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Tracer diffusion experiments on LISICON and its solid solutions by means of neutron radiography
Solid State Ionics 171 (2004) 107 – 112 www.elsevier.com/locate/ssi
Tracer diffusion experiments on LISICON and its solid solutions by means of neutron radiography Shigeomi Takai a, Katsutoshi Kurihara a, Kenji Yoneda b, Shigenori Fujine b, Yuji Kawabata b, Takao Esaka a,* a
Department of Materials Science, Faculty of Engineering, Tottori University, Minami 4-101, Koyamacho, Tottori 680-8552, Japan b Research Reactor Institute, Kyoto University, Noda, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan Received 24 February 2003; received in revised form 5 May 2003; accepted 22 July 2003
Abstract Lithium ion diffusion coefficient measurements were carried out on LISICON (Li3.5Zn0.25GeO4) and on a zinc-rich analogue (ZRA; Li3Zn0.5GeO4) using neutron radiography (NR). Smearing 6LiNO3-saturated solution on a surface of a rectangle-shaped sample consisting of 7 Li and subsequent annealing enabled the relatively low temperature diffusion experiment down to 300 jC. The measured isotope concentration profiles agreed well with the diffusion model from the surface into the semi-infinite media, and the diffusion coefficients can be obtained for both LISICON and ZRA in the temperature range between 300 and 500 jC. The diffusion coefficient of LISICON is essentially larger than that of ZRA, while similar a Haven ratio was found. This indicated that the larger conductivity in LISICON was mainly caused by the higher lithium ion mobility and not by the difference of diffusion path. D 2003 Elsevier B.V. All rights reserved. Keywords: Diffusion; Lithium; LISICON; Neutron radiography; Haven ratio
1. Introduction Neutron radiography (NR) has been developed as a nondestructive inspection method. We applied this technique to observe the distribution of lithium or hydrogen in solid electrolytes or batteries [1 – 4] using the relatively large neutron attenuation factors for these species. Moreover, we also measured the lithium ion transport numbers in solid electrolytes [5 – 10], by considering the large difference in neutron absorption cross-section between the isotopes, 6Li and 7Li [11]. We have recently successfully measured lithium ion diffusion coefficients in Li1.33Ti1.67O4 from the isotope profile of the diffusion couples annealed above 860 jC [12]. However, on annealing below 800 jC, ionic transfer was insufficient across the interface in comparison with the bulk diffusion, resulting in a discontinuous jump of the isotope profile at the interface of the diffusion couple. This denotes that, to measure the diffusion coefficient of lower temperature-type lithium ion conductors such as
* Corresponding author. Tel./fax: +81-857-31-5264. E-mail address: [email protected] (T. Esaka). 0167-2738/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0167-2738(03)00305-9
LISICON from the isotope profile obtained by NR, we have to apply the lithium isotope on a surface of the diffusion sample followed by diffusion annealing. LISICON and its solid solutions, showing the gIILi3PO4-type structure of the general formula Li2+2xZn1xGeO4, exhibit high lithium ion conductivity in the composition region of x > 0 in comparison with Li1.33Ti1.67O4 at intermediate temperatures. The composition at x=0.75, Li3.5Zn0.25GeO4, was denoted as LISICON exhibiting the highest conductivity (0.125 S cm1 at 300 jC) [13]. While a lot of investigations including electrochemical [14 – 19], structural [13,20 – 23] and NMR [24 – 27] measurements were published in late 1970s and 1980s, rather few reports discussed the lithium diffusion properties. Diffraction studies estimated that lithium ion interstitials would contribute to the high lithium ion conduction [13], and NMR measurement [26] predicted that lithium ion mobility in LISICON is larger than that in zinc-rich analogue (ZRA, x=0.5 of Li2+2xZn1xGeO4). To discuss the mobility more quantitatively, the diffusion coefficients of lithium ion should be measured. Tracer diffusion coefficients indicate not only the mobility of particular species without potential gradient, but also the diffusion mechanism. Tracer diffusion coefficients
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can be obtained from the isotope concentration, which are usually measured by counting g-rays from radioisotope tracer deposited on the sample or using SIMS. However, both of the lithium isotopes (6Li and 7Li) are not radioactive and very few reports have been published on lithium ion tracer diffusion experiments using SIMS. In the present study, we measured the tracer diffusion coefficient of LISICON (x=0.75 of Li2+2xZn1xGeO4) and ZRA (x=0.5) by means of NR in the temperature range 300 – 500 jC and compared them to each other.
of the NR images were obtained by employing an imaging reader (Fuji Film, BAS-2500). Electric conductivity was measured on cylindrical shaped samples (7 mm in diameter and 10 mm in length) by conventional two-probe a.c. methods. Gold paste was applied for the electrodes and an impedance analyzer (HP4192A) was employed in the frequency range 100– 107 Hz. Conductivity values were calculated from the minimum point of the right end of the semi-circle in the complex impedance plots.
3. Results and discussion 2. Experimental Diffusion samples of LISICON (Li3.5Zn0.25GeO4) and zinc-rich analogue (Li3Zn0.5GeO4) were prepared by conventional solid state reaction methods. Stoichiometric mixtures of ZnO (Wako Pure Chemical), GeO2 (Wako Pure Chemical) and 7 Li 2 CO 3 obtained from 7 LiOHH 2 O (Tomiyama High Purity Chemical) were calcined at 800 jC for 10 h. Thereafter, the samples were crushed in an alumina mortar, pressed under a hydrostatic pressure of 200 MPa and then fired again at 1120 (LISICON) or 1140 jC (Li3Zn0.5GeO4). The sample were cut into a rectangle shape (779 mm3) using a microcutter and lapped with 9 Am diamond lapping fluid to achieve the same dimensions precisely. For calibration of the isotope concentrations, standard samples with the same thickness as the diffusion samples were also prepared, varying the isotope ratio every 1/10 step from 7Li to the natural 6Li/7Li ratio, which is referred as NLi in the present paper. Because the relatively low isotope region should be focused on and the accurate value of natural abundance of 6Li was not necessary to calculate the diffusion coefficient, we employed NLi instead of 6Li in the standard samples. The saturated solution of 6LiNO3, obtained by dissolving the excess amount of 6Li2CO3 (Tomiyama High Purity Chemical) into nitric acid, was smeared on one face of the rectangle-shaped 7Li sample, which was thereafter set in a furnace for a given time. The annealing temperatures were selected to be 300, 400 and 500 jC, which were monitored by thermocouple (type K) and digital multimeter (HP34401A). To obtain the diffusion data with extended annealing time, the above procedure including diffusion annealing and NR measurement was repeatedly carried out on the same sample, and the diffusion time was accumulated. NR experiments were carried out at the CN-3 guide tube in the Research Reactor Institute of Kyoto Univ., Japan. Both of the standard samples and diffusion-annealed samples were aligned on an imaging plate (IP) neutron detector (Fuji Film, BAS-ND2025) and they were sledded across the beam slit of the guide tube with the constant rate of 0.8 mms1 to prevent the influence of the neutron flux inhomogeneity in the guide tube. The numerical data (gray level)
3.1. Lithium diffusion experiments on LISICON (Li3.5Zn0.25GeO4) For the sample after sintering, a nominal density of 84% of the calculated value from the sample dimensions and approximately 97% of lithium in the starting materials was found, i.e. lithium loss was negligibly small during preparation. Fig. 1 shows a typical NR image of a LISICON diffusion sample annealed at 300 jC for 2 h and those of the standard samples varying the lithium isotope ratio from NLi to 7Li. As the samples were cut to the same thickness, the higher 6Li concentration part represented the whiter image due to the large neutron attenuation coefficient of 6Li. White gradation at the left side of the diffusion sample predicted that 6Li migrated from the surface into the bulk interior. This behavior seemed not to be simply caused by the soak of 6 LiNO3 aqueous solution, because another NR image of the 6 Li-smeared sample without annealing did not show such a white gradation. The numerical gray level of this NR image was also represented in Fig. 1, where the whiter NR image, i.e. larger 6Li concentration, corresponded to the lower gray level. A calibration curve was obtained from this gray level of the standard samples, as shown in Fig. 2, giving a smooth line with very little deviation. Through the calibration curve, the gray levels of the diffusion sample were converted into the NLi concentration as shown in Fig. 3(a). The concentration profile can be expressed by a solution of Fick’s equation, pffiffiffiffiffiffiffiffiffiffi cðxÞ ¼ ðM = pD t Þexpðx2 =ð4D tÞÞ; ð1Þ where D*, t and x denote the tracer diffusion coefficient, annealing time and the distance from the surface. Therefore, ln(cN) was plotted vs. x2 as Fig. 3(b). Since the natural abundance of 6Li is incorporated into the parameter M in Eq. (1) and contributes only to the intercept in the vertical axis, the slope of these plots yields-(4D*t)1. Presumably due to the 6LiNO3 or 6Li2CO3 accumulation at the diffusion surface, the profile seemed rather steep in the vicinity of the smeared surface. On the other hand, the slope becomes gradual at x2>0.016 cm2, which might be caused by the
S. Takai et al. / Solid State Ionics 171 (2004) 107–112
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Fig. 1. NR image and the corresponding digitized gray levels of the standard and diffusion samples of LISICON. The lithium isotope ratio of standard samples varies from NLi to 7Li with 1/10 step and the diffusion sample was annealed at 300 jC for 2 h after smearing 6LiNO3 solution.
boundary diffusion or the sensitivity limit of the imaging plate. Nevertheless, the obtained data depicted by open circles gave a straight line, from which the diffusion coefficient can be calculated as 3.0107 cm2 s1 at 300 jC by least squares fitting. After various annealing times up to 4 h, the D*t values were obtained from the slope of the ln(cN)x2 diagram as shown in Fig. 3(b). These values were plotted against the actual diffusion time as depicted by circles in Fig. 4. Although the plots were scattered a little, a straight line can be drawn from the origin to provide the diffusion coefficient 3.7107 cm2 s1 at 300 jC. Diffusion experiments were also carried out at 400 and 500 jC, the data of which were plotted in Fig. 4 by triangle and rectangle symbols, respectively. In our data, D*t measured in the shorter annealing time tended to show larger values; this might be due to the fast diffusion along grain boundaries. Particularly in the case of 400 jC annealed data, D*t value would increase by 30% if the last point was missing. The finally obtained diffusion coefficients were 7.4107 and 1.5106 cm2 s1 at 400 and 500 jC, respectively.
N
Fig. 2. Calibration curve of gray level for the Li concentration in LISICON standard samples.
3.2. Lithium diffusion experiments on ZRA (Li3Zn0.5GeO4) Diffusion experiments have been also carried out on ZRA. Fig. 5 shows the typical NR images of standard and diffusion samples of ZRA annealed at 500 jC for 2 h and the corresponding gray level. After a similar procedure as carried out for LISICON, the D*t values obtained by fitting were plotted against the actual annealing time in Fig. 6, which also provided straight lines. The finally obtained diffusion coefficients were calculated to be 1.1107, 2.3107 and 1.3106 cm2 s1 at 300, 400 and 500 jC,
Fig. 3. (a) Isotope (NLi) concentration of LISICON diffusion sample annealed at 300 jC for 2 h. (b) ln(cN)Dx2 plots of the above diffusion sample.
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Fig. 4. D*t vs. t relations for LISICON. o, D and 5 denote 300, 400 and 500 jC data, respectively.
Fig. 6. D*t vs. t relations for ZRA. o, D and 5 denote 300, 400 and 500 jC data, respectively.
respectively. Although the diffusion coefficient at 500 jC seemed to be larger than that expected from the other ones, this was not supposed to be a experimental error, because diffusion annealing was carried out simultaneously with LISICON in the same furnace and all the points exhibited a well-defined straight line as observed in Fig. 6.
suggesting that they would have essentially the same diffusion mechanism, even though only three temperature data points were collected for each composition and, moreover, one of them was eliminated for calculation in ZRA. In this solid solution system, ionic conduction was thought to be associated with the lithium ion interstitials. According to the single crystal X-ray diffraction [13] and powder neutron diffraction studies [21 –23], LISICON and its solid solution consist of non-equivalent three types of tetrahedra, i.e. GeO4 and two types of (Zn/Li)O4 tetrahedra, accompanied by two types of lithium ion interstitials. Assuming that only lithium ion interstitials can migrate and those in the (Zn/Li)O4 tetrahedra are fixed, the carrier concentration corresponded to that of interstitials. Although the occupation factors of lithium ion interstitials have already been investigated by means of diffraction method [13,20 – 22], there seemed to remain a slight discrepancy in the precise position and/or occupation factors of the interstitials. We therefore adopted the nominal value for the carrier concentration n assuming all the tetrahedral sites to be filled
3.3. Comparison between the diffusion coefficient and the conductivity The temperature dependence of measured diffusion coefficients for LISICON (o) and ZRA (D) is summarized in Fig. 7 in the form of Arrhenius plots. Ignoring the 500 jC data of ZRA, LISICON showed approximately three times larger diffusion coefficients than ZRA in the measured temperature range. As the mobility is proportional to the diffusion coefficient, the higher lithium ion conduction in LISICON was supposed to be mainly due to larger lithium ion mobility. Activation energies obtained from the gradient of Arrhenius plots were 0.26 eV for both compounds,
Fig. 5. NR image and the corresponding gray level of the standard and diffusion samples of ZRA (x=0.5 of Li2+2xZn1xGeO4). Isotope concentration of the standard samples varied from NLi to 7Li with 1/10 step.
S. Takai et al. / Solid State Ionics 171 (2004) 107–112
Fig. 7. Arrhenius plots of diffusion coefficients for LISICON (o) and ZRA (D). Open and closed symbols show the diffusion coefficients obtained by NR method and conductivity measurement, respectively.
and interstitial sites partly occupied by the remaining lithium ions. The diffusion coefficients were then obtained from the conductivity (j) by using Nernst –Einstein’s relation, Dr ¼ kB T r=ðnZ 2 e2 Þ
ð2Þ
where Z and e are the valence of charge carrier and elementary electric charge, respectively. As three interstitials were incorporated into a unit cell with the volume of 351.72 ˚ 3 for LISICON, the carrier concentration n resulted in A 0.0119 molcm3 taking into account the sample density to be 84%. Similar calculations for ZRA gave a concentration n of 0.00794 molcm3. As there is some inconsistency between the reported conductivity especially in LISICON, ionic conductivity, r, was measured by a.c. methods for Eq. (2), which is consistent with the previous low-temperature data measured by Kreck and Bogusz [17] below 400 jC. The diffusion coefficients obtained from the conductivity were also plotted as the closed symbols in Fig. 7, which were approximately one order of magnitude larger than those measured by NR method (open symbols). Activation energies obtained from these plots were 0.26 and 0.35 eV for LISICON and ZRA, respectively. Although the collected data points were very few, these activation energies were not so different from those obtained by NR method. By using two types of diffusion coefficients obtained from NR method and from conductivity, Haven ratios (HR=D/Dr) were calculated and plotted in Fig. 8 except for that measured at 500 jC for ZRA. While these gave similar values for LISICON and ZRA, they seemed significantly small considering that a large number of ionic
111
conductors show HR ranging from 0.4 to 0.7. In the ideal vacancy diffusion mechanism where jump frequency and distance were not varied with applied electric field, HR corresponds to the correlation factor f derived from the correlation of successive jump directions, some of which were reported for typical structures, e.g. 0.65 for simple cubic lattice. Even in the interstitial mechanism, HR values have been reported as 0.61 for single crystalline Na halumina [28]. However, polycrystalline samples tend to show reduced HR values. For example, Ormrod and Kirk [29] reported Haven ratios of Na hW-alumina (structure is similar but rather of vacancy diffusion nature) of 0.18 – 0.16 using polycrystalline sample. They attributed such reduction of HR to the presence of an electric field, which might assist the ionic jump across the grain boundaries. While relatively plausible HR (=0.55) was obtained in our previous study using polycrystalline Li1.33Ti1.67O4 [12], this might be caused by the fact that measuring temperature was enough high above 860 jC, in which grain boundary effect would be negligible on diffusion. To discuss the absolute value of LISICON and ZRA at relatively lower temperatures, single crystalline experiments are required. In addition, the employment of a.c. conductivity instead of d.c. for the Nernst – Einstein’s equation might bring about an overestimation of Dr. Indeed, four-probe d.c. conductivity of LISICON measured by Alpen et al. [14] using Li0.6TiS4 electrodes was approximately 40% of a.c. conductivity. Notwithstanding, relatively close HR values between LISICON and ZRA suggest that the diffusion path or the mechanism was not drastically different. This was also consistent with the fact that the activation energies of conductivity were not so different between these compounds. Bose et al. [26] mentioned that the higher lithium ion conductivity in LISICON compared to ZRA was caused by the bottle neck size in the diffusion path and the number of interstitial sites. However, the latter would be denied, because the later neutron diffraction study [22] showed the occupation of Li(4) (4b position in Pnma symmetry) for ZRA, which had been reported only LISICON, and change in the number of
Fig. 8. Temperature dependence of Haven ratio, HR, for LISICON (o) and ZRA (D).
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interstitial sites would alter the correlation factor f and HR. One of the hopeful methods to discuss the further precise diffusion mechanism is molecular dynamics (MD), in which tracer diffusion coefficients obtained in the present study would be significant parameters to restrict the force field or potential parameters. Whereas there have been some ambiguity in the absolute values of Haven ratios, tracer diffusion experiment using NR enables a qualitative discussion of the diffusion mechanism in LISICON and its solid solution. Further careful experiments using single crystal would provide more precise information.
4. Conclusion Tracer diffusion coefficients of lithium ion were obtained using NR method and found to be 3.7107, 7.4107 and 1.5106 cm2 s1 at 300, 400 and 500 jC, respectively, for LISICON and 1.1107 and 2.3107 cm2 s1 for 300 and 400 jC, respectively, for ZRA. Activation energies and Haven ratios showed similar values between LISICON and ZRA. Although the Haven ratios were relatively small, their similarity indicates that these compounds have essentially the same lithium ion conduction mechanism, and the difference of the diffusion coefficient is thought to be due to the effective jump frequencies of lithium ion interstitials, as the mobility is proportional to the diffusion coefficient. We have showed the NR method to be an effective method to measure the tracer diffusion coefficient of lithium ions in solids, the data of which can be used to discuss the diffusion properties.
Acknowledgements This work has been carried out in part under the Visiting Researcher’s Program of the Research Reactor Institute, Kyoto University and partially supported by a grant-in-aid for young scientists from the Ministry of Education, Science, Sports and Culture.
References [1] M. Kamata, T. Esaka, S. Fujine, K. Yoneda, K. Kanda, Nucl. Instrum. Methods Phys. Res., Sect. A, Accel. Spectrom. Detect. Assoc. Equip. 377 (1996) 161. [2] T. Esaka, M. Kamata, H. Saito, Solid State Ionics 86 – 88 (1996) 73. [3] M. Kamata, T. Esaka, S. Fujine, K. Yoneda, K. Kanda, J. Power Sources 68 (1997) 459. [4] H. Sakaguchi, A. Kohzai, K. Hatakeyama, S. Fujine, K. Yoneda, K. Kanda, T. Esaka, Int. J. Hydrogen Energy 25 (2000) 1205. [5] M. Kamata, T. Esaka, S. Fujine, K. Yoneda, K. Kanda, Denki Kagaku 63 (1995) 1063. [6] M. Kamata, T. Esaka, K. Takami, S. Fujine, K. Yoneda, K. Kanda, Denki Kagaku 64 (1996) 984. [7] M. Kamata, T. Esaka, K. Takami, S. Takai, S. Fujine, K. Yoneda, K. Kanda, Solid State Ionics 91 (1996) 303. [8] T. Esaka, Solid State Ionics 136 (2000) 1. [9] M. Hayashi, H. Sakaguchi, S. Takai, T. Esaka, Solid State Ionics 140 (2001) 71. [10] T. Esaka, M. Hayashi, H. Sakaguchi, S. Takai, M. Matsubayashi, Solid State Ionics 147 (2002) 107. [11] V.F. Sears, in: E. Prince (Ed.), International Tables for Crystallography vol. C, Kluwer Academic Publishing, Dordrecht, 1999, pp. 440 – 450. [12] S. Takai, M. Kamata, S. Fujine, K. Yoneda, K. Kanda, T. Esaka, Solid State Ionics 123 (1999) 165. [13] H.Y.-P. Hong, Mater. Res. Bull. 13 (1978) 117. [14] U.V. Alpen, M.F. Bell, W. Wichelhaus, Electrochim. Acta 23 (1978) 1395. [15] L.-Q. Chen, C.-Q. Wang, L.-Z. Wang, C.-L. Xiao, J.-Q. Bi, Chin. Phys. 1 (1981) 93. [16] P.G. Bruce, A.R. West, J. Solid State Chem. 44 (1982) 354. [17] P. Kurek, W. Bogusz, Phys. Status Solidi (a) 78 (1983) K117. [18] P.G. Bruce, A.R. West, J. Electrochem. Soc. 130 (1983) 662. [19] P.G. Bruce, A.R. West, J. Solid State Chem. 53 (1984) 430. [20] D. Plattner, H. Vo¨llenkle, Monatsh. Chem. 110 (1979) 693. [21] I. Abrahams, P.G. Bruce, A.R. West, W.I.F. David, J. Solid State Chem. 75 (1988) 390. [22] I. Abrahams, P.G. Bruce, W.I.F. David, A.R. West, Acta Cryst. B45 (1989) 457. [23] P.G. Bruce, I. Abrahams, A.R. West, Solid State Ionics 40/41 (1990) 293. [24] Z.-R. Li, R.-J. Xue, L.-Q. Chen, Acta Phys. Sin. 3 (1981) 1388. [25] D. Mazumdar, D.N. Bose, R.L. Mukherjee, Mater. Res. Bull. 18 (1983) 79. [26] M. Bose, A. Basu, D. Torgenson, Solid State Ionics 18/19 (1986) 539. [27] R. Bertermann, W. Mu¨ller-Warmuth, Z. Naturforsch. 53a (1998) 863. [28] M.S. Whittingham, R.A. Huggins, J. Chem. Phys. 54 (1971) 414. [29] S.E. Ormrod, D.L. Kirk, J. Phys. D: Appl. Phys. 10 (1977) 1494.
Tracer diffusion experiments on LISICON and its solid solutions by means of neutron radiography Shigeomi Takai a, Katsutoshi Kurihara a, Kenji Yoneda b, Shigenori Fujine b, Yuji Kawabata b, Takao Esaka a,* a
Department of Materials Science, Faculty of Engineering, Tottori University, Minami 4-101, Koyamacho, Tottori 680-8552, Japan b Research Reactor Institute, Kyoto University, Noda, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan Received 24 February 2003; received in revised form 5 May 2003; accepted 22 July 2003
Abstract Lithium ion diffusion coefficient measurements were carried out on LISICON (Li3.5Zn0.25GeO4) and on a zinc-rich analogue (ZRA; Li3Zn0.5GeO4) using neutron radiography (NR). Smearing 6LiNO3-saturated solution on a surface of a rectangle-shaped sample consisting of 7 Li and subsequent annealing enabled the relatively low temperature diffusion experiment down to 300 jC. The measured isotope concentration profiles agreed well with the diffusion model from the surface into the semi-infinite media, and the diffusion coefficients can be obtained for both LISICON and ZRA in the temperature range between 300 and 500 jC. The diffusion coefficient of LISICON is essentially larger than that of ZRA, while similar a Haven ratio was found. This indicated that the larger conductivity in LISICON was mainly caused by the higher lithium ion mobility and not by the difference of diffusion path. D 2003 Elsevier B.V. All rights reserved. Keywords: Diffusion; Lithium; LISICON; Neutron radiography; Haven ratio
1. Introduction Neutron radiography (NR) has been developed as a nondestructive inspection method. We applied this technique to observe the distribution of lithium or hydrogen in solid electrolytes or batteries [1 – 4] using the relatively large neutron attenuation factors for these species. Moreover, we also measured the lithium ion transport numbers in solid electrolytes [5 – 10], by considering the large difference in neutron absorption cross-section between the isotopes, 6Li and 7Li [11]. We have recently successfully measured lithium ion diffusion coefficients in Li1.33Ti1.67O4 from the isotope profile of the diffusion couples annealed above 860 jC [12]. However, on annealing below 800 jC, ionic transfer was insufficient across the interface in comparison with the bulk diffusion, resulting in a discontinuous jump of the isotope profile at the interface of the diffusion couple. This denotes that, to measure the diffusion coefficient of lower temperature-type lithium ion conductors such as
* Corresponding author. Tel./fax: +81-857-31-5264. E-mail address: [email protected] (T. Esaka). 0167-2738/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0167-2738(03)00305-9
LISICON from the isotope profile obtained by NR, we have to apply the lithium isotope on a surface of the diffusion sample followed by diffusion annealing. LISICON and its solid solutions, showing the gIILi3PO4-type structure of the general formula Li2+2xZn1xGeO4, exhibit high lithium ion conductivity in the composition region of x > 0 in comparison with Li1.33Ti1.67O4 at intermediate temperatures. The composition at x=0.75, Li3.5Zn0.25GeO4, was denoted as LISICON exhibiting the highest conductivity (0.125 S cm1 at 300 jC) [13]. While a lot of investigations including electrochemical [14 – 19], structural [13,20 – 23] and NMR [24 – 27] measurements were published in late 1970s and 1980s, rather few reports discussed the lithium diffusion properties. Diffraction studies estimated that lithium ion interstitials would contribute to the high lithium ion conduction [13], and NMR measurement [26] predicted that lithium ion mobility in LISICON is larger than that in zinc-rich analogue (ZRA, x=0.5 of Li2+2xZn1xGeO4). To discuss the mobility more quantitatively, the diffusion coefficients of lithium ion should be measured. Tracer diffusion coefficients indicate not only the mobility of particular species without potential gradient, but also the diffusion mechanism. Tracer diffusion coefficients
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can be obtained from the isotope concentration, which are usually measured by counting g-rays from radioisotope tracer deposited on the sample or using SIMS. However, both of the lithium isotopes (6Li and 7Li) are not radioactive and very few reports have been published on lithium ion tracer diffusion experiments using SIMS. In the present study, we measured the tracer diffusion coefficient of LISICON (x=0.75 of Li2+2xZn1xGeO4) and ZRA (x=0.5) by means of NR in the temperature range 300 – 500 jC and compared them to each other.
of the NR images were obtained by employing an imaging reader (Fuji Film, BAS-2500). Electric conductivity was measured on cylindrical shaped samples (7 mm in diameter and 10 mm in length) by conventional two-probe a.c. methods. Gold paste was applied for the electrodes and an impedance analyzer (HP4192A) was employed in the frequency range 100– 107 Hz. Conductivity values were calculated from the minimum point of the right end of the semi-circle in the complex impedance plots.
3. Results and discussion 2. Experimental Diffusion samples of LISICON (Li3.5Zn0.25GeO4) and zinc-rich analogue (Li3Zn0.5GeO4) were prepared by conventional solid state reaction methods. Stoichiometric mixtures of ZnO (Wako Pure Chemical), GeO2 (Wako Pure Chemical) and 7 Li 2 CO 3 obtained from 7 LiOHH 2 O (Tomiyama High Purity Chemical) were calcined at 800 jC for 10 h. Thereafter, the samples were crushed in an alumina mortar, pressed under a hydrostatic pressure of 200 MPa and then fired again at 1120 (LISICON) or 1140 jC (Li3Zn0.5GeO4). The sample were cut into a rectangle shape (779 mm3) using a microcutter and lapped with 9 Am diamond lapping fluid to achieve the same dimensions precisely. For calibration of the isotope concentrations, standard samples with the same thickness as the diffusion samples were also prepared, varying the isotope ratio every 1/10 step from 7Li to the natural 6Li/7Li ratio, which is referred as NLi in the present paper. Because the relatively low isotope region should be focused on and the accurate value of natural abundance of 6Li was not necessary to calculate the diffusion coefficient, we employed NLi instead of 6Li in the standard samples. The saturated solution of 6LiNO3, obtained by dissolving the excess amount of 6Li2CO3 (Tomiyama High Purity Chemical) into nitric acid, was smeared on one face of the rectangle-shaped 7Li sample, which was thereafter set in a furnace for a given time. The annealing temperatures were selected to be 300, 400 and 500 jC, which were monitored by thermocouple (type K) and digital multimeter (HP34401A). To obtain the diffusion data with extended annealing time, the above procedure including diffusion annealing and NR measurement was repeatedly carried out on the same sample, and the diffusion time was accumulated. NR experiments were carried out at the CN-3 guide tube in the Research Reactor Institute of Kyoto Univ., Japan. Both of the standard samples and diffusion-annealed samples were aligned on an imaging plate (IP) neutron detector (Fuji Film, BAS-ND2025) and they were sledded across the beam slit of the guide tube with the constant rate of 0.8 mms1 to prevent the influence of the neutron flux inhomogeneity in the guide tube. The numerical data (gray level)
3.1. Lithium diffusion experiments on LISICON (Li3.5Zn0.25GeO4) For the sample after sintering, a nominal density of 84% of the calculated value from the sample dimensions and approximately 97% of lithium in the starting materials was found, i.e. lithium loss was negligibly small during preparation. Fig. 1 shows a typical NR image of a LISICON diffusion sample annealed at 300 jC for 2 h and those of the standard samples varying the lithium isotope ratio from NLi to 7Li. As the samples were cut to the same thickness, the higher 6Li concentration part represented the whiter image due to the large neutron attenuation coefficient of 6Li. White gradation at the left side of the diffusion sample predicted that 6Li migrated from the surface into the bulk interior. This behavior seemed not to be simply caused by the soak of 6 LiNO3 aqueous solution, because another NR image of the 6 Li-smeared sample without annealing did not show such a white gradation. The numerical gray level of this NR image was also represented in Fig. 1, where the whiter NR image, i.e. larger 6Li concentration, corresponded to the lower gray level. A calibration curve was obtained from this gray level of the standard samples, as shown in Fig. 2, giving a smooth line with very little deviation. Through the calibration curve, the gray levels of the diffusion sample were converted into the NLi concentration as shown in Fig. 3(a). The concentration profile can be expressed by a solution of Fick’s equation, pffiffiffiffiffiffiffiffiffiffi cðxÞ ¼ ðM = pD t Þexpðx2 =ð4D tÞÞ; ð1Þ where D*, t and x denote the tracer diffusion coefficient, annealing time and the distance from the surface. Therefore, ln(cN) was plotted vs. x2 as Fig. 3(b). Since the natural abundance of 6Li is incorporated into the parameter M in Eq. (1) and contributes only to the intercept in the vertical axis, the slope of these plots yields-(4D*t)1. Presumably due to the 6LiNO3 or 6Li2CO3 accumulation at the diffusion surface, the profile seemed rather steep in the vicinity of the smeared surface. On the other hand, the slope becomes gradual at x2>0.016 cm2, which might be caused by the
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Fig. 1. NR image and the corresponding digitized gray levels of the standard and diffusion samples of LISICON. The lithium isotope ratio of standard samples varies from NLi to 7Li with 1/10 step and the diffusion sample was annealed at 300 jC for 2 h after smearing 6LiNO3 solution.
boundary diffusion or the sensitivity limit of the imaging plate. Nevertheless, the obtained data depicted by open circles gave a straight line, from which the diffusion coefficient can be calculated as 3.0107 cm2 s1 at 300 jC by least squares fitting. After various annealing times up to 4 h, the D*t values were obtained from the slope of the ln(cN)x2 diagram as shown in Fig. 3(b). These values were plotted against the actual diffusion time as depicted by circles in Fig. 4. Although the plots were scattered a little, a straight line can be drawn from the origin to provide the diffusion coefficient 3.7107 cm2 s1 at 300 jC. Diffusion experiments were also carried out at 400 and 500 jC, the data of which were plotted in Fig. 4 by triangle and rectangle symbols, respectively. In our data, D*t measured in the shorter annealing time tended to show larger values; this might be due to the fast diffusion along grain boundaries. Particularly in the case of 400 jC annealed data, D*t value would increase by 30% if the last point was missing. The finally obtained diffusion coefficients were 7.4107 and 1.5106 cm2 s1 at 400 and 500 jC, respectively.
N
Fig. 2. Calibration curve of gray level for the Li concentration in LISICON standard samples.
3.2. Lithium diffusion experiments on ZRA (Li3Zn0.5GeO4) Diffusion experiments have been also carried out on ZRA. Fig. 5 shows the typical NR images of standard and diffusion samples of ZRA annealed at 500 jC for 2 h and the corresponding gray level. After a similar procedure as carried out for LISICON, the D*t values obtained by fitting were plotted against the actual annealing time in Fig. 6, which also provided straight lines. The finally obtained diffusion coefficients were calculated to be 1.1107, 2.3107 and 1.3106 cm2 s1 at 300, 400 and 500 jC,
Fig. 3. (a) Isotope (NLi) concentration of LISICON diffusion sample annealed at 300 jC for 2 h. (b) ln(cN)Dx2 plots of the above diffusion sample.
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Fig. 4. D*t vs. t relations for LISICON. o, D and 5 denote 300, 400 and 500 jC data, respectively.
Fig. 6. D*t vs. t relations for ZRA. o, D and 5 denote 300, 400 and 500 jC data, respectively.
respectively. Although the diffusion coefficient at 500 jC seemed to be larger than that expected from the other ones, this was not supposed to be a experimental error, because diffusion annealing was carried out simultaneously with LISICON in the same furnace and all the points exhibited a well-defined straight line as observed in Fig. 6.
suggesting that they would have essentially the same diffusion mechanism, even though only three temperature data points were collected for each composition and, moreover, one of them was eliminated for calculation in ZRA. In this solid solution system, ionic conduction was thought to be associated with the lithium ion interstitials. According to the single crystal X-ray diffraction [13] and powder neutron diffraction studies [21 –23], LISICON and its solid solution consist of non-equivalent three types of tetrahedra, i.e. GeO4 and two types of (Zn/Li)O4 tetrahedra, accompanied by two types of lithium ion interstitials. Assuming that only lithium ion interstitials can migrate and those in the (Zn/Li)O4 tetrahedra are fixed, the carrier concentration corresponded to that of interstitials. Although the occupation factors of lithium ion interstitials have already been investigated by means of diffraction method [13,20 – 22], there seemed to remain a slight discrepancy in the precise position and/or occupation factors of the interstitials. We therefore adopted the nominal value for the carrier concentration n assuming all the tetrahedral sites to be filled
3.3. Comparison between the diffusion coefficient and the conductivity The temperature dependence of measured diffusion coefficients for LISICON (o) and ZRA (D) is summarized in Fig. 7 in the form of Arrhenius plots. Ignoring the 500 jC data of ZRA, LISICON showed approximately three times larger diffusion coefficients than ZRA in the measured temperature range. As the mobility is proportional to the diffusion coefficient, the higher lithium ion conduction in LISICON was supposed to be mainly due to larger lithium ion mobility. Activation energies obtained from the gradient of Arrhenius plots were 0.26 eV for both compounds,
Fig. 5. NR image and the corresponding gray level of the standard and diffusion samples of ZRA (x=0.5 of Li2+2xZn1xGeO4). Isotope concentration of the standard samples varied from NLi to 7Li with 1/10 step.
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Fig. 7. Arrhenius plots of diffusion coefficients for LISICON (o) and ZRA (D). Open and closed symbols show the diffusion coefficients obtained by NR method and conductivity measurement, respectively.
and interstitial sites partly occupied by the remaining lithium ions. The diffusion coefficients were then obtained from the conductivity (j) by using Nernst –Einstein’s relation, Dr ¼ kB T r=ðnZ 2 e2 Þ
ð2Þ
where Z and e are the valence of charge carrier and elementary electric charge, respectively. As three interstitials were incorporated into a unit cell with the volume of 351.72 ˚ 3 for LISICON, the carrier concentration n resulted in A 0.0119 molcm3 taking into account the sample density to be 84%. Similar calculations for ZRA gave a concentration n of 0.00794 molcm3. As there is some inconsistency between the reported conductivity especially in LISICON, ionic conductivity, r, was measured by a.c. methods for Eq. (2), which is consistent with the previous low-temperature data measured by Kreck and Bogusz [17] below 400 jC. The diffusion coefficients obtained from the conductivity were also plotted as the closed symbols in Fig. 7, which were approximately one order of magnitude larger than those measured by NR method (open symbols). Activation energies obtained from these plots were 0.26 and 0.35 eV for LISICON and ZRA, respectively. Although the collected data points were very few, these activation energies were not so different from those obtained by NR method. By using two types of diffusion coefficients obtained from NR method and from conductivity, Haven ratios (HR=D/Dr) were calculated and plotted in Fig. 8 except for that measured at 500 jC for ZRA. While these gave similar values for LISICON and ZRA, they seemed significantly small considering that a large number of ionic
111
conductors show HR ranging from 0.4 to 0.7. In the ideal vacancy diffusion mechanism where jump frequency and distance were not varied with applied electric field, HR corresponds to the correlation factor f derived from the correlation of successive jump directions, some of which were reported for typical structures, e.g. 0.65 for simple cubic lattice. Even in the interstitial mechanism, HR values have been reported as 0.61 for single crystalline Na halumina [28]. However, polycrystalline samples tend to show reduced HR values. For example, Ormrod and Kirk [29] reported Haven ratios of Na hW-alumina (structure is similar but rather of vacancy diffusion nature) of 0.18 – 0.16 using polycrystalline sample. They attributed such reduction of HR to the presence of an electric field, which might assist the ionic jump across the grain boundaries. While relatively plausible HR (=0.55) was obtained in our previous study using polycrystalline Li1.33Ti1.67O4 [12], this might be caused by the fact that measuring temperature was enough high above 860 jC, in which grain boundary effect would be negligible on diffusion. To discuss the absolute value of LISICON and ZRA at relatively lower temperatures, single crystalline experiments are required. In addition, the employment of a.c. conductivity instead of d.c. for the Nernst – Einstein’s equation might bring about an overestimation of Dr. Indeed, four-probe d.c. conductivity of LISICON measured by Alpen et al. [14] using Li0.6TiS4 electrodes was approximately 40% of a.c. conductivity. Notwithstanding, relatively close HR values between LISICON and ZRA suggest that the diffusion path or the mechanism was not drastically different. This was also consistent with the fact that the activation energies of conductivity were not so different between these compounds. Bose et al. [26] mentioned that the higher lithium ion conductivity in LISICON compared to ZRA was caused by the bottle neck size in the diffusion path and the number of interstitial sites. However, the latter would be denied, because the later neutron diffraction study [22] showed the occupation of Li(4) (4b position in Pnma symmetry) for ZRA, which had been reported only LISICON, and change in the number of
Fig. 8. Temperature dependence of Haven ratio, HR, for LISICON (o) and ZRA (D).
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interstitial sites would alter the correlation factor f and HR. One of the hopeful methods to discuss the further precise diffusion mechanism is molecular dynamics (MD), in which tracer diffusion coefficients obtained in the present study would be significant parameters to restrict the force field or potential parameters. Whereas there have been some ambiguity in the absolute values of Haven ratios, tracer diffusion experiment using NR enables a qualitative discussion of the diffusion mechanism in LISICON and its solid solution. Further careful experiments using single crystal would provide more precise information.
4. Conclusion Tracer diffusion coefficients of lithium ion were obtained using NR method and found to be 3.7107, 7.4107 and 1.5106 cm2 s1 at 300, 400 and 500 jC, respectively, for LISICON and 1.1107 and 2.3107 cm2 s1 for 300 and 400 jC, respectively, for ZRA. Activation energies and Haven ratios showed similar values between LISICON and ZRA. Although the Haven ratios were relatively small, their similarity indicates that these compounds have essentially the same lithium ion conduction mechanism, and the difference of the diffusion coefficient is thought to be due to the effective jump frequencies of lithium ion interstitials, as the mobility is proportional to the diffusion coefficient. We have showed the NR method to be an effective method to measure the tracer diffusion coefficient of lithium ions in solids, the data of which can be used to discuss the diffusion properties.
Acknowledgements This work has been carried out in part under the Visiting Researcher’s Program of the Research Reactor Institute, Kyoto University and partially supported by a grant-in-aid for young scientists from the Ministry of Education, Science, Sports and Culture.
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