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Determination of hydrogen diffusion coefficient in metal hydride electrode by modified Warburg impedance
Journal of Alloys and Compounds 329 (2001) 115–120
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Determination of hydrogen diffusion coefficient in metal hydride electrode by modified Warburg impedance Xianxia Yuan*, Naixin Xu Shanghai Institute of Metallurgy, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, PR China Received 29 November 2000; received in revised form 10 May 2001; accepted 10 May 2001
Abstract Hydrogen diffusion coefficients in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode as a function of depth of discharge (DOD) and temperature were evaluated with modified Warburg impedance which describes more precisely the practical diffusion behavior. It was found that hydrogen diffusion coefficient in this electrode increases with the increase in DOD at ambient temperature, and for this electrode with 50% DOD, hydrogen diffusion coefficient increases with the increase of temperature and the activation energy for hydrogen diffusion in it is 35 kJ mol 21 . 2001 Elsevier Science B.V. All rights reserved. Keywords: Metal hydride electrode; Hydrogen diffusion coefficient; Modified Warburg impedance
1. Introduction Recently, nickel–metal hydride batteries (Ni / MH) have been developed and commercialized because of their inherent advantages over conventional nickel–cadmium batteries with respect to storage capacity, cleanness and tolerance to overcharging and overdischarging [1,2]. In general, the characteristics of negative electrode of Ni / MH battery, namely metal hydride electrode, is affected not only by the composition, preparation condition, particle size of the alloy powder and the forming conditions of the electrode, but also by the diffusion of hydrogen in the alloy together with charge-transfer reactions on the alloy surface [2]. Since diffusion can be a rate-determining step of the charge–discharge process of metal hydride electrode, it must be a key factor for evaluating the properties of this electrode and the integrated Ni / MH battery. The hydrogen diffusion coefficient is an important parameter to understand the diffusion behavior of hydrogen atom in metal hydride electrode, and the larger is the diffusion coefficient, the faster is the hydrogen diffusion and the better is the electrode performance [3]. So, hydrogen diffusion coefficient should be determined in the study of hydrogen storage alloy, metal hydride electrode and Ni / MH battery. Till now, there have been a large number of reports for *Corresponding author. Tel.: 186-21-6251-1070-8803; fax: 186-216225-4273. E-mail address: [email protected] (X. Yuan).
determining the diffusion coefficient of hydrogen in metals such as Pd and Ni and alloys such as TiFe, Mg 2 Ni, NiZr and LaNi 5 using quasi-elastic neutron scattering, nuclear magnetic resonance, potential or current intermittent titration, constant current discharge, potential step, current pulse relaxation, and transition region of diffusion-controlled impedance in Nyquist plot. However, Warburg impedance especially modified Warburg impedance has not been used to calculate hydrogen diffusion coefficient in metal hydride electrode. In the present research, the hydrogen diffusion coefficients in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with various depth of discharge (DOD) at room temperature and with 50% DOD at various temperatures have been evaluated with modified Warburg impedance, and the activation energy for hydrogen diffusion in it is also calculated.
2. Experimental The MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 alloy was prepared from component metals with the purity of at least 99.9 wt.% in vacuum medium frequency induction furnace. To assure the homogeneity of the alloy, the ingot was turned over and remelted five times. Then, the ingot was crushed and ground mechanically followed by capturing particles with two sequential sieves, and the particle size of the resulting powders was measured by Malvern particle analyzer
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01569-9
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Mastersizer2000 which gives an average particle diameter of 125.2 mm. The metal hydride electrodes were prepared by mixing the alloy powder and nickel powder (Inco company, Canada) in a weight ratio of 1:4 followed by pressing at room temperature onto both sides of a nickel foam under the pressure of 1.8310 8 Pa for 1 min. The resulting pellet had a diameter of 15 mm and a thickness of 1.68 mm and weighed 1.5 g. Electrochemical measurements of the metal hydride electrodes were performed in a glass cell with three compartments by means of EG&G Princeton Applied Research Potentiostat / Galvanostat Model 273A and Lockin Amplifier 5210 driven by the software of M270 or Powersine in the package of Powersuite. In addition to the metal hydride electrode as working electrode, a nickel hydroxide electrode with an excessive capacity was employed as the counter electrode, a Hg / HgO electrode (in 6 mol l 21 KOH) as the reference electrode and 6 mol l 21 KOH solution as the electrolyte. The activated metal hydride electrode was charged at 60 21 mA g (based on the amount of alloy powder) for 7.5 h, after a rest of 10 min, it was discharged at 60 mA g 21 for a certain period of time to reach a specified DOD (defined by Eq. (1)) at room temperature. After a rest of 2 h for the open-circuit potential to get stabilized, the electrochemical impedance spectrum of the electrode was measured with AC perturbation of 5 mV as amplitude and in the frequency range of 0.001 Hz|100 kHz. idtd DOD 5 ] 3 100% Q
(1)
Here, Q is the capacity of the activated metal hydride electrode, i d and t d are discharge current and discharge time, respectively. For the experiments at various temperatures, the electrodes were initially charged at 60 mA g 21 for 7.5 h and discharged at the same current to 50% DOD at ambient temperature, after a rest of 2 h at the specified temperature for the open-circuit potential to get stabilized, the electrochemical impedance of the electrode was measured.
3. Results and discussion Assuming that the alloy particles in the metal hydride electrode are in spherical form with uniform size, the diffusion equation can be written as [4]: ≠C(r, t) ≠ 2 C(r, t) 2 ≠C(r, t) ]] 5 D ]]] 1 D ] ]] 2 ≠t r ≠r ≠r
(2)
where D is the hydrogen diffusion coefficient (cm 2 s 21 ), r is the distance from the center of the sphere (cm), t is time (s), and C(r, t) is the hydrogen concentration at the site of r in the alloy and at the time of t. Supposing that the initial
hydrogen concentration in the bulk of the alloy is uniform (C0 ), when a small sinuous AC-voltage is imposed on the metal hydride electrode system, the initial and boundary conditions can be mathematically represented as [5]: [C(r, t)] t50 5 C0 ≠C(r, t) F]] G ≠r ≠C(r, t) F]] G ≠r
(3) (4)
r 50
r 5d
Imax sin v t 5 ]]] nFD
(5)
where d is the average radius of the spherical alloy particles, Imax is the amplitude of AC responding current, v is angular frequency, F is faradic constant (96485 C mol 21 ), n is the number of the transferred electrons. Solving the diffusion equation (2) with these conditions and substituting the result into Eq. (6) which is the definition of the faradic impedance of an electrochemical system yields the specific expression for the faradic impedance as Eq. (7) which is a linear combination of the charge-transfer resistance (R t ) and the diffusion impedance (Warburg impedance – Zv ) [6,7]:
F
S
D G
dh ≠i dC(r, t) ≠i Zf 5 ] 5 ]] ]] 1 ] di dh ≠h ≠(r, t)
d ≠h Zf 5 R t 1 Zv 5 ] 1 ] (1 2 j) Œ] ≠i v
21
(6) (7)
Here, h is the reaction overpotential, i is the resulting reaction current, j is the square root of 21, d is the Warburg coefficient which is given as: RT d 5 ]]]] Œ]2n 2 F 2Œ] DC0
(8)
In Eq. (8), R is the gas constant (8.314 kJ K 21 mol 21 ), T is the absolute temperature (K). According to Eq. (7), the Warburg impedance in the Nyquist plot should exhibit a straight line with the angle of 458 against the real axis, and the real (Re) or the imaginary (Im) component of the Warburg impedance is proportional to the reciprocal of the square root of the angular frequency. So, the plot of Im (or Re) vs. v 21 / 2 exhibits a straight line and the slope of it gives the Warburg coefficient d. Thus, the value of D can be evaluated with Eq. (8). This method has been used by C. Ho et al. [8] and R.D. Armstrong [9] to extract diffusion coefficients of Li 1 in WO 3 and IrCl 622 in poly(4-vinyl pyridine), respectively. However, the experimental Warburg impedance measured on metal hydride electrode is significantly different from the theoretical behavior expressed by Eq. (7), i.e. the measured Warburg straight line always deviates from 458 due to the porosity effects [10] or fractal geometry effects [11,12] of the electrode surface. Similar results have also been published in the literature concerning insertion of hydrogen in WO 3 [13], insertion of lithium in V2 O 5 [14] or
X. Yuan, N. Xu / Journal of Alloys and Compounds 329 (2001) 115 – 120
117
Fig. 3. DOD dependence of hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode at room temperature.
Fig. 1. Illustration of the determination of f3 a .
the reaction on polymer film coated electrodes [9,15]. In view of this fact, R. Cabanel and co-workers [16] modified the conventional formula of Warburg impedance into:
ap ap Zw 5 K cos ] 2 j sin ] 4 4
F
G Yw
a/2
(9)
where K is a constant, and a is between zero and two. So, the value of a can be extracted from the slope of the Warburg straight line in the Nyquist plot, and the value of D can be evaluated with 2pf3 a d 2 D 5 ]]]]]] 2 /a ap 2 cos ] 4
F
S DG
(10)
Here, f3 a is the frequency where the two asymptotes in the log(Im / K) vs. log f plot intersects as shown in Fig. 1 [16]. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with various DOD at room temperature are shown in Fig. 2 and the calculated values of D as a function of DOD is shown in Fig. 3. It can be seen that the hydrogen diffusion coefficient increases with the increase in DOD of the metal hydride electrode and increasing DOD from 0 to 100% caused the hydrogen diffusion coefficient at room temperature to increase from 4.773 10 26 to 3.75310 25 cm 2 s 21 . This is in good agreement with the result of Chiaki Iwakura [17] that the hydrogen diffusion coefficient in MmNi 4.2 Al 0.5 M 0.3 (M5Cr, Mn, Fe, Co, Ni) alloy increases with the decrease of hydrogen concentration in it. The probable reason for the DOD dependence of hydrogen diffusion coefficient is that at low DOD, the hydrogen concentration is higher and the vacant
Fig. 2. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with various DOD at room temperature (the amplitude of AC perturbation was 5 mV and the frequency covered from 100 kHz to 0.001 Hz).
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Fig. 4. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD at various temperatures (the amplitude of AC perturbation was 5 mV and the frequency covered from 100 kHz to 0.001 Hz).
sites available for hydrogen to occupy are less than that at high DOD, and as the first step of hydrogen diffusion during the discharge of metal hydride electrode, the absorbed hydrogen must transform into the adsorbed hydrogen, namely transformation of the electrode active material from metal hydride in b phase into solid solution in a phase. As a result, the diffusion of hydrogen is influenced not only by its concentration but also by phase transformation in the active material of the electrode at low DOD. At high DOD, however, hydrogen concentration is
so low that hydrogen atoms mainly exist as adsorbed hydrogen which makes the phase transformation not a necessary prerequisite, and the available sites for hydrogen to occupy is sufficient, so diffusion of hydrogen will not be limited by the two factors described above and the diffusion coefficient is larger. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD at various temperatures are shown in Fig. 4 and the calculated values of D as a function of temperature is shown in Fig. 5. It is obvious
Fig. 5. Temperature dependence of hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD.
X. Yuan, N. Xu / Journal of Alloys and Compounds 329 (2001) 115 – 120
that the hydrogen diffusion coefficient increases with the increase of temperature, and the activation energy for hydrogen diffusion in this electrode is calculated to be 35 kJ mol 21 with Arrhenius equation. This is in good agreement with the results of 35.4 kJ mol 21 obtained by ¨ Zuchner and Rauf [18] for hydrogen diffusion in LaNi 5 with current pulse relaxation method. Comparing the obtained values of hydrogen diffusion coefficient in this research with the values reported for alloys with similar composition in the literature indicates that the results of this study are much larger. For example, Lundqvist and Lindbergh [19] got the conclusion that hydrogen diffusion coefficient in MmNi 3.6 Co 0.8 Mn 0.4 Al 0.3 is (1.360.3)310 29 cm 2 s 21 , Kim et al. [20] and Chen et al. [21] showed that hydrogen diffusion coefficient in MmNi 3.55 Co 0.75 Mn 0.4 Al 0.3 varies from 10 29 to 10 210 cm 2 s 21 , Nishina et al. [22] got the value of (6.260.7)3 10 29 cm 2 s 21 for MlNi 4.0 Co 0.4 Mn 0.3 Al 0.3 , and Cai et al. [23] obtained that hydrogen diffusion coefficient in Mm 0.8 La 0.2 Ni 3.5 MnAl 0.1 Co 0.4 lies in the range from 1.94310 28 to 1.74310 27 cm 2 s 21 . Similar phenomenon has also been found in the reported values for hydrogen diffusion coefficient in the same alloy or in the alloys with similar composition. Values of 3.4310 210 [21] and (2.4660.35)310 27 cm 2 s 21 [24] have been evaluated for hydrogen diffusion coefficient in MmNi 4.5 Mn 0.5 . Hydrogen diffusion coefficient in LaNi 4.25 Al 0.75 [25], LaNi 4.5 Al 0.5 [22] and MmNi 4 Al [23] have been determined to be (2.97–3.30)310 211 , (5.260.6)310 29 and 2.86310 27 cm 2 s 21 , respectively. The values of hydrogen diffusion coefficient in LaNi 5 have been found to be scattered on the order of 10 26 [26,27], 10 27 [28], 10 28 [29–31] and 10 29 cm 2 s 21 [19], respectively. The great discrepancy in the reported values of hydrogen diffusion coefficient in alloys with the same composition or with similar composition as described above can be attributed to several reasons. Due to different preparation processes, alloys with similar composition or even the same composition might have different microstructure, thermodynamic and kinetic performance. In addition, each used technique has its own theoretical background and specific simplification has been made during the deduction of the necessary formulae for calculation of D. This results in some differences in essential significance of the defined diffusion coefficient in different techniques. Finally, the different measurement details, such as pellet electrode [21,23], alloy film [24], microelectrode with single alloy particle [19,20,22], solid–gas environment [26–30] and solid–liquid environment [25,31], are other causes of the discrepancy. From our experience, comparison of hydrogen diffusion coefficient in different alloys or in the same alloy in different states should preferentially be made with the values obtained by the same method.
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4. Conclusions 1. Hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode increases with the increase in DOD at room temperature. 2. Hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD increases with the increase in temperature, the activation energy for hydrogen diffusion in it is 35 kJ mol 21 .
References [1] C. Iwakura, M. Matsuka, Prog. Batteries & Battery Mater. 10 (1992) 81. [2] K. Naito, T. Matsunami, K. Okuno, M. Matsuoka, C. Iwakura, J. Appl. Electrochem. 23 (1993) 1051. [3] T. Nishna, H. Ura, I. Uchida, J. Electrochem. Soc. 144 (1997) 1273. [4] A.J. Bard, L.R. Faulkner (Eds.), Electrochemical Methods Fundamentals and Application, John Wiley & Sons, Inc, New York, 1980, p. 132. [5] Q. Zha (Ed.), Kinetics of Electrode Process, 2nd Edition, Science Press, Beijing, 1987, p. 278. [6] R. Greef, R. Peat, L.M. Peter et al., in: T.J. Kemp (Ed.), Instrumental Methods in Electrochemistry, John Wiley & Sons, Inc, 1986, p. 265. [7] S. Motupally, C.C. Streinz, J.W. Weidner, J. Electrochem. Soc. 142 (5) (1995) 1401. [8] C. Ho, I.D. Raistrick, R.A. Huggins, J. Electrochem. Soc. 127 (1980) 343. [9] R.D. Armstrong, B. Lindholm, M. Sharp, J. Electroanal. Chem. 202 (1986) 69. [10] L.M. Gassa, J.R. Vilche, M. Ebert, K. Juttner, W.J. Lorenz, J. Appl. Electrochem. 20 (1990) 677. [11] T. Pajkossy, L. Nyikos, Electrochim. Acta 34 (1989) 171. [12] B. Sapoval, Solid State Ionics 23 (1987) 253. [13] J.-P. Randin, R. Viennet, J. Electrochem. Soc. 129 (1984) 2349. [14] J. Farcy, R. Messina, J. Perichon, J. Electrochem. Soc. 137 (1990) 1337. [15] C. Gabrielli, O. Haas, H. Takenouti, J. Appl. Electrochem. 17 (1987) 82. [16] R. Cabanel, G. Barral, J.-P. Diard, B. Le Gorrec, C. Montella, J. Appl. Electrochem. 23 (1993) 93. [17] C. Iwakura, T. Oura, H. Inoue et al., J. Electroanal. Chem. 398 (1995) 37. ¨ [18] H. Zuchner, T. Rauf, J. Less-Common Met. 172–174 (1991) 611. [19] A. Lundqvist, G. Lindbergh, J. Electrochem. Soc. 145 (11) (1998) 3740. [20] H.-S. Kim, M. Nishizawa, I. Uchida, Electrochim. Acta 45 (1999) 483. [21] J. Chen, S.X. Dou, D.H. Bradhurst, H.K. Liu, Int. J. Hydrogen Energy 23 (3) (1998) 177. [22] T. Nishina, H. Ura, I. Uchida, J. Electrochem. Soc. 144 (4) (1997) 1273. [23] C. Cai, D. Zhao, B. Wang, Chin. J. Power Sources 17 (5) (1993) 9. [24] J. Cao, Z. Zhou, C. Wang, Y. Jia, L. He, Chem. J. Chin. Univ. 9 (9) (1988) 957. [25] G. Zheng, B.N. Popov, R.E. White, J. Electrochem. Soc. 143 (3) (1996) 834. [26] E. Khodosov, A. Linnik, G. Kobsenko, V. Ivanchenko, in: Proceedings of the 2nd International Congress on Hydrogen in Metals, Paper 1D10, Pairs, 1977, Pergamon Press, Oxford, 1977.
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[27] P. Fischer, A. Furrer, G. Busch, L. Schlapbach, Helv. Phys. Acta 50 (1977) 421. [28] E.F. Kohdosov, A.I. Linnik, G.F. Kobsenko, V.G. Evanchenko, Phys. Met. Metall. 44 (1977) 187. [29] R.C. Bowman, D.M. Gruen, M.H. Mendelsohn, Solid State Commun. 32 (1979) 501.
¨ [30] E. Lebsanft, D. Richter, J. Topler, Z. Phys. Chem., N.F. 116 (1979) 175. ¨ [31] H. Zuchner, T. Rauf, J. Less-Common Met. 172–174 (1991) 611– 617.
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Determination of hydrogen diffusion coefficient in metal hydride electrode by modified Warburg impedance Xianxia Yuan*, Naixin Xu Shanghai Institute of Metallurgy, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, PR China Received 29 November 2000; received in revised form 10 May 2001; accepted 10 May 2001
Abstract Hydrogen diffusion coefficients in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode as a function of depth of discharge (DOD) and temperature were evaluated with modified Warburg impedance which describes more precisely the practical diffusion behavior. It was found that hydrogen diffusion coefficient in this electrode increases with the increase in DOD at ambient temperature, and for this electrode with 50% DOD, hydrogen diffusion coefficient increases with the increase of temperature and the activation energy for hydrogen diffusion in it is 35 kJ mol 21 . 2001 Elsevier Science B.V. All rights reserved. Keywords: Metal hydride electrode; Hydrogen diffusion coefficient; Modified Warburg impedance
1. Introduction Recently, nickel–metal hydride batteries (Ni / MH) have been developed and commercialized because of their inherent advantages over conventional nickel–cadmium batteries with respect to storage capacity, cleanness and tolerance to overcharging and overdischarging [1,2]. In general, the characteristics of negative electrode of Ni / MH battery, namely metal hydride electrode, is affected not only by the composition, preparation condition, particle size of the alloy powder and the forming conditions of the electrode, but also by the diffusion of hydrogen in the alloy together with charge-transfer reactions on the alloy surface [2]. Since diffusion can be a rate-determining step of the charge–discharge process of metal hydride electrode, it must be a key factor for evaluating the properties of this electrode and the integrated Ni / MH battery. The hydrogen diffusion coefficient is an important parameter to understand the diffusion behavior of hydrogen atom in metal hydride electrode, and the larger is the diffusion coefficient, the faster is the hydrogen diffusion and the better is the electrode performance [3]. So, hydrogen diffusion coefficient should be determined in the study of hydrogen storage alloy, metal hydride electrode and Ni / MH battery. Till now, there have been a large number of reports for *Corresponding author. Tel.: 186-21-6251-1070-8803; fax: 186-216225-4273. E-mail address: [email protected] (X. Yuan).
determining the diffusion coefficient of hydrogen in metals such as Pd and Ni and alloys such as TiFe, Mg 2 Ni, NiZr and LaNi 5 using quasi-elastic neutron scattering, nuclear magnetic resonance, potential or current intermittent titration, constant current discharge, potential step, current pulse relaxation, and transition region of diffusion-controlled impedance in Nyquist plot. However, Warburg impedance especially modified Warburg impedance has not been used to calculate hydrogen diffusion coefficient in metal hydride electrode. In the present research, the hydrogen diffusion coefficients in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with various depth of discharge (DOD) at room temperature and with 50% DOD at various temperatures have been evaluated with modified Warburg impedance, and the activation energy for hydrogen diffusion in it is also calculated.
2. Experimental The MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 alloy was prepared from component metals with the purity of at least 99.9 wt.% in vacuum medium frequency induction furnace. To assure the homogeneity of the alloy, the ingot was turned over and remelted five times. Then, the ingot was crushed and ground mechanically followed by capturing particles with two sequential sieves, and the particle size of the resulting powders was measured by Malvern particle analyzer
0925-8388 / 01 / $ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 01 )01569-9
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Mastersizer2000 which gives an average particle diameter of 125.2 mm. The metal hydride electrodes were prepared by mixing the alloy powder and nickel powder (Inco company, Canada) in a weight ratio of 1:4 followed by pressing at room temperature onto both sides of a nickel foam under the pressure of 1.8310 8 Pa for 1 min. The resulting pellet had a diameter of 15 mm and a thickness of 1.68 mm and weighed 1.5 g. Electrochemical measurements of the metal hydride electrodes were performed in a glass cell with three compartments by means of EG&G Princeton Applied Research Potentiostat / Galvanostat Model 273A and Lockin Amplifier 5210 driven by the software of M270 or Powersine in the package of Powersuite. In addition to the metal hydride electrode as working electrode, a nickel hydroxide electrode with an excessive capacity was employed as the counter electrode, a Hg / HgO electrode (in 6 mol l 21 KOH) as the reference electrode and 6 mol l 21 KOH solution as the electrolyte. The activated metal hydride electrode was charged at 60 21 mA g (based on the amount of alloy powder) for 7.5 h, after a rest of 10 min, it was discharged at 60 mA g 21 for a certain period of time to reach a specified DOD (defined by Eq. (1)) at room temperature. After a rest of 2 h for the open-circuit potential to get stabilized, the electrochemical impedance spectrum of the electrode was measured with AC perturbation of 5 mV as amplitude and in the frequency range of 0.001 Hz|100 kHz. idtd DOD 5 ] 3 100% Q
(1)
Here, Q is the capacity of the activated metal hydride electrode, i d and t d are discharge current and discharge time, respectively. For the experiments at various temperatures, the electrodes were initially charged at 60 mA g 21 for 7.5 h and discharged at the same current to 50% DOD at ambient temperature, after a rest of 2 h at the specified temperature for the open-circuit potential to get stabilized, the electrochemical impedance of the electrode was measured.
3. Results and discussion Assuming that the alloy particles in the metal hydride electrode are in spherical form with uniform size, the diffusion equation can be written as [4]: ≠C(r, t) ≠ 2 C(r, t) 2 ≠C(r, t) ]] 5 D ]]] 1 D ] ]] 2 ≠t r ≠r ≠r
(2)
where D is the hydrogen diffusion coefficient (cm 2 s 21 ), r is the distance from the center of the sphere (cm), t is time (s), and C(r, t) is the hydrogen concentration at the site of r in the alloy and at the time of t. Supposing that the initial
hydrogen concentration in the bulk of the alloy is uniform (C0 ), when a small sinuous AC-voltage is imposed on the metal hydride electrode system, the initial and boundary conditions can be mathematically represented as [5]: [C(r, t)] t50 5 C0 ≠C(r, t) F]] G ≠r ≠C(r, t) F]] G ≠r
(3) (4)
r 50
r 5d
Imax sin v t 5 ]]] nFD
(5)
where d is the average radius of the spherical alloy particles, Imax is the amplitude of AC responding current, v is angular frequency, F is faradic constant (96485 C mol 21 ), n is the number of the transferred electrons. Solving the diffusion equation (2) with these conditions and substituting the result into Eq. (6) which is the definition of the faradic impedance of an electrochemical system yields the specific expression for the faradic impedance as Eq. (7) which is a linear combination of the charge-transfer resistance (R t ) and the diffusion impedance (Warburg impedance – Zv ) [6,7]:
F
S
D G
dh ≠i dC(r, t) ≠i Zf 5 ] 5 ]] ]] 1 ] di dh ≠h ≠(r, t)
d ≠h Zf 5 R t 1 Zv 5 ] 1 ] (1 2 j) Œ] ≠i v
21
(6) (7)
Here, h is the reaction overpotential, i is the resulting reaction current, j is the square root of 21, d is the Warburg coefficient which is given as: RT d 5 ]]]] Œ]2n 2 F 2Œ] DC0
(8)
In Eq. (8), R is the gas constant (8.314 kJ K 21 mol 21 ), T is the absolute temperature (K). According to Eq. (7), the Warburg impedance in the Nyquist plot should exhibit a straight line with the angle of 458 against the real axis, and the real (Re) or the imaginary (Im) component of the Warburg impedance is proportional to the reciprocal of the square root of the angular frequency. So, the plot of Im (or Re) vs. v 21 / 2 exhibits a straight line and the slope of it gives the Warburg coefficient d. Thus, the value of D can be evaluated with Eq. (8). This method has been used by C. Ho et al. [8] and R.D. Armstrong [9] to extract diffusion coefficients of Li 1 in WO 3 and IrCl 622 in poly(4-vinyl pyridine), respectively. However, the experimental Warburg impedance measured on metal hydride electrode is significantly different from the theoretical behavior expressed by Eq. (7), i.e. the measured Warburg straight line always deviates from 458 due to the porosity effects [10] or fractal geometry effects [11,12] of the electrode surface. Similar results have also been published in the literature concerning insertion of hydrogen in WO 3 [13], insertion of lithium in V2 O 5 [14] or
X. Yuan, N. Xu / Journal of Alloys and Compounds 329 (2001) 115 – 120
117
Fig. 3. DOD dependence of hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode at room temperature.
Fig. 1. Illustration of the determination of f3 a .
the reaction on polymer film coated electrodes [9,15]. In view of this fact, R. Cabanel and co-workers [16] modified the conventional formula of Warburg impedance into:
ap ap Zw 5 K cos ] 2 j sin ] 4 4
F
G Yw
a/2
(9)
where K is a constant, and a is between zero and two. So, the value of a can be extracted from the slope of the Warburg straight line in the Nyquist plot, and the value of D can be evaluated with 2pf3 a d 2 D 5 ]]]]]] 2 /a ap 2 cos ] 4
F
S DG
(10)
Here, f3 a is the frequency where the two asymptotes in the log(Im / K) vs. log f plot intersects as shown in Fig. 1 [16]. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with various DOD at room temperature are shown in Fig. 2 and the calculated values of D as a function of DOD is shown in Fig. 3. It can be seen that the hydrogen diffusion coefficient increases with the increase in DOD of the metal hydride electrode and increasing DOD from 0 to 100% caused the hydrogen diffusion coefficient at room temperature to increase from 4.773 10 26 to 3.75310 25 cm 2 s 21 . This is in good agreement with the result of Chiaki Iwakura [17] that the hydrogen diffusion coefficient in MmNi 4.2 Al 0.5 M 0.3 (M5Cr, Mn, Fe, Co, Ni) alloy increases with the decrease of hydrogen concentration in it. The probable reason for the DOD dependence of hydrogen diffusion coefficient is that at low DOD, the hydrogen concentration is higher and the vacant
Fig. 2. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with various DOD at room temperature (the amplitude of AC perturbation was 5 mV and the frequency covered from 100 kHz to 0.001 Hz).
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Fig. 4. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD at various temperatures (the amplitude of AC perturbation was 5 mV and the frequency covered from 100 kHz to 0.001 Hz).
sites available for hydrogen to occupy are less than that at high DOD, and as the first step of hydrogen diffusion during the discharge of metal hydride electrode, the absorbed hydrogen must transform into the adsorbed hydrogen, namely transformation of the electrode active material from metal hydride in b phase into solid solution in a phase. As a result, the diffusion of hydrogen is influenced not only by its concentration but also by phase transformation in the active material of the electrode at low DOD. At high DOD, however, hydrogen concentration is
so low that hydrogen atoms mainly exist as adsorbed hydrogen which makes the phase transformation not a necessary prerequisite, and the available sites for hydrogen to occupy is sufficient, so diffusion of hydrogen will not be limited by the two factors described above and the diffusion coefficient is larger. Nyquist plots of MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD at various temperatures are shown in Fig. 4 and the calculated values of D as a function of temperature is shown in Fig. 5. It is obvious
Fig. 5. Temperature dependence of hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD.
X. Yuan, N. Xu / Journal of Alloys and Compounds 329 (2001) 115 – 120
that the hydrogen diffusion coefficient increases with the increase of temperature, and the activation energy for hydrogen diffusion in this electrode is calculated to be 35 kJ mol 21 with Arrhenius equation. This is in good agreement with the results of 35.4 kJ mol 21 obtained by ¨ Zuchner and Rauf [18] for hydrogen diffusion in LaNi 5 with current pulse relaxation method. Comparing the obtained values of hydrogen diffusion coefficient in this research with the values reported for alloys with similar composition in the literature indicates that the results of this study are much larger. For example, Lundqvist and Lindbergh [19] got the conclusion that hydrogen diffusion coefficient in MmNi 3.6 Co 0.8 Mn 0.4 Al 0.3 is (1.360.3)310 29 cm 2 s 21 , Kim et al. [20] and Chen et al. [21] showed that hydrogen diffusion coefficient in MmNi 3.55 Co 0.75 Mn 0.4 Al 0.3 varies from 10 29 to 10 210 cm 2 s 21 , Nishina et al. [22] got the value of (6.260.7)3 10 29 cm 2 s 21 for MlNi 4.0 Co 0.4 Mn 0.3 Al 0.3 , and Cai et al. [23] obtained that hydrogen diffusion coefficient in Mm 0.8 La 0.2 Ni 3.5 MnAl 0.1 Co 0.4 lies in the range from 1.94310 28 to 1.74310 27 cm 2 s 21 . Similar phenomenon has also been found in the reported values for hydrogen diffusion coefficient in the same alloy or in the alloys with similar composition. Values of 3.4310 210 [21] and (2.4660.35)310 27 cm 2 s 21 [24] have been evaluated for hydrogen diffusion coefficient in MmNi 4.5 Mn 0.5 . Hydrogen diffusion coefficient in LaNi 4.25 Al 0.75 [25], LaNi 4.5 Al 0.5 [22] and MmNi 4 Al [23] have been determined to be (2.97–3.30)310 211 , (5.260.6)310 29 and 2.86310 27 cm 2 s 21 , respectively. The values of hydrogen diffusion coefficient in LaNi 5 have been found to be scattered on the order of 10 26 [26,27], 10 27 [28], 10 28 [29–31] and 10 29 cm 2 s 21 [19], respectively. The great discrepancy in the reported values of hydrogen diffusion coefficient in alloys with the same composition or with similar composition as described above can be attributed to several reasons. Due to different preparation processes, alloys with similar composition or even the same composition might have different microstructure, thermodynamic and kinetic performance. In addition, each used technique has its own theoretical background and specific simplification has been made during the deduction of the necessary formulae for calculation of D. This results in some differences in essential significance of the defined diffusion coefficient in different techniques. Finally, the different measurement details, such as pellet electrode [21,23], alloy film [24], microelectrode with single alloy particle [19,20,22], solid–gas environment [26–30] and solid–liquid environment [25,31], are other causes of the discrepancy. From our experience, comparison of hydrogen diffusion coefficient in different alloys or in the same alloy in different states should preferentially be made with the values obtained by the same method.
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4. Conclusions 1. Hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode increases with the increase in DOD at room temperature. 2. Hydrogen diffusion coefficient in MlNi 3.75 Co 0.65 Mn 0.4 Al 0.2 metal hydride electrode with 50% DOD increases with the increase in temperature, the activation energy for hydrogen diffusion in it is 35 kJ mol 21 .
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