mgh2-naalh4.pdf
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In this study, we report the hydrogen absorption/desorption properties and reactionmechanism of the MgH2eNaAlH4 (4:1) composite system. This composite system showedimproved dehydrogenation performance compared with that of as-milled NaAlH4 andMgH2 alone. The dehydrogenation process in the MgH2eNaAlH4 composite can be dividedinto four stages: NaAlH4 is first reacted with MgH2 to form a perovskite-type hydride,NaMgH3 and Al. In the second dehydrogenation stage, the Al phase reacts with MgH2 toform Mg17Al12 phase accompanied with the self-decomposition of the excessive MgH2.NaMgH3 goes on to decompose to NaH during the third dehydrogenation stage, and the laststage is the decomposition of NaH. Kissinger analysis indicated that the apparent activationenergy, EA, for the MgH2-relevent decomposition in MgH2eNaAlH4 composite was148 kJ/mol, which is 20 kJ/mol less than for as-milled MgH2 (168 kJ/mol). X-ray diffractionpatterns indicate that the second, third, and fourth stages are fully reversible. It is believedthat the formation of Al12Mg17 phase during the dehydrogenation process alters thereaction pathway of the MgH2eNaAlH4 (4:1) composite system and improves its thermodynamicproperties.TRANSCRIPT
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 en e r g y 3 6 ( 2 0 1 1 ) 9 0 4 5e9 0 5 0
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The hydrogen storage properties and reaction mechanismof the MgH2eNaAlH4 composite system
M. Ismail a,b, Y. Zhao a,c,*, X.B. Yu a,d,*, J.F. Mao a, S.X. Dou a
a Institute for Superconducting and Electronic Materials, University of Wollongong, Northfields Ave, Wollongong, NSW 2519, AustraliabDepartment of Physical Sciences, Faculty of Science and Technology, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, MalaysiacSchool of Mechanical, Materials and Mechatronics Engineering, University of Wollongong, NSW 2522, AustraliadDepartment of Materials Science, Fudan University, Shanghai 200433, China
a r t i c l e i n f o
Article history:
Received 14 February 2011
Received in revised form
5 April 2011
Accepted 17 April 2011
Available online 18 May 2011
Keywords:
MgH2
NaAlH4
Absorption/desorption
Perovskite-type hydride
* Corresponding authors. Institute for SupercNSW 2519, Australia. Fax: þ61 2 4221 5731.
E-mail addresses: [email protected] (Y. Zh0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.04.132
a b s t r a c t
In this study, we report the hydrogen absorption/desorption properties and reaction
mechanism of the MgH2eNaAlH4 (4:1) composite system. This composite system showed
improved dehydrogenation performance compared with that of as-milled NaAlH4 and
MgH2 alone. The dehydrogenation process in the MgH2eNaAlH4 composite can be divided
into four stages: NaAlH4 is first reacted with MgH2 to form a perovskite-type hydride,
NaMgH3 and Al. In the second dehydrogenation stage, the Al phase reacts with MgH2 to
form Mg17Al12 phase accompanied with the self-decomposition of the excessive MgH2.
NaMgH3 goes on to decompose to NaH during the third dehydrogenation stage, and the last
stage is the decomposition of NaH. Kissinger analysis indicated that the apparent activa-
tion energy, EA, for the MgH2-relevent decomposition in MgH2eNaAlH4 composite was
148 kJ/mol, which is 20 kJ/mol less than for as-milled MgH2 (168 kJ/mol). X-ray diffraction
patterns indicate that the second, third, and fourth stages are fully reversible. It is believed
that the formation of Al12Mg17 phase during the dehydrogenation process alters the
reaction pathway of the MgH2eNaAlH4 (4:1) composite system and improves its thermo-
dynamic properties.
Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights
reserved.
1. Introduction [1e6]. However, the high thermodynamic stability and slow
Because it is a promising energy carrier, intensive efforts have
been made to realize the potential of hydrogen to become
a major energy carrier, for both mobile and stationary appli-
cations. Solid-state hydrogen storage has become an attrac-
tive option due to its high volumetric hydrogen capacity and
favorable safety considerations. Its large hydrogen storage
capacity (7.6 wt.%), low cost, and superior reversibility make
MgH2 a promising candidate for on-board hydrogen storage
onducting and Electronic
ao), [email protected], Hydrogen Energy P
desorption kinetics [7,8] constrain the practical application of
MgH2. Many studies have been conducted to overcome these
problems, such as by preparing nanocrystalline Mg powder [7]
and adding catalysts [8e10]. Besides the studies mentioned
above, the “destabilization concept” was also introduced
[11,12]. The destabilization concept could be regarded as
a quite different approach. This approach is aimed at modi-
fying the thermodynamics and kinetics of the hydrogen
sorption reaction. Thermodynamic destabilization is achieved
Materials, University of Wollongong, Northfields Ave, Wollongong,
.cn (X.B. Yu).ublications, LLC. Published by Elsevier Ltd. All rights reserved.
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 9 0 4 5e9 0 5 09046
using additives that form a new compound during dehydro-
genation. Vajo et al. [13] tried to use certain elements such as
Si to destabilize MgH2. The formation of an intermediate
phase, Mg2Si, during the dehydrogenation process is benefi-
cial to MgH2 destabilization. However, the formation of Mg2Si
would reduce the gravimetric hydrogen density because Si
cannot be hydrogenated, so this intermediate phase seems
hard tomake reversible. Motivated by the studies of Vajo et al.,
many elements have been mixed with MgH2, including LiBH4
[14e18], NaBH4 [19e21], LiAlH4 [22e25], and Li3AlH6 [26].
Recently Zhang et al. [22] reported that MgH2 can be
destabilized effectively by LiAlH4 in which the onset dehy-
drogenation temperature and the enthalpies of MgH2-relevent
decomposition in MgH2eLiAlH4 composite is improved from
that of as-milled MgH2. In addition, Chen et al. [24] also
demonstrated that the combination of MgH2 and LiAlH4 by
mechanical grinding reduced the decomposition temperature
of MgH2. Both articles claimed that the formation of Al12Mg17as a reaction product during the dehydrogenation process
play a main catalytic effect in the MgH2eLiAlH4 composite
systems.
Another potential element to destabilize MgH2 is NaAlH4.
Varin et al. [27] studied the morphology and the reaction
mechanism in an MgH2 þ 73 vol.% NaAlH4 composite system
by scanning electron microscopy (SEM) and differential
scanning calorimetry. Sartori et al. [28] further reported the
reaction mechanism and hydrogen released from
NaAlH4 þ MgH2 þ Al prepared by hydrogenating a mixture of
2MgH2 þ 3Al þNaH under 160 bar and 80 �C for 12 h. However,
the hydrogen storage performances of an MgH2eNaAlH4
composite system have not been thoroughly investigated so
far. It is also necessary to verify whether the role of NaAlH4 is
similar to the role of LiAlH4 in the MgH2eLiAlH4 composite
system, since NaAlH4 and LiAlH4 are from the same alanate
family.
In the present paper, we investigated the hydrogen storage
properties and the reaction pathways of the MgH2eNaAlH4
(4:1) composite systemduring the de/rehydrogenation process
through temperature programmed desorption (TPD), Ther-
mogravimetric analysis/differential scanning calorimetry
(TGA/DSC), isothermal sorption measurements and X-ray
diffraction (XRD) measurements. The reaction mechanism of
MgH2eNaAlH4 (4:1) composite was discussed based on our
experimental results.
2. Experimental
Pure MgH2 (hydrogen storage grade) and NaAlH4 (hydrogen
storage grade, 93% purity) were purchased fromSigmaeAldrich
and were used as received with no further purification.
Approximately 2 g of a mixture of MgH2 and NaAlH4 with
a molar ratio of 4:1 was loaded into a sealed stainless steel vial
together with hardened stainless steel balls in an argon atmo-
sphere MBraun Unilab glove box. For simplicity, the mixture of
MgH2 and NaAlH4 with molar ratio of 4:1 will be referred to as
MgH2eNaAlH4 composite. The ratio of theweight of balls to the
weight of powder was 40:1. The sample was then milled in
a planetary ball mill (QM-3SP2) for 1 h, by first milling for 0.5 h,
resting for 6min, and thenmilling for another 0.5h inadifferent
direction at the rate of 400 rpm. Pure MgH2 and NaAlH4 were
also prepared under the same conditions for comparison
purposes.
The experiments for de/rehydrogenation were performed
in a Sieverts-type pressure-composition-temperature (PCT)
apparatus (Advanced Materials Corporation). The sample was
loaded into a sample vessel in the glove box. For the TPD
experiment, all the samples were heated in a vacuum
chamber, and the amount of desorbed hydrogen was
measured to determine the lowest decomposition tempera-
ture. The heating rate for the TPD experiment was 5 �Cmin�1,
and samples were heated from room temperature to 450 �C.The re/dehydrogenation kinetics measurements were per-
formed at the desired temperature with initial hydrogen
pressures of 3.0 MPa and 0.001 MPa, respectively.
XRD analysis was performed using a GBC MMA X-ray
diffractometer with Cu Ka radiation. qe2q scans were carried
out over diffraction angles from 25� to 80� with a speed of
2.00 �/min. Before the measurement, a small amount of
sample was spread uniformly on the sample holder, which
was wrapped with plastic wrap to prevent oxidation.
Thermogravimetric analysis/differential scanning calo-
rimetry (TGA/DSC) of the dehydrogenation process was
carried out on a Mettler Toledo TGA/DSC 1. The sample was
loaded into an alumina crucible in the glove box. The crucible
was then placed in a sealed glass bottle in order to prevent
oxidation during transportation from the glove box to the
TGA/DSC apparatus. An empty alumina crucible was used for
reference. The samples were heated from room temperature
to 500 �C under an argon flow of 30 ml/min, and different
heating rates were used.
3. Results and discussion
Fig. 1 displays the TPD curves of the as-milled MgH2, the as-
milled NaAlH4, and the MgH2eNaAlH4 composite. The as-
milled MgH2 starts to release hydrogen at 330 �C and desorbs
about 7.1 wt.% H2 after 420 �C. Meanwhile, the as-milled
NaAlH4 releases about 5.5 wt.% hydrogen in the dehydroge-
nation temperature range between 180 �C and 285 �C. For theMgH2eNaAlH4 composite, it is believed that there are four
stages of dehydrogenation occurring during the heating
process. The four stages of dehydrogenation process are re-
ported by Sartori et al. [28] for the dehydrogenation process of
hydrogenating 2MgH2 þ 3Al þNaH under 160 bar and 80 �C for
12 h. The first stage, which takes place within the temperature
range from 170 to 212 �C, is attributed to the reaction:
NaAlH4 þMgH2/NaMgH3 þAlþ 1:5H2 (1)
In order to clarify the dehydrogenation mechanism, XRD
was used. From the Fig. 2(a), it can be seen that, MgH2 and
NaAlH4 phases are detected in the as-milled MgH2eNaAlH4
composite. Fig. 2(b) shows the XRD pattern of the
MgH2eNaAlH4 composite after dehydrogenation at 212 �C.
Clearly, the pattern indicates the presence of perovskite-type
hydride, NaMgH3 and Al besides the unreacted MgH2. The fact
that no NaAlH4 phase was found indicates that the Eq. (1)
reaction was completed at this stage. From the result we can
Fig. 1 e TPD (temperature programmed desorption) curves
of the as-milled MgH2, the as-milled NaAlH4, and the
MgH2eNaAlH4 composite. (I, II, III, and IV refer to the first,
second, third, and fourth dehydrogenation stage,
respectively).
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 en e r g y 3 6 ( 2 0 1 1 ) 9 0 4 5e9 0 5 0 9047
see that the decomposition temperature of NaAlH4 in the
MgH2eNaAlH4 composite reduced by 10 �C compared with
that of as-milled NaAlH4 indicating that the dehydrogenation
performance of NaAlH4 is slightly improved after combining
with MgH2.
The second dehydrogenation stage, starting at about 280 �Cand completed at about 330 �C, can be attributed to the MgH2
or NaMgH3-relevent decomposition. In order to investigate the
reaction progress and mechanism, XRD measurements were
performed on the MgH2eNaAlH4 composite after dehydroge-
nation at 330 �C. As can be seen from the XRD result (Fig. 2(c)),
the peaks for MgH2 and Al disappear, and new peaks corre-
sponding to Mg17Al12 and Mg are observed. Furthermore, the
peaks for NaMgH3 still remain unchanged. These results
demonstrate that the hydrogen released in the second stage is
Fig. 2 e XRD patterns of the MgH2eNaAlH4 composite (a)
after 1 h ball milling and after dehydrogenation at (b)
212 �C, (c) 330 �C, (d) 360 �C, and (e) 375 �C.
from a mixing decomposition of (i) the reaction of MgH2 with
Al and (ii) the decomposition of the excessive MgH2. This kind
of MgH2-relevent decomposition can be speculated to be
through the reaction in Eqs. (2) and (3), which occurs at
a temperature 50 �C lower than the decomposition tempera-
ture of the as-milled MgH2.
17MgH2 þ 12Al/Mg17Al12 þ 17H2 (2)
MgH2/Mg þH2 (3)
Further heating led to the third decomposition, starting at
330 �C and completed at 360 �C, corresponding to the decom-
position of NaMgH3, as shown in Eq. (4). The last stage dehy-
drogenation is due to the decomposition of NaH, with
decomposition starting at 360 �C and ending at 375 �C (Eq. (5)).
XRD measurements at 360 and 375 �C were carried out to
clarify these dehydrogenation stages. As shown in Fig. 2(d)
and (e), the peaks of NaH appear after dehydrogenation at
360 �C, and the peaks of Na can be detected after further
heating to 375 �C. These results indicated that the reactions of
Eqs. (4) and (5) occurred in the third and fourth stages,
respectively.
NaMgH3/NaHþMg þH2 (4)
NaH/Naþ 1=2H2 (5)
Fig. 3 compares the isothermal dehydrogenation kinetics of
MgH2 þNaMgH3 in the MgH2eNaAlH4 composite at 300 �C and
320 �C. The dehydrogenation of MgH2 was also examined for
comparison under the same conditions. The dehydrogenation
kinetics test was carried out after a rehydrogenation process
under w3 MPa of H2 at 300 �C. At 320 �C, the MgH2eNaAlH4
sample desorbed about 3.5 wt.% hydrogen after 12 min, which
is much higher than for the MgH2 (desorbed about 0.4 wt.%
hydrogen). Meanwhile, after 12 min dehydrogenation, the
MgH2eNaAlH4 sample released about 1.2 wt.% hydrogen at
300 �C, but the MgH2 only released about 0.2 wt.% hydrogen at
the same time and temperature. It is important to note that
the dehydrogenation kinetics of the MgH2eNaAlH4 sample at
Fig. 3 e Isothermal dehydrogenation kinetics of the MgH2
and the MgH2eNaAlH4 composite at 300 �C and 320 �C.
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300 �C ismuch faster than the dehydrogenation kinetics of the
MgH2 at 320 �C. This result indicates that the MgH2-relevant
dehydrogenation kinetics is significantly improved after
combining with NaAlH4.
Fig. 4 presents the TGA/DSC traces of the MgH2eNaAlH4
composite and the as-milled MgH2, which is also shown for
comparison (inset plot). For the MgH2eNaAlH4 composite,
the first endothermic peak at 185 �C corresponds to the
melting of NaAlH4 [29], and the second endothermic peak at
275 �C corresponds to the reaction of NaAlH4 and MgH2 (first
stage dehydrogenation). Note that, before the first endo-
thermic peak, there is an extra exothermic peak. This
exothermic peak at 170 �C is most probably due to the pres-
ence of surface hydroxyl impurities in the powder as re-
ported in our previous paper [30,31] for LiAlH4. Furthermore,
after the second endothermic (first stage dehydrogenation),
three overlapping endothermic reactions occurred due to the
decomposition of MgH2, NaMgH3 and NaH. The first over-
lapping endothermic peak at 363 �C can be ascribed to MgH2-
relevent decomposition (second stage dehydrogenation), and
the rest are due to the decomposition of NaMgH3 and NaH
(third and fourth stage dehydrogenation). Ikeda et al. [32]
reported that there are two overlapping endothermic reac-
tions accompanying with continuous weight-loss in the
decomposition of NaMgH3 and NaH. Compared to the as-
milled MgH2 (inset plot), the temperature of the MgH2-rele-
vent decomposition in the MgH2eNaAlH4 composite is
clearly decreased. It starts to release hydrogen at about
315 �C, 50 �C below the temperature for the as-milled MgH2
(365 �C). This decrease in the hydrogen release temperature is
correlated to the results observed in the PCT measurement
(Fig. 1). From the TGA/DSC results, it can be seen that the
decomposition temperatures of the as-milled MgH2 and the
MgH2eNaAlH4 composite are higher than those from the
Sieverts-type PCT results (Fig. 1). This difference may be due
Fig. 4 e TGA/DSC traces of the MgH2eNaAlH4 composite
and the inset plot is TGA/DSC traces of the as-milled MgH2.
Heating rate: 15 �C minL1, argon flow: 30 ml/min. (I, II, III,
and IV refer to the first, second, third, and fourth
dehydrogenation stages).
to the different heating rates and the different heating
atmospheres between the two measurements.
The activation energy, EA, for the hydrogen desorption
mechanism of the MgH2eNaAlH4 composite was obtained by
performing a Kissinger analysis [33], according to the
following equation:
lnhb=T2
p
i¼ �EA=RTp þ A (6)
where b is the heating rate, Tp is the peak temperature in the
DSC curve, R is the gas constant, and A is a linear constant.
Thus, the activation energy, EA, can be obtained from the slope
in a plot of ln[b/Tp2] versus 1000/Tp.
Fig. 5 shows DSC traces for the MgH2eNaAlH4 composite at
different heating rates (b ¼ 10, 15, and 20 �C min�1, respec-
tively). All the peaks in the MgH2eNaAlH4 composite were
shifted when the heating rates increased. The inset of Fig. 5
shows a Kissinger’s plot of the dehydrogenation reaction for
the MgH2eNaAlH4 composite as compared with the as-milled
MgH2. (The plot refers to the MgH2-relevent decomposition,
the first of the overlapping endothermic peaks). The apparent
activation energy, EA, estimated from the Kissinger analysis
for the MgH2-relevent decomposition in MgH2eNaAlH4
composite is found to be 148 kJ/mol, which is lower than for
the as-milled MgH2 (168 kJ/mol). This indicates that mixing
with NaAlH4 reduced the activation energy and thus improved
the dehydrogenation behavior of MgH2.
To investigate the reversibility of MgH2eNaAlH4
composite, the rehydrogenation of the dehydrogenated
sample was performed under w3 MPa of H2 at 300 �C. TheMgH2 system was also examined for comparison. Fig. 6
compares the isothermal rehydrogenation kinetics of the
MgH2eNaAlH4 composite and the MgH2. From the results, the
MgH2eNaAlH4 sample shows slow absorption kinetics
compared with the MgH2. After 30 min, the MgH2eNaAlH4
sample has just absorbed 5.1 wt.% hydrogen relative to the
MgH2 sample, which can absorb as much as 6.1 wt.%
hydrogen.
Fig. 5 e DSC traces of MgH2eNaAlH4 composite at different
heating rates. The inset plot is the Kissinger’s analysis for
(a) as-milled MgH2 and (b) MgH2eNaAlH4 composite.
Fig. 6 e Isothermal rehydrogenation kinetics of the
MgH2eNaAlH4 composite and the MgH2 samples at 300 �Cand under 3 MPa.
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 en e r g y 3 6 ( 2 0 1 1 ) 9 0 4 5e9 0 5 0 9049
Fig. 7 displays the XRD patterns of the MgH2eNaAlH4
composite after rehydrogenation under w3 MPa of H2 at
300 �C. From the patterns, it can be seen that the peaks
correspond to MgH2, NaMgH3, Al and a small peak for Al3Mg2that appears after rehydrogenation. No NaAlH4 peak was
detected. The NaMgH3 phase confirms that reactions (4) and
(5) are reversible, as reported by Ikeda et al. [32]. After rehy-
drogenation, the Mg17Al12 peaks disappear, and peaks of
MgH2, Al, and small peaks of Al3Mg2 appear, indicating that
Mg17Al12 can be dissociated into Mg2Al3, MgH2, and Al (Eq. (7))
as reported by Yabe and Kuji [34], and Zhang and Wu [35].
Mg17Al12 þ ð17� 2yÞH2/yMg2Al3 þ ð17� 2yÞMgH2
þ ð12� 3yÞAl (7)
If higher hydrogenation pressure were applied, Mg2Al3would subsequently be transformed into MgH2 and Al, as
shown in Eq. (8) [36]:
Fig. 7 e XRD patterns of the MgH2eNaAlH4 composite after
rehydrogenation at 300 �C and under 3 MPa.
Mg2Al3 þ 2H2/2MgH2 þ 3Al (8)
In this study, Mg2Al3 was hardly to transform intoMgH2 and
Al due to the lower hydrogenation pressure applied (3 MPa).
This phenomenon is similar to that reported by Zhang et al.
[22] for MgH2eLiAlH4 (4:1) composite, in which their sample
was rehydrogenated under 4 MPa. For comparison, Chen et al.
[24] reported that no Mg2Al3 phase was detected from their
MgH2eLiAlH4 (4:1) composite sample after rehydrogenation at
350 �C and under 10 MPa, implying that reaction (8) occurred
when the higher hydrogen pressure was applied. The slow
absorption kinetics in the MgH2eNaAlH4 composite may due
to the yield of Mg2Al3.
From the results, it can be pointed out that the role of
NaAlH4 in this study is quite similar to the role of LiAlH4 in the
MgH2eLiAlH4 composite system. The formation of Mg17Al12phase as a reaction product of MgH2 with Al during the
dehydrogenation process may create a beneficial pathway for
hydrogen atom diffusion to the surface and recombination,
while it improves the thermodynamic properties of the
MgH2eNaAlH4 composite system, as reported by Zhang et al.
[22] and Chen et al. [24] for the MgH2eLiAlH4 (4:1) composite.
Besides Mg17Al12 phase, Zhang et al. [22] also claimed that
a catalytic effectmay also be contributed by Li0.92Mg4.08 phase,
which is formed as a reaction product of MgH2 with LiH during
the dehydrogenation process in the MgH2eLiAlH4 composite
system. In our study, the reaction of MgH2 with NaAlH4
formed a perovskite-type hydride, NaMgH3, and this product
may also play a catalytic role in enhancement of the dehy-
drogenation behavior of MgH2eNaAlH4 composite. This
hypothesis is still under investigation and will be presented in
a further report.
4. Conclusion
In summary, we have demonstrated that the hydrogen
desorption properties of MgH2 were improved after mixing
with NaAlH4. From the TPD results, theMgH2 in the composite
starts to release hydrogen at about 280 �C, compared with
330 �C for as-milled MgH2. This composite also showed strong
improvement in the dehydrogenation kinetics. The TPD
results show that the dehydrogenation process in the
MgH2eNaAlH4 (4:1) composite can be divided into four stages:
the first dehydrogenation stage can be attributed to the reac-
tion of NaAlH4 and MgH2. The second dehydrogenation stage
is due to the MgH2 react with Al accompanied with the self-
decomposition of excessive MgH2; the third dehydrogenation
stage can be ascribed to the decomposition of NaMgH3; and
the last dehydrogenation stage is due to the decomposition of
NaH. The Kissinger plots for different heating rates in DSC
show that the apparent activation energy, EA, for decompo-
sition of MgH2-relevent in theMgH2eNaAlH4 (4:1) composite is
reduced to 148 kJ/mol compared with 168 kJ/mol for the as-
milled MgH2. We believe that the formation of Mg17Al12phase during the dehydrogenation process plays a critical role
in the enhancement of dehydrogenation in MgH2eNaAlH4
composite. However, the rehydrogenation measurements
revealed that the MgH2eNaAlH4 (4:1) composite did not show
any improvement compared with the as-milled MgH2.
i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 9 0 4 5e9 0 5 09050
Acknowledgments
The authors thank the University of Wollongong for financial
support of this research. M. Ismail acknowledges the Ministry
of Higher Education Malaysia for a PhD scholarship. Many
thanks also go to Dr. T. Silver for critical reading of the
manuscript.
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