- Email: [email protected]
Degradation kinetics of discharge capacity for amorphous Mg–Ni electrode
Journal of Alloys and Compounds 334 (2002) 232–237
L
www.elsevier.com / locate / jallcom
Degradation kinetics of discharge capacity for amorphous Mg–Ni electrode D. Mu*, Y. Hatano, T. Abe, K. Watanabe Hydrogen Isotope Research Center, Toyama University, Gofuku 3190, Toyama 930 -8555, Japan Received 18 June 2001; received in revised form 27 June 2001; accepted 6 July 2001
Abstract Amorphous MgNi alloy was prepared by ball-milling of Mg 2 Ni and Ni powders. Current density dependence of the discharge capacity was studied in the range from 5 to 250 mA / g for the MgNi electrode by charge–discharge cycle tests in 6 M KOH electrolyte using a conventional two-electrode system. The amount of hydrogen used for the discharge decreased with cycles. The extent of capacity degradation at a given cycle increased with increasing discharge current density. The capacity degradation curves could be expressed by ¢(t)5¢` 1(¢0 2¢` ) exp[2kt], where ¢(t) is the discharge capacity at time t, that is the period of time in which the electrode was immersed in the electrolyte solution, ¢0 the ideal discharge capacity expected for the virgin electrode, ¢` the final steady discharge capacity after a number of cycles, and k the apparent rate constant for the degradation. The rate constant increased linearly with the current density. According to diffusion analyses of discharge curves under different current densities, the hydrogen diffusion in the bulk is not the rate-determining step for the measured discharge rate, but surface processes play dominant roles in affecting the MgNi electrode properties. 2002 Elsevier Science B.V. All rights reserved. Keywords: MgNi alloy; Discharge current density; Hydrogen diffusion; Degradation
1. Introduction Magnesium-based alloys have been extensively studied as one of the most promising materials for their applications to hydrogen storage and rechargeable Ni / MH batteries [1–4]. In particular, many works were done on the modification of these kind of alloys by mechanical alloying to improve their storage properties around room temperature [5–8]. It is reported that amorphous MgNi alloys prepared by ball-milling absorb and desorb hydrogen reversibly at room temperature by electrochemical charge– discharge cycles [9]. However, the cycle life of these materials is considerably shorter than other hydrogen storage materials such as AB 5 and AB 2 type alloys [10–12]. The poor cyclic behavior of MgNi electrodes is attributed to the formation of Mg(OH) 2 on the electrodes, which has been considered to arise from the charge–discharge cycles. To avoid the surface oxidation, Luo et al. examined effects of Nicoating of MgNi based alloys on the electrode properties [13]. Iwakura et al. also reported an improvement of the discharge capacity of a modified MgNi alloy [5], which was prepared by ball-milling of Mg 2 Ni, Ni and graphite. *Corresponding author. E-mail address: [email protected] (D. Mu).
Similar efforts have been done by modifying not only the surface but also bulk properties by means of ball-milling of Mg 2 Ni with Ni and some other third elements [14]. To improve the electrode properties, however, it is important to understand the degradation kinetics and mechanisms. From this viewpoint, the kinetics of discharge capacity degradation of amorphous MgNi electrodes was studied under different discharge current densities to elucidate factors affecting the degradation. In addition, discharge curves at different current densities were analyzed by a diffusion model to clarify the role of hydrogen diffusion in the bulk of electrode during the discharge process.
2. Experimental An amorphous MgNi alloy of Mg:Ni51:1 in atomic ratio was prepared by ball-milling Mg 2 Ni (below 200 mesh) and Ni (about 3–7 mm) powders. Two grams of the mixture powder were put into a chromium steel vessel of 12 ml together with 18 balls of stainless steel (5.5 mm diameter), and then the vessel was sealed by an O-ring in an argon atmosphere using a glove box. A planetary ball mill apparatus (Fritsch P5) was used to grind mechanically
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01759-5
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237
the mixture powder with a rotation speed of 350 rev. / min for 80 h. The ball-milled MgNi powder was mixed with electrolytic copper powder (2–3 mm) in a weight ratio of 1:3 in argon atmosphere. One gram of the mixture was compressed to a compact disc (10 mm diameter) with a pressure of 590 MPa for 10 min. One side of this pellet was connected with a Ni mesh to make the negative electrode. The other side was sealed by epoxy-resin. A Ni wire was spot-welded on the Ni mesh to serve as conducting lead. Electrochemical charge–discharge tests were carried out in 6 M KOH electrolyte at room temperature, where sintered Ni(OH) 2 / NiOOH was used as the counter electrode. The MgNi electrode was charged to 1.5 V at 100 mA / g for 10 h, rested for 5 min, and discharged at different current densities to a cut-off voltage of 1.0 V. The discharge current density was varied from 5 to 250 mA / g. Powder morphology and crystallinity were observed by a scanning electron microscope (SEM; Hitachi, S-3500H) and an X-ray diffractometer (XRD; Phillips, PW1825), respectively.
3. Results Fig. 1 is a typical example representing the change in the discharge capacity of an amorphous MgNi electrode
233
with charge–discharge cycles in 6 M KOH electrolyte, where the electrode was charged at 100 mA / g for 10 h and discharged at 20 mA / g. The MgNi electrode showed the maximum discharge capacity around 400 mAh / g at the first cycle, but it dropped rapidly with increasing cycle number. The inserts show XRD patterns for the electrode before use and after the 9th cycle, indicating that Mg(OH) 2 crystallites grew during the charge–discharge cycles. Similar degradation curves and Mg(OH) 2 formation have been observed for MgNi alloys by many research groups [14– 16]. Then, it has been widely recognized that the principal reason of the capacity degradation is the formation of Mg(OH) 2 caused by charge–discharge cycles. The discharge capacity and its degradation have been commonly discussed under fixed charge and discharge current densities. These properties, however, can change with current density. Figs. 2 and 3 show capacity degradation with cycles and discharge curves at the first cycle for different discharge current densities, respectively. As seen in Fig. 2, the discharge capacity decreased monotonically with increasing cycle under all discharge current densities. The discharge capacity itself, however, was highest for the discharge at 5 mA / g and became smaller with the increase in current density. For the discharge at 250 mA / g, the discharge capacity at the first cycle was only 30 mAh / g and showed no significant reduction of the capacity with cycles. For an insight into the influence of the discharge current
Fig. 1. The discharge capacity of MgNi electrode in 6 M KOH solution and results of XRD analyses. Charge current density is 100 mA / g, charge time is 10 h, discharge current density is 20 mA / g.
234
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237 Table 1 The fractional discharge in reference to C0 (C0 5550 mAh / g)
Fig. 2. The discharge capacities of MgNi electrodes in 6 M KOH solution at different discharge current densities. Charge current density is 100 mA / g, charge time is 10 h.
density, the discharge curves under different current densities were compared to each other. Fig. 3 shows the discharge curves at the first cycle for different current densities. The discharge at 5 mA / g gave a moderate decline of the cell voltage with discharge time, forming a fairly long plateau, and then the cell voltage fell down to 1.0 V, the cut-off voltage, at about 100 h. On increase in the current density, the time to attain the cut-off value became shorter and eventually the time was shortened to only about 7.5 min for the discharge at 250 mA / g. Thus, the discharge capacity at the first cycles was significantly reduced by the increase in the current density. The discharge capacities at the first cycles are compared in Table 1, where Cn refers to the discharge capacity at n mA / g discharge, and Cn /C0 gives a fractional discharge (represented by %) in reference to C0 , which is the ideal discharge capacity of the electrode discussed below. Table 1 shows that only 5.5% of charged hydrogen was discharged at 250 mA / g, suggesting that a large fraction of charged hydrogen remained in the electrode material. This
Discharge I (mA / g)
5
10
20
40
80
250
Cn (mAh / g) Cn /C0 (%)
496 90.2
435 79.1
388 70.5
255 46.4
149 27.1
30 5.5
was confirmed by the experiment shown in Fig. 4, where the electrode was discharged at 250 mA / g first and subsequently discharged at 20 mA / g without any recharging. Despite the very small discharge capacity at the first discharge, about eight times more hydrogen could be released at the second discharge. Han et al. have also observed by measuring PCT curves after charge–discharge cycles that the active material still exists in an amorphous MgNi anode [14]. These observations indicate that the high current density discharge does not simply correspond to enhancement of the discharge rate, but it causes discharge to be incomplete.
4. Discussion
4.1. Diffusion analysis To make clear the reason for the incomplete discharge, the role of hydrogen diffusion was analyzed for the following series reactions as M–H(b) → M–H(s)
(1)
M–H(s) 1 OH 2 → M 1 H 2 O 1 e 2
(2)
where M–H(b) denotes hydrogen in the bulk and M–H(s) that on the surface. It is assumed that the diffusion was the rate determining process. Then diffusion of hydrogen in a particle was analyzed following Crank [17] as
F
≠C ≠ 2 C 2 ≠C ] 5 D ]] 1] ] ≠t r ≠r ≠r 2
G
(3)
S D
≠C 2 D ] 5 F0 , r 5 a ≠r
(4)
Ca 5 C0 Fa 3Dt 1 r 3 2S]D H] 1 ] ] 2 ] D 2 a 10 a sin(a r) exp(2Da t) a 2 2] O ]]]]]] J r sin(a a)a a 2
0
2
2
2 n
`
n
n51
Fig. 3. The curves of cell voltage in the discharge process of MgNi electrode (first cycle) under different discharge current densities. Charge current density is 100 mA / g, charge time is 10 h.
n
2 n
2
(5)
where D is the diffusion constant of hydrogen in MgNi alloy, F0 the discharging hydrogen flux, a the average radius of powder particles, Ca the hydrogen concentration at the surface, C0 the hydrogen initial concentration in a particle, being set to unity in this case, and r 5 a at the surface; the aan ’s are the positive roots of aan cot aan 51. The diffusion constant was taken from Abe et al. as
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237
235
Fig. 4. MgNi electrode was charged at 100 mA / g for 10 h, and discharged at the current density of 250 mA / g in the first cycle. Then, the electrode was subsequently discharged at 20 mA / g without re-charging in the second cycle.
8.1310 210 cm 2 / s [18] and the average radius was determined to be 7.5 mm by SEM observations. It was assumed that the discharge at a given current density is continued till the hydrogen concentration at the surface becomes zero. Fig. 5 shows calculated depth profiles of hydrogen at the end of the discharge under different current densities. It is seen that hydrogen diffusion is fast enough and the amount of hydrogen remaining in the particle is very small, below 0.5% even by the discharge at 250 mA / g; namely 99.5% of charged hydrogen can be discharged at 250 mA / g if hydrogen diffusion is the rate determining step for the discharge process. This prediction exhibits a striking contrast with the observation that only about 6% of charged hydrogen could be released by the discharge at 250 mA / g. It is concluded, therefore, that the hydrogen transport in a particle does not impede the discharge, but
Fig. 5. Hydrogen depth profiles within the alloy particle at the end of discharge under different current densities.
surface electrochemical reactions play an important role for determining the discharge rate. This implies that there exist some competitive electrochemical reactions, which predominate progressively over the hydrogen discharge with increasing discharge current density.
4.2. Degradation kinetics The degradation of discharge capacity has been recognized as a result of charge–discharge cycles. Recently, however, Hatano et al. [15] showed that the degradation simply arises from a chemical reaction of the electrode with the electrolyte solution, without charge–discharge cycles. On account of this observation, the degradation curves that appear in Fig. 2 are re-plotted in Fig. 6 as a function of alkaline immersion time, which is the sum of charge–discharge times till a given number of cycles. It
Fig. 6. The changes in discharge capacities of MgNi electrodes under different discharge current densities with time. Charge current density is 100 mA / g, charge time is 10 h.
236
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237
was found that the re-plotted degradation curves obeyed a simple kinetic equation as
5. Conclusions
¢(t) 5 (¢0 2 ¢` ) exp[2kt] 1 ¢`
The discharge capacity of an MgNi electrode was measured at different current densities. The discharge capacity decreased with increasing current density and the rate of capacity degradation with cycles was strongly dependent on the discharge current. It was found that these degradation curves were described by an exponential function as ¢(t)5¢` 1(¢0 2¢` ) exp[2kt], where ¢(t) is the discharge capacity at time t, that is the period of time in which the electrode was immersed in the electrolyte solution, ¢0 the ideal discharge capacity expected for the virgin electrode, ¢` the final steady discharge capacity after a number of cycles, and k the apparent rate constant for the degradation. The rate constant increased linearly with the current density. Diffusion analyses of discharge curves under different current densities showed that almost all of the hydrogen charged should be released from the electrode during the discharge, irrespective of the discharge current density. These results indicate that the hydrogen diffusion in the bulk is not the rate-determining step for the measured discharge rates, but the reduction in the discharge capacity is ascribed to the increase in internal resistance, the impediment of hydrogen diffusion in a subsurface region, or the retardation of the electrochemical hydrogen discharge processes. There remains, however, the possibility of current induced Mg(OH) 2 formation. Further studies are required to clarify the role of Mg(OH) 2 formation on the charge and discharge processes.
(6)
where ¢(t) is the discharge capacity at the immersion time t, ¢0 the initial capacity, ¢` the final steady value at a given current density (denoted as the residual capacity) and k the rate constant (denoted as degradation constant). The solid lines in Fig. 6 were calculated by Eq. (6), where the parameters, ¢0 , ¢` and k, were obtained by non-linear fitting of respective degradation curves. These lines agreed very well with the observed degradation curves. It is seen that all of the degradation curves could be extrapolated to the same ¢0 value of 550 mAh / g, which should be the intrinsic discharge capacity of the virgin electrodes prepared in the present study. The residual capacity, on the other hand, showed a weak dependence on the discharge current density, decreasing from 80 mAh / g at 10 mA / g to 20 mAh / g at 250 mA / g discharge. It was found that the degradation constant, k, increased linearly with the discharge current density as shown in Fig. 7. But, this relation does not necessarily imply that the rate of Mg(OH) 2 formation increases with the current density because Mg(OH) 2 is formed by alkaline immersion of the electrode without any charge–discharge cycles, as already mentioned by Hatano et al. [15]. Taking these observations into account, this relation should be ascribed to: (1) the increases in internal resistance; (2) the impediment in hydrogen diffusion; or (3) the retardation in the electrochemical hydrogen discharge reactions, all of which can arise from the presence of a given amount of Mg(OH) 2 on the electrode surface. These mechanisms can cause the current dependent potential drop, which reduces the dischargeable amount of hydrogen above the cut-off voltage. But it is also plausible to assume a current induced Mg(OH) 2 formation. Those processes, however, are too complicated to clarify the contributions of each process in the present paper and further studies are required.
Acknowledgements This work was partly supported by a Grant-in-Aid for Scientific Research on Priority Areas A of ‘New Protium Function’ of the Ministry of Education, Science, Sports and Culture of Japan.
References
Fig. 7. The relationship between the degradation constant k and discharge current density.
[1] J.J. Reilly, R.H. Wiswall Jr., Inorganic Chem. 7 (11) (1968) P2254– P2256. [2] D. Sun, Y. Lei, W. Liu, J. Jiang, J. Wu, Q. Wang, J. Alloys Comp. 231 (1995) 621–624. [3] T. Kohno, S. Tsuruta, M. Kanda, J. Electrochem. Soc. 143 (9) (1996) PL198–PL199. [4] N. Cui, B. Luan, H. Zhao, H. Liu, S. Dou, J. Alloys Comp. 233 (1996) 236–240. [5] C. Iwakura, S. Nohara, H. Inoue, Y. Fukumoto, Chem. Commun. (1996) P1831–P1832. [6] S. Orimo, H. Fujii, K. Ikeda, Acta Mater. 45 (1) (1997) P331–P341. [7] L. Berlouis, E. Cabrera, E. Hall-Barientos, P. Hall, S. Dodd, S. Morris, M. Imam, J. Alloys Comp. 305 (2000) 82–89. [8] J. Woo, K. Lee, J. Electrochem. Soc. 146 (3) (1999) 819–823. [9] Y.Q. Lei, Y.M. Wu, Q.M. Wang, J. Wu, Q.D. Wang, Z. Phys. Chem. 181 (1993) 379. [10] S. Kim, J. Lee, Int. J. Hydrogen Energy 19 (11) (1994) 911–915.
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237 [11] H.H. Lee, J.Y. Lee, J. Alloys Comp. 270 (1998) 142–144. [12] J. Xue, G. Li, Y. Hu, J. Du, C. Wang, G. Hu, J. Alloys Comp. 307 (2000) 240–244. [13] J.L. Luo, N. Cui, J. Alloys Comp. 264 (1998) 299–305. [14] S. Han, P. Lee, J. Lee, A. Zuttel, L. Schlapbach, J. Alloys Comp. 306 (2000) 219–226. [15] Y. Hatano, T. Tachikawa, D. Mu, T. Abe, K. Watanabe, S. Morozumi, J. Alloys Comp. (in press).
237
[16] K. Watanabe, W. Shu, K. Mizukami, K. Kobayashi, Y. Hatano, S. Morozumi, J. Alloys Comp. 293–295 (1999) 626–631. [17] J. Crank, The Mathematics of Diffusion, 2nd Edition, Oxford University Press, Oxford, 1975. [18] T. Abe, T. Tachikawa, Y. Hatano, K. Watanabe, J. Alloys Comp. (in press).
L
www.elsevier.com / locate / jallcom
Degradation kinetics of discharge capacity for amorphous Mg–Ni electrode D. Mu*, Y. Hatano, T. Abe, K. Watanabe Hydrogen Isotope Research Center, Toyama University, Gofuku 3190, Toyama 930 -8555, Japan Received 18 June 2001; received in revised form 27 June 2001; accepted 6 July 2001
Abstract Amorphous MgNi alloy was prepared by ball-milling of Mg 2 Ni and Ni powders. Current density dependence of the discharge capacity was studied in the range from 5 to 250 mA / g for the MgNi electrode by charge–discharge cycle tests in 6 M KOH electrolyte using a conventional two-electrode system. The amount of hydrogen used for the discharge decreased with cycles. The extent of capacity degradation at a given cycle increased with increasing discharge current density. The capacity degradation curves could be expressed by ¢(t)5¢` 1(¢0 2¢` ) exp[2kt], where ¢(t) is the discharge capacity at time t, that is the period of time in which the electrode was immersed in the electrolyte solution, ¢0 the ideal discharge capacity expected for the virgin electrode, ¢` the final steady discharge capacity after a number of cycles, and k the apparent rate constant for the degradation. The rate constant increased linearly with the current density. According to diffusion analyses of discharge curves under different current densities, the hydrogen diffusion in the bulk is not the rate-determining step for the measured discharge rate, but surface processes play dominant roles in affecting the MgNi electrode properties. 2002 Elsevier Science B.V. All rights reserved. Keywords: MgNi alloy; Discharge current density; Hydrogen diffusion; Degradation
1. Introduction Magnesium-based alloys have been extensively studied as one of the most promising materials for their applications to hydrogen storage and rechargeable Ni / MH batteries [1–4]. In particular, many works were done on the modification of these kind of alloys by mechanical alloying to improve their storage properties around room temperature [5–8]. It is reported that amorphous MgNi alloys prepared by ball-milling absorb and desorb hydrogen reversibly at room temperature by electrochemical charge– discharge cycles [9]. However, the cycle life of these materials is considerably shorter than other hydrogen storage materials such as AB 5 and AB 2 type alloys [10–12]. The poor cyclic behavior of MgNi electrodes is attributed to the formation of Mg(OH) 2 on the electrodes, which has been considered to arise from the charge–discharge cycles. To avoid the surface oxidation, Luo et al. examined effects of Nicoating of MgNi based alloys on the electrode properties [13]. Iwakura et al. also reported an improvement of the discharge capacity of a modified MgNi alloy [5], which was prepared by ball-milling of Mg 2 Ni, Ni and graphite. *Corresponding author. E-mail address: [email protected] (D. Mu).
Similar efforts have been done by modifying not only the surface but also bulk properties by means of ball-milling of Mg 2 Ni with Ni and some other third elements [14]. To improve the electrode properties, however, it is important to understand the degradation kinetics and mechanisms. From this viewpoint, the kinetics of discharge capacity degradation of amorphous MgNi electrodes was studied under different discharge current densities to elucidate factors affecting the degradation. In addition, discharge curves at different current densities were analyzed by a diffusion model to clarify the role of hydrogen diffusion in the bulk of electrode during the discharge process.
2. Experimental An amorphous MgNi alloy of Mg:Ni51:1 in atomic ratio was prepared by ball-milling Mg 2 Ni (below 200 mesh) and Ni (about 3–7 mm) powders. Two grams of the mixture powder were put into a chromium steel vessel of 12 ml together with 18 balls of stainless steel (5.5 mm diameter), and then the vessel was sealed by an O-ring in an argon atmosphere using a glove box. A planetary ball mill apparatus (Fritsch P5) was used to grind mechanically
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01759-5
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237
the mixture powder with a rotation speed of 350 rev. / min for 80 h. The ball-milled MgNi powder was mixed with electrolytic copper powder (2–3 mm) in a weight ratio of 1:3 in argon atmosphere. One gram of the mixture was compressed to a compact disc (10 mm diameter) with a pressure of 590 MPa for 10 min. One side of this pellet was connected with a Ni mesh to make the negative electrode. The other side was sealed by epoxy-resin. A Ni wire was spot-welded on the Ni mesh to serve as conducting lead. Electrochemical charge–discharge tests were carried out in 6 M KOH electrolyte at room temperature, where sintered Ni(OH) 2 / NiOOH was used as the counter electrode. The MgNi electrode was charged to 1.5 V at 100 mA / g for 10 h, rested for 5 min, and discharged at different current densities to a cut-off voltage of 1.0 V. The discharge current density was varied from 5 to 250 mA / g. Powder morphology and crystallinity were observed by a scanning electron microscope (SEM; Hitachi, S-3500H) and an X-ray diffractometer (XRD; Phillips, PW1825), respectively.
3. Results Fig. 1 is a typical example representing the change in the discharge capacity of an amorphous MgNi electrode
233
with charge–discharge cycles in 6 M KOH electrolyte, where the electrode was charged at 100 mA / g for 10 h and discharged at 20 mA / g. The MgNi electrode showed the maximum discharge capacity around 400 mAh / g at the first cycle, but it dropped rapidly with increasing cycle number. The inserts show XRD patterns for the electrode before use and after the 9th cycle, indicating that Mg(OH) 2 crystallites grew during the charge–discharge cycles. Similar degradation curves and Mg(OH) 2 formation have been observed for MgNi alloys by many research groups [14– 16]. Then, it has been widely recognized that the principal reason of the capacity degradation is the formation of Mg(OH) 2 caused by charge–discharge cycles. The discharge capacity and its degradation have been commonly discussed under fixed charge and discharge current densities. These properties, however, can change with current density. Figs. 2 and 3 show capacity degradation with cycles and discharge curves at the first cycle for different discharge current densities, respectively. As seen in Fig. 2, the discharge capacity decreased monotonically with increasing cycle under all discharge current densities. The discharge capacity itself, however, was highest for the discharge at 5 mA / g and became smaller with the increase in current density. For the discharge at 250 mA / g, the discharge capacity at the first cycle was only 30 mAh / g and showed no significant reduction of the capacity with cycles. For an insight into the influence of the discharge current
Fig. 1. The discharge capacity of MgNi electrode in 6 M KOH solution and results of XRD analyses. Charge current density is 100 mA / g, charge time is 10 h, discharge current density is 20 mA / g.
234
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237 Table 1 The fractional discharge in reference to C0 (C0 5550 mAh / g)
Fig. 2. The discharge capacities of MgNi electrodes in 6 M KOH solution at different discharge current densities. Charge current density is 100 mA / g, charge time is 10 h.
density, the discharge curves under different current densities were compared to each other. Fig. 3 shows the discharge curves at the first cycle for different current densities. The discharge at 5 mA / g gave a moderate decline of the cell voltage with discharge time, forming a fairly long plateau, and then the cell voltage fell down to 1.0 V, the cut-off voltage, at about 100 h. On increase in the current density, the time to attain the cut-off value became shorter and eventually the time was shortened to only about 7.5 min for the discharge at 250 mA / g. Thus, the discharge capacity at the first cycles was significantly reduced by the increase in the current density. The discharge capacities at the first cycles are compared in Table 1, where Cn refers to the discharge capacity at n mA / g discharge, and Cn /C0 gives a fractional discharge (represented by %) in reference to C0 , which is the ideal discharge capacity of the electrode discussed below. Table 1 shows that only 5.5% of charged hydrogen was discharged at 250 mA / g, suggesting that a large fraction of charged hydrogen remained in the electrode material. This
Discharge I (mA / g)
5
10
20
40
80
250
Cn (mAh / g) Cn /C0 (%)
496 90.2
435 79.1
388 70.5
255 46.4
149 27.1
30 5.5
was confirmed by the experiment shown in Fig. 4, where the electrode was discharged at 250 mA / g first and subsequently discharged at 20 mA / g without any recharging. Despite the very small discharge capacity at the first discharge, about eight times more hydrogen could be released at the second discharge. Han et al. have also observed by measuring PCT curves after charge–discharge cycles that the active material still exists in an amorphous MgNi anode [14]. These observations indicate that the high current density discharge does not simply correspond to enhancement of the discharge rate, but it causes discharge to be incomplete.
4. Discussion
4.1. Diffusion analysis To make clear the reason for the incomplete discharge, the role of hydrogen diffusion was analyzed for the following series reactions as M–H(b) → M–H(s)
(1)
M–H(s) 1 OH 2 → M 1 H 2 O 1 e 2
(2)
where M–H(b) denotes hydrogen in the bulk and M–H(s) that on the surface. It is assumed that the diffusion was the rate determining process. Then diffusion of hydrogen in a particle was analyzed following Crank [17] as
F
≠C ≠ 2 C 2 ≠C ] 5 D ]] 1] ] ≠t r ≠r ≠r 2
G
(3)
S D
≠C 2 D ] 5 F0 , r 5 a ≠r
(4)
Ca 5 C0 Fa 3Dt 1 r 3 2S]D H] 1 ] ] 2 ] D 2 a 10 a sin(a r) exp(2Da t) a 2 2] O ]]]]]] J r sin(a a)a a 2
0
2
2
2 n
`
n
n51
Fig. 3. The curves of cell voltage in the discharge process of MgNi electrode (first cycle) under different discharge current densities. Charge current density is 100 mA / g, charge time is 10 h.
n
2 n
2
(5)
where D is the diffusion constant of hydrogen in MgNi alloy, F0 the discharging hydrogen flux, a the average radius of powder particles, Ca the hydrogen concentration at the surface, C0 the hydrogen initial concentration in a particle, being set to unity in this case, and r 5 a at the surface; the aan ’s are the positive roots of aan cot aan 51. The diffusion constant was taken from Abe et al. as
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237
235
Fig. 4. MgNi electrode was charged at 100 mA / g for 10 h, and discharged at the current density of 250 mA / g in the first cycle. Then, the electrode was subsequently discharged at 20 mA / g without re-charging in the second cycle.
8.1310 210 cm 2 / s [18] and the average radius was determined to be 7.5 mm by SEM observations. It was assumed that the discharge at a given current density is continued till the hydrogen concentration at the surface becomes zero. Fig. 5 shows calculated depth profiles of hydrogen at the end of the discharge under different current densities. It is seen that hydrogen diffusion is fast enough and the amount of hydrogen remaining in the particle is very small, below 0.5% even by the discharge at 250 mA / g; namely 99.5% of charged hydrogen can be discharged at 250 mA / g if hydrogen diffusion is the rate determining step for the discharge process. This prediction exhibits a striking contrast with the observation that only about 6% of charged hydrogen could be released by the discharge at 250 mA / g. It is concluded, therefore, that the hydrogen transport in a particle does not impede the discharge, but
Fig. 5. Hydrogen depth profiles within the alloy particle at the end of discharge under different current densities.
surface electrochemical reactions play an important role for determining the discharge rate. This implies that there exist some competitive electrochemical reactions, which predominate progressively over the hydrogen discharge with increasing discharge current density.
4.2. Degradation kinetics The degradation of discharge capacity has been recognized as a result of charge–discharge cycles. Recently, however, Hatano et al. [15] showed that the degradation simply arises from a chemical reaction of the electrode with the electrolyte solution, without charge–discharge cycles. On account of this observation, the degradation curves that appear in Fig. 2 are re-plotted in Fig. 6 as a function of alkaline immersion time, which is the sum of charge–discharge times till a given number of cycles. It
Fig. 6. The changes in discharge capacities of MgNi electrodes under different discharge current densities with time. Charge current density is 100 mA / g, charge time is 10 h.
236
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237
was found that the re-plotted degradation curves obeyed a simple kinetic equation as
5. Conclusions
¢(t) 5 (¢0 2 ¢` ) exp[2kt] 1 ¢`
The discharge capacity of an MgNi electrode was measured at different current densities. The discharge capacity decreased with increasing current density and the rate of capacity degradation with cycles was strongly dependent on the discharge current. It was found that these degradation curves were described by an exponential function as ¢(t)5¢` 1(¢0 2¢` ) exp[2kt], where ¢(t) is the discharge capacity at time t, that is the period of time in which the electrode was immersed in the electrolyte solution, ¢0 the ideal discharge capacity expected for the virgin electrode, ¢` the final steady discharge capacity after a number of cycles, and k the apparent rate constant for the degradation. The rate constant increased linearly with the current density. Diffusion analyses of discharge curves under different current densities showed that almost all of the hydrogen charged should be released from the electrode during the discharge, irrespective of the discharge current density. These results indicate that the hydrogen diffusion in the bulk is not the rate-determining step for the measured discharge rates, but the reduction in the discharge capacity is ascribed to the increase in internal resistance, the impediment of hydrogen diffusion in a subsurface region, or the retardation of the electrochemical hydrogen discharge processes. There remains, however, the possibility of current induced Mg(OH) 2 formation. Further studies are required to clarify the role of Mg(OH) 2 formation on the charge and discharge processes.
(6)
where ¢(t) is the discharge capacity at the immersion time t, ¢0 the initial capacity, ¢` the final steady value at a given current density (denoted as the residual capacity) and k the rate constant (denoted as degradation constant). The solid lines in Fig. 6 were calculated by Eq. (6), where the parameters, ¢0 , ¢` and k, were obtained by non-linear fitting of respective degradation curves. These lines agreed very well with the observed degradation curves. It is seen that all of the degradation curves could be extrapolated to the same ¢0 value of 550 mAh / g, which should be the intrinsic discharge capacity of the virgin electrodes prepared in the present study. The residual capacity, on the other hand, showed a weak dependence on the discharge current density, decreasing from 80 mAh / g at 10 mA / g to 20 mAh / g at 250 mA / g discharge. It was found that the degradation constant, k, increased linearly with the discharge current density as shown in Fig. 7. But, this relation does not necessarily imply that the rate of Mg(OH) 2 formation increases with the current density because Mg(OH) 2 is formed by alkaline immersion of the electrode without any charge–discharge cycles, as already mentioned by Hatano et al. [15]. Taking these observations into account, this relation should be ascribed to: (1) the increases in internal resistance; (2) the impediment in hydrogen diffusion; or (3) the retardation in the electrochemical hydrogen discharge reactions, all of which can arise from the presence of a given amount of Mg(OH) 2 on the electrode surface. These mechanisms can cause the current dependent potential drop, which reduces the dischargeable amount of hydrogen above the cut-off voltage. But it is also plausible to assume a current induced Mg(OH) 2 formation. Those processes, however, are too complicated to clarify the contributions of each process in the present paper and further studies are required.
Acknowledgements This work was partly supported by a Grant-in-Aid for Scientific Research on Priority Areas A of ‘New Protium Function’ of the Ministry of Education, Science, Sports and Culture of Japan.
References
Fig. 7. The relationship between the degradation constant k and discharge current density.
[1] J.J. Reilly, R.H. Wiswall Jr., Inorganic Chem. 7 (11) (1968) P2254– P2256. [2] D. Sun, Y. Lei, W. Liu, J. Jiang, J. Wu, Q. Wang, J. Alloys Comp. 231 (1995) 621–624. [3] T. Kohno, S. Tsuruta, M. Kanda, J. Electrochem. Soc. 143 (9) (1996) PL198–PL199. [4] N. Cui, B. Luan, H. Zhao, H. Liu, S. Dou, J. Alloys Comp. 233 (1996) 236–240. [5] C. Iwakura, S. Nohara, H. Inoue, Y. Fukumoto, Chem. Commun. (1996) P1831–P1832. [6] S. Orimo, H. Fujii, K. Ikeda, Acta Mater. 45 (1) (1997) P331–P341. [7] L. Berlouis, E. Cabrera, E. Hall-Barientos, P. Hall, S. Dodd, S. Morris, M. Imam, J. Alloys Comp. 305 (2000) 82–89. [8] J. Woo, K. Lee, J. Electrochem. Soc. 146 (3) (1999) 819–823. [9] Y.Q. Lei, Y.M. Wu, Q.M. Wang, J. Wu, Q.D. Wang, Z. Phys. Chem. 181 (1993) 379. [10] S. Kim, J. Lee, Int. J. Hydrogen Energy 19 (11) (1994) 911–915.
D. Mu et al. / Journal of Alloys and Compounds 334 (2002) 232 – 237 [11] H.H. Lee, J.Y. Lee, J. Alloys Comp. 270 (1998) 142–144. [12] J. Xue, G. Li, Y. Hu, J. Du, C. Wang, G. Hu, J. Alloys Comp. 307 (2000) 240–244. [13] J.L. Luo, N. Cui, J. Alloys Comp. 264 (1998) 299–305. [14] S. Han, P. Lee, J. Lee, A. Zuttel, L. Schlapbach, J. Alloys Comp. 306 (2000) 219–226. [15] Y. Hatano, T. Tachikawa, D. Mu, T. Abe, K. Watanabe, S. Morozumi, J. Alloys Comp. (in press).
237
[16] K. Watanabe, W. Shu, K. Mizukami, K. Kobayashi, Y. Hatano, S. Morozumi, J. Alloys Comp. 293–295 (1999) 626–631. [17] J. Crank, The Mathematics of Diffusion, 2nd Edition, Oxford University Press, Oxford, 1975. [18] T. Abe, T. Tachikawa, Y. Hatano, K. Watanabe, J. Alloys Comp. (in press).