Jana Radaković*,
Katarina Batalović,
Ivan Mađarević and
Jelena Belošević-Čavor
VINČA Institute of Nuclear Sciences, University of Belgrade, PO Box 522, 11001 Belgrade, Serbia. E-mail: janar@vinca.rs; Tel: +381 113408 601
First published on 17th October 2014
Understanding the microscopic aspect of the hydride formation process provides an insight into the experimentally observed properties of prospective hydrogen storage materials. In this paper, we have studied the local structural and electronic modifications induced by hydrogen absorption in cubic C15 Laves phases AB2 (A = Zr; B = Cr, Mn, Ni), as well as the stability of the formed hydrides, by means of density functional theory (DFT). To address the effect of hydrogen absorbed in one of three tetrahedral sites (96g, 32e, and 8b) on the electronic structure of its surrounding atoms, we have calculated the electric field gradient (EFG) on the position of Cr, Mn, and Ni in pure and hydrogenated compounds. EFG is associated with the hydrogen site-preference, and formation enthalpies of ZrB2H hydrides are used to examine their formation feasibility. Obtained enthalpies reveal that ZrMn2H and ZrNi2H are both unstable regardless of the occupied site, and the only attainable hydride is ZrCr2H, with comparable occupational probability of sites 96g and 32e. EFG results indicate that a hydrogen distribution within the crystal depends on the level of induced electronic structure modifications; i.e., the hydrogen site-preference is governed by the condition of minimal divergence of the electronic charge from its initial distribution.
Due to the experimentally observed storage capability of ZrCr2 and ZrMn2, as well as of the alloys from Zr–Ni phase system; all selected compounds have been previously studied. So far, the research focus has been based on their electrochemical performance and tuning of thermodynamic and kinetic properties by partial substitution of host atoms with various transition metals (e.g., V, Cr, Mn, Fe, Ni) and rare earths (La, Ce). In that regard, their hydrogen absorption capacity and absorption/desorption kinetics have been studied in the case of both pure and multicomponent systems.1,2,9,10 Pure and hydrogenated ZrCr2 is easily synthesized in cubic C15 structure, with the maximum storage capacity of 3 hydrogen atoms per formula unit. Additionally, pressure–composition–temperature (PCT) measurements revealed its satisfactory thermodynamic properties regarding the needed electrochemical stability.2,9 ZrMn2 is found to readily crystallize in the hexagonal C14 structure, and is able to store up to 3.6 hydrogen atoms per formula unit;10,11 however, several theoretical studies indicate the possibility of existing structural degeneracy at low temperatures, and forming of cubic C15 ZrMn2 compound and ZrMn2H0.5 hydride.1,7 Furthermore, optimization of the synthesis process of compounds in the Zr–Ni phase system led to the potential discovery of C15 Laves phase ZrNi2. Recently, Kumar et al.12 studied the effect of various concentrations of Ni on the ZrMn2−xNix phase transformation from hexagonal C14 ZrMn2 to cubic C15 ZrNi2 compound, and revealed the existence of cubic Laves phase ZrNi2. Acknowledging the previous studies, we have decided to examine the possibility of ZrMn2H and ZrNi2H formation in cubic configuration by calculating their heats of formation.
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Fig. 1 Cubic C15 Laves phase unit cell, with indicated 96g (A2B2), 32e (AB3), and 8b (B4) tetrahedral interstitials. Some atoms are omitted for clarity. |
Interstitial position 96g is a tetrahedral site formed by two A and two B atoms, A and B being the host atoms of AB2 Laves phase. For simplicity, this site and respective hydride will be addressed as A2B2. In analogy to previous position, 32e site, which is constructed by one A and three B atoms, will be referred to as AB3, and finally, 8b as B4.
Depending on the size of the interstitial site, and type of A and B atoms, hydrogen preferably occupies A2B2 and/or AB3 position, although, in some compounds B4 site can also be occupied, but with considerably lower probability.1,3,13 Considering that the foremost interest of this study is to observe the changes in electronic structure of atoms, in various tetrahedral arrangements, in the presence of hydrogen, and consequently provide an explanation for the hydrogen occupational site-preference, we have neglected the occupation probability and equally studied all three interstitial positions.
The used methodology assumed subsequent introduction of hydrogen into the A2B2, AB3, or B4 tetrahedral site, in order to construct AB2H hydride. It was expected that due to different hydrogen's first coordination spheres (see Fig. 1.) the local crystal structure and electronic properties of host metals would be differently modified. Because the electric field gradient (EFG) directly reflects both geometrical and electronic aspects, induced modifications were studied by calculating it on the atomic site of Cr, Mn, and Ni, before and after hydrogenation.
EFG originates from the charge density deviation from spherical symmetry in the vicinity of observed nucleus, and it is extremely sensitive even to trivial changes in the electronic structure. Mathematically, it is defined as the second partial derivative of the electrostatic potential near nucleus (V(),
→ 0) with respect to spatial coordinates Vzz = ∂2V(0)/∂xi∂xj.14,15 It is designated as a traceless, symmetric second rank tensor, diagonal in the principal-axis coordinate system, and it is always present at the atomic site with the noncubic point group symmetry. According to a convention, its three nonzero components are ordered as |Vzz| ≥ |Vyy| ≥ |Vxx|; however, it is completely described by its largest component, comparable with the experimental values. Furthermore, in full-potential formalism, used in present calculations, total EFG (Vtotii) equals a sum of the valence EFG (Vvalii), which is a linear combination of partial valence electronic charge contributions
, and the lattice EFG (Vlatii).
The heats of formation were calculated by defining the energy difference between the total energy of studied hydrides and the total energy of the reactants; details can be found in our previous work.16 Our calculations reflect the situation at 0 K, and do not incorporate the vibrational frequencies associated with zero point energy, since in various types of Laves phases they are significantly smaller then ΔH(AB2H). In addition, their values in different interstitial sites are mutually comparable; therefore, they do not disrupt the calculated trend.17
ZrNi2 | ZrMn2 | ZrCr2 | |
---|---|---|---|
C15 | 6.991 | 6.995 | 7.134 |
B4 | 7.243 | 7.238 | 7.384 |
AB3 | 7.155 | 7.147 | 7.318 |
A2B2 | 7.136 | 6.958 | 7.302 |
Total EFGs on the atomic site of Cr, Mn, or Ni, the corresponding valence component, and partial orbital p (Vppzz) and d (Vddzz) contributions, have been calculated in pure and hydrogenated compounds and results are presented in Fig. 2.
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Fig. 2 Total EFG, valence EFG, and p and d orbital contributions calculated on the atomic site of Ni, Mn, or Cr, in pure and hydrogenated C15 Laves phases. |
In all compounds total EFG is entirely determined by its valence component Vtotzz ≅ Vvalzz, that is, by the charge density within the MT sphere. In pure and hydrogenated compounds value and sign of the EFG depend on the type of B atom, while in hydrides it also depends on the atom's spatial arrangement in the tetrahedral site itself.
In series of pure compounds, stable ZrCr2 exhibits the lowest absolute EFG value, which indicates that compared to Mn or Ni a lesser charge deviation from the spherical symmetry occurs in the vicinity of Cr. In ZrCr2Hx and ZrMn2Hx (x = 0, 1) EFG exhibits an analogous increase of its absolute value throughout the series of tetrahedral sites. Established trend and its evident discrepancy in case of ZrNi2Hx can be understood in view of Cr, Mn, and Ni electronic configuration. However, to comprehend the importance of this, one should initially perceive that for all studied hydrides partial p and d terms predominantly contribute to the valence EFG in a form of linear combination Vvalzz ≅ Vppzz + Vddzz (see Fig. 2.). Atomic Cr and Mn have comparable electronic configuration (Cr: 4s1 3d5 4p0; Mn: 4s2 3d5 4p0), which differs from that of Ni (4s2 3d8). As a result of that, and their identical site symmetry, it can be expected that d and p charge in Cr and Mn are equivalently spatially distributed. Considering the spherical symmetry of s orbital, contribution from s states is negligible compared to Vppzz and Vddzz. Providing this explanation, it is relatively simple to understand the established trend and the lack of it in Ni-hydrides.
It was briefly mentioned that the governing factor in the occupation process is the volume of the interstitial position. Accordingly, because it possesses the largest volume, A2B2 site will be preferably occupied and followed by the occupation of somewhat smaller AB3 tetrahedra.21 The smallest available B4 site usually remains unoccupied; however, negative formation enthalpies for several B4 hydrides have been reported.13 At this point, we will correlate the obtained EFG values with the hydrogen occupational site-preference in studied compounds, and add a presumption to the “site-volume–site-preference” rule. According to our results, absorption of hydrogen in A2B2 site only slightly modifies the EFG values from the ones calculated in corresponding pure compounds. On the other hand, considerably pronounced divergence of the electronic charge from the original distribution is observed when hydrogen occupies B4 tetrahedral site. On the basis of this, it can be argued that the interstitial positions of studied Laves phases are being occupied under the condition that the electronic charge of its surrounding atoms minimally diverges from the initial distribution.
Further observation can be made regarding the correlation between the Fermi level position and the stability of studied structures. In pure ZrCr2, Fermi level clearly separates the bonding from the antibonding states, while in ZrMn2 it is shifted towards the antibonding area. This agrees with the pronounced stability of ZrCr2, and infers that ZrMn2 compound does not crystallize in cubic C15 structure.
In addition, according to the position of EF, all ZrMn2H interstitial hydrides are likely to be unstable. Position of EF in DOS of ZrCr2H reveals the stability of A2B2 and AB3 hydrides, and suggests the instability of B4 hydride. DOS of ZrNi2 and ZrNi2H does not afford such distinct assumptions, which is why in order to gain insight into its practical features formation enthalpies of this hydride have to be addressed.
According to the formation enthalpies of all three studied cubic Laves phase compounds the only stable monohydride is ZrCr2H. ZrNi2H and ZrMn2H have positive formation enthalpies, which indicates that, regardless of the occupied interstitial site, all suggested hydrides are physically unattainable. When hydrogen is accommodated in A2B2 or AB3 interstitial site of ZrCr2, negative formation enthalpies are obtained, according to which both hydrides are stable. On the other hand, positive enthalpy of B4 hydride suggests that occupation of this site destabilizes the initial compound. Calculated enthalpies of A2B2 or AB3 hydrides are mutually comparable (−16.98 kJ mol−1 H−1 for AB3 and −18.17 kJ mol−1 H−1 for A2B2) and lead to an assumption that in ZrCr2 their occupation is competitive. To be able to directly compare our values with those from previous studies, experimental or computational, it would be beneficial to have the formation enthalpies for ZrCr2Hx, with x = 1. However, in lack of these results we can relate our values to the existing ones in respect to the range of available hydrogen concentrations. Previously studied concentrations ranged from 0.5 H per f.u. to ∼3 H per f.u., and published formation enthalpies listed from the experimental value of −18 kJ mol−1 H−1 for ZrCr2H3 (ref. 10 and 24) to theoretical of −33.5 kJ mol−1 H−1 for ZrCr2H0.5.1–3 Our value for A2B2 hydride agrees excellently with the experimental one for 3 hydrogen atoms per formula unit.
Positive formation enthalpies of all ZrNi2H and ZrMn2H indicate that regardless of the occupied interstitial site these hydrides are always unstable. The obtained values suggest difficulties in any prospective synthesis attempt; nevertheless, hydrogenation of potentially synthesized cubic C15 ZrMn2 or ZrNi2 may also result in the phase transformation into hexagonal C14 Laves phase, or even some other stable structure. Our results are in agreement with the experimental findings of Kumar and coworkers.12 On the other hand, present computational and previous experimental results contradict the first-principles calculations conducted on hypothetical ZrMn2H0.5,1 for which the authors obtained negative formation enthalpies. In addition, it is expected that the formation of hydrides in Zr–Ni system would be less probable with increasing Ni content, given that Ni, being the late transition metal, does not form stable binary hydride, while Zr does (ZrH2). Baring in mind that ZrNi2 forms a hydride of significantly decreased stability, with respect to the pronounced stability of ZrNi hydrides,25,26 further investigation of ZrNixHy alloy system (1 < x < 2) could present a prospective way of tailoring the desired stability of the Zr–Ni hydrides.
Calculated formation enthalpies indicated that of all studied hydrides only ZrCr2H is the stable one; with hydrogen occupying A2B2 or AB3 interstitial site. Both ZrMn2H and ZrNi2H were found to be unstable, regardless of the occupied interstitial site. Our values agree with experimental results for all hydrides; however, they contradict the previously calculated formation enthalpies of Mn-hydride, according to which this hydride in cubic C15 structure can be stable.
Presented results suggest the existence of correlation between the electronic structure of atoms surrounding the absorbed hydrogen and hydride formation process in the cubic Laves phases. However, to provide a deeper insight into such correlation, and additionally study provided conclusions, it would be beneficial if an extensive investigation is conducted on a broader class of prospective hydrogen storage materials.
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