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Phase Stability, Phase Mixing and Phase Separation in Fluorinated Alkaline Earth Hydrides Ramaraj Varunaa, and Ponniah Ravindran J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03265 • Publication Date (Web): 15 Sep 2017 Downloaded from http://pubs.acs.org on September 17, 2017

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Phase Stability, Phase Mixing and Phase Separation in Fluorinated Alkaline Earth Hydrides R. Varunaa†,‡ and P. Ravindran∗,†,‡,¶,§ †Department of Physics, Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, 610101, India ‡Simulation Center for Atomic and Nanoscale MATerials, Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, 610101, India ¶Department of Materials Science, Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, 610101, India §Center for Materials Science and Nanotechnology and Department of Chemistry, University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway. E-mail: [email protected] Abstract Alkaline-earth hydrides (AH2 ) are considered as potential hydrogen storage material. Due to high decomposition temperature and slow sorption kinetics, these hydrides cannot be used for energy storage applications. As fluorine is more electro-negative than hydrogen, substitution of hydrogen by fluorine will bring anisotropic bonding interaction and hence it may improve the hydrogen storage properties. Hence, the structural stability, electronic structure, and chemical bonding of AH2 and fluorinated AH2 (AH2−x Fx ) are delineated using ab-initio calculations. From the calculated enthalpy of formation we have predicted that AH2−x Fx are relatively more stable than the

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corresponding pure hydrides. The positive and very low value of enthalpy of mixing for AH2−x Fx imply that single-phase of AH2−x Fx may form at reasonable temperatures. The band structure and density of states (DOS) calculations reveal that AH2−x Fx are insulators. Partial DOS, charge density, electron localization function and crystal orbital Hamiltonian population analyses conclude that these compounds are governed mainly by ionic bonding. The calculated H site energy increases as the fluorination increases and thus fluorination bring extra stability in the lattice. The present results suggest that hydrogen closer to fluorine can be removed more easily than that far away from fluorine. Hence the fluorination brings disproportionation in the bonding between the constituents.

Introduction Due to increase in world population and change in lifestyle of people there is a continuous demand for more energy consumption. Nonrenewable energy sources are used mostly for present energy system which exists in the form of fossil fuels such as coal, oil, and natural gases. The cost of these energies is rising continuously every year and also these resources are depleting drastically. Moreover, burning these fuels cause environmental pollution. The emission of CO2 , SO2 , benzene, nitrogen oxides, etc., from these fossil fuels causing global warming, smog, acid rain, and affecting human health. So one should look for a sustainable energy system through the utilization of renewable energy sources. As renewable energy sources are of intermittent nature and also not available sufficiently where there is energy demand, one should look for energy storage systems. If one wants to use energy storage systems for practical applications, it should be abundant, environmentally friendly as well as economically viable. 1,2 Hydrogen is an environmentally friendly energy carrier which has been used for mobile applications since it has more advantages than the other chemical energy carriers. 3–8 Hydrogen is the lightest and most abundant element in the universe. However, it needs to be stored 2


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at high densities for mobile applications. For widespread applications hydrogen storing materials should have adequate stability, fast kinetics of absorption as well as desorption, high gravimetric and volumetric storage capacity. 9 On-board hydrogen storage approaches are liquid hydrogen storage tanks, compressed hydrogen gas storage, and solid state storages in materials such as metal hydrides, complex hydrides, carbon based materials, metal-organic frameworks, etc. The liquid and high pressure storage of hydrogen is expensive and technically challenging. 10 Solid state storage of hydrogen is preferred for on-board applications 11–13 due to low cost, good stability, reversibility of charging/discharging process, easily attainable operating conditions, and high gravimetric storage capacity. The advantages of using lightweight hydrides for hydrogen storage is that they have high volumetric as well as gravimetric storage capacity. So they can be used in fuel cells, batteries, thermal energies, and other environmentally friendly energy utilization applications. The alkaline-earth hydrides such as beryllium hydride (BeH2 ), magnesium hydride (MgH2 ), calcium hydride (CaH2 ), strontium hydride (SrH2 ), and barium hydride (BaH2 ) are the interesting class of compounds for hydrogen storage applications. 14,15 It is experimentally well known that MgH2 is less stable compared with other ionic hydrides such as CaH2 , SrH2 , and BaH2 . 16 Among all the alkaline earth hydrides, MgH2 has been much studied by both experimentally 17–21 and theoretically 22–30 for energy storage applications due to its low manufacturing cost, high gravimetric hydrogen density (7.6 wt.%) as well as high volumetric hydrogen density (110 kg/m3 ). But, the dehydrogenation of MgH2 requires higher temperature, i.e. 552 K (300o C) at 1 atm. 31–35 The high enthalpy of formation (∆H= −75 kJ/mol) and very slow hydrogenation/ dehydrogenation kinetics led MgH2 as a challenging energy storage material. In order to improve the hydrogen storage property of these hydrides, understanding their stability and analysis of the chemical bonding between the constituents are important. The bonding interactions between constituents of MgH2 have been analyzed by Lu et al. 36 using ab-initio pseudo potential method. In his paper, he reported that there is no

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covalent bonding between nearest neighbor of H and Mg sites and there is about 19% of charge in the interstitial region. The stability of MgH2 has been studied by Vajeeston et al. 37 up to 20 GPa using density-functional total-energy calculations. They reported that the ground state of α-MgH2 becomes unstable at higher pressures and shown that α-MgH2 is an insulator in the whole pressure range. They have found several pressure induced structural transitions within 20 GPa and demonstrated that all the high-pressure modifications also exhibit insulating behavior. Doping hydrogen with other isovalent elements in hydrides is one of the possible ways to reduce the stability and improve the hydrogen storage properties. De Castro et al. 38 reported that the metal fluoride addition to MgH2 decreases the H-sorption temperatures. Deledda et al. 39 observed that the fluorine addition is beneficial for H sorption behavior. The decomposition reaction of LiBH4 with and without F anion doping was investigated using first-principles calculations by Yin et al. 40 They have reported that F substitution at the H site in the lattices of LiBH4 and LiH hydrides may produce single phase materials those will be suitable for on-board hydrogen storage application on both thermodynamic and capacity aspects. Malka et al. 41 have studied the influence of various halide additives milled with a magnesium hydride on its decomposition temperature. They have reported that the fluorine has a much stronger influence on the MgH2 decomposition process as compared to chlorine. Corno et al. 42 reported that the fluorination destabilize the lithium borohydride. Malka et al. 43 reported in their paper that F anion substantially increased the absorption/desorption kinetics of MgH2 . Kou et al. 44 and Xiao et al. 45 reported that if one add NbF5 additive to 2LiBH4 /MgH2 system the desorption temperature will be lowered and also the reaction kinetics get improved. Zhang et al. 46 reported that the combined effect of co-doped Ti and F in improving the dehydrogenation properties of MgH2 is superior to that of single-doped Ti. Ismail et al. 47 reported that TiF3 effectively improves the dehydrogenation properties of the MgH2 NaAlH4 composite system. Wang et al. 48 illustrated the effects of F and Cl impurities on

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the stability of MgH2 by calculating hydrogen removal energy. They have reported that F and Cl do not reduce the removal energy for neutral and negatively charged H, but can substantially reduce removal energy for positively charged H. Kou et al. 49 reported that increasing the addition amount of NbF5 to the 2LiBH4 -MgH2 composite reduce the dehydrogenation temperature, improve the hydriding-dehydriding kinetics and also leads to the re/dehydrogenation capacity loss. Pragya et al. 50 shown that MgF2 additive acts as a catalyst for MgH2 decomposition, and improve its hydrogenation/dehydrogenation kinetics due to the presence of chemically stable MgF2 powder well mixed in MgH2 matrix. Several other experimental studies 51–58 have shown that fluorinated hydrides improve the hydrogen sorption performance and reduce the dehydrogenation temperature of the materials. Malka et al. 59 reported that dehydrogenation at 325 o C leads to the formation of magnesium, iron and MgH2−x Fx phases while milled MgH2 with FeF2 and FeF3 . Pighin et al. 60 reported that the hydriding and dehydriding kinetics are faster when milling of MgH2 with (7 mol%) NbF5 than in MgH2 milled without additive. They have also noticed that the milling of MgH2 with NbF5 produces H-rich and F-rich solid solutions such as MgH2−x Fx and MgHy F2−y . Keeping in view of the above observations, we have performed ab-initio calculations for pure alkaline earth metal hydrides and F substituted in the H site with different composition in alkaline earth metal hydrides. In this paper, we have determined structural parameters, enthalpy of formation, enthalpy of mixing, and hydrogen site energy for understanding the structural stability of these AH2−x Fx systems. Compared with hydrogen, fluorine is having higher atomic weight and also each fluorine atom replace one H atom and hence the gravimetric density of hydrogen will decrease with fluorination. For example, 50% of fluorine substituted MgH2 , the gravimetric density of hydrogen reduced from 7.6 wt.% to 4.5 wt.%. The bonding features of AH2−x Fx systems are analysed with the help of density of states (DOS), electron localization function (ELF), charge density plot, and crystal orbital Hamiltonian population (COHP). In order to understand the electronic properties the band structure of these materials are analyzed.

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Computational details Density functional theory (DFT) 61 calculations were performed using projector augmented plane-wave (PAW) method

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implemented in Vienna ab-initio simulation package (VASP). 63

For the exchange and correlation functional we have used the generalized gradient approximation by Perdew, Burke and Ernzrhof (GGA-PBE) 64 since these potentials improved the accuracy in our calculations. The geometric relaxations were done using force as well as stress minimization. The PAW-PBE potentials such as H_s for H, F_s for F, Be_sv for Be, Mg, Ca_sv for Ca, Sr_sv for Sr and Ba_sv for Ba were used. These potentials treat valence electron configurations of 1s1 , 2s2 2p5 , 1s2 2s2 , 3s2 , 3s2 3p6 4s2 , 4s2 4p6 5s2 , and 5s2 5p6 6s2 for H, F, Be, Mg, Ca, Sr, and Ba, respectively. In case of Mg, we have used the standard Mg potential since it gave structural parameters (obtained equilibrium volume of MgH2 is 60.63 Å3 ) which are consistent with experimental parameters (60.85 Å3 ) than that obtained using Mg_sv (39.46 Å3 ). In order to finalize the computational parameters for all the calculations, we have made volume optimization calculations for MgH2 and MgF2 as a function of energy cutoff. We have found that the energy cutoff of 300 eV is sufficient to reproduce the experimental equilibrium volume for MgH2 and MgF2 with the accuracy of 0.36% and −0.39%, respectively. Hence, we have used an energy cutoff of 300 eV for all AH2−x Fx systems (except for BeH2−x Fx systems where 400 eV is used) for our calculations. Brillouin zone integrations were done using Monkhorst-Pack k-point mesh 65 for structural optimization while the Γ centered grid was employed to conduct electronic structure calculations. The 8x8x10 and 8x8x8 meshes comprising 160 and 114 points in the irreducible Brillouin zone were sufficient to describe structural properties of BeH2 and BeF2 structures, respectively. For MgH2 , MgF2 , CaH2 , CaF2 , SrH2 (Pnma), SrH2 (P63 /mmc), SrF2 , BaH2 and BaF2 structures, 10x10x16, 10x10x16, 10x12x10, 12x12x12, 10x10x10, 12x12x8, 12x12x12, 10x12x10, and 12x12x12 k-meshes with irreducible k points such as 120, 120, 150, 120, 125, 168, 56, 150, and 56 were used. In order to substitute fluorine in MgH2 , a 1x1x2 supercell was constructed and the cell contains four Mg atoms and eight H atoms. Out of eight H 6


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8 4.1052 (3.9500 5.7992 (5.7940 6.8337 (6.7920 6.2154 (6.2000

Pnma

P63 /mmc

Fm¯ 3m

Pnma

Fm¯ 3m

SrH2

SrH2

SrF2

BaH2

BaF2

5.4585 (5.4712 6.3411 (6.3770

Fm¯ 3m

Pnma

CaH2

4.8783 (4.6880 4.4928 (4.4982 4.6245 (4.6213 5.8806 (5.9480

8.9500 (8.9670

a

CaF2

P42 /mnm

MgF2

P31 21

BeF2

P42 /mnm

Ibam

BeH2

MgH2

Space group

Structure type

6.2154 6.2000

5.7992 5.7940 4.1609 4.1680

4.1052 3.9500

5.4585 5.4712 7.2885 7.3580

4.8783 4.6880 4.4928 4.4982 4.6245 4.6213 3.5619 3.6070

4.1321 4.1410

Unit cell(Å) b

6.2154 6.2000)

5.7992 5.7940) 7.8680 7.8580)

5.6315 5.1700)

5.4585 5.4712) 3.8489 3.8830 )

5.3345 5.1850) 3.0037 3.0075) 3.0601 3.0519) 6.7537 6.8520 )

7.6458 7.6430)

c Be(4a):0,0,0.25 Be(8j):0.1678,0.1222,0 (0.1677,0.12,0) H(16k):0.0882,0.2271,0.1525 (0.0882,0.2241,0.1520) H(8j): 0.3115,0.2771,0 (0.3102,0.2771,0) Be(3a): 0.4783,0,0.3334(0.47,0,0.3334) F(6c): 0.4189,0.2524,0.2007(0.419,0.269,0.213) Mg(2a): 0,0,0 H(4f):0.3043,0.3043,0(0.304,0.304,0) Mg(2a): 0,0,0 F(4f): 0.3027,0.3027,0(0.3029,0.3029,0) Ca(4c):0.2395,0.25,0.1105(0.26,0.25,0.11) H(4c):0.3552,0.25,0.4276(0.375,0.25,0.435) H(4c):0.9742,0.25,0.6777(0,0.25,0.66) Ca(4a):0,0,0 F(8c):0.25,0.25,0.25 Sr(4c):0.2396,0.1109,0.25(0.246,0.11,0.25) H(4c):0.3549,0.4277,0.25(0.246,0.43,0.25) H(4c):0.9735,0.6785,0.25(0.01,0.742,0.25) Sr(2c):0.3333,0.6667,0.25 H(2a):0,0,0 H(2d):0.3333,0.6667,0.75 Sr(4b):0.5,0.5,0.5 F(8c):0.25,0.25,0.25 Ba(4c):0.2605,0.25,0.8872 (0.2603,0.25,0.8886) H(4c):0.6446,0.25,0.9287 (0.646,0.25,0.9135) H(4c):0.0288,0.25,0.1799(0.043,0.25,0.174) Ba(4a): 0,0,0 F(8c): 0.25,0.25,0.25

Wyckoff position

240.11 (238.33) 76

195.03 (194.51) 74 223.72 (222.45) 75

164.38 (139.72) 73

162.64 (163.78) 71 177.88 (182.20) 72

109.94 (98.69) 67 60.63 (60.85) 68 65.44 (65.18) 69 141.47 (147.01) 70

282.76 (283.80) 66

Volume of unit cell (Å3 )

Table 1: Theoretically calculated and experimentally 66–76 observed (enclosed in the bracket) structural parameters for alkalineearth hydrides and fluorides in their ground state.

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insulator up to 100 GPa. Due to its low mass and high hydrogen content (18.2 wt.%), 80 BeH2 is considered as an interesting hydrogen storage material. In the ground state, BeF2 is preferred to be in trigonal (P31 21) structure (see Figure 1(b)). The unit cell contains 3 Be and 6 F atoms. Each Be atom is tetrahedrally coordinated with F atoms and fluorine ions are coordinated by two Be atoms. At room temperature, the α-MgH2 (rutile structure) crystallize in the tetragonal structure. In Figure 1(c) we have displayed the primitive unit cell of MgH2 which contains two Mg and four H atoms. Each Mg atom is octahedrally coordinated to six H atoms, whereas each H atom is coordinated to three Mg atoms. The bonding interaction between constituents in MgH2 is generally described as partially covalent in nature rather than purely ionic. From charge density, charge transfer, electron localization function, and Mulliken population analyses, it is shown that MgH2 has a dominant ionic character. 28 Like MgH2 , magnesium fluoride also preferred to be in tetragonal structure. As shown in Figure 1(d), the primitive unit cell of MgF2 contains two Mg atoms and four F atoms where each Mg atom is connected to six F atoms and each F atom is connected to three Mg atoms. Since F is the most electro-negative element and Mg is the electro-positive element, there will be an electron transfer from Mg to F which results a strong ionic bonding in MgF2 . At ambient conditions, CaH2 preferred to stabilize in orthorhombic (Pnma) structure while CaF2 is in face centered cubic (Fm¯3m) structure. The crystal structure of CaH2 and CaF2 is shown in Figure 1(e) and 1(f), respectively. The unit cell of CaH2 contains four calcium atoms and eight hydrogen atoms. Similarly, CaF2 also contains four calcium and eight fluorine atoms in its unit cell. In CaH2 , each Ca is surrounded by nine H atoms, whereas each hydrogen of type1 (H1) and type2 (H2) is surrounded by four and three Ca atoms, respectively. In CaF2 each F is tetrahedrally coordinated with Ca. Similar to CaH2 , SrH2 also crystallize in the orthorhombic (Pnma) structure in its ground state (see Figure 1(g)) and the unit cell contains four strontium and eight hydrogen atoms with hydrogen occupied in two inequivalent sites. It is also reported 73 that SrH2 can also stabilize in the

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hexagonal (P63 /mmc) structure (see Figure 1(h)) with four strontium and eight hydrogen atoms in the unit cell. In the ground state, SrF2 has cubic (Fm¯3m) structure (see Figure 1(i)) and that contains four strontium and eight fluorine atoms. However, hexagonal form of SrF2 is also reported in the literature. 81,82 The ground state crystal structure of BaH2 is orthorhombic (Pnma) (see Figure 1(j)) while that for BaF2 is face centered cubic (Fm¯3m) as shown in Figure 1(k). In BaH2 , each Ba atom is connected to nine H atoms and type1 hydrogen (H1) is coordinated with four Ba atoms, while type2 hydrogen (H2) is coordinated with five Ba atoms. In BaF2 , each F atom is tetrahedrally coordinate with Ba atoms, whereas each Ba atom is connected to eight F atoms.

Results and Discussion Phase stability and phase transition As fluorine is highly electro-negative compared with hydrogen, if hydrogen is present close to fluorine, charge at the H site will be drawn by F atom. As a result, the charge at the H sites will disproportionate. So, H atom closer to F will have relatively less charge than those far away from F. Due to ionic bonding, the neighboring alkaline-earth metal also will be a positive ion. Hence, the Coulombic attractive interaction between these ions will reduce and that will bring instability into the lattice. On the other hand, if the F ions are adjacent to each other, apart from having ionic interaction with neighboring alkali-earth metal, they can also form small covalent interaction between themselves which brings extra stability in the lattice. We have calculated total energies for two different cases. In the first case, we have substituted F atoms which are farer from each other in AH2−x Fx . In another case, we have substituted F atoms which are closer together in AH2−x Fx . Our total energy calculations suggest that in AH2−x Fx systems, F atoms closer with each other is energetically favorable to form. In order to understand the structural phase stability of AH2−x Fx systems, we have cal10


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Table 2: Calculated enthalpy of formation per formula unit and bandgap (Eg) of alkalineearth hydrides and alkaline-earth fluorides. Structure type

Calculated Other theoretically/ ∆Hf experimentally (kJ/mol) observed ∆Hf (kJ/mol)

Calculated Other theoretically/ Eg experimentally (eV) observed Eg (eV)

BeH2 (P31 21) BeH2 (Ibam) BeF2 (P31 21) BeF2 (Ibam) MgH2 (P42 /mnm) MgF2 (P42 /mnm) CaH2 (Fm¯3m) CaH2 (Pnma) CaF2 (Fm¯3m) CaF2 (Pnma) SrH2 (Fm¯3m) SrH2 (P63 /mmc) SrH2 (Pnma) SrF2 (Fm¯3m) SrF2 (P63 /mmc) SrF2 (Pnma) BaH2 (Fm¯3m) BaH2 (Pnma) BaF2 (Fm¯3m) BaF2 (Pnma)

−8.886 −14.654 −929.553 −929.414 −52.772 −1018.474 −154.187 −160.684 −1128.808 −1111.528 −148.066 −138.761 −154.960 −1130.505 −1055.665 −1118.454 −131.625 −140.666 −1110.299 −1100.353

5.759 5.329 8.097 8.005 3.696 7.064 0.135 3.022 7.258 7.717 0.814 1.291 3.129 6.894 6.418 7.156 1.203 2.830 6.694 6.974

14

−14.8, −18.86 −1026.8±3.3 85

83

−60.3, 14 −45.192 32 −1124.2±1.3 87 −176.7, 14 −181.5, 90 −144 91 −1221.3±0.8 93

−170.7, 14 −177 16 −1218.4±1.3 93

−157.6, 14 −171.5, 16 −188.8 95

11


5.496, 14 5.5, 78 5.78 84 8.11 86 3.6, 22 3.79, 68 3.965 14 6.78, 88 6.88 89 3.105, 14 2.97 92 7.24 94

3.221 14 7.5 94

2.9, 96 2.901 14 7.49 97



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implies that the stability of these systems is mainly govern by the ionicity and the Vegard’s law can be utilized to estimate the heat of formation for intermediate compositions. In order to substantiate this observation the enthalpy of formation of alkaline earth hydrides versus electro negativity difference between alkaline-earth metal and hydrogen are plotted in Figure 2(b). From this figure, we have observed that the enthalpy of formation is increasing from BeH2 to BaH2 due to the increase in ionicity of these systems. Gridani et al. 98 reported that BaH2 is less ionic than the SrH2 , which is less ionic than CaH2 from Mulliken’s population analysis. So our calculated enthalpy of formation decreases from CaH2 to BaH2 . This is mainly due to the electro-negativities of heavy atom along with the size factor of the ions.

Figure 3: (Color online) Difference between enthalpy of formation of pure hydride phase and pure fluoride phase for AH2−x Fx systems as a function of fluorination. In order to identify the phase transition with fluorination, we have calculated the difference between the enthalpy of formation of Pnma and P31 21 structure of BeH2−x Fx . Similarly, we have calculated the difference between the enthalpy of formation for other systems as shown in Figure 3. From this figure, it is clear that the phase transition from Pnma to P31 21 structure occur in BeH2−x Fx systems at around 68% fluorination in BeH2 . For the CaH2−x Fx , SrH2−x Fx , and BaH2−x Fx systems, the structural phase transition occurs at 18%, 13



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22%, and 36% fluorination in their corresponding pure hydrides, respectively.

Phase mixing and phase separation

Figure 4: (Color online) Calculated enthalpy of mixing of AH2−x Fx as a function of fluorination. In order to understand the stability of fluorinated systems, i.e. whether they form single fluorohydride phase or the multiphase comprised of a hydride phase and a fluoride phase, the enthalpy of mixing (∆Hm ) has been calculated using the following equation for the AH2−x Fx system, ∆Hm (AH2−x Fx ) = E(AH2−x Fx ) − [(2 − x)E(AH2 ) + (x)E(AF2 )]

(2)

The ∆Hm of AH2−x Fx as a function of fluorination are displayed in Figure 4. The calculated ∆Hm for pure metal hydrides and metal fluorides are zero. For all the AH2−x Fx systems, the estimated ∆Hm values are positive and very low, which implies that these compounds may form at room temperature. The calculated enthalpy of mixing show that it is experimentally easy to synthesize single phase of fluorinated compounds for CaH2−x Fx (Fm¯3m), SrH2−x Fx (Fm¯3m), and BaH2−x Fx (Fm¯3m) and with moderate thermodynamic conditions 14


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GGA/LDA calculation is usually underestimate with respect to the experimental values. Using hybrid functional or the GW calculations one can quantitatively predict the bandgap and this is out of the scope of the present study. The presence of flat bands in the valence band maxima indicates that the hole effective mass in this system will be high. For 50% fluorinated MgH2 (see Figure 5(b)), the bandgap increased to 5.34 eV and this is due to increase in ionicity. It is to be noted that the fluorination brings additional states in the valence band. For MgF2 (see Figure 5(c)), it is observed that the valence band maxima (VBM) and conduction band minima (CBM) occurs at the Γ-point and bandgap further increased to 7.06 eV. This bandgap value is in good agreement with the value of 6.88 eV calculated by Ramesh et al.. 104 Our calculations suggest that MgF2 can be classified as a direct bandgap insulator. The increase in value of the bandgap by fluorination in MgH2 is associated with the increase in ionicity of the system. Compared with the bands in the VBM, the bands in the CBM are well dispersed and hence the electron mobility is expected to be more than the hole mobility. In order to understand the bonding interaction between the constituents, we have made a partial DOS analysis for AH2 systems as a function of fluorine substitution. The calculated and other theoretically/experimentally observed bandgap of alkaline-earth hydrides and fluorides are listed in Table 2. Let us first analyze the DOS for α−MgH2 . The energy gap value of MgH2 obtained from our GGA calculation is 3.69 eV. The partial density of states for MgH2 are plotted in Figure 6(a). The valence band is mainly governed by the large contribution of H-s state and very small contribution of Mg-s and Mg-p states. The negligibly small Mg-s DOS in the valence band indicates charge transfer from the Mg-site to H-site. Still, there is a finite DOS present in the whole valence band of Mg. The broadband feature along with the degenerate distribution of electrons in the whole valence band of Mg sites with that in the H-site indicates the presence of finite covalent bonding between H and Mg atoms. The strong ionic bonding along with noticeable covalency bring high formation energy and hydrogen site energy in MgH2 .

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Our calculated partial DOS for BeH2 (see Figure 6(d)) shows that the Be-s,p and H-s states are energetically degenerate in the whole valence band reflecting the covalent interaction between Be and H. Partial DOS of BeH2 has broader peaks compared with MgH2 resulting from this covalent hybridization. In the high energy region of the valence band, the contribution from Be-s state has negligible DOS, which indicate that some of the charges get transfer from Be-s to H-s. From these observations one can conclude that the bonding interaction between Be and H in BeH2 has dominant covalent bonding with small ionic characters. For 50% F substituted BeH2 , the partial DOS is displayed in Figure 6(e). Due to the substitution of more electro-negative F in BeH2 , some of the electrons from Be and H get transferred to F as a result the DOS of Be and H were become narrow in the high energy region of the valence band as compared with that of pure BeH2 . Be-p and H-s states in BeHF are drastically reduced in the VBM compared with that in BeH2 , whereas Be-p and F-p states have energetically degenerate nature in the region -2 eV to 0 eV indicating the presence of iono-covalent bonding in BeHF system. For BeF2 system, the partial DOS analysis shows that the F states are dominating the valence band and also the Be states are well separated from that of F (see Figure 6(f)) indicating the presence of dominant ionic bonding between Be and F. The total DOS for BeH2−x Fx , MgH2−x Fx , and BaH2−x Fx in their ground state crystal structures are shown in Figure 7(a), 7(b), and 7(c), respectively. It is evident from these figures that the bandgap values increasing with increase in fluorine concentration in all the three systems and this could be explained from the increase in ionicity as expected from simple chemical picture. The broadband feature present in BeH2−x Fx (see Figure 7(a)) is due to the covalent bond present between Be with neighbors in these systems. On the other hand, for the BaH2−x Fx systems, the F-p states are well separated from valence band indicating the presence of ionic bonding. Further, F substitution brings an additional level in alkaline-earth hydrides which increases the DOS intensity in the valence band region. Also, the intensity of the DOS in the top of the valence band (i.e. -2 to 0 eV) systematically

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Hydrogen site energy The H site energy (H desorption enthalpy) 25,29,106 is the energy required to remove an H atom (or ion) from its host lattice. The higher H site energy indicates that the H atoms are strongly bound to the host lattice and hence high temperature is required to remove H from the system. The calculation of H site energy for the hydrogen storage materials will help one to understand more about the thermodynamical stability and desorption kinetics. To investigate the effect of F substitution on the stability of alkaline-earth hydride, the H site energy is calculated 107 using the following relation, 1 Ed (H) = E(An H2n−1 ) + ( )E(H2 ) − E(An H2n ) 2

(4)

The H site energy of MgH2 as a function of fluorination is calculated and plotted in Figure 9(a). The calculated energy which is required to remove H from Mg2 H4 is 115.69 kJ/mol (1.203 eV). This is in good agreement with the H site energy for various polymorphs of MgH2 reported by Vajeeston et al. 108 The calculated H site energy is relatively high i.e., H desorption enthalpy is high and hence one can expect that the hydrogen desorption temperature of MgH2 will be high because the desorption temperature mainly involve the breaking of Mg-H bond. Moreover, the diffusion of hydrogen atom through hydride is expected to be slow and hence the reaction kinetics will be poor. For 12.5 % and 25 % fluorine substitution in MgH2 , we have calculated H site energy to understand the role of fluorination on hydrogen desorption temperature. We have removed H which is closer to F as well as far away from F. In Figure 9(a), one can notice that the energy required to remove H closer to F is higher than that of H far away from F. Hence removing H atom nearer to F is unfavourable in MgH2−x Fx . This may be due to the difference in the electro-negativity of H and F. Our calculated H site energy as a function of fluorine substitution in MgH2 shows that the H site energy increases when fluorination increases. Hence, the H desorption enthalpy increases when F substitution in MgH2 increases. This is mainly due to the high electro-negativity of F which brings extra stability to the lattice as 21




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the Mg site due to charge transfer effect. Further, the charges in the H sites are spherically distributed and also very low charge density is present between Mg and H. These are the indication for the presence of ionic bonding in the system. It may be noted that, though there is an ionic bonding between Mg and H, there is small anisotropic charge distribution present between H atoms and between Mg and H. This charge distribution feature suggests the presence of partial covalency in the system and this is consistent with our partial DOS analysis. Figure 10(c) and 10(d) display the charge density and ELF plot of 50 % F substituted MgH2 . Owing to the higher value of electro-negativity in the F, it has drawn most of the charges from Mg and hence there is a limited amount of electrons only available to participate ionic bonding with H. It is to be noted that charges present in the interstitial region in between H atoms in MgH2 get reduced in the fluorinated system. Apart from having isotropic charge distribution, there is small anisotropic charge distribution present between constituents in MgHF indicating small covalency in the system. In MgF2 system (see Figure 10(e) and 10(f)), due to the high electro-negativity of fluorine, charges are drawn almost completely by F from Mg which clearly indicating strong ionic bonding between Mg and F. The Figures 11(a) and 11(b) show the charge density and ELF plot, respectively for BeH2 in the plane where one can see the bonding between the representative atoms. It may be noted from Figure 11(a) that there is a relatively small charge distributed on the Be site and most of the charge get accumulated in the H sites. This is the clear indication for the presence of ionic bonding interaction between Be and H. However, the nonspherical distribution of charges in the H sites and also the finite charge distribution between H sites as well as between Be and H sites and their directional nature indicating the presence of substantial covalency. The ELF distribution in Figure 11(b) clearly shows that the presence of paired electron distribution in-between H sites confirming the presence of covalent bonding. So, the chemical bonding in BeH2 can be characterized as mixed iono-covalent bond. The covalent character in BeH2 is higher than that in MgH2 as discussed above. In the case of

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interaction is present between Mg and H. On the other hand, the antibonding states are present near the Fermi level and it is relatively very less. For 50% fluorinated MgH2 , the bonding states between Mg and H is reduced in the lower region (below -2.5 eV) and the Mg-H bonding states are present in the higher region between -2.5 and 0 eV. Further, the bonding states from Mg-F interaction is strongest (magnitude is higher) compared with that from Mg-H interaction in MgHF. This implies that F substitution in MgH2 significantly reduces the bonding interaction between Mg and H. The bonding interaction between Mg and F is high which brings extra stability in the lattice compared to pure MgH2 .

Summary In order to improve the hydrogen storage properties of alkaline-earth hydrides, ab-initio total energy calculations for pure alkaline-earth hydrides, and fluorine substituted alkaline-earth hydrides (AH2−x Fx ) were performed and concludes the followings. 1. The phase stability, phase transformation, phase mixing, electronic structure, and chemical bonding of all AH2−x Fx systems were investigated. 2. The obtained enthalpy of formation of all AH2−x Fx systems reveal that fluorinated alkaline-earth hydrides are thermodynamically more stable and bonding between the constituents also very strong. This high stability leads to high dehydrogenation enthalpy as well as high decomposition temperature. We have found that the stability of these fluorinated compounds is governed by the ionicity and demonstrated a direct correlation between ionicity and stability in these compounds. 3. The phase transition of BeH2−x Fx , CaH2−x Fx , SrH2−x Fx , and BaH2−x Fx systems occured at around 68%, 18%, 22%, and 36% fluorination in BeH2 , CaH2 , SrH2 , and BaH2 , respectively. 4. The positive and very low enthalpy of mixing of AH2−x Fx systems concludes that single phase of these systems may form at a reasonable temperature.

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5. The band structure and total DOS plots show that all these compounds exhibit insulating behavior. The variation in the bandgap values for AH2−x Fx as a function of fluorination reveals that the bandgap increases with F concentration due to the substantial increase of the ionicity and hence bring narrow band behavior which can tune the optical properties of the systems. The strongest contribution to band bowing is due to chemical charge transfer, which induces the non linearity behavior of bandgap variation. 6. From the partial DOS, charge density, ELF, and COHP, we have concluded that there is ionic as well as some noticeable covalent bond is present in the fluorinated alkaline-earth hydrides and fluorination in alkaline-earth hydrides reduces the bonding interaction between alkaline-earth metal and hydrogen and also bring disproportionate bonding interaction. 7. The H site energy increases with increase in fluorine concentration due to the increase in ionicity. Moreover, the H site energy for H closer to F is smaller than that far away from F indicates that fluorination in AH2 induces disproportionation in the bonding between the constituents. The H site energy for SrH2−x Fx and CaH2−x Fx systems reveals that the hydrogen closer to fluorine can be removed more easily than that present far away from fluorine. 8. The present results suggest that the phase stability and physical properties of these AH2−x Fx systems are governed mainly by strong ionic bonding.

Acknowledgement We gratefully acknowledge the Department of Science and Technology, India for the financial support via Grant No. SR/NM/NS-1123/2013 to carry out this research and Research Council of Norway for computing time on the Norwegian supercomputer facilities.

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