiment was conducted in one or two months after neutron irradiation. Although the irradiation effects mainly originate from vacancies and helium produced by the 6Li(n, α)T reaction, we assume that the irradiation effects on the tritium release behavior are not dominant, but the large amount of native Li-vacancy are dominant. 3.2. Determination of tritium diffusion coefficients In the tritiated species released above the melting point of βLiAl (968 K) [33], the other gaseous tritiated species except HT was negligible. The percentage of aqueous tritium (HTO) collected in the cold trap was less than 2% for the total tritium released from β-LiAl. The origin of HTO was ascribed to the presence of oxygen [18] that existed in the oxide layer on the surface of β-LiAl. The typical tritium release-rate of gaseous tritiated species are shown as a function of heating time in Fig. 2. The tritium release curves were analyzed on the basis of the diffusion-controlled kinetics. The kinetics assumed that the original concentration of tritium was uniform in the crystal and the tritium was continuously removed from the rectangular parallelepiped of side length a, b and c. For this condition, owing to the solution of Fick's equation for the diffusion coefficient D, the fraction of tritium released up to the time t is written as [34] f ¼ 1−RaRbRc
ð1 1Þ
Ra ¼
raising the heating temperatures. The surface of β-LiAl crystal is active to react with oxygen and nitrogen; oxides and nitrides might be formed on the surface of crystals heated in the neon carrier gas which contained trace amounts of oxygen and nitrogen, in spite of purification before use. The oxides and nitrides on the surface lead to depression of tritium release, because the tritium release rates of oxides [35] and nitrides [36] are smaller than that of β-LiAl. Since the surface reaction of βLiAl with oxygen and nitrogen was accelerated with increasing the temperature, the start of depression of tritium release becomes earlier with increasing the temperature, i.e., 6000 s for 699 K, 1250 s for 752 K and 600 s for 886 K. Though the experimental results are not shown for all the heating time of 104 s in Fig. 2, the depressed tritium release-rate at 699 K was 0.239 for the calculated value of 0.265 in 104 s. Thus, it is reasonable to derive the diffusion coefficient from the curve fitting at the early stage of heating time, where contribution of the oxides and nitrides to the tritium diffusion in β-LiAl crystals is negligibly small. The diffusion coefficients determined from the experimental tritium release-curves are listed in Table 1. 3.3. Arrhenius plot of tritium diffusion coefficients The Arrhenius plot of the diffusion coefficients determined in Section 3.2 are shown in Fig. 3, with those of β-LiAl, Al-4.4 at. % Li alloy and pure-Al reported by Hayashi et al. [17]. The temperature T (K) dependence of diffusion coefficient in β-LiAl is expressed as D ¼ ð7:78F1:19Þ 10−5
nX ¼l
2 2
2 2
½8=ð2n þ 1Þ k exp½−ð2n þ 1Þ k Dt=a ; 2
ð1 2Þ
n¼1
where Σb and Σc are the corresponding expression of Eq. (1–2) substituted by b and c. The calculated curves for 699, 752 and 886 K are shown with the experimental data in Fig. 2. The diffusion coefficient at each temperature was derived by the curve fitting for the experimental data. As shown in Fig. 2, the fitted regions moved to the early stage of heating time with
ð2Þ
exp½−ð103:7F9:5ÞðkJ=molÞ=RT m2 s−1
in temperatures from 699 to 886 K, where R is the gas constant (J/mol·K). The probable errors of pre-exponential factor and activation energy are the standard deviation derived from the least-squares method. As shown in Fig. 3, though the present result for the diffusion coefficient is almost the same as that reported by Hayashi et al. [17] at temperatures above 700 K, the present result for the activation energy turns out nearly twice of that (64.9 ± 3.8 kJ/mol). The discrepancy comes from the reason mentioned below. Since the defect structure above 700 K is different from that below 700 K as discussed in Section 3.5, the tritium diffusion above 700 K is different from that below 700 K. Table 1 Temperature dependence of tritium diffusion coefficient D in β-LiAl Temperature, T/K
with
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699 722 747 752 776 799 822 824 849 873 886
D/m2 s− 1 − 12
1.00 × 10 1.70 × 10− 12 4.50 × 10− 12 7.00 × 10− 12 1.50 × 10− 11 1.50 × 10− 11 2.00 × 10− 11 1.75 × 10− 11 4.00 × 10− 11 4.00 × 10− 11 4.00 × 10− 11
log D/m2 s− 1 −12.00 − 11.77 − 11.35 − 11.16 −10.80 −10.80 −10.70 −10.75 −10.40 −10.40 −10.40
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Li alloy and β-LiAl at temperatures above 700 K. We consider that the dominant origin of the tritium diffusion as follows. For a migrating tritium in Al-4.48 at.% Li alloy the possibility to meet a Li atom is less than 1 in the nearest neighbor of the tritium, because Li-atom number is 0.6 per the f.c.c. unit cell of the alloy. On the other hand, a migrating tritium in β-LiAl has the attractive interaction with some Li-atoms of the nearest neighbor at the same time as supposed in Fig. 1. Thus, the tritium diffusion coefficients in Al–Li system become smaller owing to the increase of trapping sites number and the activation energy in Al–Li system becomes larger owing to the attractive interaction with some Li-atoms around the nearest neighbor of tritium with increasing CLi as shown in Fig. 3. As shown in Fig. 3, Hayashi et al. [17] obtained the value of ELiAl (64.9 ± 3.8 kJ/mol), which is smaller than EAl–Li (72.4 ± 7.5 kJ/mol). Since the fact conflicts with the tritium diffusion feature discussed in the former paragraph, the value of ELiAl (64.9 ± 3.8 kJ/mol) is not adequate. 3.5. Defect structure of β-LiAl Fig. 3. Arrhenius plot of diffusion coefficients D for tritium in β-LiAl, Al-4.4 at. % Li alloy and pure-Al (this work and Ref. [17]).
Thus, the tritium diffusion above 700 K has to be analyzed individually from that below 700 K. However, Hayashi et al. [17] continuously analyzed the tritium diffusion above and below 700 K and did not considered the defect structure of βLiAl. Furthermore, the activation energy obtained in this study is supported by the features of tritium diffusion in Al–Li system, but the activation energy by Hayashi et al. [17] conflicts with the features of tritium diffusion as discussed in Section 3.4. We believe that the diffusion coefficients and the activation energy obtained in this study have a good reliability, because CLi of β-LiAl crystals was controlled in 49.5 ± 0.5 at.% and the leastsquares methods used the enough number of data to determine the activation energy as shown in Fig. 3. On the other hand, CLi of β-LiAl crystals used by the earlier study [17] is unknown, although the intermetallic compound crystallizes in β-phase with CLi over 48–56 at.%. 3.4. Tritium diffusion in Al–Li system The activation energy of tritium diffusion in neutronirradiated β-LiAl (ELiAl = 103.7 ± 9.5 kJ/mol) in this study was larger than that in neutron-irradiated Al-4.4 at.% Li (EAl–Li = 72.4 ± 7.5 kJ/mol) [17] and that in Al (EAl = 53.4 ± 2.2 kJ/mol) [17], i.e., ELiAl N EAl–Li N EAl. Considering the results of pure-Al, Al-4.4 at.% Li alloy and β-LiAl as shown in Fig. 3, the increase of lithium concentration reduces the diffusion coefficients and raises the activation energy except the case of β-LiAl in the previous study [17]. Nakashima et al. [37] also reported that with increasing the lithium concentration in Al-0.08 at.% Li, Al-1.04 at.% Li and Al4.48 at.% Li alloy the diffusion coefficients decrease and the activation energy increases. Thus, the increase of lithium concentration not only increase the number of trapping sites but also raises the activation energy for escape from a trap in Al–
As shown in Fig. 1, the crystal structure of β-LiAl is composed of both the lithium and the aluminum sublattices, and contains two types of defects (VLi and LiAl) at room temperature. However, a neutron diffraction study [7] revealed that the crystal structure composed of the Li and Al sublattices is not changed but Li antisite atoms (LiAl) and Al antisite atoms (AlLi) are created by the exchange between Li atoms in the Li sublattice (LiLi) and Al atoms in the Al sublattice (AlAl) at temperatures above 700 K. That is, two kinds of antisite defects (LiAl and AlLi) of 10 at.% [7] are newly created for β-LiAl of 48 at.% Li and the increase of disorder in the atom arrangement of β-LiAl is induced at elevated temperatures above 700 K. The difference between the defects structure in β-LiAl above 700 K and that below 700 K suggests that the tritium diffusivity above 700 K is different from that below 700 K as discussed in the second paragraph of Section 3.6. 3.6. Diffusion mechanism There are two kinds of typical diffusion mechanisms in solids; one is an interstitial mechanism and the other is a vacancy mechanism [38]. The diffusivity of interstitial atoms is larger than that of substitutional atoms which obey the vacancy mechanism. The activation energy of interstitial atom diffusion is smaller than that of substitutional atoms. For a typical example of the interstitial mechanism, the diffusion coefficient of hydrogen in metals (e.g., V, Fe, Ni, Cu, Nb, Pd, Ta) is in the range from 10− 7 to 10− 8 m2 s− 1 around 800 K and the activation energy of hydrogen diffusion in the metals is from 4 to 40 kJ/mol [39,40]. The activation energy of hydrogen diffusion in aluminum is from 40 to 60 kJ/mol [41,42]. On the other hand, the activation energy of vacancy diffusion (self-diffusion) is 124 kJ/mol in Al and from 110 to 550 kJ/mol in the other metals mentioned above [39]. The activation energy of tritium ELiAl was 103.7 ± 9.5 kJ/mol as determined in Section 3.2. Although the activation energy is comparable with that of vacancy
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diffusion, we conclude that tritium in β-LiAl diffuses owing to the interstitial mechanism, because there is a repulsive interaction between tritium (valence-1) and VLi (valence-1). The dominant origin of the large activation energy ELiAl in the interstitial mechanism is attributed to the impeded diffusion due to the strong attractive interaction between tritium (valence-1) and LiLi (valence + 1) in β-LiAl. In view of chemical bond, the strong attractive interaction is due to the Li–T bonds. The above valence and bond features are the same as the metal hydrides like LiH and NaH [43]. Analogically, we consider that the Li–T bonds of β-LiAl play the similar role in the tritium diffusion as the O–H bonds of the perovskite-type oxide play the important role in the proton conduction [44,45]. However, the details of tritium diffusion mechanism in β-LiAl are not clear yet. As mentioned in Section 3.5, AlLi (valence + 2) and LiAl (valence-2) are created by the exchange between LiLi and AlAl at temperatures above 700 K; the interaction between tritium (valence-1) and the latter two atoms below 700 K is different from that between tritium and the former two atoms above 700 K. The above attractive and repulsive interactions possibly cause the different tritium diffusivity in β-LiAl above and below 700 K. Since the tritium release curve in β-LiAl heated at a constant rate has each peak at temperatures above and below 700 K [15,19], it was also made sure that the feature of tritium diffusion in β-LiAl at temperatures above 700 K is different from that below 700 K. 4. Conclusion Compared with the activation energy (53.4 ± 2.2 kJ/mol) [17] of tritium diffused interstitially in Al, the large activation energy (103.7 ± 9.5 kJ/mol) of that in intermetallic β-LiAl was determined at temperatures from 699 to 886 K. We conclude that tritium diffuses interstitially in β-LiAl and the large activation energy in the impeded diffusion of tritium is due to the attractive interaction with lithium atoms at the lithium sublattices. The present result in β-LiAl with the previous study [17] showed the systematics that the increase of lithium concentration in Al– Li system decreases the diffusion coefficient and increases the activation energy above 700 K, but the tritium diffusivity in β-LiAl below 700 K is not established yet. Thus, in future, we are going to examine that below 700 K. Acknowledgements I am grateful to Dr T. Hayashi of JAERI for his pioneer work of tritium diffusion in Al–Li system and helpful discussion. I would like to thank Messrs. M. Kato and K. Kurosawa of JAERI for the technical supports. I acknowledge Drs M. Tanase and M. Nishi of JAERI, Profs M. Yahagi of Aomori Univ., H. Hamanaka and K. Kuriyama of Hosei Univ., and S. Sawamura of Hokkaido Univ. for their valuable suggestions. References [1] M. Tanase, M. Kato, K. Kurosawa, S. Motoishi, S. Okane, H. Sugai, M. Fujie, K. Onoma, H. Yamabayashi, J. Nucl. Sci. Technol. 25 (1988) 198.
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