Thermodynamic changes in mechanochemically synthesized magnesium hydride nanoparticles

Article abstract of DOI:10.1021/ja908398u

The thermodynamic properties of magnesium hydride nanoparticles have been investigated by hydrogen decomposition pressure measurements using the Sieverts technique. A mechanochemical method was used to synthesize MgH₂ nanoparticles (down to ～7 nm in size) embedded in a LiCl salt matrix. In comparison to bulk MgH₂, the mechanochemically produced MgH ₂ with the smallest particle size showed a small but measurable decrease in the decomposition reaction enthalpy (IH decrease of 2.84 kJ/mol H₂ from IH_bulk = 74.06 ± 0.42 kJ/mol H₂ to IH_nano = 71.22 ± 0.49 kJ/mol H ₂). The reduction in IH matches theoretical predictions and was also coupled with a similar reduction in reaction entropy (IS decrease of 3.8 J/mol H₂/K from IS_bulk = 133.4 ± 0.7 J/mol H₂/K to IS_nano = 129.6 ± 0.8 J/mol H₂/K). The thermodynamic changes in the MgH₂ nanoparticle system correspond to a drop in the 1 bar hydrogen equilibrium temperature (T_{1 bar}) by ～6 A°C to 276.2 ± 2.4 A°C in contrast to the bulk MgH₂ system at 281.8 ± 2.2 A°C. The reduction in the desorption temperature is less than that expected from theoretical studies due to the decrease in IS that acts to partially counteract the effect from the change in IH.

Full text of DOI:10.1021/ja908398u

Published on Web 03/22/2010
Thermodynamic Changes in Mechanochemically Synthesized
Magnesium Hydride Nanoparticles
Mark Paskevicius,† Drew A. Sheppard,† and Craig E. Buckley*,†,‡
Department of Imaging and Applied Physics, Curtin UniVersity of Technology, GPO Box U
1987, Perth WA 6845, Australia and CSIRO National Hydrogen Materials Alliance, CSIRO
Energy Centre, 10 Murray Dwyer Circuit, Steel RiVer Estate NSW 2304, Australia
Received October 2, 2009; E-mail: C.Buckley@curtin.edu.au
Abstract: The thermodynamic properties of magnesium hydride nanoparticles have been investigated by
hydrogen decomposition pressure measurements using the Sieverts technique. A mechanochemical method
was used to synthesize MgH2 nanoparticles (down to ∼7 nm in size) embedded in a LiCl salt matrix. In
comparison to bulk MgH2, the mechanochemically produced MgH2 with the smallest particle size showed
a small but measurable decrease in the decomposition reaction enthalpy (∆H decrease of 2.84 kJ/mol H2
from ∆Hbulk ) 74.06 ( 0.42 kJ/mol H2 to ∆Hnano ) 71.22 ( 0.49 kJ/mol H2). The reduction in ∆H matches
theoretical predictions and was also coupled with a similar reduction in reaction entropy (∆S decrease of
3.8 J/mol H2/K from ∆Sbulk ) 133.4 ( 0.7 J/mol H2/K to ∆Snano ) 129.6 ( 0.8 J/mol H2/K). The thermodynamic
changes in the MgH2 nanoparticle system correspond to a drop in the 1 bar hydrogen equilibrium temperature
(T1 bar) by ∼6 °C to 276.2 ( 2.4 °C in contrast to the bulk MgH2 system at 281.8 ( 2.2 °C. The reduction
in the desorption temperature is less than that expected from theoretical studies due to the decrease in ∆S
that acts to partially counteract the effect from the change in ∆H.
Introduction
the onset temperature can be determined by kinetics, leading
to problems with this method of thermodynamic determination.8
Recent theoretical work9 suggests that a reduction in MgH2
particle size below 10 nm can result in thermodynamic
destabilization of the hydride phase with a consequent lowering
of the desorption temperature. This effect is expected to be
pronounced for particles below 3 nm in diameter.9-12 As a result
of the promising theoretical investigations a number of recent
attempts have been made to experimentally synthesize Mg or
MgH2 nanoparticles in this size range which include the
following: a melt infiltration technique being applied to syn-
thesize <5 nm13 Mg nanocrystallites or <30 nm Mg nanopar-
ticles14 supported in carbon frameworks, the sonoelectrochem-
ical production of Mg particles reported to be 4 nm,15 the
formation of MgH2 embedded within a carbon aerogel scaffold
by deposition of a dibutylmagnesium precursor,16 and the
Magnesium hydride has a high gravimetric hydrogen storage
capacity (7.7 wt %) and has been studied in detail over the past
50 years.1 However its use as a commercial hydrogen storage
material has been impeded by a high thermal stability and poor
sorption kinetics. Recently the kinetics issue has largely been
overcome by introducing catalytic oxides during ball milling,2,3
but to the authors’ knowledge no alterations to the thermody-
namics of pure MgH2 have been experimentally achieved to
date. Some studies in the literature utilize Differential Scanning
Calorimetry (DSC) to measure changes in the desorption
temperature of MgH2.4-6 However these studies often overlook
the fact that the DSC signal contains both a thermal and kinetic
component7 and in many hydride systems (including MgH2)
† Curtin University of Technology.
‡ CSIRO Energy Centre.
(8) Rongeat, C.; Llamas-Jansa, I.; Doppiu, S.; Deledda, S.; Borgschulte,
A.; Schultz, L.; Gutfleisch, O. J. Phys. Chem. B 2007, 111, 13301–
13306.
(1) Manchester, F. D.; San-Martin, A. H-Mg (Hydrogen-Magnesium). In
Phase Diagrams of Binary Hydrogen Alloys; Manchester, F. D., Ed.;
ASM International: OH, 2000.
(2) Barkhordarian, G.; Klassen, T.; Bormann, R. J. Alloys Compd. 2004,
364, 242–246.
(9) Kim, K. C.; Dai, B.; Johnson, J. K.; Sholl, D. S. Nanotechnol. 2009,
20, 204001.
(10) Liang, J. J. Appl. Phys. A: Mater. Sci. Proc. 2005, 80, 173–178.
(11) Wagemans, R. W. P.; van Lenthe, J. H.; de Jongh, P. E.; van Dillen,
A. J.; de Jong, K. P. J. Am. Chem. Soc. 2005, 127, 16675–16680.
(12) Cheung, S.; Deng, W. Q.; vanDuin, A. C. T.; Goddard, W. A. J. Phys.
Chem. A 2005, 109, 851–859.
(3) Aguey-Zinsou, K. F.; Nicolaisen, T.; Ares Fernandez; J, R.; Klassen,
T.; Bormann, R. J. Alloys Compd. 2007, 434-435, 738–742.
(4) Dobrovolsky, V. D.; Ershova, O. G.; Solonin, Y. M.; Khyzhun, O. Y.;
Paul-Boncour, V. J. Alloys Compd. 2008, 465, 177–182.
(5) Ershova, O. G.; Dobrovolsky, V. D.; Solonin, Y. M.; Khyzhun, O. Y.;
Koval, A. Y. J. Alloys Compd. 2008, 464, 212–218.
(6) Yu, X. B.; Guo, Y. H.; Yang, Z. X.; Guo, Z. P.; Liu, H. K.; Dou,
S. X. Scr. Mater. 2009, 61, 469–472.
(13) de Jongh, P. E.; Wagemans, R. W. P.; Eggenhuisen, T. M.; Dauvillier,
B. S.; Radstake, P. B.; Meeldijk, J. D.; Geus, J. W.; de Jong, K. P.
Chem. Mater. 2007, 19, 6052–6057.
(14) Gross, A. F.; Ahn, C. C.; Van Atta, S. L.; Liu, P.; Vajo, J. J.
Nanotechnol. 2009, 20, 204005.
(7) Marsh, K. N.; Ott, J. B.; Wormald, C. J.; Yao, H.; Hatta, I.; Claudy,
P. M.; Herwaarden, S. V.; A.R.H. Goodwin, K. N. M.; Wakeham,
W. A. Calorimetry. In Experimental Thermodynamics; Elsevier: 2003;
Vol 6, pp 325-385.
(15) Haas, I.; Gedanken, A. Chem. Commun. 2008, 1795–1797.
(16) Zhang, S.; Gross, A. F.; Van Atta, S. L.; Maribel, L.; Liu, P.; Ahn,
C. C.; Vajo, J. J.; Jensen, C. M. Nanotechnol. 2009, 20, 204027.
9
10.1021/ja908398u  2010 American Chemical Society
J. AM. CHEM. SOC. 2010, 132, 5077–5083 5077

A R T I C L E S
Paskevicius et al.
formation of 5 nm colloidal Mg17 that appears to be stabilized
by an adduct.18 Despite the number of nano-Mg and nano-MgH2
synthesis methods there is still no experimental evidence of the
thermodynamic destabilization of the Mg-H system being
attributed solely to particle size effects.
Table 1. Summary of Thermodynamic Data for MgH2
Decomposition Available in the Literature
Temperature
Range (°C)
Enthalpy
(∆H, kJ/mol H2)
Entropy
(∆S, J/mol H2/K)
Source
Stampfer 196021
Reilly 196822
314-576
276-350
303-390
280-370
270-345
350-400
74.4 ( 0.3
77.4 ( 4.2
70
74.3 ( 0.5
81.86
135.1 ( 1.9
138.3 ( 2.9
126
136 ( 1
146.1
Herein, MgH2 nanoparticles were produced using a mechan-
ochemical method, allowing for control over the size of the
MgH2 particles produced by the addition of an inert LiCl
buffering material.18 Mechanochemical synthesis involves a
chemical reaction that is initiated using mechanical milling.
Usually a reaction byproduct phase is also formed during milling
that can act to separate the desired reaction product. The phase
separation can be enhanced by the addition of large quantities
of a buffer material to the chemical reagents leading to product
particle sizes down to 4 nm.19 The buffer is often chosen as the
reaction byproduct phase for simplicity and to facilitate its
extraction if so desired. The MgH2 samples and the effect of
the buffering material (LiCl) on the microstructure evolution
have previously been characterized by synchrotron X-ray
Diffraction and Transmission Electron Microscopy.18
Pedersen 198323
Friedlmeier 198824
Klose 199525
Shao 200426
75.0
135.6
is taken into account using a fundamental parameters approach in
Topas (Bruker AXS) that was verified using a NIST 660a LaB6
reference standard. The sample was loaded into an XRD sample
holder in an argon glovebox and sealed with a poly(methyl-
methacrylate) (PMMA) airtight bubble to prevent oxygen/moisture
contamination during data collection. The crystallite sizes were
determined from an LVol-IB method (volume averaged column
height calculated from the integral breadth)20 that provides a good
measure of the volume-weighted average crystallite size.
Hydrogen sorption experiments were performed in a manometric
apparatus. The digital pressure gauge (Rosemount 3051S) had a
precision and accuracy of 14 mbar, while room temperature
measurements were recorded using a 4-wire platinum resistance
temperature detector (RTD). The determination of correct thermo-
dynamic properties requires measurements with high levels of
accuracy and precision. The Sieverts apparatus that was utilized
allows for small thermodynamic changes to be discerned due to
the high precision pressure and temperature data that are collected.
Due to limitations with extremely slow kinetics full pressure-
composition isotherms were not generated. As such, equilibrium
pressure data were collected over the hydrogen equilibrium plateau
between hydrogen to metal ratios (H/M) of 0.8 to 1.8 in the
temperature range 300 to 360 °C. Due to the flat nature of the
equilibrium plateau in the Mg-H system, repeat equilibrium
measurements over this range were found to be equivalent within
reported uncertainties. For example, at 360 °C equilibrium pressures
of 8.05 ( 0.02 bar and 8.06 ( 0.03 bar were measured at H/M
ratios of 1.28 and 1.78 respectively for a given sample. Further
details are provided in the Supporting Information on the hydrogen
sorption apparatus and on the methods and uncertainties involved
in equilibrium measurements and thermodynamic calculations.
Experimental Details
All handling of chemicals and sealable milling canisters was
undertaken in an argon-atmosphere glovebox to minimize oxygen
(O2 < 1 ppm) and water (H2O < 1 ppm) contamination. LiH (Sigma-
Aldrich, 95%), MgCl2 (Sigma-Aldrich, g98%), and LiCl (Sigma-
Aldrich, g99%) were used as starting reagents. The reagents were
all individually milled for 3 h using a ball to powder ratio (B/P) of
30:1 prior to use. Ball milling was performed at room temperature
with a custom-made 316 stainless steel ball milling canister (650
cm3 internal volume) attached to a Glen Mills Turbula T2C shaker
mixer. All samples were milled for 18 h using a 90:1 B/P with
equal numbers of 7.9 mm and 12.7 mm 316 stainless steel balls in
5-10 g batches.
Magnesium hydride was synthesized mechanochemically at room
temperature according to the following reaction:
2LiH + MgCl2 f MgH2 + 2LiCl ∆rG298K ) -72.8 kJ/mol
(1)
To promote nanoparticle production a LiCl reaction buffer was
used to separate the as-synthesized MgH2 particles. The amount of
LiCl added to each sample corresponded to 0 (sample MgH2-A),
1.05 (sample MgH2-B), 2.62 (sample MgH2-C), and 6.82 (sample
MgH2-D) mol of LiCl added to the left-hand side of eq 1. A
purchased MgH2 (Sigma-Aldrich, g96.5%) powder sample was also
ball milled without LiCl for 18 h using a B/P of 90:1 for use as a
MgH2 reference material, designated forthwith as MgH2-Purchased.
Further synthesis details can be found in Sheppard et al.18
Transmission electron microscopy (TEM) was conducted on a
JEOL 3000F FEGTEM instrument operating at 300 kV. Samples
were loaded onto 200 mesh copper grids with holey carbon support
films dropwise via suspension in toluene. Samples must be exposed
to air before being loaded into the TEM column; however the air-
exposure time was kept as short as possible (up to a few minutes).
X-ray diffraction (XRD) on MgH2-Purchased was performed
using a Bruker D8 Advance diffractometer (Cu KR radiation) with
a 2θ range of 10°-100° using 0.02° steps with 0.8 s of count time
per step with operating conditions of 40 kV and 40 mA. The XRD
instrument was equipped with a LynxEye 3° linear position sensitive
detector (PSD) with 192 pixels. The instrumental line broadening
Results and Discussion
Bulk MgH2 Thermodynamic Properties. The generally ac-
cepted thermodynamic properties for the Mg-H system were
provided by Stampfer, J. F., Jr. et al. in 196021 (see Table 1).
Stampfer’s data are often preferred due to the large number of
data points collected over a wide temperature range.1 However
it must be noted that the accuracy of this data set is quite low.
Listed equilibrium pressure values vary by up to 9% at the same
sample temperature. The percentage error in Stampfer’s pressure
data is lower at high temperatures, but repeated equilibrium
pressures still vary by 3 bar at 444 °C. The thermodynamic
data from a number of sources provided in Table 1 illustrate
the wide spread in the reported decomposition enthalpy (∆H)
and entropy (∆S) data for MgH2 as measured under similar
temperature conditions. The large discrepancies between the
determined ∆H and ∆S values are likely a result of the poor
MgH2 desorption kinetics not being adequately accounted for
in some studies. If the Mg-H system does not reach a true
(17) Aguey-Zinsou, K.-F.; Ares-Ferna´ndez, J.-R. Chem. Mater. 2008, 20,
376–378.
(18) Sheppard, D. A.; Paskevicius, M.; Buckley, C. E. J. Alloys Compd.
2010, 492, L72–L74.
(20) Coelho, A. A. Topas User Manual, 3.0 ed.; Bruker AXS GmbH:
Karlsruhe, Germany, 2003.
(21) Stampfer, J. F., Jr.; Holley, C. E., Jr.; Suttle, J. F. J. Am. Chem. Soc.
1960, 82, 3504–3508.
(19) McCormick, P. G.; Tsuzuki, T.; Robinson, J. S.; Ding, J. AdV. Mater.
2001, 13, 1008–1010.
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Thermodynamics of Magnesium Hydride Nanoparticles
A R T I C L E S
Table 2. Summary of MgH2 Particle and Crystal Size Information
equilibrium pressure then the resultant thermodynamic values
calculated from these pressures will be biased.
As Determined by TEM and XRD18
Hydrogen equilibrium pressure measurements can be used
to determine thermodynamic quantities using the van’t Hoff
relationship for hydrogen desorption:
TEM average
particle size
XRD average
crystallite size
MgH2-A
MgH2-B
MgH2-C
MgH2-D
1-2 µm
15-40 nm
12-20 nm
2-7 nma
N/A
10.1 ( 0.3 nm
7.6 ( 0.3 nm
6.7 ( 0.4 nm
6.7 ( 0.7 nm
6.4 ( 0.1 nm
feq
∆H
RT
∆S
R
ln
) -
+
(2)
( )
f0
MgH2-Purchased
a Only crystallites could be discerned from the homogeneous sample.
where feq is the fugacity of hydrogen under equilibrium at a
given temperature T, f0 is a reference fugacity of 1 bar, and R
) 8.3145 J/K/mol H2 is the gas constant. The fugacity is the
activity of the real gas which provides a better representation
of the chemical potential of the system than pressure. In turn,
the fugacity (and hence pressure) can be calculated from ∆H
and ∆S using the exponential of eq 2 as follows (where f0 )
1):
pressure data extend up to ∼280 bar where the compressibility
of hydrogen is vital in determining accurate fugacity values.
Reprocessing Stampfer’s pressure data reveals that the fugacity
values that were calculated using the Beattie-Bridgeman EOS
do not match fugacities calculated using more recent EOS
models.30,33 The disparity leads to a change in Stampfer’s
reported ∆H and ∆S values from 74.4 ( 0.3 kJ/mol H2 and
135.1 ( 1.9 J/mol H2/K to 76.2 ( 1.1 kJ/mol H2 and 137.4 (
1.4 J/mol H2/K respectively. The uncertainties for the repro-
cessed data were calculated using the weighted least-squares
method explained in the Supporting Information. Given the large
∼2% difference in calculated ∆H and ∆S values by using
different EOS models, it can be seen that an accurate fugacity
is essential in determining accurate thermodynamics from a van’t
Hoff plot, especially when dealing with high measured pressures.
Reilly and Wiswall22 also calculated the decomposition ther-
modynamics of the Mg-H system as shown in Table 1. Although
they report that the enthalpy and entropy are converted to 25
°C, reprocessing their data shows that these thermodynamic
properties are in fact not converted and are valid at their
temperature range midpoint (313 °C). Reprocessing of Reilly’s
raw pressure data using fugacity (calculated using a modern
EOS) also results in different enthalpy and entropy values (∆H
) 78.8 kJ/mol H2 and ∆S ) 140.9 J/mol H2/K) than those
originally reported in Table 1.
MgH2 Samples. Four samples of MgH2 were mechanochemi-
cally synthesized according to eq 1 using various amounts of
LiCl buffer added to premilled starting reagents prior to milling.
Large quantities of LiCl buffer act to separate the synthesized
MgH2 particles, essentially restricting particle growth and
promoting nanoparticle formation. The LiCl is also essential in
forming a barrier to particle growth during thermodynamic
investigations where samples are heated up to 360 °C. Each of
the four mechanochemically synthesized samples differed
dramatically in its structural features as investigated with
transmission electron microscopy (TEM) in the synthesis
study.18 MgH2 particle and crystal sizes are provided in Table
2 for all of the samples analyzed.
∆H ∆S
-
+
(
)
feq ) e
(3)
RT
R
The determination of ∆H and ∆S from a van’t Hoff plot (ln
feq against 1/T) relies upon a straight line fit to the experimental
data. The thermodynamic parameters are only weakly temper-
ature dependent27 allowing the linear approximation to be valid
over a limited but large temperature range.28 The pressure and
fugacity can be related when the compressibility of hydrogen
is taken into account by using29
Vm
p
f
p
1
p
ln
)
-
dp
(4)
∫
(
)
( )
0
RT
where Vm is the molar volume of H2 which is calculated from
an equation of state (EOS) for hydrogen. The Hemmes equation
of state (EOS)30 and the method of McLennan and Gray31 were
used to account for the compressibility of hydrogen. The
fugacity is often assumed to be equal to pressure due to the
small deviation from the ideal gas law at low pressures.
However, for our equilibrium measurements at 360 °C the
difference between the measured pressure and the fugacity was
of a similar magnitude to the uncertainty in the measured
pressure. Consequently all measured pressures were converted
to their fugacities using eq 4 to provide higher accuracy
thermodynamic data.
The requirement of fugacity in determining thermodynamics
from a van’t Hoff plot is especially important when dealing
with higher pressure data. For example Stampfer, J. F., Jr. et
al.21 utilize the Beattie-Bridgeman EOS32 to account for the
compressibility of hydrogen and to calculate the fugacity of
hydrogen at a given pressure and temperature. Stampfer’s
The MgH2 particle size decreases from several micrometers
in size for MgH2-A to 12-20 nm for MgH2-C. Comparison of
the particle size from TEM of MgH2-C with its crystallite size
from XRD suggests that the MgH2 particles consist of a few
individual crystallites. TEM of MgH2-D was largely homoge-
neous with no obvious particle morphology. Thus only crystallite
(22) Reilly, J. J.; Wiswall, R. H. Inorg. Chem. 1968, 7, 2254–2256.
(23) Pedersen, A. S.; Kjøller, J.; Larsen, B.; Vigeholm, B. Int. J. Hydrogen
Energy 1983, 8, 205–211.
(24) Friedlmeier, G. M.; Bolcich, J. C. Int. J. Hydrogen Energy 1988, 13,
467–474.
(25) Klose, W.; Stuke, V. Int. J. Hydrogen Energy 1995, 20, 309–316.
(26) Shao, H.; Wang, Y.; Xu, H.; Li, X. Mater. Sci. Eng., B 2004, 110,
221–226.
(27) Atkins, P.; Paula, J. d. Atkins’ Physical Chemistry, 7th ed.; Oxford
University Press: New York, 2002.
(32) Holley, C. E., Jr.; Worlton, W. J.; Zeigler, R. K. Compressibility
Factors and Fugacity Coefficients Calculated from the Beattie-
Bridgeman Equation of State for Hydrogen, Nitrogen, Oxygen, Carbon
Dioxide, Ammonia, Methane and Helium; Los Alamos Scientific
Laboratory, LA-2271, 1958.
(33) Lemmon, E. W.; McLinden, M. O.; Friend, D. G. Thermophysical
Properties of Fluid Systems. In NIST Standard Reference Database
Number 69; Linstrom, P. J., Mallard, W. G., Eds.; National Institute
of Standards and Technology: Gaithersburg, MD, 2005.
(28) Ragone, R.; Colonna, G. J. Phys. Chem. 1995, 99, 13050.
(29) Marchi, C. S.; Somerday, B. P.; Robinson, S. L. Int. J. Hydrogen
Energy 2007, 32, 100–116.
(30) Hemmes, H.; Driessen, A.; Griessen, R. J. Phys. C: Solid State Phys.
1986, 19, 3571–3585.
(31) McLennan, K. G.; Gray, E. M. Meas. Sci. Technol. 2004, 15, 211–
215.
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A R T I C L E S
Paskevicius et al.
Figure 1. Transmission electron microscope (TEM) micrograph of lattice
fringing in MgH2-D occurring from the MgH2 hkl ) 020 plane. The
crystallites are 2-7 nm in size.
Figure 3. Kinetic hydrogen desorption data for MgH2-D illustrating that
equilibrium was reached at all temperatures.
unless the preferential cleavage along particular γ-MgH2 crystal
planes is taken into account.
Thermodynamics. Thermodynamic investigations were un-
dertaken by measuring hydrogen desorption equilibrium pres-
sures at 300, 320, 340, and 360 °C for each of the mecha-
nochemically synthesized samples in addition to the MgH2-
Purchased sample. Kinetic pressure and temperature data was
collected at 120 s intervals for every measurement, and very
long collection times (g48 h) were implemented to ensure true
Mg-H equilibrium was reached in each case. It is often
ambiguous as to whether MgH2 data presented in the literature
are actually at equilibrium or whether data collection was ceased
prematurely. Certain studies present pressure-composition
isotherms (PCIs) that appear to be severely affected by kinet-
ics.26 PCI curves often display large amounts of hysteresis that
could simply be due to an inadequate measurement time. If one
does not wait until true equilibrium is met, then measured
absorption pressures will be higher than the true equilibrium
and measured desorption pressures will be lower than the true
equilibrium, leading to an apparent hysteresis. Kinetic plots
allow for an assessment of whether true equilibrium is met.
Certain PCI features such as a shortened equilibrium plateaux
at low temperatures can also indicate that the true equilibrium
has not been met. These features can be due to the slower
kinetics at low temperatures and the slower kinetics at extreme
hydrogen to metal ratios not being accounted for adequately.
In our research, care was taken in an effort to provide high
quality equilibrium data for MgH2 to provide accurate bulk
thermodynamic data and to study the variation in thermodynam-
ics with changes in MgH2 particle size.
Figure 2. X-ray diffraction (XRD) pattern for MgH2-Purchased after 18 h
of ball milling with 90:1 B/P. A Rietveld fit to the data is shown along
with a difference plot.
sizes could be determined from high magnification lattice
fringing as shown in Figure 1. Of note is that only the hkl )
020 plane of MgH2 could be discerned from TEM. It may be
possible that there is MgH2 crystal growth along a preferred
crystallographic axis in the mechanochemically synthesized
nanoparticles.
The MgH2-Purchased sample was analyzed with XRD after
being ball milled for 18 h as shown in Figure 2. Two MgH2
crystalline phases (ꢀ and γ) were detected along with small
quantities of MgO and Mg impurities. The γ-MgH2 phase has
previously been shown to form during ball milling.34 The
Rietveld fit to the XRD data for MgH2-Purchased does not
adequately model the peak intensities from the γ-MgH2 phase
The kinetics of decomposition are quite slow for the mecha-
nochemically synthesized MgH2 samples. This can be attributed
to the fact that the MgH2 particles are embedded within a LiCl
salt byproduct matrix. Kinetic hydrogen desorption data are
provided in Figure 3 that illustrates the majority of decomposi-
tion occurs within 2-5 h; however minor but significant changes
in pressure are still evident until 24 h have passed. It is likely
that small MgH2 nanoparticles that are not embedded within a
LiCl matrix would present very fast hydrogen sorption kinetics.
However removal of the LiCl byproduct phase has proven
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Thermodynamics of Magnesium Hydride Nanoparticles
A R T I C L E S
Table 3. Measured Equilibrium Pressures and Thermodynamic Properties for Mechanochemically Synthesized and Purchased MgH2
Samplesa
MgH2-Purchased
MgH2-A
MgH2-B
MgH2-C
MgH2-D
Pressure at 300 °C (bar)
1.636 ( 0.020
2.789 ( 0.019
4.581 ( 0.021
7.196 ( 0.019
74.06 ( 0.42
133.4 ( 0.7
1.622 ( 0.018
2.763 ( 0.019
4.506 ( 0.022
7.092 ( 0.027
73.92 ( 0.45
133.1 ( 0.7
1.671 ( 0.019
2.837 ( 0.020
4.622 ( 0.021
7.370 ( 0.020
74.75 ( 0.42
134.7 ( 0.7
1.824 ( 0.017
3.146 ( 0.018
5.086 ( 0.017
8.053 ( 0.023
74.15 ( 0.37
134.5 ( 0.6
1.919 ( 0.018
3.134 ( 0.020
5.019 ( 0.019
7.862 ( 0.044
71.22 ( 0.49
129.6 ( 0.8
Pressure at 320 °C (bar)
Pressure at 340 °C (bar)
Pressure at 360 °C (bar)
Decomposition enthalpy (∆H, kJ/mol H2)
Decomposition entropy (∆S, J/mol H2/K)
Calculated 1 bar H2 equilibrium
temperature (T1 bar) (°C)
281.8 ( 2.2
282.2 ( 2.2
281.7 ( 2.1
278.1 ( 2.1
276.2 ( 2.4
a Uncertainties are calculated with a 95% confidence interval with further details provided in the Supporting Information.
difficult due to the reactivity of MgH2 with a range of solvents
capable of dissolving LiCl. For example, the ball-milled MgH2-
Purchased as well as the mechanochemically synthesized MgH2
showed obvious gas evolution on addition to tetrahydrofuran
unlike the early work of Ashby35 in synthesizing MgH2 in
tetrahydrofuran and diethyl ether. If the LiCl phase was removed
however, it is also very likely that the MgH2 nanoparticles would
agglomerate into much larger particles, especially at the high
temperatures required for decomposition.
Given the slow kinetics of desorption, the hydrogen equilib-
rium pressures were determined by averaging the final 6 h of
pressure data as presented in Table 3, with uncertainties
calculated with a 95% confidence interval from the 180 averaged
data points. It is evident that there is a change in the hydrogen
equilibrium pressures between the samples analyzed. The
equilibrium pressures for MgH2-A and MgH2-B are similar to
the pressures obtained for MgH2-Purchased at all measured
temperatures. The similarity in equilibrium pressures is expected
for MgH2-A due to the large MgH2 particle size (1-2 µm) which
is effectively bulk MgH2. However the similarity between the
equilibrium pressures of MgH2-B and MgH2-Purchased is
interesting as the MgH2-B particle size from TEM was found
to be in the range of 15-40 nm. The result indicates that MgH2
particle sizes smaller than this are required to observe measur-
able thermodynamic changes, as is predicted by theoretical
studies. An appreciable increase in the equilibrium pressure is
found for both MgH2-C and MgH2-D in comparison to MgH2-
Purchased at all measured temperatures (Table 3). It can be
deduced that the change in equilibrium pressure is a result of
thermodynamic changes within the Mg/MgH2 system due to
nanoscopic particle size, as this is the only variable between
the mechanochemically synthesized samples.
A van’t Hoff plot was constructed as shown in Figure 4 that
illustrates the change in measured pressures for MgH2-C and
MgH2-D that have average particle sizes below 20 nm. The
decomposition reaction enthalpy (∆H) and entropy (∆S) were
calculated by a weighted least-squares method (explained in
detail in the Supporting Information) and are provided in Table
3. ∆H for MgH2-Purchased is equivalent to ∆H for MgH2-A,
MgH2-B, and even MgH2-C within uncertainty; however a
reduction in ∆H of 2.84 kJ/mol H2 is determined for MgH2-D
in contrast to the bulk. The measured change in ∆H for MgH2-D
is similar to theoretical predictions for ∼4 nm MgH2 nanopar-
ticles by Kim et al.9 The average MgH2 particle size in MgH2-D
cannot be smaller than the average crystallite size (6.7 ( 0.7
nm) as determined by XRD. The small difference between the
experimentally measured minimum particle size (6.7 nm) and
Figure 4. van’t Hoff plot for the decomposition of MgH2 in the four
mechanochemically synthesized samples as well as the bulk reference
(MgH2-Purchased).
the theoretically predicted particle size (4 nm) for the given
change in ∆H may simply relate to minor inaccuracies in the
theoretical model. However it is also likely that some MgH2
particle size polydispersity exists within MgH2-D. If significant
levels of polydispersity exist, the hydrogen equilibrium pressure
will be controlled by certain MgH2 particle sizes at different
H/M ratios. Desorption measurements for each sample began
at H/M ) 2. It follows that initially the particles with the
smallest size will contribute to the equilibrium pressure (above
the bulk value) due to their larger change in ∆H and hence
higher inherent equilibrium pressure. As the hydrogen in the
smallest particles is exhausted, the elevated equilibrium pressure
will no longer be maintained and the equilibrium pressure will
begin to approach the bulk value. In the present work the
equilibrium pressure was found to be repeatable (within
uncertainty) at the different H/M ratios (0.8-1.8) in which
measurements were taken. Given the change in ∆H measured
for MgH2-D, it is likely that the equilibrium pressure in this
H/M range is controlled by small MgH2 particles while larger
particles (with larger crystallite sizes) may dominate equilibrium
pressures at lower H/M ratios.
Figure 5a provides a visual representation of the calculated
∆H and ∆S quantities for each of the samples analyzed. There
is an interesting correlation between ∆H and ∆S where a lower
(34) Bououdina, M.; Grant, D.; Walker, G. Int. J. Hydrogen Energy 2006,
31, 177–182.
(35) Ashby, E. C.; Schwartz, R. D. Inorg. Chem. 1971, 10, 355–357.
9
J. AM. CHEM. SOC. VOL. 132, NO. 14, 2010 5081

A R T I C L E S
Paskevicius et al.
predicting the 1 bar desorption temperature.9,11 Recently Fich-
tner37 noted that nothing had been reported to date on whether
changes in ∆S with particle size would positively or negatively
affect equilibrium pressures. In a bulk system the reaction
entropy (∆S) upon MgH2 f Mg + H2 at 25 °C can be expressed
as SMg (32.5 J/mol H2/K) + SH (130.0 J/mol H2/K) - SMgH
2
2
(31.1 J/mol H2/K) ) ∆S (131.4 J/mol H2/K).38 SH is not affected
2
by alterations in the particle structure, but it can be seen that a
disproportionate change in the entropy of Mg and MgH2 with
particle size would lead to a change in ∆S. A lower ∆S will be
generated if the entropy of a MgH2 nanoparticle increases by a
greater quantity than the entropy for a Mg nanoparticle as
particle size is reduced.
The measured thermodynamics for MgH2-D acts to lower the
1 bar hydrogen equilibrium temperature (T1 bar) (see Table 3)
as predicted by theoretical investigations.9-12 However, the
measured reduction in T1 bar is not in line with the magnitude
of the changes predicted. Herein T1 bar is reduced by ∼6 °C for
MgH2-D in contrast to the bulk (MgH2-Purchased). A reduction
in T1 bar of ∼4 °C is also found for MgH2-C even though its
enthalpy was found to be close to that of the bulk. The result
indicates that entropy also plays a large part in determining
changes in T1 bar. Given the change in ∆H determined for
MgH2-D (2.84 kJ/mol H2) a reduction in T1 bar is theoretically
predicted to be ∼15 °C9 when using a constant bulk ∆S. This
result is in contrast to the calculated ∼6 °C reduction in T1 bar
because of the change in ∆S relative to the bulk. The fact that
a decrease in T1 bar is still observed indicates that the change in
∆H due to particle size reduction has a larger impact on T1 bar
than the corresponding change in ∆S.
Conclusions
Figure 5. (a) Calculated thermodynamic values for MgH2 decomposition
from the van’t Hoff plot in Figure 4. (b) Calculated thermodynamic values
from repeat measurements on freshly synthesized MgH2-Purchased and
MgH2-D. Uncertainties are calculated with a 95% confidence interval as
described in the Supporting Information.
Hydrogen equilibrium pressure measurements have been used
to determine the decomposition enthalpy and entropy for MgH2
nanoparticles that were mechanochemically synthesized. A
reduction in both the decomposition enthalpy and entropy was
found for ∼7 nm MgH2 nanoparticle in relation to bulk MgH2.
The consequence of this thermodynamic destabilization is a drop
in the 1 bar hydrogen equilibrium temperature of ∼6 °C. The
temperature drop is not as large as theoretical predictions due
to the effect of the decrease in reaction entropy which partially
counteracts the decrease in reaction enthalpy. It is not known
if the thermodynamics of smaller nanoparticles will be domi-
nated by changes in either the reaction enthalpy or entropy.
Further theoretical and experimental studies on MgH2 nano-
particles will need to be performed with a focus on reaction
entropy changes to accurately quantify the thermodynamic
destabilization of the Mg-H nanoparticle system to determine
whether large reductions in the 1 bar hydrogen equilibrium
temperature are possible. Though the mechanochemical syn-
thesis of MgH2 is a suitable method for producing nanosized
particles and comparing their thermodynamics to theoretical
predictions, the minor thermodynamic alterations achievable do
not justify the added level of synthesis complexity or the
hydrogen density penalties for its use as a hydrogen storage
solution.
decomposition reaction enthalpy in MgH2-D is matched by a
lower reaction entropy, and even subtle changes in enthalpy
are closely matched by corresponding changes in entropy. Mg
and MgH2 particles that have nanoscopic sizes contain a large
number of atoms that are influenced by the particle surface.36
The influence of the particle surface affects the Mg and MgH2
phases to different degrees resulting in a reduction in the overall
MgH2 decomposition reaction enthalpy (∆H). The same phase-
preferred destabilization also appears to apply to ∆S (between
Mg and MgH2). Given the contentious claim of a measured
change in the thermodynamics of nanosized MgH2 particles,
the thermodynamic measurements of MgH2-Purchased and
MgH2-D were repeated by synthesizing two completely new
batches of these samples. The values for the enthalpy and
entropy of the freshly synthesized samples both agree, within
uncertainties, of the original measurements (Figure 5b). This is
particularly encouraging given (1) ball milling does not produce
perfectly homogeneous samples and (2) the desorption equi-
librium pressures at each temperature were measured at different
H/M ratios for each sample. This confirms that the measured
changes in enthalpy and entropy for MgH2-D are real and not
an artifact of the measurement technique.
Acknowledgment. This work was carried out with the support
of the National Hydrogen Materials Alliance (NHMA). C.E.B.
acknowledges the financial support of the Australian Research
Changes in ∆S are not considered in the theoretical investiga-
tions, and instead constant bulk ∆S quantities are assumed when
(37) Fichtner, M. Nanotechnol. 2009, 20, 204009.
(38) Outukumpu. HSC Chemistry, 6.1 ed.; Chemistry Software: Houston,
(36) Sergeev, G. B. Nanochemistry; Elsevier: Amsterdam, 2006.
2006.
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Thermodynamics of Magnesium Hydride Nanoparticles
A R T I C L E S
Council through a 2007 LEIF grant LE0775551, which enabled
the XRD studies to be undertaken. The authors acknowledge the
facilities, scientific, and technical assistance of the Australian
Microscopy & Microanalysis Research Facility at the Centre for
Microscopy, Characterization & Analysis, The University of
Western Australia, a facility funded by The University, State and
Commonwealth Governments. M.P. thanks the Australian govern-
ment for the granting of Australian Post Graduate Awards with
Stipend (APAWS) and the Australian Institute of Nuclear Science
and Engineering (AINSE) for the granting of a postgraduate research
award (PGRA).
Supporting Information Available: Detailed information is
provided regarding the Sieverts apparatus, the associated
uncertainty calculations, and the reproducibility of the acquired
data. This material is available free of charge via the Internet
at http://pubs.acs.org.
JA908398U
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