Study of the hydriding kinetics of LaNi4.7Al0.3H system by a step-wise method

Journal of the Less-Common

Metals, 159 ( 1990) 109-

STUDY OF THE HYDRIDING A STEP-WISE METHOD

X.-L. WANG*

June

KINETICS

OF LaNi,.,AI,,,-H

SYSTEM

BY

and S. SUDA

Llepurtment of Chemical Engineering, I92 (Japan) (Received

109

119

Kogakuin University 2665-I, Nakano-machi,

Hachioji-shi, Tokyo

10, 1989)

Summary

The hydriding kinetics of activated LaNi,,,Al,,,-H were determined under isochoric and variable pressure conditions by applying step-wise changes of the hydrogen concentration. Experiments were performed in three different phases from the a to p phases under isothermal conditions. A rate equation was derived by taking account of the reversible nature of the hydriding and dehydriding reactions

Reactions were observed to proceed differently in the three phases, i.e. in the a, a + B and B phases. Reaction rates in the a and ,4 phases are much faster than those in the two-phase (a + p) region. The reaction orders with respect to hydrogen pressure and hydrogen concentration H/M were found to be considerably different in each phase. It is concluded that the rate-controlling step in the hydriding reaction changes with the phase changes. In the a, a + /?and /I phase regions, the rate-controlling step was characterized as the surface reaction, nucleation and growth, and diffusion of hydrogen atoms to the hydride layer respectively.

1. Introduction

The most important factor in the study of hydriding kinetics is the reduction in thermal effects during the course of the reaction. It is also important to establish an appropriate kinetic model which can reproduce experimental data by employing an appropriate rate-controlling step. As one of the typical hydriding materials, LaNi, generates heat during the hydriding reaction (exothermal reaction) at about - 7.2 kcal (mol H,))’ [l]. This

*On leave from The Department 0022-5088/90/$3.50

of Chemistry,

Nankai

University,

0 Elsevier

Tianjin,

Sequoia/Printed

China. in The Netherlands

110

evolution of heat would cause considerable temperature changes of the metal hydride bed if there were no device to release the heat and, as a result, hydrogen transfer rates would reduce dramatically. To avoid this, much effort has been taken to design reactors to secure rapid heat transfer [2-41. Among them, the doublewalled cell [2] which consists of two tubes with a 0.5 mm annular space as the reacting space has been used for detailed studies of metal hydride kinetics [5-81. Another method has been proposed in which hydride powders are mixed with inactive metallic compounds as thermal ballast such as nickel, aluminium or manganese in order to increase the heat capacity of the reacting materials and also to enhance the heat transmission through the hydride bed [9-131. Thermal effects have been significantly reduced by this method, although the high weight fraction (approximately 98%) of the ballasting materials might cause other experimental difficulties. Although Goode11 and Rudman [9] reported that it did not significantly affect the results, the catalytic effect of nickel powders cannot be ignored. Schlapbath et al. [14] has pointed out that the metallic nickel acts as a catalyst for the dissociation of hydrogen at the beginning of the hydriding process. Many equations have been proposed [2,3,5,8, 10-12, 15-191 although the kinetic models employed have been considered inappropriate to represent the experimental data. The rates were expressed only as a function of hydrogen pressure or otherwise as a function of H/M [9, 10, 19,201. Different rate constants at different levels of hydrogen pressure [21] and hydrogen concentration in MH [4] were reported. The aim of this paper is to present an experimental procedure suitable for a detailed study of the reaction kinetics in different phases, and to propose a rate equation by taking account of the reversible nature of the hydriding and dehydriding reactions. The equation proposed here will make it possible to account for both the effects of hydrogen pressure and H/M. An experimental technique called the step-wise method has been introduced in which consecutive changes of H/M caused by controlling the hydrogen pressure at any desired level lead the experimental runs as precisely as possible. By applying the proposed technique and using the double-walled reactor, temperature changes in the metal hydride bed can be reduced to a minimum level.

2. Experimental details The experiments were performed under isochoric and variable pressure conditions. A double-walled cell [2] immersed in a thermostated bath was used to secure high heat transfer. A sample of about 5 g was placed in the 0.5 mm thick space between the outer and inner tubes. Water of a given temperature was pumped through the inner tube to release heat and to maintain a uniform temperature in the sample bed. Data were taken after more than 40 times of repeated hydriding-dehydriding cycles at temperatures of 40-90 “C. The pressure changes were measured by an electronic pressure transducer with a Hewlett-Packard 3052A data acquisition system. Data were stored in a tape cartridge at 0.2 s intervals for 2 min after starting each experimental run.

111

Composition

[H/MI

Fig. 1. A schematic diagram showing the experimental hydriding reaction kinetics.

Atom

procedures

10

0.5

0.0

Ratio

[H/Ml

for determining

the isothermal

Fig. 2. Hydriding isotherms of the LaNi, ,A& 3-H system at 40-90 “C.

The experimental procedure of the step-wise method employed in this work is illustrated in Fig. 1. The hydriding reaction proceeds linearly from PO to P, or from n,, to n, in each run, where n, refers to the hydrogen concentration at the point where the reaction was started and POis the initial pressure. P, and + are the final equilibrium pressure and concentration respectively. The concentration YES in turn becomes the next starting concentration. Each run can be continued by changing the pressure in the gas reservoir to a higher level than the equilibrium pressure of the previous run. Figure 2 illustrates the hydriding P-C curves taken under several isothermal conditions.

3. Rate equation of hydriding reaction Solid particles and ideal gas law have been assumed under uniform temperature and composition conditions throughout the sample bed. The reversible relations between hydriding and dehydriding reactions are expressed by the following chemical equation:

The hydriding reaction rates can be expressed as a function of pressure and H/M under isothermal conditions. Both the rate constant k and the plateau pressure P, increase with temperature, the plateau pressure P, being defined as the average pressure in the plateau region at each P-C isotherm. For a given pressure, k is proportional to the reaction rate. However, the reaction rate is inversely proportional to the plateau pressure. Those effects of the rate constant k and plateau pressure P, on the reaction rates can be expressed by a specific term k/P,. As P, is a constant at a given isothermal condition, P/P, is

112

introduced instead of l/P, to express the temperature effect on the reaction rates. Subsequently, (P/P,)a is employed to reveal the reaction order with respect to hydrogen pressure as given in eqn. (2) a

0$

v+=k,

(2)

e

Similarly, the rate of the backward reaction (dehydriding order b is expressed as V_ =k,d

reaction) with reaction

(3)

The net rate of the hydriding reaction is given by the difference between the forward and backward reaction rates and the corresponding equation can be written as: dn dt = v+ - v=k,

$ ‘-kg’ 0 e

(4)

When dynamic equilibrium is reached, the net rate of the hydriding reaction must be zero as both reactions proceed at equal rates, so that:

(5) By substituting eqn. (5) into eqn. (4) one obtains

(6) Equation (6) is taken as the general rate equation in this work. P and Pf in eqn. (6) are pressures corresponding to the reacting condition and to the final equilibrium condition. The quantities 12and nr represent the hydrogen concentrations H/M at a given time elapsed t and at the final equilibrium pressure Pf respectively. The hydriding and dehydriding reaction rate constants are denoted by k, and k, respectively. The constant a is the order of the reaction with respect to the hydrogen pressure and the constant b is the order of the reaction with respect to H/M. In the above rate equation, the reaction rate is a function of both the hydrogen pressure and H/M. The rate constant k and the reaction orders a and b should be kept constant under isothermal conditions if there is no phase change from the a region to the a + /3 region or from the a + /3 region to the /? region.

113

4. Results 4.1. Effects of hydrogen concentration Hydriding kinetics have been observed at intervals of 10 “C in the temperature range of 40-90 “C and H/M has been varied from the a phase to the /3 phase. Figure 3 illustrates the reaction rates as a function of the hydrogen pressure and H/M at 40°C where the reaction order a and b were determined as 2 and 1 respectively. The reaction rate was found to be proportional to the pressure of the system and to H/M, although we found different slopes for the different phase regions. The values of a and b were determined as 1.5 and 1.0 in the a phase region, and as 2.0 and 1.0 in the a + /3 phase region. There were not enough data in this investigation to determine the a and b values for the B phase region. Similar behaviour was obtained for various hydrides corresponding to the a phase region at 60 “C, as shown in Fig. 4. Figure 5 presents data for the a phase region under various isothermal conditions, where each isotherm was taken starting from approximately 0.02 H/M and terminating at H/M close to 0.03. The relationships for H/M in the a + /3 phase region, ranging from 0.40 to 0.55, are illustrated in Fig. 6. The values determined from the slopes and the intercepts of each straight line are shown in Fig. 7 as a function of H/M. It is clear from Fig. 7 that the rate constants are classified into three groups according to the phases studied, i.e. the a, a + /3 and p phase regions. For the sake of clarity, the values at 60 “C in each phase region are listed in Table 1. The results indicate that the rate constants are constant regardless of the hydrogen concentration H/M in a given phase region. It was observed that the values of the rate constant in the a and /3 phase regions are much larger than in the a + p phase region.

F

.0020

E 1 6

.0015

.OOlO .0005

I(

,028.

.037

0

.037-

043

0 0 (P/P,)2

[l

Fig. 3. Hydriding reaction each phase at 40 “C. Fig. 4. Hydriding phase at 40 “C.

rates

(Pf/P)Z wq

rates

V.S.(P/PC)’ ‘{I

CP/PJ1.5

I

VS. ( P/Pe,)‘( 1-

.EJ

(P,/P)‘n/n,] at different

-(P,/F)’ ‘n/n,} at different

.lO I1

(Pf/Pl’.5

hydrogen

hydrogen

.15 hhfl

.20 I

concentrations

concentrations

in

in the GI

114 ,003

.

.

.

’

“, 80°C

* I..

”

70 “c

A

(P/PJ’.5 I1 (Pf/P)‘.5 b/n$

1

(P/P,)2 11 (Pr/PF wwl

Fig. 5. Hydriding reaction rates vs. (Pip,)’ ‘(1 - (P,/P)J,5 n / nr] a t several temperatures Reactions start from about 0.02 H/M and terminate at about 0.03 H/M. Fig. 6. Hydriding reaction rates vs. ( P/PC)‘{1 - ( Pf/P)2 n/n,) a t several temperatures region. Reactions start from about 0.40 H/M and terminated at about 0.55 H/M.

0

.l

2

3

.4

.5

.6

.7

.8

1

in the a phase.

in the a + p phase

.9

Hydride composition IWMI

Fig. 7. Rate constants at different hydrogen concentrations

at 60 “C.

4.2. Effects of hydrogen pressure The initial reaction rate is proportional to the hydrogen pressure in the reactor system. However, the rate constants are not influenced by the pressure within a given phase region (see Table 1). A detailed investigation has also been carried out by holding the initial pressure constant at a given H/M in order to study the pressure dependency of the reaction rates. The curves found for the hydriding reaction are shown in Fig. 8, the data pertaining to 0.35 MPa at 60 “C. The measured reaction rates depend on the phases present, the rates in the a and B phase regions being much faster than those in the a + /3 phase region. The rate constants calculated from these data are listed in Table 2.

TABLE 1 Rate constants under various hydrogen pressures and hydrogen concentrations concentration

at 60 “C Rate constants (sc’)x IO’

Hydrogen pressure

Hydrogen

(MPa)

(HIM)

0.039-0.033 0.067-0.062

0.0 12-0.020 0.020-0.028

1.70

0.105-0.098 0.1 18-O.114 0.147-0.135 0.276-0.165 0.334-0.187 0.347-0.2 I 1 0.362-0.242 0.409-0.3 14 1.062-0.952

0.028-0.037 0.037-0.043 0.043-0.054 0.054-0.183 0.183-0.370 0.370-0.540 0.540-0.690 0.600-0.804 0.804-0.886

1.70 1.60 1.80 0.49 0.52 0.5 I 0.49 0.55 12.70

I A0

0.6

Fig. 8. Hydriding curves under constant initial hydrogen pressure of 0.35 MPa at different hydrogen concentrations at 60 “C.

TABLE 2 Rate constants under the determining conditions of constant hydrogen pressure at 60 “C Hydrogen pressure

Hydrogen

Wa)

l HIM

(SC’)

181 1 0.3501-0.2057 0.350 l-O.232 1 0.3500-0.2462

0.077-0.289 0.289-0.47 1 0.47 l-0.6 19 0.6 I Y-O.725

0.00478 0.00456 0.00308 0.00433

0.3498-O.

concentration

Rate constants

116

It is clearly shown in eqn. (6) that the rate constant is independent of the pressure although the reaction rate is a function of the hydrogen pressure. The present study revealed that the rate constant is not a function of the hydrogen pressure. 4.3. Influence of hydriding-dehydriding cycles From the experimental point of view, two different types of experimental variables have been examined: (1) the number of hydriding-dehydriding cycles and (2) the volume of the gas reservoir. The number of hydriding-dehydriding cycles have been observed to influence the order of the reaction. This order has been determined to be equal to 2.0 with respect to the pressure after 40 repeating cycles. However, it is approximately 2.5 for the earlier stages of the activation treatments. The influence of the number of cycles and the time intervals during cycling have been extensively studied by Nomura [22]. Other factors which are considered to be of influence for the apparent discrepancies of kinetic data have been studied systematically by a Japanese group organized by the national research institutions, universities and private industries [22]. The rate constants were found to be not affected by the volume of the system. The results calculated by eqn. (6) for the two different cases (120.03 and 37.64 ml) are shown in Table 3. The activation energies in the a and a + /3phase regions can be evaluated from the experimental results shown in Fig. 9, i.e. from the Arrhenius plots of the rate constants of the hydriding reaction. The apparent activation energy is determined from the slope of each straight line to be 56.4 and 36.8 kJ (mol HZ)-’ respectively.

5. Discussion The results obtained in the present work indicate that a single step as the ratecontrolling step does not account for the hydriding reaction which starts in the a phase region and terminates in the /3 phase region, across the a + /?phase region.

TABLE 3 Rate constants at different system volumes at 60 “C 120.03 ml

37.64 ml

HIM

k(s-‘)

HIM

k(s-‘)

0.054-0.183 0.183-0.370 0.370-0.540 0.540-0.690 0.690-0.804

0.0049 0.0052 0.0051 0.0049 0.0050

0.033-0.081 0.081-0.197 0.197-0.360 0.360-0.52 1 0.521-0.675

0.0048 0.0048 0.0042 0.0045 0.0047

2.6

2.7

2.6

2.9

looo/r

3.0

3.1

II/K1

3.2

3.2

Solid solution

I

Hydride

m

phase

Fig. 9. Arrhenius plot for the hydriding reaction in the a phase region and the a + /3 phase region. Fig. 10 Schematic model of hydride formation during hydriding reaction: (a) formation of a hydrogen saturated solid solution (the a phase); (b) formation of the metal hydride near the surface (the a + /3 phase); (c) the growing hydride layer surrounds the a-solid solution; (d) the /I hydride.

The rate constant in a given phase region remains constant regardless of the changes in H/M. For an apparent reaction which does not involve a single phase but which overshoots directly from the a phase region to the /3 phase region via the a + /3phase region, the calculated rate constant might be an average of the different phases concerned. Recent reports which explain the dependency of the rate constant on the pressure [2 l] and the hydrogen concentration (H/M) [4] might not be able to explain the characteristic features of each phase. In the hydriding process, several steps can be considered as rate-controlling steps, e.g. the surface reaction, diffusion, and nucleation and growth. During the progress of a reaction, the rate-controlling step must change at the phase transition point when going from one phase to another. This can be clearly seen from the different rate constants and reaction orders in the various phases. For the hydriding reaction of LaNi,, Goode11 and Rudman [9] stated that the hydriding reaction might involve the mixed states of the hydrogen chemisorption at the surface and the diffusion of hydrogen atoms into the hydride. Park and Lee [23] stated that the rate-controlling step changes with the reaction time elapsed. These two observations might correspond to the experimental conditions where the hydriding reaction switches directly from the a phase region to the p phase region via the a + ,Ll phase region. In this study, the reaction order is determined to be a = 1.5 in the a phase and a = 2.0 in the a + p phase region. The hydriding reaction in the a + p phase region remains constant, independent of H/M. The rate in the GL+ /3 phase region is much slower than that in the a and /3 phases (see Fig. 8). Hydrogen diffusion from the surface into the hydride phase as the ratecontrolling step in the a + p phase region can be excluded in view of the hydriding rates observed. As illustrated in Fig. 10(c), the diffusion of hydrogen atoms to the interface between the a phase and the /3 hydride proceeds through a grown layer of the p hydride. Diffusion of hydrogen atoms in the a phase proceeds through the solid solution (Fig. 10(a)), and in the /? phase proceeds through the hydride layer

118

(Fig. 10(d)). If the diffusion is the rate-controlling step, the reaction rate in the a + /3 phase region has to be faster than that in the /3 phase region because the outer layer of a hydride particle in the a + p phase region is the /I hydride (see Fig. 10). Further evidence for this can be derived from the fact that in the a + /3 phase region the reaction rate stays below a constant level regardless of the changes in the hydrogen concentration. Therefore it is assumed that the nucleation and growth process is the rate-controlling step in the a + /I phase region. This agrees with results of Gerard and other workers [3,19,24,25]. Regarding the reaction in the a and /I phases, there are two possible ratecontrolling steps, i.e. the surface process and the diffusion process, although it is difficult to draw a clear conclusion as to the rate-controlling step in the a phase. Chemisorption was supposed to be the rate-controlling step in the a phase [8, 23, 261. This can be derived from the fact that the reaction order with respect to hydrogen pressure is close to unity in a region where the reaction rate is proportional to the hydrogen pressure. However, the reaction order a = 1.5 indicates that another controlling step might be involved. In the /3 phase, the diffusion of hydrogen atoms through the hydride phase can be considered as the rate-controlling step. This is based on the fact that the reaction rate in the /I phase is lower than that in the a phase (see Fig. 8), but the hydrogen pressure applied in the p phase is much higher than that in the a phase.

6. Conclusions A rate equation for the hydriding reaction is derived based on the reversible nature of the hydriding and dehydriding reactions. The equation proposed reproduces the experimental results with considerable accuracy. The intrinsic nature of the reaction kinetics in the different phases has been explained reasonably well. The rate constants are found to be maintained constant within a given phase region independent of the hydrogen concentration (H/M) and the hydrogen pressure under isothermal conditions. The rate-controlling step changes from chemisorption in the a phase region to nucleation and growth in the a + p phase region, and finally to the diffusion-limited motion of hydrogen atoms into the hydride layer of the p phase.

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2 3 4 5 6 7

119 H. Bjurstrom and S. Suda, J. Less-Common Met., 131 ( 1987) 6 1. P. D. Goode11 and P. S. Rudman, J. Less-Common Met., 89 (1983) 117. A. J. Goudy and R. A. Wallingford, J. Less-Common Met., 99 (1984) 249. P. S. Rudman, G. D. Sandrock and P. D. Goode& J. Less-Common Met., 89 (1983) 437. 12 P.S. Rudman, J. Less-Common Met., 89 (1983) 93. 13 H. S. Chung and J. Y. Lee, Int. J. Hydrogen Energy, IO (1985) 537. 14 L. Schlapbach, A. Seiler, H. C. Siegmann, T. v. Waldkirch and P. Zurcher, lnt. .I. Hydrogen Energy,

8 9 10 11

4(1979)21. 15 J. S. Han and J. Y. Lee, Int. J. Hydrogen Energy, 6 (1987) 417. 16 E. Akiba, K. Nomura and S. Ono, J. Less-Common Met., 89 (1983) 145. 17 J. Y. Lee, S. M. Byun, C. N. Park and J. K. Park, J. Less-Common Met., 87 ( 1982) 149. 18 J. S. Han and J. Y. Lee, Int. J. Hydrogen Energy, 11 (1985) 767. 19 L. Belkbir, E. Joly and N. Gerard, J. Less-Common Met., 81 (1981) 199. 20 T. Hirata, T. Matsumoto, M. Amano and Y. Sasaki, J. Less-Common Met., 89 (1983) 85. 2 1 C. M. Stander, J. Inorg. Nucl. C’hem., 39 (1977) 22 1. 22 Reports of the activities on the research and development of metal hydride (in Japanese),

23 24 25 26

The Science and Technology Center of Osaka, Japan, 1986, 1987,1988. C. N. Park and J. Y. Lee, J. Less-Common Met., 8.3 (1982) 39. N. Gerard, J. Less-Common Met., 131 (1987) 13. 0. Boser, J. Less-Common Met., 46 (1976) 91. P.-W. Shen. G.-S. Wang, D.-X. Zhang, X.-L. Wang and J.-H. Zhang, Hydrogen Syst., 1 (1985) 355.