i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 1 9 5 1 – 1 9 5 7

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Investigation on kinetics mechanism of hydrogenabsorption in the La2Mg17-based composites

Jing Liua, Xu Zhanga, Qian Lia,*, Kuo-Chih Choua,b, Kuang-Di Xua

aShanghai Key Laboratory of Modern Metallurgy and Materials Processing, Shanghai University, Shanghai 200072, ChinabDepartment of Physical Chemistry, University of Science and Technology Beijing, Beijing 100083, PR China

a r t i c l e i n f o

Article history:

Received 19 November 2008

Received in revised form

13 December 2008

Accepted 13 December 2008

Available online 22 January 2009

Keywords:

Hydrogen storage materials

La2Mg17

Hydrogen absorption

Kinetics mechanism

Model

* Corresponding author. Tel.: þ86 21 5633404E-mail address: shuliqian@shu.edu.cn (Q

0360-3199/$ – see front matter ª 2008 Interndoi:10.1016/j.ijhydene.2008.12.040

a b s t r a c t

A new model has been successfully used to investigate the hydrogen absorption kinetics

mechanism of La2Mg17-based composites. The results indicate that different preparation

conditions lead to different rate-controlling steps during hydrogen absorption process. For

La2Mg17–LaNi5 composite synthesized by the method of melting, the rate-controlling step is

the surface penetration of hydrogen atoms, which does not change by addition agent

(LaNi5). However, mechanical milling can change the rate-limiting steps of hydriding

reaction in the La2Mg17–LaNi5 composite from surface penetration to diffusion of hydrogen

in the hydride layer. With the enhancement of milling intensity, the rate-controlling step

in La1.8Ca0.2Mg14Ni3 alloy changes from surface penetration to diffusion. In addition,

the activation energies of hydrogen absorption for La2Mg17�20 wt%LaNi5 and

La1.8Ca0.2Mg14Ni3 are obtained by this model.

ª 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights

reserved.

1. Introduction additions to improve the absorption properties of La2Mg17

The magnesium-rich alloys Mg–RE (RE¼ La, Ce or mischmetal)

hold a special position among hydride-forming metals and

alloys. They are characterized by the high gravimetric storage

capacity of the magnesium and the mild condition of hydride

formation owing to the catalytic effect of the rare earth

components [1,2]. However, one of their significant disad-

vantages is the very poor hydrogen absorption and desorption

kinetics, about 10 times slower than that of the well-known

hydrogen storage alloy LaNi5 [3]. An applicable hydrogen

storage material requires not only a large hydrogen capacity

but also a fast hydriding/dehydriding reaction rate. To accel-

erate the hydriding/dehydriding process, the elements in the

La2Mg17 were substituted by a small amount of calcium for

lanthanum and a 3d element for magnesium, respectively [4].

Moreover, Dutta et al. [5] selected LaNi5 and FeTi(Mn) as

5; fax: þ86 21 56338065.. Li).ational Association for H

intermetallics, since they easily become activated and possess

good kinetics at ambient condition.

In fact, it is significant to elucidate the hydriding/dehy-

driding process mechanism for improving the kinetics prop-

erties with good pertinence. Khrussanova et al. [6] used the

kinetics equations describing hydrogen chemisorption on the

alloy surface, three-dimensional hydrogen diffusion through

the product layer and chemical reaction between hydrogen

and the alloy to obtain the hydriding mechanism of La2Mg17,

La1.8Ca0.2Mg17 and La1.6Ca0.4Mg17. Their results indicated that

at low values of the reacted fraction (0< x< 0.4), hydrogen

chemisorption on the alloy surface is the rate-controlling step

and at higher x values, the hydriding process is controlled by

hydrogen diffusion through the hydride layer. But, to date

most measurements of hydrogen absorption and desorption

of La2Mg17-based composites are simply presented as plots of

ydrogen Energy. Published by Elsevier Ltd. All rights reserved.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 1 9 5 1 – 1 9 5 71952

reacted fraction or percentage of reacted amount versus time

[7–9]. It is well known that an analytical expression is benefi-

cial to discussion and analysis on the kinetics mechanism.

However, the research in experiments of the hydriding/

dehydriding mechanisms of La2Mg17-based composites has

lagged behind its theory level.

The present paper firstly summarizes the experimental

kinetics data of La2Mg17–LaNi5 and La1.8Ca0.2Mg14Ni3 from the

literature [10–12]. A new kinetics model [13,14] is then applied

to study their hydrogen absorption kinetics mechanisms. The

influences of the additions, the preparation methods, and the

element substitution on the hydriding reaction kinetics

mechanisms of La2Mg17-based composites are systematically

investigated.

2. Kinetics model

The kinetics of many solid–gas reactions can be represented

by the general equation f(x)¼ kt, where x is the fraction reacted

in time t and the function f(x) is closely related to the reaction

mechanism. The equations for solid–gas reactions have been

known for decades. Most solid state reactions involving the

precipitation of a new phase can be characterized by an

equation derived by Avrami [15] and Johnson and Mehl [16].

In its simplest form, the equation can be written as

ln[�ln(1� x)]¼ ln Bþmln t [17,18], where B is a constant which

depends on the rates of nucleation and growth and m is

a constant that can vary according to the geometry of the

system. Hancock and Sharp [17] had tabulated the values of m

corresponding to 9 different reaction models, as shown in Table

1, which can be separated into three different groups: diffusion

controlled, interface controlled and nucleation and growth

models. Theoretically, the rate-controlling step can be deter-

mined by comparing their empirical results with the value of m.

However, it is not precise enough to determine which intra

group model is appropriate. Moreover, the parameters B and m

have no obvious physical significance. In addition, numerous

published articles have also reported the useful approximations

of the kinetics functions [19–27] which are also summarized in

Table 1 – Set of reaction models to describe the reaction kineti

Mechanism

One-dimensional diffusion

Two-dimensional diffusion (bidimensional particle shape)

Three-dimensional diffusion (Jander equation)

Three-dimensional diffusion (Gisling–Braunshtein equation)

First order kinetics

Two-dimensional phase-boundary reaction

Three-dimensional phase-boundary reaction

Zero order

Random nucleation and growth of nuclei (Avrami–Erofeev equation)

Random nucleation and growth of nuclei (Avrami–Erofeev equation)

Phase-boundary controlled reaction (n¼ 0, 1/2, and 2/3)

Three-dimensional diffusion (Kroger–Ziegler equation)

Three-dimensional diffusion (modified Jander relation)

Three-dimensional diffusion (Valensi–Carter model)a

a Z represents the volume of the reaction product formed per unit volum

Table 1. Some of them have the same forms as in the literature

[17]. Although many kinetics functions are available in litera-

ture, as far as most of kinetics equations are concerned, if one

treats each step rigorously, that will lead to solve a group of

differential or integral equations. The situation now is that

some treatments are so complicated that they cannot offer an

explicit analytic expression and give an intuitionistic quantita-

tive discussion. The other situation is that some equations are

often difficult to be applied owing to the lack of parameter

values [21]. From the practical point of view, we introduced

a new kinetics model (Chou model) proposed in our lab with

much calculation accuracy to analyze the hydrogen absorption

kinetics mechanism for the La2Mg17-based composites. It is

necessary to point out that Chou model has a series of simpler

and physical meaningful explicit analytic expressions.

Chou model assumes that all particles of the metal or alloy

could be regarded as spherical balls with the same density and

radius. The whole particle is a ball of radius R0. A general

process of hydriding reaction for a particle can be described as

the following seven steps: (1) Hydrogen transfer from the bulk

gas phase to the surface of metal particle; (2) Hydrogen

diffusion through the boundary layer between gas phase and

solid particle; (3) Physisorption of hydrogen molecules on the

solid surface; (4) Dissociation of hydrogen molecules and

chemisorption; (5) Surface penetration of hydrogen atoms; (6)

Diffusion of hydrogen atoms through the hydride product

layer to the hydride/metal interface; (7) Chemical reaction and

nucleus formation producing hydride.

In the most cases, the first two steps are very fast and the

steps (5) and (6) could be the rate-controlling steps. Some-

times, the process may have different controlling steps at

different stages. When the rate-controlling step is the surface

penetration, the relation of the hydriding reacted fraction

x and time t can be expressed as [13]

x ¼ 1�

0@1�

kfspK

12paK

12ca

�P

12H2� P

eq12

H2

�nmR0

t

1A

3

(1)

where ym represents the constant coefficient that depends

on the density of the storage material, kspf represents the

cs from the literatures.

Equation m Ref.

x2¼ kt 0.62 [17,19]

(1� x) ln(1� x)þ x¼ kt 0.57 [17,19]

[1� (1� x)1/3]2¼ kt 0.54 [17,19,20]

1� 2x/3� (1� x)2/3¼ kt 0.57 [17,21,22]

�ln(1� x)¼ kt 1.00 [17,19]

1� (1� x)1/2¼ kt 1.11 [17,19]

1� (1� x)1/3¼ kt 1.07 [17,19]

x¼ kt 1.24 [17]

[�ln(1� x)]1/2¼ kt 2.00 [15,17]

[�ln(1� x)]1/3¼ kt 3.00 [15,17]

[1� (1� x)1�n]/(1� n)¼ kt [23]

[1� (1� x)1/3]2¼ kln t [21,24]

[(1/(1� x))1/3� 1]2¼ kt [21,25]

{Z� (Z� 1)(1� x)2/3� [1þ(Z� 1)x])2/3}/(Z� 1)¼ kt [21,26,27]

e of reactant consumed.

Fig. 1 – Kinetics data of hydrogen absorption at 623 K and

4.0 MPa H2 for La2Mg17Lx wt%LaNi5 (x [ 5, 20 and 40) [10]

together with the fitted curves.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 1 9 5 1 – 1 9 5 7 1953

equilibrium constant for the surface penetration of hydrogen

atoms in the forward direction, Kpa and Kca are equilibrium

constants for the physisorption and chemisorption, respec-

tively, and PH2and Peq

H2represent the hydrogen partial pres-

sures in the gas phase and in equilibrium with hydride.

Define tc(sp), ‘the characteristic reaction time’ of the

hydriding reaction controlled by surface penetration of

hydrogen atoms, as

tcðspÞ ¼nmR0

kfspK

12paK

12ca

�P

12H2� P

eq12

H2

� (2)

Substituting Eq. (2) into Eq. (1), we have

x ¼ 1��

1� ttcðspÞ

�3

(3)

When the rate-controlling step is the diffusion of hydrogen

in hydride, the relation of the hydriding reacted fraction x and

time t is given by [13]

x ¼ 1� 1�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2Db

HðCHðbÞ � CeqH ða=bÞÞ

R20nm

t

s 31A0@ (4)

where DHb represents the diffusion coefficient of hydrogen in

b phase, CH(b) is the concentration of hydrogen atoms in the

hydride phase just underneath the particle surface at radius

R0 and CHeq(a/b) represents the equilibrium composition of

hydrogen in hydride as hydrogenation reaction reaches

equilibrium.

Define

tcðdÞ ¼1

2Db

HðCHðbÞ�CeqHða=bÞÞ

R20

nm

(5)

as ‘the characteristic reaction time’ of the hydriding reaction

controlled by diffusion of hydrogen in hydride. Substituting

Eq. (5) into Eq. (4), we have

x ¼ 1�

1�ffiffiffiffiffiffiffiffi

ttcðdÞ

s !3

(6)

In addition, for the surface penetration, the relation of the

hydriding reacted fraction x and time t can also be expressed

as

x ¼ 1��1� exp

��Ev

RTv

�1Bt

t

�3

(7)

When the rate-controlling step is the diffusion of hydrogen

atoms in the solid solution, the relation of the hydriding

reacted fraction x and time t is

x ¼ 1� 1� exp

��Ev

2RTv

� ffiffiffiffiffiffiffi1Bt

t

s 3375

264 (8)

where Ev is activation energy (J/mol), t is reacted time (s), TV

is thermodynamic temperature (K), x is reacted fraction, R

is gas constant, Bt is a coefficient. If the particle radius and

temperature are fixed and the relation between tc and Bt is

tc ¼ Bt$exp

�Ev

RTv

�(9)

As mentioned above, Chou model [13] involves a series of

analytic equations for various kinds of rate-controlling steps.

These equations describe the reacted fraction (x) of hydriding/

dehydriding reaction as an explicit function of time (t),

temperature (T ), hydrogen partial pressure (PH2) and particle

radius (R0). Among them, a very important and useful

parameter is the new concept of ‘‘characteristic reaction time

tc’’, the physical meaning of which is the required time for the

particle to be completely hydrogenated. The smaller the tc, the

faster the hydriding reaction rate. It indicates the hydriding/

dehydriding kinetics performance of hydrogen storage mate-

rials is quantified with accuracy using the characteristic

reaction time directly. Since this method gives the possible

formulae for calculating the reacted fraction x at the different

reaction times corresponding to different kinds of controlling

steps, the rate-controlling step for any hydriding reaction can

be determined by comparing the experimental results with

the theoretical modeling results. If we know the value of tc, the

kinetics of the hydriding/dehydriding reaction can be

described conveniently. However, in most cases, tc is not easy

to be measured accurately. In this study, we use linear

regression method to obtain tc. Moreover, the activation

energy Ev in the two rate-controlling steps can be attained by

non-linear fitting. The detail derivation of Chou model was

given in the Ref. [13].

3. Results and discussion

3.1. The effect of the amount of addition agent onhydriding kinetics of La2Mg17

Pal [10] had investigated the hydriding property of La2Mg17�x

wt% LaNi5 composite, which was synthesized by melting the

La2Mg17 and LaNi5 with the proper stoichiometric ratios in

a radiofrequency induction furnace. Fig. 1 shows the hydrogen

absorption kinetics of La2Mg17�x wt%LaNi5 (x¼ 5, 20 and 40) at

623 K and at a pressure of 4.0 MPa H2.

The relationship between x and t is modeled by fitting

the experimental data with the rate equations of each step

Table 2 – The linear regression results of La2Mg17Lx wt%LaNi5 (x [ 5, 20 and 40) at 623 K.

rate-controlling step Parameters x¼ 5 x¼ 20 x¼ 40

Surface penetration R2 0.9983 0.9992 0.9967

tc(sp)/s 5137 4017 1493

Diffusion R2 0.7533 0.6872 0.7331

tc(d)/s 10,057 9703 3406

Fig. 3 – Kinetics data for hydrogen absorption of samples

a [11], b [10] and c [11] together with the fitted curves

(solid curves: surface penetration step; dotted curves:

diffusion step).

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 1 9 5 1 – 1 9 5 71954

(Eqs. (3) and (6)) using the least squares and the results are

listed in Table 2. For the surface penetration step, the corre-

sponding R2 of the linear regression equations are 0.9983,

0.9992 and 0.9967 for x¼ 5, 20 and 40, respectively. On the

contrary, these experimental data cannot be fitted by the

model with the rate-controlling step of diffusion. From these

results, the surface penetration can be considered as the rate-

controlling step.

Based on Eq. (3) and Table 2, a series of fitted curves were

also drawn in Fig. 1 together with the experimental data. It can

be seen that the fitted results are in good agreement with the

experimental data. Table 2 shows that tc(sp)5> tc(sp)20> tc(sp)40,

where tc(sp)5, tc(sp)20 and tc(sp)40 are the characteristic reaction

time at 623 K for La2Mg17�x wt%LaNi5 (x¼ 5, 20 and 40),

respectively.

Fig. 2 shows the hydrogen absorption kinetics of

La2Mg17�20 wt%LaNi5 at 623 K, 648 K, and 673 K. The param-

eters Ev and Bt can be evaluated using Eq. (7) by non-linear

fitting method. The corresponding R2 is 0.9915, which indi-

cates that the experimental data can be fitted with good

accuracy by Chou model and the surface penetration is

the rate-controlling step for this system from 623 K to 673 K.

The calculated activation energy is 61.79� 0.67 kJ/mol H2.

By the same method, Chou model was also used to analyze the

hydriding kinetics of La2Mg17�x wt%LaNi5 (x¼ 5, 40) at 623 K,

648 K and 673 K, and the activation energy can be calculated as

64.83� 1.25 and 69.70� 0.95 kJ/mol H2, respectively.

Therefore, for the La2Mg17�x wt%LaNi5 materials synthe-

sized by melting, the hydrogen absorption rates are improved

by increasing the amount of addition agent (LaNi5) and rising

Fig. 2 – Kinetics data of hydrogen absorption at different

temperatures (623 K, 648 K and 673 K) and under 4.0 MPa H2

for La2Mg17L20 wt%LaNi5 [10] together with the fitted curves.

temperature and the reaction rate can be compared quanti-

tatively. The hydrogen absorption mechanism is surface

penetration of hydrogen atoms and cannot be changed by

addition agent or increased temperature.

3.2. The effect of mechanical milling on hydridingkinetics of La2Mg17–LaNi5

Gross et al. [11] had investigated the hydriding property of

La2Mg17–LaNi5 composite formed by mechanical milling. They

had measured the hydriding kinetics at 523 K for the samples

of pure La2Mg17 and La2Mg17�50 wt%LaNi5, which had been

milled for 25 min. Fig. 3 gives the plot of x versus t for the

different samples mentioned above. To compare the effect of

mechanical milling on hydriding kinetics, the kinetics data at

623 K of un-milled La2Mg17�40 wt%LaNi5 prepared by Pal [10]

were included in Fig. 3. The milled pure La2Mg17 was labeled as

‘a’, the un-milled La2Mg17�40 wt%LaNi5 was labeled as ‘b’ and

the milled La2Mg17�50 wt%LaNi5 was labeled as ‘c’. The rela-

tionship between x and t is modeled by fitting the experi-

mental data with the rate equations of each step (Eqs. (3) and

(6)) using the least squares and the results are listed in Table 3.

It can be seen from Table 3 that the R2 of sample a is 0.9920

for surface penetration model. For sample b, the quality of

fitting is also better for the surface penetration model than

for diffusion model. On the contrary, for sample c, the

Table 3 – The linear regression results of the samples a,b and c.

rate-controllingstep

Parameters Samplesa

Samplesb

Samplesc

Surface penetration R2 0.9920 0.9967 0.7916

tc(sp)/s 2306 2692 38.66

Diffusion R2 0.9674 0.7134 0.9873

tc(d)/s 23,750 5605 65.33

Fig. 4 – Hydriding data at 473 K and under 4.0 MPa H2 for

La1.8Ca0.2Mg14Ni3 alloys milled for different times [12]

together with the fitted curves (solid curves: surface

penetration step; dotted curves: diffusion step).

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 1 9 5 1 – 1 9 5 7 1955

corresponding R2 is 0.9873 for the diffusion model, which is

much higher than that for the surface penetration model.

Fig. 3 shows the hydrogen absorption curves of samples a,

b and c fitted by models. It can be seen that the surface

penetration model can represent the experimental curves of

the samples a and b and the diffusion model fits the experi-

mental data of sample c very well. From Section 3.1, we know

that the hydrogen absorption rate-limiting step is surface

penetration of hydrogen atoms and cannot be changed with

the increase of LaNi5. So it can be concluded that mechanical

milling combined with the catalyzer not only to improve the

hydriding kinetics (tc for samples a and b are much longer

than that for sample c), but also change the hydrogen

absorption rate-limiting step of La2Mg17-based material from

surface penetration to the diffusion of hydrogen atoms

through the hydride layer. The increase in the specific surface

area and the introduction of defects by the intensive milling

contribute to the improvement of kinetics [28].

3.3. The effect of combination of mechanical milling andelement substitution on kinetics of La2Mg17

Gao et al. [12] studied the hydriding behaviors of

La1.8Ca0.2Mg14Ni3 alloy modified by ball-milling under argon.

Fig. 4 shows the initial hydriding data at 473 K and 4.0 MPa H2

of the alloy milled for different periods of time. To better

Table 4 – The linear regression results of the La1.8Ca0.2Mg14Ni3

rate-controlling step Parameters Milled 0 h

Surface penetration R2 0.9909

tc(sp)/s 3374

Diffusion R2 0.7387

tc(d)/s 11,130

interpret the data, the term ‘‘percentage of reacted amount’’ is

used to describe the hydriding kinetics of the alloy. The rela-

tion between the ‘‘reacted fraction’’ x and the ‘‘percentage of

reacted amount’’ is

x ¼ DmDmmax

¼Dmm0

Dmmaxm0

(10)

where m is the reacted amount, m0 is the initial weight of the

sample, m/m0 is the percentage of reacted amount and mmax

represents the maximum reacted amount.

The relationship between x and t is modeled by fitting the

experimental data with the rate equations of each step (Eqs.

(3) and (6)) using least squares and the results are listed in

Table 4. It can be seen that the R2 of the linear regression

equation is strongly affected by milling time. For the un-

milled sample, the R2 is 0.9909 for surface penetration model

but only 0.7387 for diffusion model. On the contrary, for the

samples milled for 15 h and 20 h, the corresponding R2 for

diffusion model are 0.9786 and 0.9855, which are higher than

that for surface penetration model. For the sample milled for

10 h, the situation is more complex. It is possible that more

than one controlling step in whole process. There is a trend

that the R2 for diffusion model becomes higher and higher

with the increase of milling time, which indicates that the

rate-controlling step of the alloy has been changed from

surface penetration to the diffusion of hydrogen in the

hydride layer with increases of milling time.

Fig. 4 shows the fitted curves for the La1.8Ca0.2Mg14Ni3 alloy

modified by ball-milling. For the alloy milled for 10 h, it looks

like that at the beginning of hydriding reaction (t< 700 s), the

controlling step is the surface penetration and at a later stage

(t> 700 s), the diffusion of hydrogen in the hydride changes

into the controlling step due to a longer diffusion path.

Fig. 5 shows the hydrogen absorption kinetics at 300 K,

373 K, and 473 K and under a hydrogen pressure of 4.0 MPa

for La1.8Ca0.2Mg14Ni3 alloys milled for 20 h. The parameters

Ev and Bt can be evaluated using Eq. (8) by non-linear fitting

method. The corresponding R2 is 0.9908, which indicates

that the experimental data can be fitted with good accuracy

by Chou model and the diffusion of hydrogen in the hydride

is the rate-controlling step for this system from 300 K to

373 K. The calculated activation energy is 28.62� 0.63 kJ/mol

H2, which is much lower than that of La2Mg17�x wt%LaNi5.

The result was probably due to the effect of mechanical

milling as mentioned in Section 3.2. Moreover, the element

substitution also plays an important role in the hydroge-

nation process [29].

From the mathematical treatment and comparison of

model prediction with experimental data in the La2Mg17-based

alloy milled for different times.

Milled 10 h Milled 15 h Milled 20 h

0.9764 0.9223 0.9211

1550 1437 948.2

0.9095 0.9786 0.9855

3510 3780 1890

Fig. 5 – Hydriding data at different temperatures and under

4.0 MPa H2 for La1.8Ca0.2Mg14Ni3 alloys milled for 20 h [12]

together with the fitted curves.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 4 ( 2 0 0 9 ) 1 9 5 1 – 1 9 5 71956

intermetallics system, we can see that the rate-limiting

step of hydrogen absorption changes with preparation

conditions.

4. Conclusion

Chou method has been used to investigate the hydrogen

absorption kinetics mechanism of La2Mg17-based composites.

For La2Mg17–LaNi5 composite synthesized by the method of

melting, the rate-controlling step is the surface penetration

and cannot be changed by addition agent (LaNi5). However,

mechanical milling combined with the catalyzer not only

improves the hydrogenation kinetics, but changes the reac-

tion rate-controlling step from surface penetration to diffu-

sion. Similarly, mechanical milling can also change the

reaction rate-limiting step of La1.8Ca0.2Mg14Ni3 alloy. There is

a trend that the rate-controlling steps change from surface

penetration to diffusion with the enhancement of milling

intensity. From Chou model and the non-liner regression

method, the activation energies of hydrogen absorption for

La2Mg17�20 wt%LaNi5 and for La1.8Ca0.2Mg14Ni3 can be calcu-

lated as 61.79� 0.67 kJ/mol H2 and 28.62� 0.63 kJ/mol H2,

respectively.

Acknowledgement

The authors gratefully acknowledge the financial supports

from the National High Technology Research and Develop-

ment Program of China (2007AA05Z118), the National Natural

Science Foundation of China (50804029), a Foundation for the

Author of National Excellent Doctoral Dissertation of P.R.

China (200746), the Program for Changjiang Scholars and

Innovative Research Team in University (IRT0739) and the

Innovation Fund for Graduate Student of Shanghai

University.

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