Hydrogen Dissociation and Diffusion on Ni and Ti -doped Mg(0001) Surfaces
HHydrogen Dissociation and Diffusion on Ni and Ti -doped Mg(0001) Surfaces
M. Pozzo , and D. Alf`e , , , ∗ Department of Earth Sciences, University College London,Gower Street, London WC1E 6BT, United Kingdom Department of Physics and Astronomy, University College London,Gower Street, London WC1E 6BT, United Kingdom Material Simulation Laboratory, University College London,Gower Street, London WC1E 6BT, United Kingdom London Centre for Nanotechnology, University College London,17-19 Gordon Street, London WC1H 0AH, United Kingdom
A. Amieiro, S. French and A. Pratt † Johnson Matthey Plc, Technology Centre,Blounts Court, Sonning Common,Reading, RG4 9NH, United Kingdom (Dated: November 4, 2018)It is well known, both theoretically and experimentally, that alloying MgH with transition ele-ments can significantly improve the thermodynamic and kinetic properties for H desorption, as wellas the H intake by Mg bulk. Here we present a density functional theory investigation of hydrogendissociation and surface diffusion over Ni-doped surface, and compare the findings to previouslyinvestigated Ti-doped Mg(0001) and pure Mg(0001) surfaces. Our results show that the energybarrier for hydrogen dissociation on the pure Mg(0001) surface is high, while it is small/null whenNi/Ti are added to the surface as dopants. We find that the binding energy of the two H atoms nearthe dissociation site is high on Ti, effectively impeding diffusion away from the Ti site. By contrast,we find that on Ni the energy barrier for diffusion is much reduced. Therefore, although both Ti andNi promote H dissociation, only Ni appears to be a good catalyst for Mg hydrogenation, allowingdiffusion away from the catalytic sites. Experimental results corroborate these theoretical findings,i.e. faster hydrogenation of the Ni doped Mg sample as opposed to the reference Mg or Ti dopedMg. PACS numbers:
I. INTRODUCTION
Safe and efficient hydrogen storage is one of the biggestbarriers to the more wide spread usage of hydrogen as anenergy carrier or fuel. Currently, commercial solutionsare based on liquid or compressed gas storage methods,which are inefficient and have safety issues. Alterna-tive storage methods include metal hydrides, which areformed by the interaction between a suitable metal andhydrogen. The relatively strong metal-hydrogen bondsprovide an intrinsically safe storage medium. The re-lease of hydrogen from the hydride is then achieved byheating the material above a certain decomposition tem-perature. There are a large number of metals in naturethat form hydrides, however, only the lighter ones arethought to be suitable candidates for mobile hydrogenstorage purposes (see [2] for an overview). Beside beinglight weight, a hydride will need to have good cyclability(several hundred times with little loss of performance),fast adsorption/desorption kinetics (the hydride should ∗ Electronic address: [email protected] † URL: form/decompose on a time scale of minutes) and lowdecomposition temperature (ideally between 20 and 100Celsius).Magnesium is a good case study due to its lightweight,low cost, cyclability and the high H storage capacity of7.6% by weight once the hydride MgH is formed [3].However, its commercial application is still on hold forpractical issues due to low H absorption/desorption ki-netics and high working temperatures [4]. The strongbond between Mg and hydrogen provides MgH withhigh thermodynamic stability, which has an enthalpy offormation of about -76 kJ/mol [5], and a decompositiontemperature of more than 300 Celsius [6]. The slow ki-netics may be explained by the high energy barrier whichneeds to be overcome (see for example [7]) to dissociatethe H molecule due to the tendency of Mg to repel the s-electron of H because of the Pauli exclusion principle [8].A step forward in improving hydrogen reaction kineticshas been achieved by the mechanical ball milling of MgH with transition elements (see [9] and references therein).The hydrogen storage properties of mechanically milledpowders improves because of the reduced powder size (seefor example [10, 11, 12, 13] and references therein), whichshorten the diffusion distance of H into bulk Mg for theformation of the hydride. There are many experimental a r X i v : . [ c ond - m a t . m t r l - s c i ] J a n and theoretical papers in the literature showing that thehydriding properties of MgH are further enhanced bythe addition of traces of transition metals which act asa catalyst (see for example [13, 14, 15, 16, 17] and ref-erences therein). In particular, alloying Mg with Ni canslightly improve the thermodynamic properties of the hy-dride by favouring H adsorption/dissociation and con-sequent atomic hydrogen absorption/desorption due to aweakening of the bonding between Mg and H atoms (seefor example [11, 13, 16, 17, 18] and references therein).While from theoretical calculations the destabilizationeffect of Ni on MgH appears second only to Cu (see [16]),experimentally Ni shows the highest kinetics, with Cufalling behind. As suggested by Shang et al. [13], Cu re-sults are disadvantageous for H desorption probably be-cause of the formation of a MgCu compound. Recently,a new method of chemical fluid deposition in supercrit-ical fluids has been used on metal hydrides [19]. Evensparser literature exists for the activation barrier of hy-drogen dissociation on a transition metal doped surface,which includes only the theoretical calculations made byDu et al. [1, 20, 21] within DFT (RPBE) for both thepure Mg(0001), and Ti and Pd incorporated Mg surfaces.Their results show that the dissociation barrier of hydro-gen on the Ti doped Mg surface is greatly reduced (infact, there is no barrier at all) due to the strong interac-tion between the hydrogen s orbital and the Ti d orbital,however, strong binding of the two H atoms near the Tisite prevents easy diffusion, reducing therefore the effi-cacy of the catalyst for Mg hydrogenation [1]. Palladiumdoping appears to both lower the dissociation barrier andthe diffusion barrier, suggesting a better catalytic activ-ity. Their findings are consistent with the experimentallyobserved trend of generally improved hydrogen absorp-tion kinetics when Mg surfaces are doped with transitionmetals, as previously mentioned.To our knowledge, so far there is no published theo-retical investigation of H dissociation and correspond-ing activation barrier on a Ni-incorporated Mg surface,nor a systematic investigation of the catalytic effect ofother transition metal dopants apart from the above men-tioned studies on the Ti-doped and Pd-doped Mg sur-faces presented by Du et al. [1, 20, 21]. There are afew theoretical papers about the dissociation of molec-ular hydrogen on a pure Mg surface where the corre-sponding activation barrier has been effectively calcu-lated. These investigations were based on a jellium modeland potential energy surface(PES) calculations withindensity functional theory (DFT) with the local densityapproximation(LDA) or generalised gradient corrections(RPBE) [22, 23, 24, 25, 26].For the purpose of a larger scale investigation, we haveperformed DFT calculations for hydrogen dissociationand diffusion on a Ni-doped Mg surface, accompaniedby analogous calculations on a Ti-doped Mg surface fora consistency check with the recently reported theoreti-cal values. This study should be regarded as a first stepin order to build up a global picture of the dissociative chemisorption of hydrogen when doping the Mg surfacewith different transition metals. The main purpose ofthis article is to try to understand the observed largeenhancement of the kinetics of hydrogen adsorption byMg when it is doped with a small quantity of Ni, butnot when it is doped with Ti. The computational resultsare supported by experimental data where a Ni dopedMg sample is hydrogenated substantially faster than thereference Mg or Ti doped Mg. II. COMPUTATIONAL METHOD
DFT calculations were performed with the ab-initiosimulation package VASP [27] using the projector aug-mented wave (PAW) method [28, 29] and the PBEexchange-correlation functional [30]. An efficient chargedensity extrapolation was used to speed up the calcula-tions [31]. A plane-wave basis set was used to expand theelectronic wave-functions with a plane-wave energy cut-off of 270 eV, which guarantees convergence of adsorptionenergies within 1 meV. For completeness, Mg bulk pa-rameters were also calculated using the LDA functional.Monkhorst-Pack k -points were used to sample the Bril-louin zone [32]. A smearing function of the Methfessel-Paxton (MP) type (product of a Gaussian times a n th-order Hermite polynomial) [33] was used throughout.Figs. 1, 3 - 9 and 13 have been made using the XCRYS-DEN software [34]. The exact values of the various pa-rameters used in the calculations will be reported belowin the relevant sections.Activation energies have been calculated using thenudged elastic band (NEB) method [35]. A sufficientnumber of replicas has to be used in order to predict ac-curately a minimum energy path (MEP), for most caseswe repeated the calculations with a different number ofreplicas until convergence of the activation energy andmain features of the MEP were observed. The total num-ber of images actually used in each case is reported whererelevant in the following sections. III. THEORETICAL RESULTSA. Bulk Mg, Ti and Ni, and the Mg(0001) surface
Magnesium bulk crystal at ambient conditions has thehexagonal closed packed (hcp) structure. Several prelim-inary tests were first carried out using the PBE versionof the PAW potential of magnesium, which only includesthe 3 s electrons in valence and has a core radius of 1.1 ˚A.These included: the energy dependence on the c/a ratiofor different k -points meshes, from a minimum of 56 toa maximum of 880 k -points in the irreducible wedge ofthe Brillouin zone (IBZ); different values of n for the MPsmearing functions and different smearing widths; anddifferent plane-wave cutoffs. To calculate the bulk struc-tural properties of Mg, energy versus volume curves werefitted to a Birch-Murnaghan equation of state [36]. Wefound that with a 18x18x12 k -point mesh (259 points inthe IBZ), n = 1 and a smearing width of 0.2 eV, thezero pressure equilibrium volume V and bulk modulus B of bulk Mg were converged to within 0.2% and 0.3%respectively. Similar convergence results were obtainedwith the standard LDA potentials, which also has onlythe 3 s electrons in valence and a core radius of 1.1 ˚A.Results are summarised in Table I, together with resultsfrom previous theoretical calculations. The well knowntrend of LDA to overestimate the bulk modulus and un-derestimate the lattice parameter [37] is apparent.Finally, we have tested PBE and LDA PAW potentialswith 2 p and 3 s electrons in valence. These potentialsstill have core radii of 1.1 ˚A but require an higher en-ergy cut-off value of 350 eV. The structural parametersobtained with these potentials are essentially identical tothose obtained with the previous potentials. Therefore,in the rest of the work we only used the standard Mgpotentials.From our PBE calculations (see Table I), we derivea lattice constant of 3.19 ˚A, in error of just 0.6% withrespect to the experimental value [39]. The zero pressurebulk modulus B is 36.8 GPa, and the value of c/a at theequilibrium volume is 1.621, both in very good agreementwith the experimental values (we note however that thesecalculations do not include room temperature thermalexpansion, which are present in the experimental data).Titanium is also hcp crystal. We used the standardversion of the PBE PAW pseudopotential for Ti, whichhas a core radius of 1.2 ˚A, and we used a 18x18x12 k -point grid. The resulting values for the structural pa-rameters were a = 2 .
923 ˚A and B = 120 GPa, and thevalue of c/a at the equilibrium volume was 1.583, in goodagreement with those previously found with theoreticaland experimental investigations (see Refs. 47, 48, 49 andreferences therein).To study bulk Ni we also used the standard versionof the PBE PAW potential, which has a core radius of1.1 ˚A. Ni bulk has a face centred cubic crystal structure,with a small magnetic moment of 0.61 µ B under ambi-ent conditions [42], so we performed spin polarised to-tal energy calculations. The calculations were performedwith a 13x13x13 grid of k -points. We found a latticeparameter a = 3 .
524 ˚A and a bulk modulus B = 194GPa, which compare well with the experimental data of3.524 ˚A and 186 GPa respectively [42, 50]. The zero pres-sure magnetic moment is 0.63 µ B , which is also close tothe experimental value of 0.61 µ B . The values we foundfor a , B and µ B are in agreement with those from otherGGA and PBE calculations [51, 52, 53].Surfaces have been modelled using periodic slabs, withseveral atomic layers (from 3 to 13) and a large vacuumthickness (5-18 ˚A), defined as the distance between twoopposite facing surfaces. We used a 18x18x1 k -point gridfor the 1x1 surface primitive cell. The positions of theatoms in the three topmost layers were allowed to relax,while the rest were kept at the bulk interatomic distances. Good convergence in the calculated surface energies andrelaxations of the topmost atomic layers was achievedwith five layer slabs (corresponding to a slab thicknessof about 13 ˚A) and a vacuum region thickness of about10 ˚A. We found that the topmost layer has an inward re-laxation of about 1.4 %, in good agreement with the in-ferred experimental zero temperature value of 1.7% [54].We found that with 5 atomic layers the surface energyis converged to within 2 meV to the value 0.30 eV/atom.This compares well with the experimental findings whichare in the range 0.28-0.33 eV/atom [45, 46]. B. H dissociation and H diffusion on the pure Mgand the Ti-doped Mg surfaces Hydrogen adsorption energies on the Mg(0001) surfacewere determined at low coverage in four possible sites:top, bridge, hollow-fcc and hollow-hcp (see Fig. 1). Theseadsorption energies are defined as E ads (H)= E slab (MgH)-[ E slab (Mg) + 1/2 E (H )], where E slab (MgH) is the en-ergy of the slab with one H adsorbed on the surface, E slab (Mg) is the energy of the bare slab and E (H ) theenergy of the isolated hydrogen molecule, calculated byplacing the H molecule in a large cubic box of sides13.5 ˚A.Calculations have been performed on 2x2 (correspond-ing to 0.25 ML coverage, ML=monolayer) and checkedagainst results obtained from 3x3 (corresponding to 0.11ML coverage) surface unit cells, with differences betweenthe two sets of calculations of less than 0.01 eV, thusimplying that the results effectively correspond to thosefor an isolated H molecule. The two sets of calculationshave been performed with equivalent grids of k -points,9x9x1 and 6x6x1 for the 2x2 and the 3x3 surface unitcells respectively.The values for the adsorption energies of atomic hydro-gen in different adsorption sites on the pure Mg surfaceare reported in Table II. These compare well with pre-vious theoretical results [25]. It is clear that there is astrong preference for the hollow sites, with a small pref-erence for the fcc hollow site.We performed NEB calculations for H dissociationover two possible sites (bridge and top). These have beenaccompanied by careful tests on supercell size, number oflayers in the slab and number of replicas in the NEB cal-culation to obtain the minimum energy path and the ac-tivation barrier. We found that a 2x2 supercell, 5 layersand 5 replicas are enough to obtain activation energiesconverged to within 0.02 eV. The first MEP is ratherfeatureless (IS → TS → FS), and it is well approximatedalso by 5 replicas, although in Fig. 2 we report the MEPobtained with 17 replicas.Of the two sites investigated, we found that H prefersto dissociate over a bridge site (see Fig. 3) with an acti-vation energy of about 0.87 eV (about 0.6 eV lower thanthat obtained for dissociation over a top site), in agree-ment with previous DFT calculations [20, 24, 25, 26] and TABLE I: Bulk and surface properties of pure Mg.a (˚A) c/a V ( cell/atom )0 (˚A ) k (GPa) dk This work 3.19(3.13) a a a a a Other calculations 3.19 b , 3.18(3.13) c , 1.615(1.616) c , 22.97(21.66) d c , 4.0(4.1) d d d d [Expt.] [3.21] e [1.624] e [23.24] f [35.4] e , [36.8 ± g [4.3 ± g E coh (eV) -1.50 a , -1.50(-1.78) c [Expt.] -1.51 h E surf (eV/atom) 0.30 a , 0.30(0.35) c , 0.34 i , 0.32 j [Expt.] 0.28 k , 0.33 la Reported values are those from PAW PBE(LDA) calculationswhich do not include room temperature thermal expansion. b Ref. 20. c Ref. 37 from DFT GGA(LDA) calculations. d Ref. 38 from PAW GGA(LDA) calculations. e Ref. 39. f Ref. 40. g Ref. 41. h Ref. 42. i Ref. 43 from ab initio LDA calculations. j Ref. 44 from ab initio LDA calculations. k Ref. 45. l Ref. 46.
TABLE II: Hydrogen adsorption energies (E ads ) in differentadsorption sites on the pure Mg surface, for the 2x2 and the3x3 surface unit cells.Ads. sites E ads (eV) E ads (eV)(2x2) (3x3)Top 0.75 0.74bridge 0.12 0.13hollow (hcp) -0.03 -0.03hollow (fcc) -0.05 -0.04 experimental findings [7], as reported in Table III.The small difference between our findings and those ofVegge [17] and Du et al. [20] are due to their use of RPBEinstead of PBE, and different k -point meshes.We then performed a second NEB calculation to ob-tain the MEP for the diffusion of one of the H atomson the surface from one fcc to a second fcc site (FS → TS2 → LS → TS3 → FS2; see Fig. 4). This MEP (cal-culated with 17 replicas) is also displayed in Fig. 2, asa continuation of the dissociation MEP, and shows thatthe highest energy barrier for surface diffusion is only ∼ .
18 eV, which agrees very well with the calculationsof Du et al. [1]. This low energy barrier clearly indicatefast diffusion even at room temperature.Before repeating the calculations on the Ti-doped sur-face, we tested all four possible sites for H adsorptionafter dissociation (see Fig. 5), and we found that atomichydrogen prefers to adsorb into two of the possible threehollow-fcc sites around the Ti atom. The dissociation
TABLE III: Activation energy (E a ) for hydrogen dissociationon the pure Mg, Ni-doped and Ti-doped Mg surfaces.E a (pure Mg) 0.87 a , 0.4 b , c , 0.5 d , e , 1.15 f , 1.05 g , 0.95 h [Expt.] 1.0 i E a (Ni-doped Mg) 0.06 a E a (Ti-doped Mg) null a , negligible ga This work. b Ref. 22 for a jellium system. c Ref. 25, from DFT LDA calculations ans PES. This lower valueas compared to other calculations is explained as due to the wellknown LDA overbinding. d Ref. 23 for a jellium system. e Ref. 24 for a jellium system and PES. f Ref. 26 from DFT RPBE. g Ref. 20, from DFT PAW RPBE calculations (see also discussionin main text). h Ref. 55 from PES calculations. i Ref. 7. activation barrier was calculated using 9 and 17 replicas,with 9 being enough to display the main features of theMEP (IS → FS; see Fig. 6), although in Fig. 2 we dis-play the results obtained with 17 replicas. Our findingsare very similar to the previous results of Du et al. [1, 20],i.e. there is no barrier for hydrogen dissociation on a Ti-doped Mg surface, and a barrier of almost 0.8 eV fordiffusing away from the Ti sites (FS → TS2 → FS2; seeFig. 7), which therefore becomes the rate limiting step inthe reaction [1].
C. H dissociation and diffusion on a Ni-doped Mgsurface Having benchmarked our calculations on the pure Mgand the Ti-doped Mg surfaces, we now come to the mainpurpose of the paper, which is to study the effect of Nidoping of the Mg(0001) surface on the activation barriersfor H dissociation and diffusion on the surface.On the Mg(0001) surface, we found that Ni is non-magnetic, so all calculations have been performed with-out including spin-polarisation.After dissociating on top of a Ni atom, the two H atomscan adsorb into four different hollow sites, as shown inFig. 5. The most stable final state is found to be the onewhere the H atoms adsorb into two nearby hollow-hcpsites (see Fig. 5, bottom-right corner. We also found thatthe configuration on the bottom-left corner was unstable,with the hydrogen atoms repelled by the Nickel atom andsqueezed between nearby Mg atoms). Figure 8 showsthe dissociation of the hydrogen molecule over the Niatom as viewed from side (top panel figures) and top(bottom panel figures) positions respectively at the IS,TS and FS. Note that on the Ni-doped Mg surface themolecule at the TS is much higher than on the pure Mg(0001) surface (see respectively Figs. 8 and 3), being at ∼ ∼ dissociation on aNi-incorporated Mg surface is only 0.06 eV, against 0.87eV found for the pure Mg surface. In Fig. 2 we displaythe MEP obtained from a calculation with 17 replicas (IS → TS → FS).The NEB diffusion calculation was also performed with17 replicas (FS → TS2 → FS2; see Fig. 9) and showsan energy barrier of only 0.27 eV, which is only slighltyhigher than the diffusion barrier on the pure Mg surface,and would also allow fast diffusion even at room tem-perature. We note that this barrier is similar to the onefound on the Pd-doped surface by Du at al. [1], althoughin that case the rate limiting step is the dissociation ofthe H molecule with an energy barrier of 0.305 eV.This suggests that Ni should be an even better catalystthan Pd for the hydrogenation of Mg.As a final note we would like to point out an inter-esting analogy with H dissociation on pure transitionmetal surfaces. In particular, on the pure Ni(111) sur-face Kresse [56] calculated an energy barrier of only 0.015eV using DFT PAW GGA. This is similar to our value of0.06 eV on the Ni-doped Mg surface, however, we notethat when the same 4x4x1 k -point sampling grid is usedwe find an energy barrier of 0.014 eV on the Ni-dopedMg surface, which is therefore very close to the valuefound by Kresse [56]. These calculations are also con-sistent with potential energy calculations of Arboleda etal. [55], also performed with a 4x4x1 k -point grid. Thesmall barrier for hydrogen dissociation on Ni(111) is also confirmed by experiments [57]).Analogously, the behaviour of H dissociation over theTi-doped Mg surface appears to be similar to that ob-tained on the pure Ti(111) surface: the null activationbarrier we find with a smaller 4x4x1 grid compares withtheoretical results found over a Ti (0001) surface with ananalogous grid [55, 58]. In other words, this seems to sug-gest that the value of the activation barrier for hydrogendissociation over a transition-metal doped Mg surface issimilar to the activation barrier for H dissociation overthe corresponding pure transition-metal surface. D. Electronic structure
To study the electronic properties of the system, weprojected the electronic density of states onto sphericalharmonics functions of type s , p and d , centred on Mg,Ni, Ti and H atoms. It is well known that the catalyticreactivity of a surface is correlated to the position of the d -band (i.e., in this case the projection of the electronicdensity of states onto d type spherical harmonics) withrespect to the Fermi energy E f . In particular, it wasshown by Hammer and Norskov [8](see also [59]) that aconvenient parameter to monitor the catalytic reactivityis the first energy moment of the d -band, or d -band cen-tre, defined as E d = (cid:82) E −∞ dE ( E − E f ) p d ( E ), where p d ( E )is the density of states projected onto spherical harmonicof type d centred on some specified atom, and E is somecutoff energy which we chose to be at 7 eV above theFermi energy. Then, if the centre of the band is close to E f it follows that there are many d electrons availablefor donation, as well as a significant number of empty d -levels available for back-donation, and the results of thisis that the system is very reactive. The d electrons of Nion Mg(0001) form a band which is relatively close to theFermi energy and for this reason the system is very reac-tive. By contrast, Mg has no d electrons (although in thesolid state a projection onto d type spherical harmonicsis not zero), and therefore its reactivity is much reducedby comparison.Ni is a late transition metal with almost all the d or-bitals filled with electrons, by contrast Ti only has 2 elec-trons in the d orbitals. It is therefore clear that the posi-tion of the d -band centre will be much higher in Ti thanin Ni, which explains the higher reactivity of Ti.Our calculated values for E d on the Ni/Ti-doped Mgsurfaces are -0.79 eV and +1.08 eV for Ni and Ti respec-tively (see Table IV).Using DFT RPBE, Vegge et al. [17] calculated the d -band center position for MgTM (TM = transition metal)alloys, allowing an expansion of the alloy lattice to acco-modate the hydrogen atoms. They found -0.82 and +0.48for TM=Ni,Ti respectively. Although the value we findfor Ti is much larger, the same trend is observed in thecase of our Ni/Ti-doped Mg surfaces.Figures 10-12 show the projected density of states(PDOS) found for the pure Mg, Ni-doped and Ti-doped TABLE IV: The d-band center position with respect to the Fermi energy ( E d − E f ), H s peak shift between the initialand transition state (H sTS − IS ), activation barrier (E a ) and energy difference between the final and initial state (E FS − IS ) forhydrogen dissociation on the pure Mg surface as opposed to the Ni/Ti-doped Mg surfaces.Surface E db − E F (eV) H sTS − IS (eV) E a (eV) E FS − IS (eV)Mg pure – -1.43 0.87 -0.04Ni-doped Mg -0.79 -0.77 0.06 -0.66Ti-doped Mg +1.08 – null -1.34 Mg surfaces respectively. The PDOS are given for a num-ber of configurations along the MEP: the initial state(IS), the transition state (TS), the replica just after thetransition state (TS+1) and the final state (FS). For theTi-doped Mg surface, the PDOS are given for IS and FSonly since there is no transition state in the dissociationprocess. For somplicity of notation, we call here the tran-sition state and the final state simply TS and FS, as weonly refer to the part of the MEP which deals with thedissociation of the H molecule.In the IS the hydrogen molecule is still far from themetal surface and there is no overlap between the H molecular orbitals and the orbitals of the metal surface.At the transition state, instead, when gaseous hydrogenhas started dissociating over the surface, there is clearinteraction between the H s orbital and the Mg s and p orbitals on the pure Mg surface (see Fig. 10, top-rightcorner). On the Ni-doped surface the overlap appearsto be non-zero with all the Ni s , p and d orbitals (seeFig. 11, top-right corner). In the final state it is evidentthat the magnitude of the Mg p electron peaks below theFermi level are increased in the Ni/Ti-doped surfaces (seerespectively Fig. 11, bottom-right corner, and Fig. 12,right) with respect to the pure Mg surface (see Fig. 10,bottom-right corner).Interestingly, we note that there appears to be a clearnegative shift of the position of the hydrogen s orbital ingoing from the initial state to the transition state, whichis more pronounced for the pure Mg surface as opposedto the Ni-doped Mg surface.Besides the d -band center positions, in Table IV wealso report the corresponding activation barriers ( E a ),the energy difference between the initial and final states( E F S − IS ) for hydrogen dissociation, and the H s peakshift between the initial and transition states (H sT S − IS ).The correlation between the position of the d -band andthe height of the activation barrier is evident, as wellas the correlation with E F S − IS , i.e., the d -band centerposition is smaller for larger values of the former andsmaller values of the latter.Furthermore, from the results obtained for the pureMg and Ni-doped Mg surfaces, another interesting corre-lation emerges. In fact, as shown in Table IV, it appearsthat H sT S − IS correlates with both E a and E F S − IS , i.e.,it is smaller for smaller values of the former and forlarger values of the latter, following a reversed trend withrespect to that noticed for the d -band center position.In other words, this means that the shift of the hydro- gen s orbital between initial state and transition state islarger when the bond between the dopant and H atomsis weaker. E. Charge distribution
To conclude our analysis we decided to have a look atthe charge distributions in the systems as the dissociationprocesses take place on the pure Mg and metal-doped Mgsurfaces.To do this, we calculated the total charge at eachstep of the MEP, and for convenience, we subtractedthe charge densities obtained from calculations which in-cluded only the substrate and only the H fragments re-spectively, with the atoms in exactly the same positions.This charge difference obviously integrates to zero, andhas the advantage of showing point by point where thecharge is being transferred to. The analysis reveals someinteresting effects. In particular, on the pure Mg(0001)surface we find that at the transition state there is a sig-nificant charge transfer from the Mg substrate to the Hatoms (see Fig. 13 - left). This extra charge fills the H an-tibonding orbitals which eventually leads to dissociation,and builds up on the molecule because the Mg surface isunwilling to accept back-donation of electrons from theH atoms. The Coulomb energy of this charge transfer isprobably the main contribution for the energy barrier.By contrast, on the Ni doped surface there is almostno charge transfer from the substrate to the molecule atthe transition state (see Fig. 13 - right). This is becausewhile some Ni d charge fills up the H antibonding or-bitals, charge from the molecular bonding orbital is back-donated to the empty d states available on the surface.As a result, the energy barrier is reduced to almost zero. IV. EXPERIMENTALA. Sample preparation
The three samples prepared were MgH , 2%Ni/MgH and 2%Ti/MgH . Three batches of 25 gram samples wereprepared by ball milling the different compositions for 2hours under 4 bar of hydrogen. The MgH used for all isGoldschmidt 98% pure. The Ni used (99.9% pure) wasfrom Alfa Aesar 0.8 - 0.03 µ m diameter as was the Tiused ( < µ m and 93% pure). 25 g of both 2%Ni/MgH and 2%Ti/MgH were mixed in a tubular mixer beforemilling for one hour. Samples were then milled using theFritsch planetary ball mill pulverisette 5. The millingpots have a special stainless steel jacket with an o-ringfitted on the top seal, this can allow a gas atmospherethrough a feeding valve, to be used during the millingprocess of up to 5 bar. 25 grams of sample were milledusing agate pots (around 300cc volume) and 15 balls ofthe same material. The milling process was 2 hours using350 rpm in a 15 minute mill 10 minute pause sequence. B. Sample testing
The rig used for testing the sample has a 10 cc reactorpot containing 1 gram of sample. The main lines of therig are a hydrogen line regulated to a 7 bar gauge, anArgon line and a vacuum line. The inert gas line anda vacuum line are used for purging the system. The re-actor is connected to an inlet flow controller, a pressuretransducer to read the internal pressure and a mass flowmeter outlet. A thermocouple in close contact with thepowder load reads the sample temperature. A heatingjacket cartridge is attached to the reactor allowing thesystem to operate in isothermal conditions or be tem-perature programmed from a control box which uses thesample thermocouple as a reference value. An interfacecard records inlet flow, outlet flow, temperature and pres-sure every second.Volumetric hydrogenation and dehydrogenation cycleswere possible to monitor using this arrangement. Hydro-genations were performed at 300 C using 25 cc min − of hydrogen from a regulator set at 7 bar gauge. Duringthe hydrogenation the pressure increases to a point wherethe sample starts absorbing and forms a plateau pressure,once the sample is fully hydrogenated the reactor keepsbuilding pressure until seven bar are reached. Dehydro-genations were recorded by flowing 25cc/min of hydrogenthrough the reactor using an inlet flow controller. Thesystem is then open to vent for a chosen temperature orheating slope and any hydrogen evolving from the sam-ple is recorded as an increase in the 25cc min flow by anoutlet flowmeter. C. Experimental Results
The hydrogenation plots of the 2% Ni/Mg sample atdifferent temperatures in the range between 290 and320 C are shown in Fig. 14. The hydrogenation of the2%Ti/Mg sample in the temperature range between 290and 310 C is shown in Fig. 15. Both graphs of hydro-genation show P mbar gauge vs time in seconds. Thehydrogenation of pure Mg gave results close to the Tidoped samples and is therefore not shown.The catalytic activation of Mg by Ni during hydro-genation is clear. The plateau pressures for each temper-ature hydrogenation are lower for the 2%Ni/Mg sample than those of Mg and 2%Ti/Mg. The fact that at 290 Cthe hydrogenation curve for 2%Ni/Mg is still lower thanthe hydrogenation in the same conditions at 300 C con-firms this. At 290 C both Mg and 2%Ti/Mg showed ahigher hydrogenation pressure than at 300 C suggestingTi catalysisof Mg hydrogenation is not evident.
V. CONCLUSIONS
We have presented a DFT study of hydrogen dissocia-tion and diffusion over Ni-doped and Ti-doped Mg(0001)surfaces, and compared these with dissociation and diffu-sion on pure Mg(0001). Our results show that the energybarrier for hydrogen dissociation is high on the pure Mgsurface (0.87 eV), and it is small (0.06 eV) or even nullwhen Ni or Ti are used as dopants respectively. We alsofound that although on the pure Mg(0001) surface thebinding energy of the H fragments is nearly zero, on theNi/Ti -doped surfaces this binding energy is significant,being 0.66 and 1.34 eV respectively, with diffusion energybarriers of ∼ . ∼ .
27 and ∼ . dissociationover the Ni/Ti-doped Mg surface are similar to the valuesfound on the corresponding pure Ni/Ti surfaces [55, 56,58].More insight in the behaviour of these systems can begained by inspecting the partial density of states and bylooking at the electronic charge density distributions. Inparticular, the higher reactivity of Ti with respect to Nican be understood in terms of a lower position of the d -band centre, which correlates with both the height of theenergy barriers for the dissociation of the H moleculeand with the binding energy of the H fragments whenadsorbed on the surface.The charge density distributions on the different sys-tems also shows some interesting behaviour. In partic-ular, we argued that the presence of a barrier on thepure Mg(0001) surface may be understood in terms of thebuild up of extra charge on the H molecule as it movescloser to the surface. This happens because the closedshell Mg surface is unwilling to accept back-donation ofcharge from the H molecule. One consequence of this isthat the molecule needs to arrive very close to the sur-face before starting to dissociate. By contrast, Ni andeven more so Ti have many available empty d -states,and this avoids significant charge transfer from the sub-strate to the molecule. In this case, the dissociation ofthe molecule begins much further away from the surface.The low dissociation barrier, coupled with the low dif-fusion barrier, make Ni a very useful promoter for thehydrogenation of Mg. By contrast, the high dissociationbarrier on the pure Mg surface, and the high diffusionbarrier on the Ti-doped surface, are responsible for theslow kinetics of hydrogenation on both systems.Our experimental findings show faster hydrogenationfor the 2%Ni/Mg sample with respect to the reference Mgor the 2%Ti/Mg, in good agreement with our theoreticalresults of a lower activation energy for the dissociation-diffusion process in the 2%Ni/Mg system. The behaviourof Mg and 2%Ti/Mg upon hydrogenation is found to bevery similar, again agreeing very well with the theoreticalfindings of large and similar activation energies: a disso-ciation energy barrier of 0.87 in the pure Mg system, anda diffusion energy barrier of 0.8 eV in the 2%Ti/Mg sys-tem, making the dissociation-diffusion process similarlydifficult in both cases.We deliberately chose to study Ni and Ti as dopantsbecause they are at the two ends of the first row of tran- sition metals, and so their behaviour may be expectedto be representative of a range of properties. In fact, weare now extending our investigations to other transitionmetals, and we plan to report on these new results in thenear future. Acknowledgments [1] A. J. Du, S. C. Smith, X. D. Yao, and G. Q. Lu, J. Am.Chem. Soc. , 10201 (2007).[2] L. Schlapbach and A. Z¨uttel, Nature (London) , 353(2001).[3] R. B. Schwarz, MRS Bull. , 40 (1999).[4] J.-L. Bobet, C. Even, Y. Nakamura, E. Akiba and B.Darriet, J. Alloys Compd. , 279 (2000).[5] M. Yamaguchi and E. Akiba, in Material Science andTechnology , vol. 3B, edited by R. W. Cahn, P. Haasenand E. J. Kramer (New York: VCH, 1994), p. 333.[6] B. Bogdanovic, K. Bohmhammel, B. Christ, A. Reiser,K. Schlichte, R. Vehlen and U. Wolf, J. Alloys Comp. , 84 (1999).[7] P. T. Sprunger and E. W. Plummer, Chem. Phys. Lett. , 559 (1991).[8] B. Hammer, J. K. Nørskov, Surf. Sci. , 211 (1995).[9] W. Oelerich, T. Klassen and R. Bormann, J. AlloysCompd. , L5 (2001).[10] L. Zaluski, A. Zaluska, P. Tessier, J. O. Str¨om-Olsen andR. Schulz, J. Alloys Compd. , 53 (1995).[11] G. Liang, J. Huot, S. Boily, A. Van Neste and R. Schulz,J. Alloys Compd. , 247 (1999).[12] A. Zaluska, L. Zaluski and J. O. Str¨om-Olsen, J. AlloysCompd. , 217 (1999).[13] C. X. Shang, M. Bououdina, Y. Song and Z. X. Guo, Int.J. Hydrogen Energy , 73 (2004).[14] A. R. Yavari, J. F. R. de Castro, G. Heunen, and G.Vaughan, J. Alloys Compd. , 246 (2003).[15] G. Liang, J. Alloys Compd. , 123 (2004).[16] Y. Song, Z. X. Guo and R. Yang, Phys. Rev. B , 094205(2004).[17] T. Vegge, L. S. Hedegaard-Jensen, J. Bonde, T. R.Munter and J. K. Nørskov, J. Alloys Compd. , 1(2005).[18] N. Hanada, T. Ichigawa and H. Fujii, J. Phys. Chem. B , 7188 (2005).[19] J.-L. Bobet, C. Aymonier, D. Mesguich, F. Cansell, K.Asano and E. Akiba, J. Alloys Compd. , 250 (2007).[20] A. J. Du, S. C. Smith, X. D. Yao, and G. Q. Lu, J. Phys.Chem. B , 18037 (2005).[21] A. J. Du, S. C. Smith, X. D. Yao, and G. Q. Lu, J. Phys.Chem. B , 21747 (2006).[22] H. Hjelmberg, Surf. Sci. , 539 (1979).[23] P. K. Johansson, Surf. Sci. , 510 (1981).[24] J. K. Nørskov, A. Høumoller, P. K. Johansson, and B. I.Lundqvist, Phys. Rev. Lett. , 257 (1981). [25] D. M. Bird, L. J. Clarke, M. C. Payne and I. Stich, Chem.Phys. Lett. , 518 (1993).[26] T. Vegge, Phys. Rev. B , 035412 (2004).[27] G. Kresse and J. Furthm¨uller, Phys. Rev. B , 11169(1996).[28] P. E. Bl¨ochl, Phys. Rev. B , 17953 (1994).[29] G. Kresse and J. Joubert, Phys. Rev. B , 1758 (1999).[30] J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev.Lett. , 3865 (1996).[31] D. Alf`e, Comp. Phys. Comm. , 31 (1999).[32] H. J. Monkhorst and J. D. Pack, Phys. Rev. B , 5188(1976).[33] M. Methfessel and A. Paxton, Phys. Rev. B , 3616(1989).[34] A. Kokalj, Comp. Mater. Sci.
305 (1995); H. Jonsson, G. Mills, and K.W. Jakobsen, in
Classical and Quantum Dynamics in Condensed PhaseSimulations , edited by B.J. Berne, G. Ciccotti and D.F.Coker (World Scientific 1998); G. Henkelman and H.Johnsson, J. Chem. Phys. , 9978 (2000); G. Henkel-man, B.P. Uberuaga, and H. Johnsson, J. Chem. Phys.113, 9901 (2000).[36] F. Birch, Phys. Rev. , 809 (1947).[37] E. Wachowicz and A. Kiejna, J. Phys.: Condens. Matter , 10767 (2001).[38] S. Mehta, G. D. Price, and D. Alf`e, J. Chem. Phys. ,194507 (2006).[39] N. W. Ashcroft and N. D. Mermin, in Solid State Physics , 1277 (2003).[42] C. Kittel, Introduction to Solid State Physics , 7th ed.(Wiley, New York, 1996).[43] A. F. Wright, P. J. Feibelman and S. R. Atlas, Surf. Sci. , 215 (1994).[44] Ismail, Ph. Hofmann, E. W. Plummer, C. Bungaro, andW. Kress, Phys. Rev. B , 17012 (2000).[45] B. E. Hayden, E. Schweitzer, R. K¨otz, and A. M. Brad-shaw, Surf. Sci. , 26 (1981).[46] W. R. Tyson and W. A. Miller, Surf. Sci. , 267 (1977).[47] Y. K. Vohra and P. T. Spencer, Phys. Rev. Lett. , 3068(2001).[48] R. R. Zope and Y. Mishin, Phys. Rev. B , 024102 (2003).[49] M. Jahn´atek, M. Krajˇc´ı, and J. Hafner, Phys. Rev. B ,024101 (2005).[50] CRC Handbook of Chemistry and Physics , 83rd ed.,edited by D. R. Lide (CRC, New York, 2002).[51] G. Kresse and J. Hafner, Surf. Sci. , 287 (2000).[52] J. Greeley and M. Mavrikakis, J. Phys. Chem. B ,3460 (2005).[53] M. Pozzo, G. Carlini, R. Rosei and D. Alf`e, J. Chem.Phys. , 164706, 2007.[54] H. L. Davis, J. B. Hannon, K. B. Ray, and E. W. Plum-mer, Phys. Rev. Lett. , 2632 (1992).[55] N. B. Arboleda Jr., H. Kasai, K. Nobuhara, W. A. Dinoand H. Nakanishi, J. Phys. Soc. Jpn. , 745 (2004).[56] G. Kresse, Phys. Rev. B , 8295 (2000).[57] K. D. Rendulic, G. Anger and A. Winkler, Surf. Sci. ,404 (1989).[58] K. Nobuhara, H. Kasai, W. A. Din˜o, and H. Nakanishi,Surf. Sci. , 703 (2004).[59] M. Mavrikakis, B. Hammer and J. K. Nørskov, Phys.Rev. Lett. , 2819 (1998). FIG. 1: (Colour) Possible adsorption sites (top, bridge,hollow-hcp and hollow-fcc) for hydrogen (dark red) on theMg(0001) surface (light blue).FIG. 2: Minimum Energy Path for H dissociation and dif-fusion on a pure Mg(0001), Ni-doped Mg(0001) and Ti-dopedMg(0001) surface. FIG. 3: (Colour) H (dark red) dissociation on the pureMg (light blue) surface as viewed from side (top figures) andtop (bottom figures). Figures show positions at IS (left-handpanel), TS (central panel) and FS (right-hand panel).FIG. 4: (Colour) H (dark red) diffusion on the pure Mg (lightblue) surface as viewed from top. Figures show positions atFS (top-left), TS2 (top-centre), LS (top-right), TS3 (bottom-left) and FS2 (bottom-right). FIG. 5: (Colour) Possible final state adsorption sites for H (dark red) dissociation over the metal-doped (Ti/Ni) (darkgreen) Mg surface (light blue). In the case of the Ni dopedsurface the bottom-left site was not a stable configuration.FIG. 6: (Colour) Same as Fig. 3 but for H dissociating overthe Ti-doped Mg surface at IS and FS (there is no TS in thiscase). The Mg, Ti and H atoms are represented respectivelyby light blue, dark green and dark red colours. FIG. 7: (Colour) Same as Fig. 4 but for H diffusion overthe Ti-doped Mg surface. Figures show positions at FS (left),TS2 (centre) and FS2 (right). The Mg, Ti and H atoms arerepresented respectively by light blue, dark green and darkred colours.FIG. 8: (Colour) Same as Fig. 3 but for H dissociatingover the Ni-doped Mg surface. The Mg, Ni and H atoms arerepresented respectively by light blue, dark green and darkred colours. FIG. 9: (Colour) Same as Fig. 4 but for H diffusion overthe Ni-doped Mg surface. Figures show positions at FS (left),TS2 (centre) and FS2 (right). The Mg, Ni and H atoms arerepresented respectively by light blue, dark green and darkred colours.FIG. 10: Projected density of states for H dissociating overa pure Mg surface as a function of the energy relative to theFermi level, respectively for the initial state (IS, top-left cor-ner), transition state (TS; top-right corner), transition stateplus one further step along the MEP (TS+1; bottom-left cor-ner) and final state (FS; bottom-right corner). FIG. 11: As in Fig. 10 but for the Ni-doped Mg surface. Thedashed vertical line shows the position of the d-band centre.FIG. 12: As in Fig. 10 but for the Ti-doped Mg surface.Note that there is no barrier for hydrogen dissociation for thissurface, therefore the dos are those for IS and FS only. Thedashed vertical line shows the position of the d-band centre. FIG. 13: (Colour) Charge distribution during H (dark red)dissociation at the TS of the MEP respectively on the pureMg (left) and Ni-doped Mg (right) surfaces (see text for de-tails). White shows positive charge and black negative charge.Isolines are also shown in white.FIG. 14: (Colour) Different temperature hydrogenation plotsfor 1 gram of 2%Ni/Mg using 25 cc/min of H . FIG. 15: (Colour) Different temperature hydrogenation plotsfor 1 gram of 2%Ti/Mg using 25 cc/min of H2