- Email: [email protected]
Investigation of surface and near-surface effects on hydrogen desorption kinetics of MgH2
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 8 6 2 e8 6 7
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Investigation of surface and near-surface effects on hydrogen desorption kinetics of MgH2 Sandra Kurko, Igor Milanovic, Jasmina Grbovic Novakovic, Nenad Ivanovic, Nikola Novakovic* Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia
article info
abstract
Article history:
Desorption of hydrogen atoms from the (110) surface of rutile magnesium hydride (MgH2)
Received 20 April 2013
was investigated using density functional theory (DFT) and pseudopotential method.
Received in revised form
System was represented by (110) (22) slab MgH2 supercell with 12 atomic layers along the
12 October 2013
z-axis. The H-desorption was modeled by the successive release of the four two-fold
Accepted 20 October 2013
bonded H atoms from the (110) surface of MgH2. Dependence of the H-desorption energy
Available online 17 November 2013
on number and configuration of remaining surface hydrogen atoms has been determined. The features of the H atoms diffusion from the bulk towards the surface have been
Keywords:
investigated, too. The results suggest that decrease in number of surface H atoms
MgH2
generally lowers the H-desorption energy in each desorption step and that both the HeH
Hydrogen kinetics
and the MgeH interatomic interactions strongly influence the H-desorption process. The
Ab initio calculations
hydrogen vacancy formation energy in the first three sub-surface layers also exhibits a
Surface effects
pronounced dependence on concentration. These findings lead to the conclusion that tendency of the MgH2 (110) surface to preserve a maximum possible surface H concentration in its most stable configuration is the limiting factor for the H-desorption kinetics. In principle, the obtained results allow us to determine preferred paths of surface and subsurface H-diffusion for a wide range of H concentrations and the principle features of the MgH2 dehydrogenation process, at least for the H-rich region. Being rather comprehensive, the approach is applicable for other metal hydrides, as well. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Even though fuel cells and hydrogen energy are promising alternatives for fossil fuels, for practical applications it is still necessary to provide cheap, safe and non-toxic hydrogen storage materials with high gravimetric and volumetric density [1]. One of the most investigated and the most promising material that can meet these demands is MgH2. However, several drawbacks, such as slow kinetics and relatively high dehydrogenation temperature prevent its practical
application. To overcome these problems many different experimental and theoretical approaches have been proposed [1e8]. For example, nanostructuring of MgH2 by mechanical milling and addition of various dopants [2e4], irradiation by heavy ions or microwaves [5,6] decrease the dehydrogenation temperature and improve the sorption kinetics. Theoretical investigations of MgH2 by ab initio DFT calculations provide insight into the nature of compound bonding and cohesion at the fundamental electronic level [7e13] and also demonstrate the role of dopants and defects such as H-
* Corresponding author. Tel.: þ381 11 3408 610; fax: þ381 2453681. ). E-mail address: [email protected] (N. Novakovic 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.10.107
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 8 6 2 e8 6 7
vacancy on H-desorption [9e13]. For instance, it has been shown that a small amount of Fe may significantly improve thermodynamics and kinetics of Mg hydrogenation by lowering the energy barrier for the H-adsorption on the Mg (0001) surface to 0.1 eV [9]. Comparison of the DFT and experimental results has led to the conclusion that the ratecontrolling step of the MgH2 dehydrogenation is surface recombination of hydrogen [9,10]. Du et al. have found that the (110) MgH2 surface has the lowest energy barrier for the recombinative hydrogen desorption, that formation energy of a single H-vacancy increases slightly, going from the surface toward the bulk layers [11,12]. They have also found that barrier for the H-vacancy diffusion from the surface to the sub-surface layers is 0.7 eV, much smaller than the hydrogen desorption energy from the (110) MgH2 surface (1.78e2.80 eV) [11,12]. Investigation of the charged native point defects in MgH2 indicates that in absence of impurities and under extreme H-poor conditions, the lowest formation energies are for positively and negatively charged hydrogen vacancies [13]. In extreme H-rich conditions, the lowest formation energies are for negatively charged magnesium vacancy and negatively charged interstitial hydrogen. The hydrogen-related vacancies are found to be highly mobile, with migration barriers between 0.10 and 0.63 eV, depending on the vacancy type. However, little data exist about dependence of the Hdesorption energy and the sub-surface vacancies formation energy on number and distribution of surface H atoms. In this work we present the results of calculations of these dependences for the (110) MgH2 surface, that provide all details necessary to understood the H-desorption kinetics from MgH2 at high H concentration.
2.
Computational details
Abinit code [14e17] and TroulliereMartins pseudopotentials were used for all calculations. Brillouin zone of the MgH2 supercell (see Fig. 1) was sampled with regular twodimensional Monkhorst-Pack grid. The energy cutoff of the plane wave basis set was 544 eV. As a preparation step for the slab supercell construction, the original rutile MgH2 unit
863
cell was fully relaxed with respect to interatomic forces. The obtained cell parameters were 1% smaller than experimental values, while c/a ratio was practically left unchanged. The next step was 45 rotation of the relaxed MgH2 unit cell around the z-axis in order to “expose” its (110) plane. Then, a new coordinate system with the z-axis perpendicular to the (110) plane was adopted. The supercell was formed by repetition of the transformed unit cell two times along the x- and y- axes directions. Along the supercell z-axis there are 12 parallel atomic planes with total of 96 atoms, with H two-fold bonded surface atoms exposed to vacuum (see Fig. 1(a)). For initial calculations of surface related processes, the nine bottom atomic planes of the supercell were fixed, playing the role of bulk. The top three atomic planes: the first consisting of hydrogen atoms double bonded to the nearest Mg atoms marked as H2s, the second consisting of Mgs atoms and H3s atoms triple coordinated with Mg and the third one, consisting of “regular” bulk Hb atoms, (see Fig. 1(b)), were relaxed in order to simulate the close-to-surface conditions [18]. For the sub-surface calculations down to the seventh atomic layer, the structure was fully relaxed with the three bottom atomic layers fixed, to simulate crystal bulk. The top surface of the supercell was separated from its perpendicularly trivially translated periodic image by a vacuum approximately 15 A thick. The atomic ground state and molecular hydrogen binding energy, were obtained as Eat(H) ¼ 12.988 eV and Ebind(H2) ¼ 5.027 eV, respectively.
3.
Results and discussion
Different arrangements of H vacancies at the (110) surface and sub-surface layers were investigated. These arrangements are presented in Fig. 2. The following nomenclature for different surface vacancies configurations is adopted: hH2s vacanciesihH3s vacanciesihHb vacanciesiABC. Different hydrogen vacancies arrangements for the same configuration are marked with capital letters. Thus, the configuration without H vacancies is 000; 100 stands for the
Fig. 1 e (a). 232 (110) supercell used in calculations. Gray spheres e Mg, white spheres e H atoms. (b). The side view of 12 atomic layers (marked on the right) of the supercell slab. Four distinct types of the surface sites are denoted. Top 7 layers (3 in case of surface hydrogens studies) were used in calculations.
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i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 8 6 2 e8 6 7
configuration with a single surface H vacancy (corresponding to the real sample surface 75% covered with H), 200A,B,C for different configurations with two H2s atoms missing (50% surface coverage), 110 and 101 for configurations with single surface vacancy and single vacancy in the second and the third layer respectively, and so on. Calculations of these configurations allowed us to determine atomic and molecular hydrogen desorption energies and preferred channels for surface and sub-surface H-diffusion.
Energies of H and H2 desorption were calculated using following general equations: Enk ðHÞ ¼ Etot ððn kÞHÞ þ kEat ðHÞ Etot ðnHÞ
(1)
and Enk ðH2 Þ ¼ Enk ðHÞ þ ðk=2ÞEbind ðH2 Þ;
(2)
where Enk(H) and Enk(H2) are energies required for desorption of k H atoms and k/2H2 molecules, respectively, Etot(nH) is total energy of the Mg slab with n hydrogen atoms. Symbols n and k stand for the initial configuration with n and a final configuration with nek hydrogen atoms. Vacancy formation energies used for estimation of vertical mobility of hydrogen atoms were calculated as difference between reference energy (configurations of type n00, with only H2s vacancies present) and energy of configurations with the same number of H2s vacancies present and one extra H vacancy in some of the sub-surface layers. For example, the following equation: Eðn01Þ ¼ Etot ðn01Þ þ Eat ðHÞ Etot ðn00Þ
(3)
gives vacancy formation energy for third sub-surface layer.
3.1. Calculations of various surface configurations of H atoms Structural parameters of three different types of H atoms for configuration 000 are presented in Table 1. Atomic hydrogen desorption energies along the principle desorption paths from the MgH2 (110) surface are shown in Fig. 3(a). Together with desorption energies (labeled with grey bold line), corresponding final configurations of surface H2s atoms are shown. There are three different 200 surface hydrogen configurations, determining the three different H-desorption paths with different energies for 100e200x and 200xe300 desorption steps. The figure illustrates a general trend of lowering of the H-desorption energy as surface hydrogen concentration decreases, making desorption from the less populated surface easier. The energies of the second desorption step 100e200x are indicative also for the estimation of the HeH interaction influence on the H-desorption process. It appears that it is more difficult to desorb the “double bonded” H (desorption of the top-left H of the 100 configuration, path 3), than the “single-bonded” ones. Also, it is more difficult to desorb H by
Table 1 e Local coordination of three different types of H atoms at the fully occupied (110) MgH2 surface and in the two sub-surface layers. Atom H2s
H3s
Fig. 2 e Configurations of surface and sub-surface H atoms used in calculations. H3s atoms from the second layer are represented by shifted small circles, while Hb atoms are represented by smaller dashed circles within the circles representing the surface H2s atoms.
Hb
Neighbor atom/Coord. number/distance [A] Mgs 2 1.875 Mgs 2 1.941 5Mg 1 1.939
Mgs 1 1.991 Mgs 2 2.052
Hb 1 2.503 H3s 1 2.404 H2s 1 2.503
H3s 4 2.749 H2s 2 2.749 5H 4 2.751
4H 2 2.819
Hb 2 2.842 H3s 4 2.842
H2s 2 3.019 H3s 2 3.019 Hb 2 3.019
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 8 6 2 e8 6 7
breaking the short HeH bond (desorption of the bottom-left H of the 100 configuration, path 2), than by breaking the long HeH bond (desorption of the top-right H of the 100 configuration, path 1). Only path 3 exhibits a monotonic decrease of H-desorption energy, while both of the more favorable desorption paths, path 1 and path 2 have slight increases of desorption mainly due to an easy desorption of the “singlebonded” H surface atoms from the 100 configuration. Energies of simultaneous desorption of two surface hydrogen atoms followed by immediate formation of H2 molecule, are shown in Fig. 3(b). The results are in accordance with those of successive single H atom desorption. It has been also shown that it is most difficult to desorb the H2 molecule, which leaves the 200A configuration, because for this process it is necessary that each of the desorbing H atoms break two HeH “bonds”, one short and one long. Further, desorption that leaves the 200C configuration at the surface requires more energy than the one that leaves the 200B configuration,
865
because in the first case each of the desorbing H atoms must break one short, and in the second one long HeH “bond”. In this calculation scheme (Eq. (2)), which considers only the energy difference of the final and the initial state there is only one 100e300 transition. Differences of this and of the corresponding transitions obtained during successive H-desorption (see Fig. 3(a)) are kind of measure of surface relaxation along these particular paths. Due to the low desorption energy of the 000e200B step and the relatively high energy necessary to desorb the final tightly bounded H2 pair in the 200Be400 transition, only the 000e200Be400 path experiences a small rise of hydrogen desorption energy. For the other two paths, the desorption energy from the low populated surface is lower than from the fully populated. This is in good accordance with the atomic H-desorption results.
3.2.
Sub-surface processes
To investigate the influence of the (110) sub-surface processes on the MgH2 dehydration kinetics, calculations of the H-vacancy formation energy in the seven successive sub-surface layers have been performed. The influence of the surface was included by performing the sub-surface calculations for different arrangements and concentrations of surface H2s vacancies (see Fig. 2). The results obtained using Formula (3) are presented in Fig. 4, with particular configurations marked according to the number of surface vacancies. Energies for several possible hydrogen single vacancy positions in configurations without and with one single surface hydrogen vacancy present are given in Table 2. Energies are calculated per hydrogen molecule using Formula (2), so that values can be comparable to data available from literature [11,12]. Agreement is very good, which gives us confidence in our results and observed trends. For fully populated surface (configuration with 0 surface vacancies) the increase of the H-vacancy formation energy
Fig. 3 e (a). Characteristic paths of H-desorption from the (110) MgH2 surface. The presented desorption energies are calculated relative to the energy of the surface fully relaxed after the previous desorption step. (b). Energies of simultaneous desorption of surface hydrogen atoms pairs into the molecular final state.
Fig. 4 e The H-vacancy formation energies in the (110) MgH2 sub-surface layers as a function of surface coverage with H2s atoms, calculated using Formula (3). Configurations with 1 and 3 H vacancies in 3rd and 6th layer are connected with dashed line.
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Table 2 e Diffusion energies for configurations with one and two H vacancies. Single H vacancy Configuration Layer This work Literature [11,12]
100 1 1.336 1.32
010 2 1.558 1.50
e 4 1.606 1.52
001 3 1.519 1.43
going from the surface towards the bulk is almost monotonic, with a small deviation from the trend in the first sub-surface layer (see second layer in Fig. 4). Quite different picture is obtained if H vacancies are already present at the surface. The H-vacancy formation energy in the first sub-surface layer is approximately 1.1 eV lower if two vacancies are present at the surface and about 1.35 eV in the case of one and four surface vacancies, than for the completely populated surface. The trend reverses in the third layer, with the exception of configuration 1. Going further into the bulk, as screening of the surface effects increases, all properties approach those corresponding to the completely full surface, as can be seen for the 6th layer H-vacancy formation energies of configurations 1 and 3. Obviously, removal of the surface hydrogen atoms makes the hydrogen vacancy formation in first several sub-surface layers easier. At the same time, the H-desorption energy from vacant surface slightly increases with appearance of the sub-surface vacancies. The influence of surface coverage on surface barrier profile emphasizes the importance of rate of hydrogen recombination at surface in order to keep the surface as “hydrogen-free” as possible [18]. The additional details of the surface H-coverage influence on the H-vacancy formation energy in the second and in the third atomic layer calculated using Eq. (2) with stoichiometric surface configuration 000 as the reference level are presented in Fig. 5. The configurations with the same surface coverage and the same number of the sub-surface H vacancies in different arrangements are connected with dashed lines. The first to notice is that energies of both 010 and 001 configurations with all H2s atoms present at the surface are significantly higher than for any vacant surface configuration. This result is in accordance with the already established fact that surface H-
Fig. 5 e H-vacancy formation energies for different configurations of surface and sub-surface vacancies calculated using Formula (2). Configurations with same surface arrangements are connected with dashed lines.
Two H vacancies e 5 1.643 1.57
200 2.153 2.22e2.2 [12]
110 1.560 1.50
vacancies make vacancy formation in the sub-surface layers easier. However, it is a bit surprising that the lowest subsurface H-vacancy formation energies are for the 110 and 101A configurations, for which only one surface vacancy exists. After that, configurations with two surface vacancies start to prevail, the 210B having approximately the same energy as 101B and all of them, together with 201and 210C having the lower energies than 101C. It is also apparent (see Figs. 1 and 2) that sub-surface vacancies tend to form as close as possible to the surface ones and that their formation bellow the depleted part of the surface is easier when the remaining surface H configuration itself is stronger bonded, probably because the effects of the surface H-depletion are better localized and more pronounced in this case. The lowering of the H-vacancy formation energy from 101C to 101A is a good example for the case when horizontal diffusion of vacancies could be preferred to the vertical one, especially if the initial vacancy is high in energy. However, for energetically most favorable cases a vertical (zigzag) diffusion of vacancies is more probable, as well as the vacancy repopulation, for instance from 210A into 110, or 101A configuration. The dependence of the sub-surface H-vacancy formation energy on the vacancy position is weak for surface configurations with high number of vacancies (three and four), as in these cases the surface is already completely reconstructed.
4.
Conclusions
The hydrogen desorption from the (110) MgH2 surface and the possibilities of the surface repopulation from the sub-surface layers were investigated using ab initio calculations and the slab-supercell approach. It has been demonstrated that the Hdesorption energy strongly depends on number of surface H atoms and their configuration. The importance of the HeH interaction between the surface hydrogen atoms and the surface reconstruction on the H-desorption process has been emphasized, too. The presented calculations show that the largest H-desorption energy is required for desorption of the first H-atom from the surface, which correspond to the first 25% of the surface H atoms of a real sample. Much lower energy is needed for desorption of the second H atom (next 25% of hydrogen surface atoms)and the same trend of the Hdesorption energy decrease (except for small deviations observed for some particularly stable surface H configurations) is noticed for further lowering of the surface H concentration. Different H-desorption energies along the investigated desorption paths point out the importance of the HeH interaction between the surface hydrogen atoms. However, the observed deviations from the desorption trends suggest that relaxation of the surface after each H-desorption,
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 8 6 2 e8 6 7
governed mostly by the MgeH interaction, has also a large influence on the H-desorption process. Both these interactions are strongly influenced by concentration and actual distribution of surface hydrogen atoms. The H-vacancy formation energies down to the seventh sub-surface layer from the (110) MgH2 surface is calculated for the completely populated surface and the similar dependences for the various numbers of surface vacancies down to the third, i.e. the sixth atomic layer. It has been noticed that surface vacancies considerably lower the H-vacancy formation energies in the sub-surface layers, especially below the surface vacancy and (or) the weakly bonded surface H atoms. These results suggest that the role of surface hydrogen concentration and distribution is decisive for the H-desorption kinetics, not only because an increased number of surface hydrogen vacancies lowers the potential barrier for further H-desorption, but also as they support creation of the sub-surface vacancies network and make diffusion of bulk hydrogen atoms toward the surface easier. The presented method provides the basis for general explanation of the experimental temperature and H-pressure dependences of H-desorption from MgH2. It also gives the reason for the low H-desorption kinetics, especially in the early stages of the process (H-rich region of the phase diagram). The results strongly suggest that by maintaining the optimal surface concentration of H atoms (about two out of four, or 50% of the full surface coverage) during the as long as possible period of the H-desorption process, it would be possible to improve its kinetics tremendously. This could be done, for instance, by incorporation of suitable impurities, or defects, at the (110) MgH2 surface and in the immediate subsurface layers, which would facilitate the initial stages of the H-desorption process (surface vacancies creation) and control the subsequent H-diffusion from the bulk toward the surface, by creation of an appropriate sub-surface network of H-vacancies. As the dependence of the H-binding energy on the surrounding charge distribution is in principle known, the more precise answers about design of the (110) MgH2 surface and sub-surface layers, in the sense mentioned above, should be expected in the recent future.
Acknowledgment This work is financially supported by the Ministry of Education, Science and Technological Development of Republic of Serbia under grant III45012.
references
[1] Varin RA, Czujko T, Wronski ZS. In: Bansal NP, editor. Nanomaterials for solid state hydrogen storage. 1st ed. New York: Springer ScienceþBusiness Media; 2009.
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Lj, Novakovic N, Matovic B, Jovanovic Z, [2] Kurko S, Matovic Paska s Mamula B, et al. Hydrogen storage properties of MgH2 mechanically milled with a and b SiC. Int J Hydrogen Energy 2011;36:1184e9. Novakovic I, Milo S, Ra -Lovre Z, N, [3] Milanovic sevic skovic Lj, et al. Microstructure and hydrogen Vujasin R, Matovic storage properties of MgH2eTiB2eSiC composites. Ceram Int 2013;39(1):51e6. [4] Malka IE, Bystrzycki J, Plocinski T, Czujko T. Microstructure and hydrogen storage capacity of magnesium hydride with zirconium and niobium fluoride additives after cyclic loading. J Alloys Compd 2011;509(2):S616e20. [5] Ares JR, Leardini F, Dı´az-Chao P, Bodega J, Ferna´ndez JF, Ferrer IJ, et al. Ultrasonic irradiation as a tool to modify the H-desorption from hydrides: MgH2 suspended in decane. Ultrason Sonochem 2009;16:810e6. Lj, Novakovic N, Kurko S, Siljegovi M, Matovic B, [6] Matovic c evic N, et al. Structural destabilisation of MgH2 Romc obtained by heavy ion irradiation. Int J Hydrogen Energy 2009;34:7275e82. N, Grbovic Novakovic J, Matovic Lj, Radisaljevic I, [7] Novakovic N. Ab initio calculation of MgH2, Manasijevic M, Ivanovic MgH2:Ti and MgH2:Co compounds. Int J Hydrogen Energy 2009;34(17):598e608. [8] Giusepponi S, Celino M. Hydrogen desorption from Mg hydride: an ab initio study. Crystals 2012;2:845e60. [9] Wu G, Liu S, Zhang J, Li Q, Wu Y, Chou K, et al. Density functional theory study on hydrogenation mechanism in catalyst-activated Mg(0001) surface. Trans Nonferrous Met Soc China 2009;19:383e8. [10] Wu G, Zhang J, Li Q, Wu Y, Chou K, Bao X. Dehydrogenation kinetics of magnesium hydride investigated by DFT and experiment. Comput Mater Sci 2010;49:S144e9. [11] Du AJ, Smith SC, Yao XD, Lu GQ. Ab initio studies of hydrogen desorption from low index magnesium hydride surface. Surf Sci 2006;600:1854e9. [12] Du AJ, Smith SC, Lu GQ. First-principle studies of the formation and diffusion of hydrogen vacancies in magnesium hydride. J Phys Chem C 2007;111:8360e5. [13] Park MS, Janotti A, Van de Walle CG. Formation and migration of charged native point defects in MgH2: firstprinciples calculations. Phys Rev B 2009;80:064102e6. [14] Gonze X, Amadon B, Anglade P-M, Beuken J-M, Bottin F, Boulanger P, et al. ABINIT: first-principles approach of materials and nanosystem properties. Comput Phys Commun 2009;180:2582e615. [15] Gonze X, Rignanese G-M, Verstraete M, Beuken J-M, Pouillon Y, Caracas R, et al. A brief introduction to the ABINIT software package. Zeit Kristallogr 2004;220:558e62. [16] Goedecker S. Fast radix 2, 3, 4and 5 kernels for fast Fourier transformations on computers with overlapping multiply e add instructions. SIAM J Sci Comput 1997;18(6):1605e11. [17] Torrent M, Jollet F, Bottin F, Zerah G, Gonze X. Implementation of the projector augmented-wave method in the ABINIT code: application to the study of iron under pressure. Comput Mater Sci 2008;42:337e51. [18] Dai JH, Song Y, Yang R. Intrinsic mechanisms on enhancement of hydrogen desorption from MgH2 by (001) surface doping. Int J Hydrogen Energy 2011;36:12939e49.
Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Investigation of surface and near-surface effects on hydrogen desorption kinetics of MgH2 Sandra Kurko, Igor Milanovic, Jasmina Grbovic Novakovic, Nenad Ivanovic, Nikola Novakovic* Vinca Institute of Nuclear Sciences, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia
article info
abstract
Article history:
Desorption of hydrogen atoms from the (110) surface of rutile magnesium hydride (MgH2)
Received 20 April 2013
was investigated using density functional theory (DFT) and pseudopotential method.
Received in revised form
System was represented by (110) (22) slab MgH2 supercell with 12 atomic layers along the
12 October 2013
z-axis. The H-desorption was modeled by the successive release of the four two-fold
Accepted 20 October 2013
bonded H atoms from the (110) surface of MgH2. Dependence of the H-desorption energy
Available online 17 November 2013
on number and configuration of remaining surface hydrogen atoms has been determined. The features of the H atoms diffusion from the bulk towards the surface have been
Keywords:
investigated, too. The results suggest that decrease in number of surface H atoms
MgH2
generally lowers the H-desorption energy in each desorption step and that both the HeH
Hydrogen kinetics
and the MgeH interatomic interactions strongly influence the H-desorption process. The
Ab initio calculations
hydrogen vacancy formation energy in the first three sub-surface layers also exhibits a
Surface effects
pronounced dependence on concentration. These findings lead to the conclusion that tendency of the MgH2 (110) surface to preserve a maximum possible surface H concentration in its most stable configuration is the limiting factor for the H-desorption kinetics. In principle, the obtained results allow us to determine preferred paths of surface and subsurface H-diffusion for a wide range of H concentrations and the principle features of the MgH2 dehydrogenation process, at least for the H-rich region. Being rather comprehensive, the approach is applicable for other metal hydrides, as well. Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
1.
Introduction
Even though fuel cells and hydrogen energy are promising alternatives for fossil fuels, for practical applications it is still necessary to provide cheap, safe and non-toxic hydrogen storage materials with high gravimetric and volumetric density [1]. One of the most investigated and the most promising material that can meet these demands is MgH2. However, several drawbacks, such as slow kinetics and relatively high dehydrogenation temperature prevent its practical
application. To overcome these problems many different experimental and theoretical approaches have been proposed [1e8]. For example, nanostructuring of MgH2 by mechanical milling and addition of various dopants [2e4], irradiation by heavy ions or microwaves [5,6] decrease the dehydrogenation temperature and improve the sorption kinetics. Theoretical investigations of MgH2 by ab initio DFT calculations provide insight into the nature of compound bonding and cohesion at the fundamental electronic level [7e13] and also demonstrate the role of dopants and defects such as H-
* Corresponding author. Tel.: þ381 11 3408 610; fax: þ381 2453681. ). E-mail address: [email protected] (N. Novakovic 0360-3199/$ e see front matter Copyright ª 2013, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijhydene.2013.10.107
i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 9 ( 2 0 1 4 ) 8 6 2 e8 6 7
vacancy on H-desorption [9e13]. For instance, it has been shown that a small amount of Fe may significantly improve thermodynamics and kinetics of Mg hydrogenation by lowering the energy barrier for the H-adsorption on the Mg (0001) surface to 0.1 eV [9]. Comparison of the DFT and experimental results has led to the conclusion that the ratecontrolling step of the MgH2 dehydrogenation is surface recombination of hydrogen [9,10]. Du et al. have found that the (110) MgH2 surface has the lowest energy barrier for the recombinative hydrogen desorption, that formation energy of a single H-vacancy increases slightly, going from the surface toward the bulk layers [11,12]. They have also found that barrier for the H-vacancy diffusion from the surface to the sub-surface layers is 0.7 eV, much smaller than the hydrogen desorption energy from the (110) MgH2 surface (1.78e2.80 eV) [11,12]. Investigation of the charged native point defects in MgH2 indicates that in absence of impurities and under extreme H-poor conditions, the lowest formation energies are for positively and negatively charged hydrogen vacancies [13]. In extreme H-rich conditions, the lowest formation energies are for negatively charged magnesium vacancy and negatively charged interstitial hydrogen. The hydrogen-related vacancies are found to be highly mobile, with migration barriers between 0.10 and 0.63 eV, depending on the vacancy type. However, little data exist about dependence of the Hdesorption energy and the sub-surface vacancies formation energy on number and distribution of surface H atoms. In this work we present the results of calculations of these dependences for the (110) MgH2 surface, that provide all details necessary to understood the H-desorption kinetics from MgH2 at high H concentration.
2.
Computational details
Abinit code [14e17] and TroulliereMartins pseudopotentials were used for all calculations. Brillouin zone of the MgH2 supercell (see Fig. 1) was sampled with regular twodimensional Monkhorst-Pack grid. The energy cutoff of the plane wave basis set was 544 eV. As a preparation step for the slab supercell construction, the original rutile MgH2 unit
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cell was fully relaxed with respect to interatomic forces. The obtained cell parameters were 1% smaller than experimental values, while c/a ratio was practically left unchanged. The next step was 45 rotation of the relaxed MgH2 unit cell around the z-axis in order to “expose” its (110) plane. Then, a new coordinate system with the z-axis perpendicular to the (110) plane was adopted. The supercell was formed by repetition of the transformed unit cell two times along the x- and y- axes directions. Along the supercell z-axis there are 12 parallel atomic planes with total of 96 atoms, with H two-fold bonded surface atoms exposed to vacuum (see Fig. 1(a)). For initial calculations of surface related processes, the nine bottom atomic planes of the supercell were fixed, playing the role of bulk. The top three atomic planes: the first consisting of hydrogen atoms double bonded to the nearest Mg atoms marked as H2s, the second consisting of Mgs atoms and H3s atoms triple coordinated with Mg and the third one, consisting of “regular” bulk Hb atoms, (see Fig. 1(b)), were relaxed in order to simulate the close-to-surface conditions [18]. For the sub-surface calculations down to the seventh atomic layer, the structure was fully relaxed with the three bottom atomic layers fixed, to simulate crystal bulk. The top surface of the supercell was separated from its perpendicularly trivially translated periodic image by a vacuum approximately 15 A thick. The atomic ground state and molecular hydrogen binding energy, were obtained as Eat(H) ¼ 12.988 eV and Ebind(H2) ¼ 5.027 eV, respectively.
3.
Results and discussion
Different arrangements of H vacancies at the (110) surface and sub-surface layers were investigated. These arrangements are presented in Fig. 2. The following nomenclature for different surface vacancies configurations is adopted: hH2s vacanciesihH3s vacanciesihHb vacanciesiABC. Different hydrogen vacancies arrangements for the same configuration are marked with capital letters. Thus, the configuration without H vacancies is 000; 100 stands for the
Fig. 1 e (a). 232 (110) supercell used in calculations. Gray spheres e Mg, white spheres e H atoms. (b). The side view of 12 atomic layers (marked on the right) of the supercell slab. Four distinct types of the surface sites are denoted. Top 7 layers (3 in case of surface hydrogens studies) were used in calculations.
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configuration with a single surface H vacancy (corresponding to the real sample surface 75% covered with H), 200A,B,C for different configurations with two H2s atoms missing (50% surface coverage), 110 and 101 for configurations with single surface vacancy and single vacancy in the second and the third layer respectively, and so on. Calculations of these configurations allowed us to determine atomic and molecular hydrogen desorption energies and preferred channels for surface and sub-surface H-diffusion.
Energies of H and H2 desorption were calculated using following general equations: Enk ðHÞ ¼ Etot ððn kÞHÞ þ kEat ðHÞ Etot ðnHÞ
(1)
and Enk ðH2 Þ ¼ Enk ðHÞ þ ðk=2ÞEbind ðH2 Þ;
(2)
where Enk(H) and Enk(H2) are energies required for desorption of k H atoms and k/2H2 molecules, respectively, Etot(nH) is total energy of the Mg slab with n hydrogen atoms. Symbols n and k stand for the initial configuration with n and a final configuration with nek hydrogen atoms. Vacancy formation energies used for estimation of vertical mobility of hydrogen atoms were calculated as difference between reference energy (configurations of type n00, with only H2s vacancies present) and energy of configurations with the same number of H2s vacancies present and one extra H vacancy in some of the sub-surface layers. For example, the following equation: Eðn01Þ ¼ Etot ðn01Þ þ Eat ðHÞ Etot ðn00Þ
(3)
gives vacancy formation energy for third sub-surface layer.
3.1. Calculations of various surface configurations of H atoms Structural parameters of three different types of H atoms for configuration 000 are presented in Table 1. Atomic hydrogen desorption energies along the principle desorption paths from the MgH2 (110) surface are shown in Fig. 3(a). Together with desorption energies (labeled with grey bold line), corresponding final configurations of surface H2s atoms are shown. There are three different 200 surface hydrogen configurations, determining the three different H-desorption paths with different energies for 100e200x and 200xe300 desorption steps. The figure illustrates a general trend of lowering of the H-desorption energy as surface hydrogen concentration decreases, making desorption from the less populated surface easier. The energies of the second desorption step 100e200x are indicative also for the estimation of the HeH interaction influence on the H-desorption process. It appears that it is more difficult to desorb the “double bonded” H (desorption of the top-left H of the 100 configuration, path 3), than the “single-bonded” ones. Also, it is more difficult to desorb H by
Table 1 e Local coordination of three different types of H atoms at the fully occupied (110) MgH2 surface and in the two sub-surface layers. Atom H2s
H3s
Fig. 2 e Configurations of surface and sub-surface H atoms used in calculations. H3s atoms from the second layer are represented by shifted small circles, while Hb atoms are represented by smaller dashed circles within the circles representing the surface H2s atoms.
Hb
Neighbor atom/Coord. number/distance [A] Mgs 2 1.875 Mgs 2 1.941 5Mg 1 1.939
Mgs 1 1.991 Mgs 2 2.052
Hb 1 2.503 H3s 1 2.404 H2s 1 2.503
H3s 4 2.749 H2s 2 2.749 5H 4 2.751
4H 2 2.819
Hb 2 2.842 H3s 4 2.842
H2s 2 3.019 H3s 2 3.019 Hb 2 3.019
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breaking the short HeH bond (desorption of the bottom-left H of the 100 configuration, path 2), than by breaking the long HeH bond (desorption of the top-right H of the 100 configuration, path 1). Only path 3 exhibits a monotonic decrease of H-desorption energy, while both of the more favorable desorption paths, path 1 and path 2 have slight increases of desorption mainly due to an easy desorption of the “singlebonded” H surface atoms from the 100 configuration. Energies of simultaneous desorption of two surface hydrogen atoms followed by immediate formation of H2 molecule, are shown in Fig. 3(b). The results are in accordance with those of successive single H atom desorption. It has been also shown that it is most difficult to desorb the H2 molecule, which leaves the 200A configuration, because for this process it is necessary that each of the desorbing H atoms break two HeH “bonds”, one short and one long. Further, desorption that leaves the 200C configuration at the surface requires more energy than the one that leaves the 200B configuration,
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because in the first case each of the desorbing H atoms must break one short, and in the second one long HeH “bond”. In this calculation scheme (Eq. (2)), which considers only the energy difference of the final and the initial state there is only one 100e300 transition. Differences of this and of the corresponding transitions obtained during successive H-desorption (see Fig. 3(a)) are kind of measure of surface relaxation along these particular paths. Due to the low desorption energy of the 000e200B step and the relatively high energy necessary to desorb the final tightly bounded H2 pair in the 200Be400 transition, only the 000e200Be400 path experiences a small rise of hydrogen desorption energy. For the other two paths, the desorption energy from the low populated surface is lower than from the fully populated. This is in good accordance with the atomic H-desorption results.
3.2.
Sub-surface processes
To investigate the influence of the (110) sub-surface processes on the MgH2 dehydration kinetics, calculations of the H-vacancy formation energy in the seven successive sub-surface layers have been performed. The influence of the surface was included by performing the sub-surface calculations for different arrangements and concentrations of surface H2s vacancies (see Fig. 2). The results obtained using Formula (3) are presented in Fig. 4, with particular configurations marked according to the number of surface vacancies. Energies for several possible hydrogen single vacancy positions in configurations without and with one single surface hydrogen vacancy present are given in Table 2. Energies are calculated per hydrogen molecule using Formula (2), so that values can be comparable to data available from literature [11,12]. Agreement is very good, which gives us confidence in our results and observed trends. For fully populated surface (configuration with 0 surface vacancies) the increase of the H-vacancy formation energy
Fig. 3 e (a). Characteristic paths of H-desorption from the (110) MgH2 surface. The presented desorption energies are calculated relative to the energy of the surface fully relaxed after the previous desorption step. (b). Energies of simultaneous desorption of surface hydrogen atoms pairs into the molecular final state.
Fig. 4 e The H-vacancy formation energies in the (110) MgH2 sub-surface layers as a function of surface coverage with H2s atoms, calculated using Formula (3). Configurations with 1 and 3 H vacancies in 3rd and 6th layer are connected with dashed line.
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Table 2 e Diffusion energies for configurations with one and two H vacancies. Single H vacancy Configuration Layer This work Literature [11,12]
100 1 1.336 1.32
010 2 1.558 1.50
e 4 1.606 1.52
001 3 1.519 1.43
going from the surface towards the bulk is almost monotonic, with a small deviation from the trend in the first sub-surface layer (see second layer in Fig. 4). Quite different picture is obtained if H vacancies are already present at the surface. The H-vacancy formation energy in the first sub-surface layer is approximately 1.1 eV lower if two vacancies are present at the surface and about 1.35 eV in the case of one and four surface vacancies, than for the completely populated surface. The trend reverses in the third layer, with the exception of configuration 1. Going further into the bulk, as screening of the surface effects increases, all properties approach those corresponding to the completely full surface, as can be seen for the 6th layer H-vacancy formation energies of configurations 1 and 3. Obviously, removal of the surface hydrogen atoms makes the hydrogen vacancy formation in first several sub-surface layers easier. At the same time, the H-desorption energy from vacant surface slightly increases with appearance of the sub-surface vacancies. The influence of surface coverage on surface barrier profile emphasizes the importance of rate of hydrogen recombination at surface in order to keep the surface as “hydrogen-free” as possible [18]. The additional details of the surface H-coverage influence on the H-vacancy formation energy in the second and in the third atomic layer calculated using Eq. (2) with stoichiometric surface configuration 000 as the reference level are presented in Fig. 5. The configurations with the same surface coverage and the same number of the sub-surface H vacancies in different arrangements are connected with dashed lines. The first to notice is that energies of both 010 and 001 configurations with all H2s atoms present at the surface are significantly higher than for any vacant surface configuration. This result is in accordance with the already established fact that surface H-
Fig. 5 e H-vacancy formation energies for different configurations of surface and sub-surface vacancies calculated using Formula (2). Configurations with same surface arrangements are connected with dashed lines.
Two H vacancies e 5 1.643 1.57
200 2.153 2.22e2.2 [12]
110 1.560 1.50
vacancies make vacancy formation in the sub-surface layers easier. However, it is a bit surprising that the lowest subsurface H-vacancy formation energies are for the 110 and 101A configurations, for which only one surface vacancy exists. After that, configurations with two surface vacancies start to prevail, the 210B having approximately the same energy as 101B and all of them, together with 201and 210C having the lower energies than 101C. It is also apparent (see Figs. 1 and 2) that sub-surface vacancies tend to form as close as possible to the surface ones and that their formation bellow the depleted part of the surface is easier when the remaining surface H configuration itself is stronger bonded, probably because the effects of the surface H-depletion are better localized and more pronounced in this case. The lowering of the H-vacancy formation energy from 101C to 101A is a good example for the case when horizontal diffusion of vacancies could be preferred to the vertical one, especially if the initial vacancy is high in energy. However, for energetically most favorable cases a vertical (zigzag) diffusion of vacancies is more probable, as well as the vacancy repopulation, for instance from 210A into 110, or 101A configuration. The dependence of the sub-surface H-vacancy formation energy on the vacancy position is weak for surface configurations with high number of vacancies (three and four), as in these cases the surface is already completely reconstructed.
4.
Conclusions
The hydrogen desorption from the (110) MgH2 surface and the possibilities of the surface repopulation from the sub-surface layers were investigated using ab initio calculations and the slab-supercell approach. It has been demonstrated that the Hdesorption energy strongly depends on number of surface H atoms and their configuration. The importance of the HeH interaction between the surface hydrogen atoms and the surface reconstruction on the H-desorption process has been emphasized, too. The presented calculations show that the largest H-desorption energy is required for desorption of the first H-atom from the surface, which correspond to the first 25% of the surface H atoms of a real sample. Much lower energy is needed for desorption of the second H atom (next 25% of hydrogen surface atoms)and the same trend of the Hdesorption energy decrease (except for small deviations observed for some particularly stable surface H configurations) is noticed for further lowering of the surface H concentration. Different H-desorption energies along the investigated desorption paths point out the importance of the HeH interaction between the surface hydrogen atoms. However, the observed deviations from the desorption trends suggest that relaxation of the surface after each H-desorption,
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governed mostly by the MgeH interaction, has also a large influence on the H-desorption process. Both these interactions are strongly influenced by concentration and actual distribution of surface hydrogen atoms. The H-vacancy formation energies down to the seventh sub-surface layer from the (110) MgH2 surface is calculated for the completely populated surface and the similar dependences for the various numbers of surface vacancies down to the third, i.e. the sixth atomic layer. It has been noticed that surface vacancies considerably lower the H-vacancy formation energies in the sub-surface layers, especially below the surface vacancy and (or) the weakly bonded surface H atoms. These results suggest that the role of surface hydrogen concentration and distribution is decisive for the H-desorption kinetics, not only because an increased number of surface hydrogen vacancies lowers the potential barrier for further H-desorption, but also as they support creation of the sub-surface vacancies network and make diffusion of bulk hydrogen atoms toward the surface easier. The presented method provides the basis for general explanation of the experimental temperature and H-pressure dependences of H-desorption from MgH2. It also gives the reason for the low H-desorption kinetics, especially in the early stages of the process (H-rich region of the phase diagram). The results strongly suggest that by maintaining the optimal surface concentration of H atoms (about two out of four, or 50% of the full surface coverage) during the as long as possible period of the H-desorption process, it would be possible to improve its kinetics tremendously. This could be done, for instance, by incorporation of suitable impurities, or defects, at the (110) MgH2 surface and in the immediate subsurface layers, which would facilitate the initial stages of the H-desorption process (surface vacancies creation) and control the subsequent H-diffusion from the bulk toward the surface, by creation of an appropriate sub-surface network of H-vacancies. As the dependence of the H-binding energy on the surrounding charge distribution is in principle known, the more precise answers about design of the (110) MgH2 surface and sub-surface layers, in the sense mentioned above, should be expected in the recent future.
Acknowledgment This work is financially supported by the Ministry of Education, Science and Technological Development of Republic of Serbia under grant III45012.
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