Thermodynamic modeling of the Na–Al–Ti–H system and Ti

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Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 624–636

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Computer Coupling of Phase Diagrams andThermochemistry

journal homepage: www.elsevier.com/locate/calphad

Thermodynamic modeling of the Na–Al–Ti–H system and Ti dissolution insodium alanatesCaian Qiu a,∗, Susanne M. Opalka b, Ole M. Løvvik c,d, Gregory B. Olson e,fa Caterpillar Champaign Simulation Center, 1901 S. First Street, Champaign, IL 61820, USAb United Technologies Research Center, 411 Silver Lane, East Hartford, C T 06108, USAc Department of Physics, University of Oslo, N-0316 Oslo, Norwayd Institute for Energy Technology, P.O. Box 24 N-2027 Kjeller, Norwaye Department of Materials Science & Engineering, Northwestern University, Evanston, IL 60201, USAf QuesTek Innovations LLC, 1820 Ridge Ave., Evanston, IL 60201, USA

a r t i c l e i n f o

Article history:Received 23 March 2008Received in revised form18 July 2008Accepted 28 August 2008Available online 17 September 2008

Keywords:Sodium alanatesTitanium dissolutionDirect method lattice dynamicsThermodynamic modelingPhase diagrams

a b s t r a c t

Thermodynamic assessments were made to optimize thermodynamic models and parameter fits toselected experimental and first principles hypothetical predicted phase data within the Na–Al–Ti–Hsystem. This enabled thermodynamic modeling of Ti solubility within the sodium alanates: NaAlH4 andNa3AlH6, and the relative stability of Ti-bearing phases. Themodeling provides insights into the role of Tioriginating from Ti-based activating agents commonly referred to as ‘catalysts’ in promoting reversibilityof the Na–Al–H dehydrogenation and rehydrogenation reactions under moderate temperature andpressure conditions relevant to H storage applications. Preliminary assessments were made to evaluateH solubility in bcc-Ti and hcp-Ti, and stability of the hydride δ-TiH2. To model possible Ti dissolutionin NaAlH4 and α-Na3AlH6, sub-lattice models were applied. A repulsive interaction is predicted by firstprinciples calculations when Ti is dissolved in NaAlH4 or α-Na3AlH6, which becomes stronger withincreasing temperature. Although Ti is virtually insoluble in NaAlH4 or α-Na3AlH6, a small addition ofTiCl3will induce a thermodynamic driving force for formation of TiH2 and/or TiAl3. The addition of pure Tishows a weaker effect than TiCl3 and leads to formation of TiH2 only. Based on a combined interpretationof present thermodynamic modeling and prior experimental observations, the TiAl3 and TiH2 phases areascribed to have a catalytic effect, not a thermodynamic destabilization effect, on the reversibility of thedehydrogenation/rehydrogenation reactions in the Na–Al–H system.

© 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Titanium and other transition metal additives have showngreat utility for tailoring the functional properties of ceramiccomponents, including: microwave dielectrics, tunable solid-statelasers, thermo-optic devices, waveguide amplifiers, lithium ionbattery electrodes, superconductor wires, semiconductors, stabi-lized and/or densified structural ceramics, and solid lubricationfilms. Recently, Ti and other transition metal activating agentshave also been shown to significantly increase the kinetics ofthe dehydrogenation and rehydrogenation reactions of the com-plex covalent sodium alanate stoichiometric compounds, NaAlH4and α-Na3AlH6, promoting their consideration to be one of the

∗ Corresponding author. Tel.: +1 217 255 8576; fax: +1 217 255 8505.E-mail addresses: [email protected] (C. Qiu), [email protected]

(S.M. Opalka), [email protected] (O.M. Løvvik), [email protected](G.B. Olson).

premier moderate temperature and pressure H storage materialcandidates [1–3]. Titanium additives also effectively enhance thekinetics of a wide range of other solid-state inorganic hydride Hstorage materials.A number of experimental and theoretical studies have sought

to elucidate the Ti activation mechanisms in the sodium alanatesin order to lay a foundation for further H storage materialdevelopment. Overall, it can be concluded from the summary inRef. [4] as well frommore recent reports [5–12], that these studieshave hypothesized that Ti phases could affect the sodium alanate Hcycling kinetics either by changing the dehydrogenation reactionproducts, altering the properties of the sodium alanate phases,and/or catalyzing surface reactions or solid-state transformations.Experimentally, Ti has been observed in Ti-activated sodiumalanate samples as an ordered TiAl3 alloy [6,13–15], amorphousTi–Al compounds [5,8,9,11,12,15–19], Ti-hydrides [12,20,21] andTi interstitials in NaAlH4 [16]. The formation of these newphases incorporating Ti could shift the favorability of the sodiumalanate reactions, akin to the destabilization of metal or covalent

0364-5916/$ – see front matter© 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.calphad.2008.08.005


C. Qiu et al. / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 624–636 625

Fig. 1. The Al–H phase diagram calculated at 1 atm from Ref. [36].

Fig. 2. The Al–Na phase diagram calculated at 1 atm from Ref. [37].

hydride dehydrogenation bymetal ormetal hydride additives [22],to achieve lower temperatures for equilibrium H reversibility.Titanium dissolution in sodium alanate phases, and modificationof these alanates caused by such dissolution has been investigatedboth experimentally and theoretically. It has been interpreted fromthese studies that the most favorable Ti substitution in the sodiumalanate structures, may be either on the Na sublattice [4,23–25], oron the Al sublattice [26–30], albeit in some cases in a metastablestate and others a stable state. It has also been reported from somestudies that Ti may act as a heterogeneous catalyst on the reactingphase surfaces, activating H recombination and H2 gas desorptionupon dehydrogenation, H2 gas dissociation and adsorption uponrehydrogenation, and/or nucleation and growth of the associatedreaction products [5,9,11,12,31–34].A recent study created ground state chemical potential maps of

the Na–Al–Ti–H system from first principles phase formation en-thalpies and predicted favorable Ti substitution for Al under Al-poor/H-rich conditions [35]. Thermodynamic methodologies can

Fig. 3. The Na–H phase diagram calculated at 1 atm from Ref. [38].

be used to model the equilibrium distribution and behavior ofTi-bearing bulk phases formed from Ti-activated sodium alanatesover an even wider range of temperature and pressure conditions.This is accomplished in the present study by the thermodynamicassessment of combined experimental measurements of knownphases and first principles finite temperature predictions of hy-pothetical Ti-substituted phases. In the present work the ther-modynamic mixing interactions of Ti with NaAlH4 or α-Na3AlH6and the thermodynamic properties of the fully Ti-substituted hy-pothetical end-member compounds are predicted with densityfunctional theory ground state minimizations and direct methodlattice dynamics. The CALPHAD (CALculation of PHAse Diagrams)methodology is used to simultaneously fit thermodynamic mod-els to the large set of experimental and predicted data, wherethe latter effectively reduces the number of fit parameters. TheNa–Al–Ti–H assessment is progressively built in increasing ele-mental order, first establishing the unassessed binary Na–Ti andTi–H systems, then merging these with the other established rel-evant binary and ternary assessments, and finally incorporatingthemodeled quaternary interactions. A thermodynamic parameterdatabase constructed in this way for the Na–Al–Ti–H system en-ables equilibrium thermodynamic modeling of Ti-doping in bulksodium alanates, the stability of sodium alanates, and the effectof Ti on the formation of Ti–Al compounds and Ti-hydrides. Thismethodology does not intend to address surface catalytic effectson sodium alanate dehydrogenation/rehydrogenation kinetics; in-stead it describes the ideal thermodynamic upper bound that canbe achieved for sodium alanate reversibility in the presence of Tiadditives.

2. Review of experimental data and modeling methodologies

2.1. Thermodynamic modeling and evaluation of binary systems

To model the quaternary Na–Al–Ti–H system, it is essentialto have thermodynamic descriptions of all six constituent binarysystems. The Al–H [36], Al–Na [37], and Na–H [38] systems wereevaluated by the present authors, while the Al–Ti system wasmodeled by Ansara et al. [39]. Their phase diagrams are shownin Figs. 1–4. Modeling of the Na–Ti system is not available fromliterature and is conducted in the presentwork. Therewere several


626 C. Qiu et al. / Computer Coupling of Phase Diagrams and Thermochemistry 32 (2008) 624–636

Fig. 4. The Al–Ti phase diagram calculated from Ref. [39].

attempts to evaluate the Ti–H system thermodynamically [40–42]. Most recently, Königsberger and co-workers [42] modeled theTi–H and Zr–H systems using the CALPHAD approach. However,they set interstitial sites as one per metallic atom for hcp, and 1.5for bcc when modeling the metal-H interstitial solutions. Thosemodels could not be combined with the Na–Al–H system. As aconsequence, a new evaluation of the Ti–H system had to be madein the present work.A review on the Na–Ti system by Bale [43] in 1989 showed

that the published experimental data were not available. Byanalogy with binary phase diagrams of alkali metal and GroupIVA elements, Bale suggested that the Na–Ti system is almostcompletely immiscible in both the solid and liquid states. SinceNa and Ti have extremely low mutual solubilities, a univarianttemperature in the Na–Ti system would be very close to acorresponding transition temperature of a pure element. Usingthermodynamic models, the liquid and solution phases (bcc andhcp) are treated as substitutional solutions, while the gaseousphase is approximated as an ideal gas in the present work.Thermodynamic descriptions of gaseous species were taken fromRef. [44], which are available in SGTE (Scientific Group ThermodataEurope) database [45]. According to the substitutional solutionmodel, the molar Gibbs energy of liquid, bcc, or hcp is given by

Gm =∑i

xi oGi + RT∑i

xi ln xi + xNaxTiL (1)

where xi is the molar fraction of Na or Ti, and oGi is the Gibbsenergy of pure elements in the liquid, bcc, or hcp phases, referredto the enthalpy of the so-called Stable Element Reference (SER)at 298.15 K and 1 bar (same thereafter). The Gibbs energy of allthe pure elements are compiled in Ref. [46], and are also availablein the SGTE database [45]. The last term in Eq. (1) is the excessenergy due to the interaction between Na and Ti in the liquid, bcc,fcc, or hcp phases. The interaction parameter L can be expressedas a linear function of temperature, L = A + BT , fitted torelevant experimental data. The goal of the present modeling wasto evaluate interactionparameters for liquid, bcc, andhcpphases inorder to reproduce reasonable phase diagram and solubility data.This was done using an optimization module in Thermo-Calc [47].Due to the extremely low solubility, a strong positive interaction,i.e. a repulsive interaction, between Na and Ti should be expectedfor all the phases. From the preliminary optimizations it was found

Fig. 5. The Na–Ti phase diagram calculated at 1 atm according to the presentmodeling.

that a temperature dependent parameter with an approximatevalue of 75 J/mol/Kwas necessary for the liquid phase. On the otherhand, a constant interactionparameter is efficient for the bcc or hcpsolid solutions.With the presentmodels andparameters, theNa–Tidiagram was calculated as presented in Fig. 5. It shows almost nomutual solubility in solid and liquid states, and each three-phaseequilibrium temperature is almost the same as the correspondingtransformation temperature of a pure element. It is worth notingthat similar thermodynamic descriptionswould be expectedwhenmodeling theNa–Sc, Na–Y, Na–Ce, Na–Zr, Na–Hf, Na–V, andNa–Nbsystems.The Ti–H system is of importance to the present work

since titanium hydrides may be formed during dehydrogenationof Ti-activated sodium alanates. The Ti–H binary system wasinvestigated experimentally several times. A literature reviewwasconducted by San-Martin and Manchester [48], who compiledmost of the experimental information on the Ti–H phase diagram,H solubility in bcc-Ti and hcp-Ti, and thermodynamic propertiesof the hydride δ-TiH2. Hydrogen solubility in both the hcp and bccphases is very high. They are described together with vacancies(Va) in the interstitial solution model, using (Ti)1(H,Va)3 for thebcc phase and (Ti)1(H,Va)0.5 for the hcp phase in the presentwork.Accordingly, the Gibbs energy for one mole of formula unit of bccor hcp is given by

Gm = yHoGTi:H + yVaoGTi + cRT (yH ln yH + yVa ln yVa)+ yHyVaL (2)

where c = 3 for bcc, and 0.5 for hcp. The variable yi is the fractionof occupied H atoms or vacancies in the second sublattice. Thequantity oGTi is Gibbs energy of the pure element bcc-Ti or hcp-Ti, while oGTi:H is Gibbs energy of the hypothetical compoundsbcc-TiH3 or hcp-TiH0.5. These two quantities are evaluated fromexperimental information using the following expressionsoGTi:H(TiH3) = a1 + b1T + c1T ln T +

oGTi(hcp)+ 1.5oGH2(gas) (3a)

oGTi:H(TiH0.5) = a2 + b2T + c2T ln T +oGTi(hcp)

+ 0.25oGH2 (gas). (3b)

The last term in Eq. (2) represents excess energy due tointeraction between H and vacancies in second sublattice. It isdetermined from experimental data.According to Ref. [48], δ-TiH2 has a cubic structure similar to

CaF2 and is the only stable hydride in the Ti–H system. It exhibits a



Fig. 6. Enthalpy of formation of δ-TiH1.6 and δ-TiH2.0 calculated as a function oftemperature, in comparison with experimental data.

Fig. 7. Entropy of formation of δ-TiH1.6 and δ-TiH2.0 calculated as a function oftemperature, in comparison with experimental data.

considerable concentration range from 60 to 66 at.% H, but H nevercompletely occupies all available tetrahedral vacancy sites. As aconsequence, a two-sublattice model (Ti)1(H,Va)2 is applied toaccount for H deficiency in the vacancy sites, and its Gibbs energyis also expressed with Eq. (2). There are two quantities of Gibbsenergy: one for hypothetical Ti with the same structure as TiH2,and another for the stoichiometric composition TiH2. The former isassumed to the same as the Gibbs energy ofmetastable fcc-Ti givenin Ref. [46]. The latter is modeled as a function of temperaturewiththe following polynomial

oGTiH2 = a+ bT + cT ln(T )+ dT2+ eT 3 + f /T (4)

where the parameters a, b, c, . . . are evaluated from experimentaldata. The liquid phase is modeled as a substitutional solution.However, model parameters can not be evaluated due to the lackof relevant experimental information.

Fig. 8. Gibbs energy of formation of δ-TiH1.6and δ-TiH2.0 calculated as a functionof temperature, in comparison with experimental data.

Experimental data compiled in Ref. [48] were used as input tooptimize the model parameters for bcc, hcp, and δ-TiH2 throughthe optimizationmodule in Thermo-Calc. These data include phaseboundaries, pressure–composition data, and thermodynamic dataof δ-TiH2. In addition, conditions are also introduced in theoptimization to ensure the metastable status of hypotheticalbcc-TiH3 and hcp-TiH0.5 when evaluating the coefficients in Eqs.(3a) and (3b). The condition for bcc-TiH3 was set as oGTiH3 >

Gibbs energy of the mixture of TiH2 and gas, or, bcc and gas, atxH = 0.75; while the condition for TiH0.5 was set as oGTiH0.5>Gibbs energy of the mixture of hcp, bcc, TiH2, and gas at xH =0.33. During the optimization, it was found that a regular solutionmodel was sufficient to describe H solubility in bcc-Ti and hcp-Ti. The final results were obtained when most experimental datawere accounted for within the expected uncertainty limits by thecalculations. All the model parameters are given in Appendix.Using the present models and parameters, the enthalpy,

entropy, and Gibbs energy of formation of δ-TiH1.6 and δ-TiH2.0were calculated as a function of temperature, as shown in Figs. 6–8 in comparison with experimental data [49–55]. It is seen thatthe present modeling is in good agreement with most of theexperimental data. Nevertheless, the enthalpy of formation ofδ-TiH2 predicted from the present modeling differs somewhatfrom those by Arita and co-workers [49] based on analysis ofexperimental H dissolution in Ti. It is noted that their data aremorenegative than the other experiments [50–55] including their ownprevious data [50], as shown in Fig. 6. Obviously, it is impossible tofit their data and others simultaneously.The Ti–H diagram calculated at 1 atm is presented in Fig. 9,

where the symbols represent the experimental phase boundariesfrom literature compiled in Ref. [48]. It is seen from this diagramthat the present calculations are in satisfactory agreement withexperimental data on the equilibria between hcp and bcc, butsome differences remain for the phase boundary bcc/bcc +δ-TiH2. A significant effort was made to improve the fittingby applying a subregular solution model to the bcc phase,but improvement could not be achieved. It is noted that theexperimental phase boundary data are based on isothermalmeasurements of pressure–composition, and thus would bearsome uncertainty. It is more straightforward to directly comparethe isothermal measurements, as shown in Fig. 10, where



Fig. 9. The Ti–H phase diagram calculated at 1 atm according to the presentmodeling, where the symbols represent experimental phase boundaries fromliterature compiled in Ref. [48].

Fig. 10. Pressure–composition isotherms of the Ti–H system calculated at differenttemperatures, where the symbols represent experimental data from variousinvestigators cited in Ref. [48].

the experimental data are from various investigators as citedin Ref. [48]. The agreement between the present calculationsand experiments is reasonably good, which can be taken asan indication that the H solubility in bcc is modeled well attemperatures below 1000 ◦C. A potential diagram of the Ti–Hsystem in Fig. 11 calculated from the present modeling shows thedissociation pressure of TiH2.

2.2. Thermodynamic modeling and evaluation of ternary systems

TheNa–Al–Ti–H systemconsists of four ternary systems, amongwhich the Na–Al–H description encompassing the ternary sodiumalanate stoichiometric compounds was previously developed bythe present authors [37] and was the only ternary systemincorporated in the present work. A potential diagram of theNa–Al–H system is presented in Fig. 12 to show the stability

Fig. 11. Potential diagramof the Ti–H system calculated from the presentmodelingto show dissociation pressures of TiH2 .

Fig. 12. Potential diagram of the Na–Al–H system calculated from Ref. [37] toillustrate stability of various hydrides under equilibrium condition.

of various phases and their relationships. There are no ternarycompounds with known crystal structures in the other threeconstituent ternary systems: Al–Ti–H, Al–Na–Ti, and Na–Ti–H.Hydrogen solubility in Ti-rich Ti–Al phases is on the order of ppmand decreasesmarkedlywith increasing Al content [56]. Therefore,thermodynamic evaluation of the three ternary systemswould notaffect the present modeling for the Na–Al–Ti–H system. Amongthe three ternary systems, it is worth to examine the effect ofH2 pressures on the stability of Ti–Al metallic compounds andhydrides. This is illustrated in Fig. 13 by a diagram of the Al–Ti–Hcalculated at 100 ◦C by combining all binary models from thepresent work and previous studies [36,39]. It is interesting tonote that TiAl3 can coexist with TiH2 under H2 pressure rangeof 0.0012–9293 bar at 100 ◦C, while TiAl2 remains stable onlyat pressures below 0.0012 bar. Further calculations indicate thatTiAl3 still remains stable togetherwith TiH2within the H2 pressurerange of 0.102–33299 bar at 200 ◦C.



Table 1Ti substitution level and substituted compound stoichiometries for first principles thermodynamic predictions

Phase-structure Mol % Ti substitution(Cell formula)

Mol % Ti substitution(Cell formula)



NaAlH4 I41/a 0.0 6.25 25.0 100.0(Na4Al4H16) (Na16TiAl15H64) (Na4TiAl3H16) (Na4Ti4H16)

α-Na3AlH6 P21 0.0 – 50.0 100.0(Na6Al2H12) – (Na6TiAlH12) (Na6Ti2H12)

Fig. 13. Effect of H2 pressure on the formation ofmetallic compounds and hydridesin the Al–Ti system at 100 ◦C calculated by combining all binary models frompresent work and previous study [36].

2.3. Thermodynamicmodeling and evaluation of Na–Al–Ti–H quater-nary system

2.3.1. First principles predictionsTwo atomic theoretical methodologies were used to predict

the finite temperature thermodynamic properties of hypotheticalTi substitution in the NaAlH4 and α-Na3AlH6 phases. First, theperiodic structures were predicted with the density functionaltheory Vienna ab initio simulation package (VASP) code [57,58] full minimizations. The prediction used the standard Aland H, and hard valence Na and Ti projector augmented wavepotentials [59] with the generalized gradient PW91 exchangecorrelation corrections [60]. The VASP parameters and approachused in the present study are given in detail in our previous workin Ref. [26]. The Materials Design Phonon module [61,62] wasthen used with VASP to calculate direct method lattice dynamicswith the harmonic approximation for the minimized hypotheticalTi-substituted structures and to predict their finite temperaturethermodynamic properties, following the methodology fullydescribed in Refs. [37,38].Our first principles predictions approximated the thermody-

namic convention of referring to the elements in their standardstates (SER), by referring the electronic enthalpies of formation ofthe Ti-substituted sodium alanates with respect to the standardstate elemental phase structures, all simulated at the ground state.Following this approach, we previously determined the substitu-tion of Ti on the Al sublattice to be more favorable than the sub-stitution on the Na sublattice, regardless of whether the Ti formalcharge state was varied from +1 to +4 by the introduction of va-cancies [26]. Based on this premise, only the most favorable Ti in-teraction with the Al sublattices of the sodium alanate phases wassimulated in this study,where one Ti atomwas directly substituted

for one Al atom effectively as the+3 formal charge state, in the ab-sence of any vacancies. Various levels of Ti substitution for Al, givenin Table 1, were simulated by changing the supercell size of thesodium alanate phases, where Ti was substituted into each super-cell for the intermediate substitution stoichiometries. The interac-tions between the single Ti atoms in the periodic supercell wereassumed to be negligible. Full Ti substitution was modeled as thehypothetical compounds, NaTiH4 and α-Na3TiH6, whichwere sim-ulated as the structural analogs of NaAlH4 and α-Na3AlH6, respec-tively.It has been shown in previous studies that spin polarization

alters the ground state energetics of Ti-substituted NaAlH4 [4,29].It can thus be expected that the use of non-restricted spin wouldhave changed some of the results of the present study; we believehowever that all the qualitative conclusions of this work are valid.

2.3.2. Thermodynamic modeling and evaluationWith thermodynamic modeling, the Gibbs energy of a com-

pound is often expressed as a function of temperature with a poly-nomial form. Such a polynomial is quite acceptable in many casesand is often used in the CALPHAD approach. However, the poly-nomial cannot model heat capacity well at very low temperatures.On the other hand, Einstein’s model based on harmonic lattice vi-brations can describe heat capacity reasonably well under normalconditions. In the present case, the heat capacity of NaTiH4 andα-Na3TiH6 is available from direct method predictions within therange from 0 K to 2000 K, see Fig. 14(a) and (b). To model heatcapacity within the whole temperature range, it is necessary tocombine Einstein’s model and the polynomial method, as demon-strated in our previous work [37,38]. The Gibbs energy per onemole of formula of NaTiH4 or Na3TiH6 is given byoGm = Eo + nRT ln[exp(0.5θE/T )− exp(−0.5θE/T )]

− 0.5AoT 2 for 0 K < T < 298.15 K (5a)oGm = a+ bT + cT ln T + dT

2+ eT 3 + f /T

for 298.15 K < T < 2000 K (5b)where θE in Eq. (5a) is the Einstein temperature. The coefficientsEo and Ao in Eq. (5a) and a, b, c, . . . in Eq. (5b) are constants. Theconstant n in Eq. (5a) is equal to 3 for NaTiH4 and 6 for Na3TiH6.This choice is in line with the treatment in our previous workfor NaAlH4 and α-Na3AlH6 [26]. The enthalpy, entropy, and heatcapacity can be derived from the above equations using standardthermodynamic relations. As an example, the heat capacity CP isgiven below:

CP = 3R[θE

T

]2 exp(θE/T )[exp(θE/T )− 1]2

+ AoT

for 0 K < T < 298.15 K (6a)CP = −c − 2dT − 6eT 2 −−2f /T 2

for 298.15 K < T < 2000 K (6b)The first term in Eq. (6a) describes the harmonic lattice

vibrations based on Einstein’s model, and the second term is usedto account for electronic excitation and low-order anharmonicvibrations.We shall assess the properties of NaTiH4 andα-Na3TiH6using the above models. The first step was to evaluate thecoefficients θE and Ao in Eq. (5a) and c , d, e, f in Eq. (5b) for the twocompounds based on the heat capacity from the lattice dynamics



(a) NaTiH4 . (b) α-Na3TiH6 .

Fig. 14. Heat capacity of hypothetical compounds (a) NaTiH4 and (b) α-Na3TiH6 calculated from the present thermodynamic modeling and lattice dynamics predictions.

(a) NaAlH4 and NaTiH4 . (b) α-Na3AlH6g and α-Na3TiH6 .

Fig. 15. Gibbs energy of (a) stableNaAlH4 and hypothetical NaTiH4 and (b) stableα-Na3AlH6 and hypotheticalα-Na3TiH6 calculated according to the present thermodynamicmodeling and lattice dynamics predictions

predictions. Tomaintain a smooth variation of CP around 298.15 K,a condition was applied in the optimization that the difference ofEqs. (6a) and (6b) at 298.15 K should be less than 0.1 J/mol/K. Thenext step was to evaluate coefficient Eo in Eq. (5a) and constantsa and b in Eq. (5b) by best fitting to the Gibbs energy from firstprinciples calculations, as shown in Fig. 15(a) and (b).To describe possible Ti dissolution in the sodium alanates, as

mentioned earlier, it is assumed that Al in NaAlH4 and α-Na3AlH6can be substituted by Ti. By applying the sublattice models, theGibbs energy per mole of formula of (Na)x(Al, Ti)(H)y is given by

Gm = yAl oGNaxAlHy +yAloGNaxTiHy

+ RT (yAl ln yAl + yTi ln yTi)+ yAlyTiL (7)where yAl and yTi are site-fractions of Al and Ti in the secondsublattice, and oGNaxAlHy and

oGNaxTiHy aremolar energies ofNaxAlHy

(NaAlH4 or α-Na3AlH6) and NaxTiHy (NaTiH4 or α-Na3TiH6),respectively, modeled with Eqs. (5a) and (5b). The parameterL represents the interaction between Al and Ti on the secondsublattice, and can be evaluated from the mixing propertiesbetween NaAlH4 and NaTiH4 or between α-Na3AlH6 and Na3TiH6from first principles calculations at different temperatures.

3. Results and discussion

Using the present models and parameters, the heat capacity ofhypothetical NaTiH4 and α-Na3TiH6 was calculated as a functionof temperature, as shown in Fig. 14(a) and (b), respectively, incomparison with the lattice dynamics predictions. It is seen thatthe combination of modified Einstein’s model at low temperaturesand polynomial at high temperatures is capable of describing



(a) Na(Al, Ti)H4 at lower temperatures. (b) Na(Al, Ti)H4 at higher temperatures.

Fig. 16. Composition dependence of Gibbs energy of Na(Al, Ti)H4 calculated at different temperatures according to the present thermodynamic modeling, in comparisonwith lattice dynamics predictions.

(a) Na3(Al, Ti)H6 at lower temperatures. (b) Na3(Al, Ti)H6 at lower temperatures.

Fig. 17. Composition dependence of Gibbs energy of α-Na3(Al, Ti)H6 calculated at various temperatures according to the present thermodynamic modeling, in comparisonwith lattice dynamics predictions.

the heat capacity very well within the whole temperature range.A comparison of Gibbs energy between the present modelingand lattice dynamics predictions is presented in Fig. 15(a) and(b), where the Gibbs energy is referred to the enthalpy of theStable Element Reference (SER) at 298.15 K and 1 bar. Forconvenience of discussion, Gibbs energy of NaAlH4 and α-Na3AlH6was also plotted in Fig. 15(a) and (b). It is noted in these figuresthat the Gibbs energy of NaAlH4 or α-Na3AlH6 predicted fromthermodynamic modeling shows almost the same temperaturedependence as the Phonon direct prediction within wholetemperature range, but it slightly shifts towards more negativevalues. As explained in our previous work [37], this is becausethe thermodynamic model is intended to fit to experimental datarather than the data predicted from the Phonon direct method.

There is no experimental data available for the hypothetical NaTiH4and α-Na3TiH6 phases. The present thermodynamic models wereused to fit the Gibbs energy predicted from the Phonon directmethod. Compared to NaAlH4 or α-Na3AlH6, thermodynamicmodeling of NaTiH4 or α-Na3TiH6 fit the Phonon direct predictionsquite well within the whole temperature range, although somedifferences still remain.With the thermodynamic descriptions of these stable and

hypothetical compounds, it was possible to model the mixingproperties between NaAlH4 and NaTiH4 and between α-Na3AlH6and Na3TiH6. The Gibbs energy of Na(Al, Ti)H4 and Na3(Al, Ti)H6at different Ti contents was predicted as a function of temperaturefrom the first principles calculations, and some results are plottedin Figs. 16 and 17 to show the composition dependence at different



(a) 1 atm H2 . (b) 25 atm H2 .

(c) 100 atm H2 .

Fig. 18. Isothermal sections of the Na–Al–Ti system calculated at 100 ◦C to show equilibrium of TiAl3 with different hydrides under (a) 1 atm H2 , (b) 25 atm H2 , and(c) 100 atm H2 .

temperatures. The data for Na(Al, Ti)H4 in Fig. 16 shows almosta linear relation between the Gibbs energy of NaAlH4 and thatof NaTiH4 at 0 K and 298 k, and then it deviates from the linearrelation with increasing temperature. Nonlinear effects alreadyexist for Na3(Al, Ti)H6 at 0 K and 298 K, as seen in Fig. 17, andits deviation from the linear relation also becomes stronger withincreasing temperature. The deviation from the linear relationin Figs. 16 and 17 indicate a repulsive interaction when mixingNaAlH4 and NaTiH4, or mixing α-Na3AlH6 and Na3TiH6, andthe repulsion becomes stronger with increasing temperature.In order to model such behavior, a temperature dependentinteraction parameter has to be used for both Na(Al, Ti)H4 andNa3(Al, Ti)H6. With such interaction parameters, the mixing Gibbsenergy of Na(Al, Ti)H4 and Na3(Al, Ti)H6 was calculated at varioustemperatures in comparisonwith the lattice dynamics predictions,as shown in Figs. 16 and 17. In general, the present thermodynamicmodel describes quitewell the repulsive behavior betweenNaAlH4and NaTiH4, or between α-Na3AlH6 and Na3TiH6 as predicted bythe Phonon direct method.By combining the Na–Al–H system [37] with the modeling of

all the binary systems, it is possible to examine the phase stability

of alanates in the Na–Al–Ti–H system and effect of temperatureand pressures through thermodynamic calculations. To illustratepossible formation of Ti–Al compounds and Ti-hydride duringthe dehydrogenation of NaAlH4 and α-Na3AlH6 doped with Ti,isothermal sections of the Na–Al–Ti system were calculated at100 ◦C under various pressures of H2, as shown Fig. 18(a), (b) and(c). It is very interesting to see that α-Na3AlH6 is in equilibriumwith NaH and TiAl3 at 1 atm, Fig. 18(a). At 25 atm α-Na3AlH6 isin equilibrium with NaH and TiH2, while NaAlH4 is in equilibriumwith α-Na3AlH6 and TiAl3, Fig. 18(b). At 100 atm, TiH2 is inequilibrium with both α-Na3AlH6 and NaAlH4, Fig. 18(c). Sincethe pressure will vary during the dehydrogenation process, it ispossible to form both TiAl3 and TiH2 at different stages. This isconsistent with experimental observation [14,15]. The formationof TiAl3 and/or TiH2 will also depend on kinetic conditions such assurface energy, nucleation, etc. Any amorphous Ti–Al compoundsmight be early forms of TiAl3 precipitation. The formation of TiH2may be taken as an indication of H loss as observed in practice.From Figs. 16 and 17 it is seen that the dissolution of Ti

in NaAlH4 or α-Na3AlH6 will increase Gibbs energy and thusis thermodynamically unfavorable. The present thermodynamic



calculation indicates that Ti is virtually insoluble in NaAlH4 orα-Na3AlH6 under normal conditions. It has been shown in previouspredictions, however, that the stability of the substitution is highernear the surface [26]. Thus, we should expect that any inclusion ofTi in the alanate sublattice is close to the surface.Although the mechanism of Ti or TiCl3 as a catalyst is not well

known for the dehydrogenation processes, it is very interestingto examine reactions of Ti or TiCl3 with NaAlH4, especially duringball milling. If a typical amount of 2.5 mol % Ti or TiCl3 additive iscombined with NaAlH4 the possible reactions that could occur:

NaAlH4 →13Na3AlH6 +

23Al+ H2 (8a)

NaAlH4 +140Ti→

13Na3AlH6 +

140TiH2 +

23Al+

3940H2 (8b)

NaAlH4 +140Ti→

13Na3AlH6 +

140TiAl3 +

71120Al+ H2 (8c)

NaAlH4 +140TiCl3 →

37120Na3AlH6 +

340NaCl

+140TiH2 +

83120Al+

2120H2 (8d)

NaAlH4 +140TiCl3 →

37120Na3AlH6 +

340NaCl

+140TiAl3 +

74120Al+

4340H2. (8e)

A necessary condition for each reaction to proceed is an energydecrease. The more the energy decreases, the higher driving forcefor a reaction to proceed. Since thermodynamic models for allphases are now available, it is possible to calculate Gibbs energyof each phase at different temperatures, and plot energy changefor each reaction at 1 bar. This is illustrated in Fig. 19(a). It isseen that the reaction equations (8d) and (8e) show a considerableenergy decrease relative to reaction equation (8a) due to additionof 0.025 mol TiCl3 in one mole of NaAlH4. The reaction equations(8d) and (8e) have a much higher driving force, and thus bothreactions are very possible. As a consequence, TiH2 and TiAl3 can bereaction products depending on the kinetic competition betweenreaction equations (8d) and (8e). Reaction equation (8d) has aslightly higher driving force than reaction equation (8e). On theother hand, a small addition of Ti will promote reaction equation(8b) to a certain extent, which produces TiH2, but not reactionequation (8c) with TiAl3 as a reaction product.Similarly, we can examine the energy change for possible

reactions of Na3AlH6 with Ti or TiCl3:

Na3AlH6 → 3NaH+ Al+32H2 (9a)

Na3AlH6 +140Ti→ 3NaH+

140TiH2 + Al+

5940H2 (9b)

Na3AlH6 +140Ti→ 3NaH+

140TiAl3 +

3740Al+

32H2 (9c)

Na3AlH6 +140TiCl3 →

11740NaH+

340NaCl+

140TiH2

+Al+12180H2 (9d)

Na3AlH6 +140TiCl3 →

11740NaH+

340NaCl+

140TiAl3

+3740Al+

12380H2. (9e)

The Gibbs energy change for each reaction at 1 bar wascalculated as a function of temperature, as presented in Fig. 19(b). It

Fig. 19. Gibbs energy change for each reaction listed in reaction equations (8) and(9), showing effect of 0.025 mole Ti or TiCl3 addition in one mole of NaAlH4 orNa3AlH6 on their dehydrogenation processes.

is noted that the energy decrease is very small for reaction equation(9a) around 100 ◦C, and this reaction would hardly proceed, asis observed in practice. Nevertheless, an addition of 0.025 molTiCl3 in one mole of Na3AlH6 will result in considerable energydecrease, as in reaction equations (9d) and (9e) which yield TiH2or TiAl3. The addition of Ti will induce a limited driving force forreaction equation (9b) with TiH2 as a reaction product, but notfor reaction equation (9c) with TiAl3 as a reaction product. Thisis consistent with experimental observation that an addition of Tipowder usually results in formation of TiH2 instead of TiAl3 [63].The present thermodynamic phase stability and reaction

modeling reinforces hypotheses that Ti-bearing phases enhancedehydrogenation and rehydrogenation of the Na–Al–H phasesby surface-mediated catalysis and not by a destabilizationmechanism. Since the most favorable proposed reaction equations(8d), (8e), (9d) and (9e) of NaAlH4 or α-Na3AlH6 with TiCl3 arenot reversible under reasonable conditions, the possible reactionsof the Na–Al–H phases with the resulting favorable TiH2 or



TiAl3 products were examined for evidence of destabilization.Thermodynamic modeling showed that only the NaAlH4 orα-Na3AlH6 dehydrogenation reactions with TiH2

3NaAlH4 + TiH2 = 3NaH+ TiAl3 +112H2 (10a)

3Na3AlH6 + TiH2 = 9NaH+ TiAl3 +112H2 (10b)

were more favorable than those of the pure NaAlH4 and Na3AlH6phases given by reaction equations (8a) and (9a), respectively.However, increases in dissociation pressure have not been ob-served experimentally to support the occurrence of a destabi-lization effect. In addition, that lack of favorability for analogousreactions with the commonly observed TiAl3 phase does not lendcredence to a destabilization argument. Indeed, our previous com-pilation [37] of predicted and experimental dehydrogenation datafor NaAlH4 and Na3AlH6 phases did not show evidence for destabi-lization or change in dissociation pressure by Ti-doping. True catal-ysis of NaAlH4 or Na3AlH6 dehydrogenation by the TiAl3 or TiH2products can not involve destabilization or the change in reactionenergy. Also, only a catalyticmechanism, not destabilization, couldexplain the observed benefit of Ti-additives improving the kinet-ics of rehydrogenation reactions, the reverse of reaction equations(8a) and (9a).

4. Conclusions

The Ti–H system was evaluated using thermodynamic models,and model parameters were optimized by best fitting to selectedexperimental data, including H solubility in bcc-Ti and hcp-Ti, and stability of the hydride δ-TiH2. To model possible Tidissolution in sodium analates, NaAlH4 and α-Na3AlH6, sub-lattice models were applied. Thermodynamic properties of thehypothetical compounds NaTiH4 and Na3TiH6, as well as theirmixing properties with NaAlH4 or α-Na3AlH6 were predicted fromfirst-principles calculations based on density functional theoryground state minimizations and direct method lattice dynamics.The predictions have proved very effective for thermodynamicmodeling. As predicted by the first principles calculations, arepulsive interaction is also described with the model when Ti isdissolved inNaAlH4 orα-Na3AlH6. The repulsion becomes strongerwith increasing temperature. As predicted by the modeling, Tiis virtually insoluble in NaAlH4 or α-Na3AlH6 under normalconditions. On the other hand, a small amount of added TiCl3 inNaAlH4 or α-Na3AlH6 will result in a considerable driving force forthe formation of TiH2 and/or TiAl3. A small addition of Ti inducesa limited driving force for the formation of TiH2 only. Based ona combined interpretation of present thermodynamic modelingand prior experimental observations, the TiAl3 and TiH2 phasesare ascribed to have a catalytic effect, not a destabilization effect,on the reversibility of the dehydrogenation/rehydrogenationreactions in the Na–Al–H system.

Acknowledgements

This work was financially supported by the US Department ofEnergy under contract DE-FC04-02AL67610, managed by UnitedTechnology Research Center, East Hartford, Connecticut, USA.During the preparation of this work the authors did not

see the work by Ukita and co-workers [64] who modeledthermodynamically the Ti–H and Zr–H systems. It is interestingto note that their model for δ-TiH2 is same as what we used in

our work, and their prediction of enthalpy of formation at thestoichiometric composition is also very close to our evaluation. Onthe other hand, their models for the solution phases bcc and hcpare different from ours.

Appendix

Summary of thermodynamic parameters describing theNa–Al–Ti–H system. Values are given in SI units (Joule, mole,Kelvin, and Pa) and correspond to one mole of formula units of thephases. The parameters marked with an asterisk (∗) were evalu-ated in the present work. Gibbs energy for pure elements and gascan be found in [46].Liquid with formula (Al, H, Na, Ti)

oGliqH = 8035+ 25T + 2T ln(T )+ 0.5oGgasH2

LliqAl,H = 50 942− 11.1007T

LliqAl,Na = 14 130+ 56.0985T − 1827(xAl − xNa)

LliqAl,Ti = −108 250+ 38T + (−6000+ 5T )(xAl − xTi)+ 15 000(xAl − xTi)2

LliqH,Na = −70 264+ 45.2458T + (−56 577+ 21.8825T )(xH − xNa)

LliqNa,Ti = 22 520+ 75T (∗)

BCC_A2 with formula (Al,Na, Ti)1(H,Na)3oGbccAl:H = 200 000+

oGAlH3Al:HoGbccNa:H = 215 965+ 3RT ln[exp(0.5× 215/T )

− exp(−0.5× 215/T )] − 0.0095113T 2

for 0 K < T < 298.15 K= 206 754+ 258.2187T − 42.90288T ln(T )− 0.004047T 2

+ 1.889× 10−7T 3 + 696 986/Tfor 298.15 K < T < 2000 KoGbccTi:H = −124 220− 233.8955T + 56.1833T ln(T )

+oGhcpTi +1.5

oGgasH2 (∗)

LbccAl,Na:Va = 27 715

LbccAl,TiVa = −128 500+ 39T + 6000(yAl − yTi)+ 212 00(yAl − yTi)2

LbccNa,Ti:Va = 110 800 (∗)

LbccTi:H,Va = −44 910+ 22.8047T (∗)

FCC_A1 with formula (Al,Na)1(H,Va)1oGfccAl:H = 100 000+

oGfccAl +0.5oGgasH2

oGfccNa:H = 130T +oGbccNa +0.5

oGgasH2LfccAl:H,Va = −45 805+ 56.4302T

LfccAl,Na:Va = −6210+ 76.4864T

HCP_A3 with formula (Al,Na, Ti)1(H,Va)0.5oGhcpTi:H = 64 310− 766.9133T + 103.9079T ln(T )+

oGhcpTi+ 0.25 oGgasH2 (∗)

LhcpAl,Ti:Va = −133 500+ 39T + 750(yAl − yTi)+ 17 500(yAl − yTi)2

LhcpNa,Ti:Va = 102 025 (∗)

LhcpTi:H,Va = −21 155 (∗)

AlH3 with formula (Al)1(H)3oGAlH3Al:H = −28 415+ 213.712933T − 41.75632T ln(T )

− 0.014548469T 2 + 446 400/T



NaH with formula (Na)1(H)1oGNaHNa:H = −66 593+ 3RT ln[exp(0.5× 268/T )

− exp(−0.5× 268/T )] − 0.0188755T 2

for 0 K < T < 298.15 K= −75768+ 293.7188T − 48.6935T ln(T )− 2.614× 10−4T 2

+ 1.8048× 10−8T 3 + 632 658/Tfor 298.15 K < T < 2000 K

δ-TiH2 with formula (Ti)1(H,Va)2oGδTi:H = 6150− 0.2965T + F11032T (∗)

oGδTi:Va = 6000− 0.1T +oGhcpTi (∗)

NaAlH4 with formula (Na)1(Al, Ti)1(H)4oGNaAlH4Na:Al:H = −128 890− 0.10258T

2+ 3RT ln[exp(0.5× 220/T )

− exp(−0.5× 220/T )] for 0 K < T < 298.15 K= −150 434+ 592.2826T − 99.0677T ln(T )− 0.018466T 2

+ 1.0858× 10−6T 3 + 1091 420/Tfor 298.15 K < T < 2000 KoGNaAlH4Na:Ti:H = −42 990− 0.070095T

2+ 3RT ln[exp(0.5× 278/T )

− exp(−0.5× 278/T )] for 0 K < T < 298.15 K (∗)

= −739 86+ 638.3327T − 100.71T ln(T )− 0.0117834T 2

+ 1.16× 10−6T 3 + 2034 843/Tfor 298.15 K < T < 2000 K (∗)

LNaAlH4Na:Al,Ti:H = 12 040+ 155T (∗)

α-Na3AlH6 with formula (Na)3(Al, Ti)1(H)6oGαNa:Al:H = −267 960− 0.17245T

2+ 6RT ln

×[exp(0.5× 217/T )− exp(−0.5× 217/T )]for 0 K < T < 298.15 K= −309 621+ 1122.177T − 187.24T ln(T )− 0.0226T 2 + 1.3138× 10−6T 3 + 2200 845/T

for 298.15 K < T < 2000 KoGαNa:Ti:H = −177 660− 0.16314T

2+ 6RT ln

×[exp(0.5× 186/T )− exp(−0.5× 186/T )]for 0 K < T < 298.15 K (∗)

= −216 673+ 1071.4252T − 180.5633T ln T − 0.019227T 2

+ 1.26× 10−6T 3 + 1997 745/Tfor 298.15 K < T < 2000 K (∗)

LαNa:Al,Ti:H = 41 600+ 220T (∗)

β-Na3AlH6 with formula (Na)3(Al)1(H)6oGβNa:Al:H = 3497− 6.6587T +

oGαNa:Al:H

TiAl3(D022)with formula (Al, Ti)3(Ti)1oGD022Al:Ti = 3

oGfccAl +oGhcpTi −144592+ 37.024T

oGD022Ti:Ti = 4oGfccTi

LAl,Ti:Ti = −60 000

Ti5Al11 with formula (Al)17(Ti)8oGD022Al:Ti = 17

oGfccAl +8oGhcpTi −971 125+ 236.4T

TiAl2 (tI24) with formula (Al)2(Ti)1oGTiAl2Al:Ti = 2

oGfccAl +oGhcpTi −121500+ 31.2T

TiAl (L10)with formula (Al, Ti)1(Al, Ti)1oGL10Al:Al = 2

oGfccAl +4oGL10Ti:Al =

oGhcpTi +oGfccAl −79644+ 19.2T

oGL10Al:Ti =oGfccAl +

oGhcpTi −79644+ 19.2ToGL10Ti:Ti = 2

oGfccTiLAl,Ti:Al = −89 892+ 44T + 30 000(yAl − yTi)

+ 20 000(yAl − yTi)2

LAl:Al,Ti = −89 892+ 44T + 30 000(yAl − yTi)

+ 20 000(yAl − yTi)2

LTi:Al,Ti = −15 134− 2.36TLAl,Ti:Ti = −15 134− 2.36T

Ti3Al(D019)with formula (Al, Ti)3(Al, Ti)1oGD019Al:Al = 4

oGhcpAloGD019Ti:Al = 3

oGhcpTi +oGfccAl −110 080+ 23.88T

oGD019Al:Ti = 3oGfccAl +

oGhcpTi −99120+ 32.28ToGTiAl3Ti:Ti = 4

oGhcpTi +4LAl,Ti:Al = −99 120+ 32.28TLAl:Al,Ti = −98 968+ 33.3TLTi:Al,Ti = +10 656− 1.332TLAl,Ti:Ti = +32 000− 4T

Symbol:

F11032T = −147306.064− 47.3294265T + 8.608496T ln(T )− 0.0736384T 2 + 1.21497783× 10−5T 3 − 56239.65/T

for 298.15 K < T < 700 K= −164291.412+ 195.657589T − 28.70262T ln(T )− 0.036229465T 2 + 4.955565× 10−6T 3 + 1435710.5/T

for 700 K < T < 1100 K= −162 657.97+ 260.226786T − 39.95143T ln(T )− 0.020358905T 2 + 2.02269833× 10−6T 3 − 365.22975/T

for 1100 K < T < 15000 K= −167412.472+ 333.609415T − 50.93267T ln(T )− 0.01208971T 2 + 9.99446× 10−7T 3 − 14332.105/T

for 1500 K < T < 2000 K

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Thermodynamic modeling of the Na–Al–Ti–H system and Ti