The structural, elastic, electronic, vibrational and gravimetric hydrogen storage capacity properties of the Perovskite type Hydrides: DFT study

: The structural, elastic, anisotropic elastic, electronic and vibrational properties of the 1 Perovskite type Hydrides RbXH 3 (X = Be, Ca, Mg) were performed via Vienna Ab – initio 2 Simulation Package (VASP) based on Density Functional Theory (DFT). Our results have exhibited 3 a well–agreement with previous calculations and experiments for each compound. In order to 4 determine physical properties of RbXH 3 has been used the Generalized Gradient Approximation 5 (GGA) with Perdew–Burke–Ernzerhof (PBE) functional at this study. Present compounds were 6 found to be mechanically stable as well as their gravimetric hydrogen storage capacities has been 7 investigated. The Perovskite type Hydrides RbBeH 3 and RbMgH 3 has an indirect bandgap of 0.274 8 eV and 2.209 eV while RbCaH 3 has a direct bandgap of 3.274 eV respectively and therefore these 9 compounds has shown a semiconductor behaviour at equilibrium. Besides directional dependence 10 of anisotropic properties was visualized by representing them with maximum–minimum points. 11


Introduction
Nowadays, the greenhouse effect and air pollution caused by the long-term high use 14 of fossil fuels have been marked. While fossil fuels is decreased, negative impact arisen 15 from fossil fuels has increased incrementally need for extendable and durable energy 16 resources. For extendable and durable energy resources, there have many suggestions 17 such as solar energy, wind energy, hydro energy etc. in literature. Among these resources 18 Hydrogen is obviously stepped forth since Hydrogen is both clean and plentiful material 19 in the universe and the earth. Although it has many gains, hydrogen still has not been 20 the prime energy resource that it is very active chemically and it is too difficult to find it 21 in pure form in the nature. Which makes possible new research areas to investigators 22 so as to understand the nature of Hydrogen energy storage and its capabilities. That 23 means more important than ever to look for molecules or compounds that can able to 24 bond with hydrogen.[1-3] Furthermore the high energy ratio of hydrogen per unit mass 25 is among the other reasons for this. In addition to, it has a wide range of usage due to 26 next-generation solar cells and gravimetric hydrogen storage capacity. [4][5][6] 27 Firstly, Vajeeston et al. has been reported MBeH 3 (M=Li, Na, K, Rb, Cs) compounds 28 and that study contains phase stability of present compounds. Which was represented 29 mechanical properties such as Wyckoff position and Bulk Modulus(B 0 ), electronic proper-30 ties such as band structure and charge density as well as estimated gravimetric hydrogen 31 storage capacity of a monoclinic structure of RbBeH 3 using VASP in this study. Also 32 that parameter plays an important role in determining crystal structure as well [7]. In compound is stable in different structures [8]. 36 Shinzato et al. have analyzed chemical bonding with depend on energy density anal-37 ysis for RbCaH 3 compound [9]. Gheboli et al., was contributed to by calculate structural, 38 elastic, electronic and optical properties under pressure for the same compound [10]. Both 39 works were done using CASTEP code. Another study, Vajeeston et  properties such band structure and charge density as well as vibrational properties of 42 cubic structure of RbCaH 3 using VASP in this study [11]. As for Lamichhane et al., 43 structural and electronic properties of RbCaH 3 compound have been investigated via 44 TB-LMTO-ASA program based on local density approximation [12]. RbCaH 3 compound, 45 one of the components of this finding, has been largely-studied compound in literature. 46 Gingl et al., has synthesized hexagonal structure of RbMgH 3 compound experimentally 47 by sintering stoichiometric mixtures of binary hydrides at 675°K, 200 bar H 2 for 10 days 48 [13].

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In this study, structural, elastic, electronic and vibrational properties of the Per-

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The DFT calculations of RbXH 3 (X=Be, Ca, Mg) Perovskite type hydrides has been 55 carried out Vienna Ab-initio Simulation Package (VASP) [15]. VESTA [16] software was 56 used to visualize these structures. The electron-ion interaction with cut-off Energy 57 of 700 eV was taken up with the projector augmented wave (PAW) [17,18] method.

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The Generalized Gradient Approximation (GGA) with Perdew-Burke-Ernzherhof (PBE) 59 [19]functional was decided upon for the exchange and correlation terms in electron-60 electron interaction. 61 Kpoints sampling has been applied Gamma-centered 16x16x16 kpoints with a  The stress-strain method have been used for elastic constant calculation and during 68 that calculations have been performed by setting IBRION = 6 and ISIF = 3 implemented in 69 VASP. To get an anisotropic elastic properties of compounds have been used ELATE [21] 70 program which is an open-source software was complied from EIAM code [22].The 71 electron configuration has been approved of 4s 2 4p 6 5s 1 for Rb atom, 2s 2 2p 0 for Be atom, 72 3s 2 3p 6 4s 2 for Ca atom, 2p 6 3s 2 for Mg atom and 1s 1 for H atom.

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The lattice dynamical properties of RbXH 3 compounds were investigated linear 74 response method through Phonopy [23] software whose method has been depended on 75 density functional perturbation theory (DFPT) [24]. The phonon dispersion curves and 76 density of states of RbXH 3 compounds were plotted using Phonopy, in which the their 77 unit cell of compounds has been expanded 2x2x2. Thermal properties has been plotted 78 for each compound. For calculations of lattice dynamical properties of these compounds, 79 the ENCUT value has been chosen 500 eV for each compound.    bulk modulus and derivative of bulk modulus with the other theoretical work is also 112 seen in Table 1.

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The formation enthalpy has been calculated using Eq. 1.
where, E  respectively. As is seen Figure 2A, RbBeH 3 have been evaluated within this study, but 122 it is seen that the present compound is unstable due to soft mode. That's why, the 123 fundamental properties of RbBeH 3 will be presented in order not to go out of the subject 124 and to contribute to the literature.

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Depended on Phonon dispersion curves of these atoms, it can be said that RbBeH 3 126 is the no stable as dynamical since there was discovered soft mode, but the other two are and around 0-40 THz for RbCaH 3 , respectively. As is seen these figures, it is clearly seen that the phonon band is split in two. This situation is a widely and expected result of 131 ma-terials with semiconductor behaviour. In two separate regions, acoustic and optic 132 braches have been meshed for each compound.

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Because RbBeH 3 has soft mode, it is unstable dynamically. For RbMgH 3 As is seen Table 2., since C 11 value is higher than C 44 value for each compound, our The directionality of any compound, i.e., the degree of anisotropy, is defined by the 154 elastic anisotropy factor given by the formula for cubic crystals in Eq. 5, which is also 155 known as the Universal Elastic Anisotropy Index (A U ) [27]. This value is 0 for isotropic 156 crystals. A greater A U value shows directionality of the compound.

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In this study, bulk, shear, Young's modulus and Poissons's Ratio have been calculated 158 using Voigh-Reuss-Hill (VRH) approximation and and it is given by Eq. 6 and 7, respec-159 tively as well as calculated results is listed in Table 2.
In addition to that parameters the other parameters such as Kleinman parameter, There are many suggestions in the literature to predict whether a material ductile or 172 brittle. The most common of these is look at the B/G ratio.  values are below the super hardness limit as 40 GPa.
In Eq. 13, h is Planck constant, k b is Boltzmann constant, r is a density, n is the number of    Table 3 as well as their visualizations are viewed 225 in Figure 3 to be represented by Figure 3A linear compressibility, Figure 3B Poisson's Ra-226 tio, Figure 3C Shear Modulus and Figure 3D Young's Modulus of RbCaH 3 , respectively.

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Following visualizations presented belong to RbCaH 3 . Others are similar and it is also 228 shown in Appendix A, Figure 1 and 2. As is known, the Poisson's Ratio is a measure of the distortion of a material. The 230 maximum value is 0.5 while the minimum value of the Poisson's Ratio is -1. Since the 231 maximum Poisson's Ratio value (n max ) of RbBeH 3 falls outside that limit, it is thought 232 that the deformation will be permanent for this material. Also, these results shown that 233 high pressure, investigate is required for this material.

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For the thermal properties of these compounds, it was used in quasi-harmonic 250 approximation to determined of their thermodynamic properties such as Helmholtz free 251 energy, enthalpy, entropy, and constant volume heat capacity in 0 to 2000°K temperature 252 range for RbMgH 3 and RbCaH 3 . Figure 6A and Figure   Eq. 14, C wt% decreases as X increases since C wt% depends on the atomic mass of X and  investigate is the first study of presented these values. As for the other two, to the best 300 our knowledge, this work is the first study of these compounds.

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Calculated values of gravimetric hydrogen storage capacities are between 1.325 302 and 1.165 wt%, here the highest value belong to RMgH 3 , the lowest one is RbCaH 3 .

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These calculated capacities can be made a sensation about the potential of hydrogen 304 applications and to possible uses. As for anisotropic properties of these compounds, 305 thanks to elate, it has been determined to anisotropic properties of these molecules.

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When it investigated to their anisotropic properties, Poisson Ratio of RbBeH 3 stands out 307 dramatically. Since that value is outside -1 to 0.5, it can be mentioned that deformation 308 will be permanent for this material.

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The electronic properties of these compounds are found to be semiconductor behavi- and RbMgH 3 is thought to be mainly over the p-band, RbCaH 3 is thought to be over the 314 mainly d-band.

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The vibrational properties, RbBeH 3 was unstable due to soft mode and the other 316 two was stable.

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As can be understood phonon dispersion curves and corresponding density of 318 states, Rb is dominant between 0-5 THz frequencies, Be atom is dominant at 5-15 319 THz and H atom is dominant between 20-30 THz for RbBeH 3