Published on Web Date: June 11, 2010

r 2010 American Chemical Society 1982 DOI: 10.1021/jz100386j |J. Phys. Chem. Lett. 2010, 1, 19821986

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Tuning the Hydrogen Storage in Magnesium AlloysSuleyman Er, Gilles A. de Wijs, and Geert Brocks*,

Computational Materials Science, Faculty of Science and Technology and MESA Institute for Nanotechnology, University ofTwente, P.O. Box 217, 7500 AE Enschede, The Netherlands, and Electronic Structure of Materials, Institute for Molecules andMaterials, Faculty of Science, Radboud University Nijmegen, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands

ABSTRACT Mixing Mg with Ti leads to an alloy with markedly faster hydrogena-tion kinetics as compared to that of pure Mg, but the resulting hydrides are toostable for hydrogen storage applications. Moreover, Mg-Ti alloys are thermody-namically unstable with respect to decomposition into the elements. In this Letter,we show by means of first-principles density functional theory calculations thataddingAl or Si toMg-Timakes the alloysmore stable and their hydrides less stable.Controlling the structure of Mg-Ti-X (X= Al or Si) alloys by growing multilayersof Mg and TiX allows for tuning the hydrogenation energy and improves the alloysas hydrogen storage materials.

SECTION Energy Conversion and Storage

M agnesium, an inexpensive andabundantmetal, canstore up to 7.7 weight% hydrogen. The applicationof MgH2 as a hydrogen storage material is howeverobstructed by its high thermodynamic stability and very low(de)hydrogenation rates, which lead to excessively high oper-ating temperatures T J 300 C.1 A large amount of researchhas been devoted to reducing the stability of MgH2 andenhancing its (de)hydrogenation kinetics. Experiments onthin films have shown that alloying magnesium with earlytransition-metal (TM) elements can markedly improve the(de)hydrogenation kinetics.2 The improved kinetics has beencorrelated with a cubic, fluorite-type Mg(1-x)TMxH2 phase,whereas the tetragonal rutile phase of MgH2 would hamperthe (de)hydrogenation kinetics.3,4 From first-principles cal-culations, we have shown that a fluorite-type phase ofMg(1-x)TMxH2 is stable with respect to a rutile-type phasefor TM = Sc, Ti, V, and Cr, and x J 0.2.5,6

The dehydrogenation enthalpies of Mg(1-x)TMxH2 are how-ever either larger or at least not significantly smaller than that ofMgH2, implicating that the thermodynamic properties are notmarkedly improved. In addition, the stability of the Mg(1-x)TMxalloys decreases along the series Sc, Ti, V, Cr. In fact, onlyMg(1-x)Scx is thermodynamically stable with respect to decom-position into the elemental metals (Mg and Sc). Scandium is arare element, however, which prevents its large-scale use in ahydrogen storage material. Mg(1-x)Vx and Mg(1-x)Crx are ther-modynamically quite unstable, hampering their use in a rever-sible system, which needs to undergo repeated (de)hydroge-nation cycles.Mg(1-x)Tix is an interesting case. Thebinaryphasediagram of Mg and Ti indicates that a thermodynamicallystable alloy between these two elements cannot be formed.Studies of kinetically stabilized bulk Mg-Ti samples have beeninconclusive,7,8 butmetastableMg-Ti alloys are readily formedin thin films by codepositing the elements. Such films have atypical thickness of 200 nm and survive repeated (de)hydroge-nation cycles at room temperature.4,9

The high stability of Mg-Ti hydride remains a problem,however. The calculated dehydrogenation enthalpy ofMg0.75Ti0.25H2 is 0.76 eV/H2, which is close to the valuesreported for MgH2.

5,6 Recently, Vermeulen et al. have sug-gested that incorporating Al or Si into Mg-Ti thin filmsimproves their hydrogen storage properties, whereas theirhydrogen storage capacity does not deteriorate.10 In thispaper, we study the energetics of Mg-Ti-Al,Si alloys andtheir hydrides for several possible compositions by means offirst-principles density functional theory (DFT) calculations.Simultaneous deposition of themetals in thin films very likelyresults indisordered structures.We show thatnanostructuringthe alloys as atomic multilayers enables one to significantlyimprove their hydrogen storage properties.

Starting from the binary alloys, the phase diagrams ofTi with Al or Si show that, for example, alloys with a 1:1composition are very stable.11,12 Both TiAl and TiSi crystallizein a tetragonally distorted fcc structure, the so-called L10structure. The calculated formation energies per atom (Ef) ofTiAl and TiSi are -0.409 and -0.495 eV/atom, respectively,with respect to the elements in their ground-state metalstructures. In contrast, MgTi alloys are particularly unstable,and so far, no compositionsor structures have been found thatgive a negative formation energy. As an example, the calcu-lated Ef of MgTi in the L10 structure is 0.206 eV/atom.Adding Al or Si to form ternary Mg-Ti-Al,Si compoundscould improve Ef via the formation of stable Ti-Al or Ti-Sibonds. In addition, the formation energies of MgAl and MgSi(in the L10 structure) are-0.015 and 0.099 eV/atom, respec-tively, which shows that Mg-Al and Mg-Si bonds are muchmore advantageous than Mg-Ti bonds. So already fromarguments based upon a simple structure, one may suspect

Received Date: March 24, 2010Accepted Date: June 8, 2010

r 2010 American Chemical Society 1983 DOI: 10.1021/jz100386j |J. Phys. Chem. Lett. 2010, 1, 19821986

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that adding Al or Si toMg-Timay lead to a stabilized alloy notonly by forming stable Ti-Al or Ti-Si bonds but also bypreventing unstable Mg-Ti bonds.13

Mg and Si can form the very stable compound Mg2Si with afluorite structure. If one adds Si to Mg-Ti, the formation ofMg2Si needs to be prevented since that compound does notabsorb hydrogen.14 If we consider the reaction Mg2Si Ti TTiSi 2Mg, thenour calculations show that thematerials on theright-hand side of this reaction are more stable by 0.35 eV perTiSi unit. This leaves room for designing a Mg-Ti-Si com-poundsuch that Ti captures theSi andprevents the formationofMg2Si. The samereasoningholds forMgandAl,which can formstable alloys, albeit with a relatively small formation energy.15

The large formation energy of TiAl then leaves room for pre-venting these Mg-Al alloys from being formed.

Considering the stability of TiAl and TiSi, it makes sense tolook at ternary Mg-Ti-X, X= Al,Si, alloys whose Ti-X ratiois fixed at 1:1, that is, Mg(1-2y)TiyXy. We study the composi-tions y = 0.125, 0.1875, and 0.25, which cover the experi-mentally reported range of compositions that showinteresting hydrogen storage properties.10One could envisiongrowing multilayers of TiX and Mg by atomic beam epitaxy,for instance. Figure 1 shows examples of such multilayersgrown in the (001) direction of a fcc structure. Alternating onelayer of TiX and one layer of Mg leads to the compositionMg0.5Ti0.25X0.25. Mg0.75Ti0.125X0.125 can then be formed byalternating one layer of TiX with three layers of Mg andMg0.625Ti0.1875X0.1875 by a more complex stack of one TiXlayer and one or two Mg layers. We optimize the unit cellswithout imposing any constraints. Calculations on Mg-Tialloys have shown that the difference between fcc and hcpstructures is only 0.04 eV/atom.5,6 Starting from hcp struc-tures would alter the formation energies somewhat, but itdoes not change the trend.

The formation energies per atom of these Mg(1-2y)TiyXystructures are given in Table 1. They can be compared to the

formation energies of layered Mg(1-2y)Ti2y compounds withthe same amount of Mg. Adding Al or Si indeed increases thestability. Mg-Ti is quite unstable over the whole compositionrangewith respect to phase separation into the elements. Theformation energy of these layered Mg-Ti structures scaleslinearly with the Ti content, which one may attribute to theformation of Mg-Ti interfaces. A linear fit with the Ti contentgives an interface energyof 0.20 eVper interface andTi atom.The increased stability of Mg(1-2y)TiyXy can be attributed tothe stability of TiX layers. The effect decreases with increasedMg content, which can be interpreted as a strain effect. Thelattice constants of TiAl and TiSi are 11 and 14% smaller thanthat of Mg, respectively. The in-plane lattice constant ofmultilayer Mg(1-2y)TiyXy scales roughly linearly with the Mgcontent in the range considered. Therefore, an increased Mgcontent exerts an increased tensile strain on the TiX layers,which increases the formation energy.

Depositing all three metals simultaneously most likelyleads to disordered structures.10 A full search in the completeconfiguration space for the optimal structure ofa ternaryalloy,as a function of its composition, is computationally prohibi-tive. Therefore, we apply the following scenario to model adisordered structure. We position all metal atoms at fcc sitesand assume that binaryMg-Ti alloys have randompositionaldisorder. Such random structures aremodeled in finite super-cells by special quasirandom structures (SQSs).17,18 We usesupercells containing 32 metal atoms to model SQSs of

Figure 1. Layered Mg(1-2y)TiyXy structures for y = (a) 0.25, (b) 0.1875, and (c) 0.125. Mg, Ti, and X (=Al or Si) atoms are shown asblue, black, and red colored spheres, respectively.16

Table 1. Calculated Formation Energies, Ef (eV/atom), ofMg(1-2y)TiyXy in the Layered Structures with Respect tothe Elements (see Figure 1)

compound X = Ti X = Al X = Si

Mg0.5Ti0.25X0.25 0.206 -0.083 -0.132Mg0.625Ti0.1875X0.1875 0.141 -0.015 -0.040Mg0.75Ti0.125X0.125 0.093 0.010 0.006

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Mg(1-x)Tix, x=0.25, 0.375, 0.5.6,19 Adding a third element in

the compositionMg(1-2y)TiyXy, X=Al or Si,means that half ofthe Ti atoms should be replaced by X atoms. To examine thepreferential binding sites of the X atoms, the coordinationnumbers N of each Ti by Ti atoms in their nearest-neighborshells are calculated for the SQSs of Mg(1-x)Tix. We order theTi atoms in the SQSs of Mg(1-x)Tix according to their N valuesand consider two scenarios for replacing half of them byX atoms. In the first scenario, Ti atoms with the largest N arereplaced, which leads to amaximum coordination of X atomsby Ti or X atoms. We call this the high coordination (hc)structure in the following. In the second scenario, Ti atomswith the smallest N are replaced, giving X atoms that aremostly surrounded by Mg atoms, which we call low coordina-tion (lc). Note that in the lc (hc) structure, the Ti atoms thatremain in Mg(1-2y)TiyXy all have a large (small) N. The hc andlc structures represent extreme cases, and we have checkedthatother scenarios of replacingTi byXatoms give results thatare intermediate between these two cases.

The formation energies with respect to the elements ofthese Mg(1-2y)TiyXy structures are given in Table 2. They canbe compared to the formation energies of the correspondingMg(1-2y)Ti2y structures. Al and Si both have a stabilizing effecton the Mg-Ti compounds, irrespective of where these atomsare positioned, with Si having a larger effect than Al. Inaddition, the stability ofMg(1-2y)TiyXydecreaseswith decreas-ing y. On an absolute scale, only the structures with y= 0.25for Al and y=0.25 and 0.1875 for Si are thermodynamicallystable with respect to decomposition into the elements. Bycomparing the formation energies of the lc and hc structuresin Table 2, one observes that the relative ordering of themetalatoms can have a sizable effect on the formation energies.Perhaps somewhat counterintuitive, the lc case yields thelowest energy. In the lc structures, the Al or Si atoms aremainly surrounded by Mg atoms, and as discussed above,Mg-Al and Mg-Si bonds are not particularly strong. How-ever, the Ti atoms that remain in the lc structure all aremainlysurrounded by Ti atoms. Thisminimizes the number of directMg-Ti contacts that severely decrease the stability.

Comparing the formation energies of the layered struc-tures, Table 1, to those of the disordered structures, Table 2,one observes that the layered structures aremore stable. Thiscan provide new ideas for structures with interesting proper-ties, formed by immiscible elements.

We now turn to the energetics of the Mg-Ti-Al,Si hy-drides. A fluorite-type cubic structure ofMg(1-x)TixH2 is stablefor xJ 0.2.5,6 In the following, we assume that replacing half

of the Ti atoms by Al or Si maintains the fluorite structure. Weuse the structural models of the Mg-Ti-X alloys discussedabove and position hydrogen atoms in the tetrahedral inter-stitial sites. For the disordered systems, we use the lc struc-tures since these give the lowest energies for the alloys.Subsequently, all cell parameters and geometries of thehydrides are optimized.

The hydrogenation energies Eh are given in Table 3,calculated by subtracting the total energies of the alloyMg(1-2y)TiyXy and the hydrogen molecule from that of thehydride Mg(1-2y)TiyXyH2.

The results clearly show that the hydrides Mg(1-2y)TiyXyH2aremuch less stable than their correspondingMg(1-2y)Ti2yH2,whether in the layered or in the disordered structures. Incontrast, the alloys Mg(1-2y)TiyXy are more stable than thecorresponding Mg(1-2y)Ti2y; see Tables 1 and 2. This is anexample of van Mal's or Miedema's rule of reversed stability,which states that stabilization of an alloy phase is accompa-nied by a destabilization of its hydride.20 Apparently, this rulealso holds if one compares the layered to the disorderedstructures. The layered structures of the Mg(1-2y)TiyXy alloysare more stable then their corresponding disordered struc-tures (compare Tables 1 and 2), whereas the hydridesMg(1-2y)TiyXyH2 are less stable in the layered structures thanthose in the disordered structures; see Table 3. Moreover, asMg-Ti-Si alloys are more stable than Mg-Ti-Al alloys, onemay expect that Mg-Ti-Si hydrides are less stable thanMg-Ti-Al hydrides. The results in Table 3 confirm this.

The hydrides of the layered alloys have a well-orderedstructure, with hydrogen atoms occupying positions at orclose to the tetrahedral interstitial sites, as one would expectof a fluorite-type structure. In a fluorite MH2 structure, eachmetal atom M is cubically coordinated by eight hydrogenatoms. Indeed, the radial distribution functions (RDFs) of theM-H distances in layered Mg(1-2y)TiyXyH2 clearly show thiseight-fold coordination; see Figure 2. Such an atomic arrange-ment is thought to be advantageous for fast hydrogenkinetics.4 The hydrides of the disordered lc structures ofMg(1-2y)TiyXyH2 show a larger degree of disorder in thepositions of the H atoms, in particular, for compounds witha highMg content, as can be clearly observed in the RDF. Onemay expect that H atoms close to Mg atoms like to assumepositions that are more typical for the six-fold octahedralcoordination observed in MgH2.

6 Around Al or Si atoms, oneexpects to find a preference for a tetrahedral or an octahedralcoordination. Such competing preferential coordinations can

Table 2. Calculated Formation Energies, Ef (eV/atom), ofMg(1-2y)TiyXy in the Disordered Structures with Respect to theElementsa

X = Ti X = Al X = Si

compound lc hc lc hc

Mg0.5Ti0.25X0.25 0.156 -0.008 0.052 -0.066 0.006Mg0.625Ti0.1875X0.1875 0.153 0.025 0.091 -0.020 0.064Mg0.75Ti0.125X0.125 0.110 0.035 0.058 0.038 0.058

a The construction of the lc and hc structures is discussed in the text.

Table 3. Calculated Hydrogenation Energies, Eh (eV/H2), ofMg(1-2y)TiyXyH2 in the Layered and the Disordered lc Structures

a

layered disordered lc

compound X = Ti X = Al X = Si X = Ti X = Al X = Si

Mg0.5Ti0.25X0.25H2 -1.118 -0.178 0.335 -1.120 -0.358 -0.156

Mg0.625Ti0.1875X0.1875H2 -0.906 -0.278 0.093 -0.981 -0.468 -0.240

Mg0.75Ti0.125X0.125H2 -0.711 -0.317 -0.086 -0.807 -0.501 -0.434

a The second and the fifth columns represent the formation energiesof the corresponding Mg(1-2y)Ti2yH2 structures.

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be observed in the RDF of the disordered structures.The layered structures enforce cubic coordination of all metalatoms by hydrogens, thereby reducing the hydrogenationenergy.

A hydrogenation energy of -0.4 eV/H2 gives an equilib-riumhydrogen pressure of1 bar at room temperature. Evenwith this hydrogenation energy, the amount of heat releasedin a very short time when a bulk material is loaded withhydrogen can be a problem in some applications. Therefore,depending on the application, a hydrogenation energy bet-ween -0.15 and -0.4 eV/H2 is required.21 The hydro-genation energies of pure Mg-Ti alloys are clearly outside ofthis range. They are in fact larger or comparable to thehydrogenation energy of pure Mg.5,6 The addition of Al or Simarkedly destabilizes the hydrides and brings the hydrogena-tion energies into the range required for possible applications,where Si has a larger effect than Al.

The effects are particularly large in the layered struc-tures. Mg(1-2y)TiySiyH2 in a layered structure is eitherunstable or marginally stable for the compositions thatwe studied. In contrast, the hydrogenation energy ofMg(1-2y)TiyAly is-0.18 to-0.32 eV/H2. Moreover, the alloyMg(1-2y)TiyAly is stable with respect to decomposition intothe elements for y= 0.1875 and 0.25 and only marginallyunstable for y = 0.125; see Table 1. These propertiesindicate that Mg(1-2y)TiyAly in layered form is a potentialmaterial for hydrogen storage. Also, in the disorderedstructures, the addition of Al or Si does destabilize thehydrides, although the effects are not as large as those inthe layered structures. Again, Si has a larger effect than Al,but the hydrogenation energies of all compositions studiedare markedly better than those of pure Mg or Mg-Ti. If onedemands that disordered Mg(1-2y)TiyXy alloys are stablewith respect to decomposition into the elements, thenfor X = Al and Si, one needs y = 0.25 and y = 0.1875,0.25, respectively (see Table 2), which gives hydrogenationenergies ranging from -0.16 to -0.36 eV/H2.

COMPUTATIONAL METHODS

DFTcalculations are performed at the level of the general-ized gradient approximation (GGA) using the PW91functional.22 We employ the projector augmented wave(PAW) technique and a plane wave basis set,23,24 as imple-mented in the Vienna ab initio simulation package(VASP).25,26 Standard frozen core PAW potentials are used,where the H 1s, Mg 3s, Al 3s3p, Si 3s3p, andTi 3p4s3d shellsare treated as valence shells. The plane wave kinetic energycutoff is set at 518 eV, and the Brillouin zone is integratedusing a regular k-point mesh with a spacing of at most0.02 -1. The volumes and shapes of the unit cells areoptimized, aswell as the positions of the atoms. Total energiesof the optimized structures are finally calculated using thetetrahedron method.27 Details of the computational pro-cedure can be found in ref 6.

AUTHOR INFORMATION

Corresponding Author:*To whom correspondence should be addressed. E-mail: g.brocks@tnw.utwente.nl.

ACKNOWLEDGMENT The authors acknowledge P. J. Kelly forstimulating discussions. This work is part of the researchprograms of Advanced Chemical Technologies for Sustainability(ACTS) and the Stichting voor Fundamenteel Onderzoek derMaterie (FOM). The use of supercomputer facilities wassponsored by the Stichting Nationale Computerfaciliteiten (NCF).These institutions are financially supported by the NederlandseOrganisatie voor Wetenschappelijk Onderzoek (NWO).

REFERENCES

(1) Buschow, K. H. J.; Bouten, P. C. P.; Miedema, A. R. HydridesFormed from Intermetallic Compounds of Two TransitionMetals; A Special Class of Ternary Alloys. Rep. Prog. Phys.1982, 45, 9371039.

(2) Niessen, R. A. H.; Notten, P. H. L. Electrochemical HydrogenStorage Characteristics of Thin Film MgX (X = Sc, Ti, V, Cr)Compounds.Electrochem. Solid-State Lett.2005,8, A534A538.

(3) Niessen, R. A. H.; Notten, P. H. L. Hydrogen Storage in ThinFilm Magnesium-Scandium Alloys. J. Alloys Compd. 2005,404, 457460.

(4) Vermeulen, P.; Niessen, R. A. H.; Notten, P. H. L. HydrogenStorage in Metastable MgyTi1-y Thin Films. Electrochem.Commun. 2006, 8, 2732.

(5) Er, S.; Tiwari, D.; de Wijs, G. A.; Brocks, G. Tunable HydrogenStorage in Magnesium-Transition Metal Compounds: First-Principles Calculations. Phys. Rev. B 2009, 79, 024105.

(6) Er, S.; van Setten, M. J.; de Wijs, G. A.; Brocks, G. First-Principles Modelling of Magnesium Titanium Hydrides.J. Phys.: Condens. Matter 2010, 22, 074208.

(7) Liang, G.; Schulz, R. Synthesis of Mg-Ti Alloy by MechanicalAlloying. J. Mater. Sci. 2003, 38, 11791184.

(8) Rousselot, S.; Bichat, M. P.; Guay, D.; Roue, L. Structure andElectrochemical Behaviour of Metastable Mg50Ti50 Preparedby Ball Milling. J. Power Sources 2008, 175, 621624.

(9) Borsa, D. M.; Baldi, A.; Pasturel, M.; Schreuders, H.; Dam, B.;Griessen, R.; Vermeulen, P.; Notten, P. H. L. Mg-Ti-H ThinFilms for Smart Solar Collectors. Appl. Phys. Lett. 2006, 88,241910.

Figure 2. Optimized structures of Mg0.75Ti0.125Al0.125H2 in the(a) layered and (b) disordered lc structures. The dashed and solidlines give the RDFs and the integrated RDFs of metal-hydrogenpairs, respectively.

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(10) Vermeulen, P.; van Thiel, E. F. M. J.; Notten, P. H. L. TernaryMgTiX-Alloys: A Promising Route towards Low-Temperature,High-Capacity, Hydrogen-Storage Materials. Chem.-Eur. J.2007, 13, 98929898.

(11) Ekman, M.; Ozolin-s, V. Electronic Structure and BondingProperties of Titanium Silicides. Phys. Rev. B 1998, 57,44194424.

(12) Ohnuma, I.; Fujita, Y.; Mitsui, H.; Ishikawa, K.; Kainuma, R.;Ishida, K. Phase Equilibria in the Ti-Al Binary System. ActaMater. 2000, 48, 31133123.

(13) Kerimov, K. M.; Dunaev, S. F.; Sljusarenko, E. M. Investigationof the Structure of Ternary Phases in Al-Mg-Ti, Al-Mg-Vand Al-Mg-Cr Systems. J. Less-Common Met. 1987, 133,297302.

(14) Vajo, J. J.; Mertens, F.; Ahn, C. C.; Bowman, R. C., Jr.; Fultz, B.Altering Hydrogen Storage Properties by Hydride Destabili-zation through Alloy Formation: LiH and MgH2 Destabilizedwith Si. J. Phys. Chem. B 2004, 108, 1397713983.

(15) Wang, N.; Yu, W.-Y.; Tang, B.-Y.; Peng, L.-M.; Ding, W.-J.Structural and Mechanical Properties of Mg17Al12 andMg24Y5 from First-Principles Calculations. J. Phys. D: Appl.Phys. 2008, 41, 195408.

(16) Momma, K.; Izumi, F. VESTA: AThree-dimensional Visualiza-tion System for Electronic and Structural Analysis. J. Appl.Crystallogr. 2008, 41, 653658.

(17) Zunger, A.; Wei, S. H.; Ferreira, L. G.; Bernard, J. E. SpecialQuasirandom Structures. Phys. Rev. Lett. 1990, 65, 353356.

(18) Ruban, A. V.; Simak, S. I.; Shallcross, S.; Skriver, H. L. LocalLattice Relaxations in Random Metallic Alloys: EffectiveTetrahedron Model and Supercell Approach. Phys. Rev. B2003, 67, 214302.

(19) van Setten, M. J.; Er, S.; Brocks, G.; de Groot, R. A.; de Wijs,G. A. First-Principles Study of the Optical Properties ofMgxTi(1-x)H2. Phys. Rev. B 2009, 79, 125117.

(20) van Mal, H. H.; Buschow, K. H. C.; Miedema, A. R. HydrogenAbsorption in LaNi5 and Related Compounds: ExperimentalObservations and Their Explanation. J. Less-Common Met.1974, 35, 6576.

(21) Er, S.; de Wijs, G. A.; Brocks, G. Hydrogen Storage by Poly-lithiated Molecules and Nanostructures. J. Phys. Chem. C2009, 113, 89979002.

(22) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.;Pederson, M. R.; Singh, D. J.; Fiolhais, C. Atoms, Molecules,Solids, and Surfaces: Applications of the Generalized Gradi-ent Approximation for Exchange and Correlation. Phys. Rev.B 1992, 46, 66716687.

(23) Blochl, P. E. Projector Augmented-Wave Method. Phys. Rev. B1994, 50, 1795317979.

(24) Kresse, G.; Joubert, D. FromUltrasoft Pseudopotentials to theProjector Augmented-Wave Method. Phys. Rev. B 1999, 59,17581775.

(25) Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for LiquidMetals. Phys. Rev. B 1993, 47, 558561.

(26) Kresse, G.; Furthmuller, J. Efficient Iterative Schemes for AbInitio Total-EnergyCalculations Using a Plane-WaveBasis Set.Phys. Rev. B 1996, 54, 1116911186.

(27) Blochl, P. E.; Jepsen, O.; Andersen, O. K. Improved Tetrahe-dron Method for Brillouin-Zone Integrations. Phys. Rev. B1994, 49, 1622316233.