APPLIED PHYSICS LETTERS 88, 161917 共2006兲
Stability of Ti in NaAlH4
O. M. Løvvika兲
Centre for Materials Science and Nanotechnology, University of Oslo, P.O. Box 1126,
Blindern, NO-0318 Oslo, Norway
S. M. Opalka
United Technologies Research Center, 411 Silver Lane, East Hartford, Connecticut 06108
共Received 7 January 2006; accepted 7 March 2006; published online 20 April 2006兲
There has been confusion which external reference should be used for predicting ground state Ti
substitution enthalpies in NaAlH4: element gaseous atomic states or standard states. It is proposed
instead to use all the relevant product phases for the Ti-enhanced sodium alanate system as internal
reference states. The results are similar to when external reference element standard states are used:
Ti doping is unstable in NaAlH4, and substitution on the Al sublattice is the least unfavorable.
Substitution near the surface is more favorable than in the bulk, thus metastable Ti substitution may
occur close to interfaces, grain boundaries, or defects. © 2006 American Institute of Physics.
关DOI: 10.1063/1.2197291兴
Sodium alanate 共NaAlH4兲 has become a model system
for solid-state storage of hydrogen in complex hydrides.1–3 It
is one of the compounds that comes closest to the international targets for hydrogen storage media, having the combination of moderate reversible hydrogen gravimetric capacity
and relatively rapid hydrogenation kinetics within the typical
temperature and pressure ranges for polymer electrolyte
membrane fuel cell operation.4–6 An improved understanding
of sodium alanate hydrogenation mechanisms would guide
the development of higher capacity hydrogen storage media
with reversible hydrogenation at moderate temperature.
A central problem is the elucidation of the role of added
Ti, which greatly enhances the kinetics of sodium alanate
solid-state transformations associated with hydrogen desorption and adsorption. The dynamical processes leading to the
fast kinetics are poorly understood, and several different
models have been introduced to explain the improvement. Ti
has been found experimentally to be bound in a dispersed,
amorphous Al1−uTiu phase,7–9 as Al3Ti 共Refs. 10 and 11兲 or
as TiH2.12 There are also claims that a part of the Ti enters
the NaAlH4 lattice.13–16
A few studies have investigated the doping hypothesis
by calculating the ground state stability of various models of
Ti-doped NaAlH4.17–21 These studies leave an apparent discrepancy: Yildirim and co-workers concluded that Ti doping
could be stable, with Ti substitution for Na being the most
favorable model,18,19 while the conclusion of our previous
work was that Ti doping was not stable, and that the most
favorable metastable model was Ti substitution for Al.17 It
was noted by Araujo et al. that this was due to the choice of
reference state,20 and their results were consistent with the
preceding articles.17–19
The present work aims to overcome the ambiguity posed
by the choice of different external reference states by introducing an internal reference. This is based on a comparison
of the products of the doping process using a number of
different models for Ti substitution in the NaAlH4 lattice,
including all the relevant phases in the reactions. This eliminates the need for an external system of reference and proa兲
Electronic mail: o.m.lovvik@fys.uio.no
vides a robust means for evaluating the relative stability of
such doping models.
All of our ground state density-functional band-structure
calculations are made with the plane-wave VASP code utilizing projector augmented wave potentials22–24 with the PW91
generalized gradient approximation,25 following the same
methodology as presented previously.17 The present calculations do in addition allow spin polarization for all the models, since this has been shown to give significant contributions to the Ti-doped models in a cluster study.26
We investigate two possibilities: Ti addition via TiCl3
salt or as Ti powder. This allows us to examine the hypothesis that the favorable formation of NaCl from the reaction of
TiCl3 with sodium alanate promotes the direct substitution of
Ti for Na in the lattice. We describe the reaction for the
addition of a molar fraction x of TiCln 共n = 0 or 3.兲
Aided by experiment, we consider the following phases
as possible outcomes of the doping reaction: NaCl, Al, Al3Ti,
as well as the doped and undoped NaAlH4 phases. We also
tried to include Na3AlH6 and TiH2 in our analysis, but this
did not change any of our results, neither quantitatively nor
qualitatively. It is also possible to avoid the formation of
these phases by tuning the temperature and compositions
used in the doping and hydrogenation procedures. We have
thus for clarity and brevity chosen to disregard those phases
in what follows, without any loss of generality.
When we assume that all Cl added in the form of TiCl3
is reacted to form NaCl, the balanced reaction equation with
no doped phase formed reads as follows;
NaAlH4 + xTiCln → nxNaCl + 共1 − nx兲NaAlH4
+ 共nx − 3x兲Al + xAl3Ti + 共2nx兲H2 .
共1兲
The right-hand side of this reaction represents all the possible observed phases in the system with Ti and corresponds
in this sense to an internal reference system of the alternative
phases that we want to investigate.
Suppose now that w moles of a doped phase are formed
by substituting either Na or Al with ␣ moles Ti in NaAlH4.
We also open the possibility that additional vacancies are
0003-6951/2006/88共16兲/161917/3/$23.00
88, 161917-1
© 2006 American Institute of Physics
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161917-2
Appl. Phys. Lett. 88, 161917 共2006兲
O. M. Løvvik and S. M. Opalka
TABLE I. The calculated substitution enthalpy Hsubst of Ti-doped NaAlH4 共in kJ/mol at.兲 for the models using 16 unit cells 共96 atoms兲. Positive enthalpies are
unstable compared to the chosen reference state, either the internal reference 共defined in the text兲 or the standard state. Results are shown both for fully relaxed
and fixed unit cells. ␣ = 1 / 16 for all the models, and ␤, ␥, and ␦ have been specified for the models.
Internal reference
Model
Standard state
Relaxed
Fixed
Relaxed
Fixed
␤
␥
␦
3.44
3.51
2.90
3.03
3.17
3.55
3.54
3.05
3.03
3.29
1.83
2.97
1.27
1.38
2.63
1.93
3.00
1.42
1.38
2.75
0
1 / 16
0
0
1 / 16
0
0
1 / 16
1 / 16
1 / 16
0
0
0
1 / 16
0
Ti@Interst
Ti@Na
Ti@Al
Ti@Al+ Hv
Ti@Al+ Nav
formed simultaneously in the doped phase. Then the modified version of Eq. 共1兲 becomes
NaAlH4 + xTiCln
→ nxNaCl + 共1 − nx − w + w␤兲NaAlH4
+ 共nx − 3x + 3w␣ − w␤ + w␥兲Al
冉
冊
1
+ 共x − w␣兲Al3Ti + 2nx − 2w␤ + w␦ H2
2
+ wTi␣Na1−␤Al1−␥H4−␦ ,
共2兲
where ␤ is the fraction of Na sublattice sites substituted with
Ti, ␥ is the fraction of Al sublattice sites substituted with Ti,
and ␦ is four times the fraction of vacant H sublattice sites.
When the right-hand sides of Eqs. 共1兲 and 共2兲 are set
equal to one another and algebraically simplified by removing like terms, we arrive at the following effective disproportionation reaction for the doped phase:
Ti␣Na1−␤Al1−␥H4−␦
→ 共1 − ␤兲NaAlH4 + 共− 3␣ + ␤ − ␥兲Al + ␣Al3Ti
冉
冊
1
+ 2␤ − ␦ H2 .
2
共3兲
The resulting “internal” substitution enthalpy from this is
Hsubst共Ti␣Na1−␤Al1−␥H4−␦兲 = E共Ti␣Na1−␤Al1−␥H4−␦兲
− 共1 − ␤兲E共NaAlH4兲 − 共− 3␣ + ␤ − ␥兲E共Al兲 − ␣E共Al3Ti兲
冉
− 2␤ −
␦
2
冊
E共H2兲,
共4兲
where E共NaAlH4兲 is the calculated ground state electronic
energy 共at 0 K without zero point motion corrections兲 of the
NaAlH4 phase, etc. That is, the doped phases compete directly with the undoped sodium alanate, the mixture of Al
and Al3Ti, and hydrogen gas. Its substitution enthalpy is independent of the NaCl phase and also of the number of
moles formed of the doped phase, w. Even more interestingly, it is independent of the amount of 共x兲 and form of 共n兲
the added TiCln.
We have used ␣ = 1 / 16 in our calculations for substituting Ti in a 2 ⫻ 2 ⫻ 1 NaAlH4 supercell. This is the same as in
our previous calculations17 and was also used in the other
modeling papers.18–20 This gives a minimum distance of
1 nm between the Ti inclusions and is a reasonable model of
dilute substitution. We present here results for fully relaxed
cells and for cells with the lattice parameters fixed to the
undoped NaAlH4 ground state dimensions–the ionic posi-
tions were relaxed in both cases. The former case represents
an upper bound for the influence of dopant interactions on
the crystalline lattice, while the latter case represents the
dilute limit where there are no interactions between
dopant atoms.
Table I shows the resulting substitution enthalpies obtained for the most favorable doping models. The “internal
reference” results are the substitution enthalpies calculated
with reference to the undoped state, using Eq. 共4兲. The “standard state” results refer to the element standard states following the methodology previously described by us,17 and are
included in the table for comparison. All results are given for
both the fully relaxed and fixed lattice models. Several different representative models for Ti substitution have been
included in the table. Ti@Na and Ti@Al means that Ti was
substituted at the Na and Al sublattices, respectively. Hv
means that a hydrogen vacancy was created, allowing for
varying Ti valences. Ti@Interst denotes Ti absorption at an
interstitial site in the NaAlH4 lattice. Positive enthalpy values represent endothermic or unstable substitution of Ti.
We first note that none of the doped models are stable,
neither compared to the internal reference nor to the standard
state. Also, Al substitution is the least unstable of all the
investigated possibilities. It has been proposed that Na substitution should have been more beneficial, since the Na displaced from the substitution then could combine with Cl to
form the very stable NaCl phase, reducing the necessary
amount of NaAlH4 disproportionation. In spite of this, the Ti
substitution for Na is less favorable. It has been shown in
another theoretical study that formation of Na vacancies in
the lattice would be followed by spontaneous H desorption,21
which supports this view. Al substitution is on the other hand
probably less unfavorable because Ti is closer in size,
valence, and coordination to Al.
The difference between the fixed and relaxed cells is not
very large. Since the relaxed cells change cell parameters
significantly, even down to ␣ = 1 / 32,17 and it is known that
no change in lattice parameters was observed in Ti-enhanced
NaAlH4,9 we believe that the most relevant energies are from
the fixed cells. They are even more unstable than the relaxed
cells by up to 0.13 kJ/ mol per atom.
The description could have been improved by including
other phases such as the Al1−uTiu phase. However, this would
give the same effect for all the substitution models, since an
equal amount of Al would be transferred to the Al1−uTiu
phase.
Ti could also be added by other means; as a salt of other
halides,14,27 as TiH2,14 as Ti共OBu兲4 in solution,1,28 or as colloidal Ti clusters.29 However, for most addition schemes the
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161917-3
Appl. Phys. Lett. 88, 161917 共2006兲
O. M. Løvvik and S. M. Opalka
hydrogenation rate is very similar after a number cycles,
which means that the relevant phases for the long-term kinetics must be the same for all the various addition routes.
We thus believe that our results are valid for all working
schemes.
Very few experimental studies have given support to the
picture of Ti substitution in the alanate lattice. This does not,
however, rule out the possibility of Ti existing within alanate
particle aggregates. There is some experimental evidence
that this may actually be the case. It has been shown that the
concentration of Ti is lower at the surface of particles than in
the bulk after ball milling.16,30 Further IR spectroscopy
showed that doping 共and milling兲 affects the frequency of the
Al–H asymmetric stretching mode, which may be ascribed to
Ti in the vicinity of the AlH4 unit.15 This may be explained
by Ti going into interfaces between particles or grain boundaries within particles, either along with Al or alone. Another
study has shown that Ti addition is followed by transport of
point defects,31 which indicates that defects may play a role.
There is also a possibility that Ti acts in a transient state to
enhance 共de-兲hydrogenation kinetics.26
Thus a picture of the addition of Ti that is consistent
with most experimental and theoretical results is as follows:
Ti moves into interfaces, grain boundaries, or defects of the
NaAlH4 particles, but does not substitute in the perfect
NaAlH4 lattice. The microstructure of the particles is most
probably affected by the added Ti. The mechanism behind
the enhanced kinetics is still not clarified, but there are signs
that relate the effect to defects and impurities, in addition to
the classical picture of heterogeneous catalysis. Work along
this direction is in progress.
In conclusion, there is overall consistency between
modeling results and experiments. When all possible relevant
phases in the hypothetical formation reaction of Ti-doped
NaAlH4 are taken into account, none of the investigated
substitution models shows stable substitution. The least
unfavorable substitution scheme is to replace Al near the
surface. The most likely function of Ti is related to interfaces, grain boundaries, and defects, as well as working as a
heterogeneous catalyst.
Financial support from the Nanomat program in the
Norwegian Research Council and a computational grant via
the Notur concortium are gratefully acknowledged by one of
the authors 共O.M.L.兲. Another author 共S.M.O.兲 acknowledges
financial support under US DOE Contract No. DE-FC0402AL67610.
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