Structural phase stability, electronic structure and mechanical properties of alkali metal hydrides AMH4 (A=Li, Na; M=B, AL)

Author’s Accepted Manuscript Structural phase stability, electronic structure and mechanical properties of alkali metal hydrides AMH4 (A=Li, Na; M=B, AL) M. Santhosh, R. Rajeswarapalanichamy www.elsevier.com/locate/jpcs

PII: DOI: Reference:

S0022-3697(15)30066-4 http://dx.doi.org/10.1016/j.jpcs.2015.09.013 PCS7638

To appear in: Journal of Physical and Chemistry of Solids Received date: 8 March 2015 Revised date: 10 September 2015 Accepted date: 26 September 2015 Cite this article as: M. Santhosh and R. Rajeswarapalanichamy, Structural phase stability, electronic structure and mechanical properties of alkali metal hydrides AMH4 (A=Li, Na; M=B, AL), Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2015.09.013 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Structural phase stability, Electronic structure and Mechanical properties of Alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) M. Santhosha, and R. Rajeswarapalanichamya* a

N.M.S.S. Vellaichamy Nadar College, Madurai, Tamilnadu-625019, India.

Abstract The structural stability of Alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) is analyzed among the various crystal structures, namely hexagonal (P63mc), tetragonal (P42/nmc), tetragonal (P421c), tetragonal (I41/a), orthorhombic (Pnma) and monoclinic (P21/c). It is observed that, orthorhombic (Pnma) phase is the most stable structure for LiBH4, monoclinic (P21/c) for LiAlH4, tetragonal (P42/nmc) for NaBH4 and tetragonal (I41/a) for NaAlH4 respectively at normal pressure. Pressure induced structural phase transitions are observed in LiBH4, LiAlH4, NaBH4 and NaAlH4 at the pressures of 4 GPa, 36.1 GPa, 26.5 GPa and 46 GPa respectively. The electronic structure reveals that these metal hydrides are wide band gap insulators. The calculated elastic constants indicate that these metal hydrides are mechanically stable at normal pressure.

Keywords: C. Ab-initio calculations; D. Crystal structure; D. Electronic structure; D. Mechanical properties. PACS No.: 31.15.A- , 61.50 Nw, 31.15.ae, 62.20.-x

*Corresponding author; E-mail: [email protected] Address: Department of Physics, N.M.S.S.V.N College, Madurai, Tamilnadu-625019, India. Phone: 0452-2459187 Fax: 0452-2458358

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1. INTRODUCTION The alkali metal hydrides are considered as promising materials for hydrogen storage [1, 2]. The alanates and borohydrides of alkali and alkaline-earth metals are widely studied because of their light weight and high hydrogen content. The mechanisms of reverse hydrogen storage at the interface LiBH4/MgH2/graphite were investigated [3]. A high degree of structural and compositional dynamics was observed in the LiBH4 – LiCl system as a function of temperature and time [4]. Ikeshoji et al. [5] have explained the problems in the structural analysis using first principles molecular dynamics (FPMD) calculation. Li et al. [6] reviewed the synthesis and structure dynamics of intermetallic compounds of LiBH4. Yao et al. [7] investigated the high pressure phase transformations using first principles calculation and they reported that I41/acd structure is the most stable for LiBH4. Structural phase transition properties of the LiBH4 + x LiI (x = 0 – 1.00) pseudo binary system were examined by powder x-ray diffraction and differential scanning calorimetry combined with density functional theory calculations [8]. Miyazaki et al. [9] investigated the effect of addition of LiI to LiBH4. The low temperature crystal structures of the ABH4 (A = Li-Cs) series have been investigated by Vajeeston et al. [10]. George et al. [11] reviewed the structural stability of metal hydrides, alanates, borohydrides of alkali and alkalineearth metals. Skipov et al. [12] reviewed the recent progress in the nuclear magnetic resonance studies of atomic motion in metal borohydrides. The structural stability of alkali borohydrides MBH4 (M = K, Rb, Cs) have been investigated by X-ray and neutron powder diffraction methods [13]. Kang et al. [14] investigated the crystal structures and dehydrogenation reaction mechanism in the intermediate phases of LiAl hydride systems. The electronic structure of alkali aluminum and alkali gallium tetrahydrides was systematically investigated using ab initio calculations [15]. The pressure-temperature phase relation in complex metal hydrides was reported by Sundqvist 2

[16]. The stability of complex hydrides NaBH4, NaAlH4 and Na3AlH6 was analyzed [17]. Huan et al. [18] discovered a large number of the low energy structures for LiAlH4 and they found that P21/c structure has the lowest energy. The phase transformations in pure LiAlH4 under pressure have been studied using Raman spectroscopy [19]. Damian et al. [20] carried out the inelastic neutron scattering experiments on NaBH4 and KBH4. Nakamori et al. [21] investigated the thermodynamical stabilities of metal borohydrides M (BH4)n (M = Li, Na, K, Cu, Mg, Zn, Sc, Zr, and Hf; n = 1-4). Kawashima et al. [22] investigated the quadrupole hyperfine structure of NaBH4 and KBH4. Herbst et al. [23] investigated the elastic properties of alkali gallium hydrides AGaH4 (A = Li, Na, K, Rb and Cs). The crystal and electronic structures of the alkali aluminum and alkali gallium tetrahydrides (ABH4; A = Li, Na, K, Rb and Cs; B = Al or Ga) were analyzed by Vajeeston et al. [24]. The structural stability of RbBH4 was analysed by using high pressure synchrotron powder X-ray diffraction and Raman techniques [25]. To the best of our knowledge, the mechanical properties of alkali complex metal hydrides are not yet reported. In this work, the structural stability, electronic structure and mechanical properties of alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) are investigated for six different crystal structures namely hexagonal (P63mc), tetragonal (P42/nmc), tetragonal (P-421c), tetragonal (I41/a), orthorhombic (Pnma) and monoclinic (P21/c) phases under normal and high pressures. 2. COMPUTATIONAL DETAILS The ab initio calculations are performed using density functional theory within the generalized gradient approximation (GGA) [26-28] as implemented in the VASP code [29–31]. The interaction between the ion and electron is described by the projector augmented wave method [27]. Ground state geometries are determined by minimizing stresses and Hellman– 3

Feynman forces using conjugate-gradient algorithm with force convergence less than 10-3 eV Å-1 and the Brillouin zone integration is performed with a Gaussian broadening of 0.1 eV. The Khon-Sham orbitals are expanded using the plane wave energy cutoff of 420 eV. The Brillouin zone integrations are carried out using Monkhorst–Pack K-point mesh [32] with a grid size of 4x4x4 for the total energy calculation. The valence electron configurations are Li 2s1, Na 3s1, B 2s2 2p1, Al 3s2 3p1 and H 1s1 atoms. The crystal structures for the considered phases of Alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) are shown in Fig.1. 3. RESULTS AND DISCUSSION 3.1 Structural stability and ground state properties The structural stability is analyzed among the various crystal structures, namely hexagonal (P63mc), orthorhombic (Pnma) and tetragonal (P42/nmc) for LiBH4. For LiAlH4 and NaAlH4, tetragonal (I41/a), orthorhombic (Pnma) and monoclinic (P21/c) structures are considered. For NaBH4, tetragonal (P42/nmc), tetragonal (P-421c) and monoclinic (P21/c) structures are considered. The total energies of LiBH4, LiAlH4, NaBH4 and NaAlH4 are computed for various phases as a function of cell volume and their plots are given in Fig. 2. It is observed that the most stable structure are orthorhombic (Pnma), monoclinic (P21/c), tetragonal (P42/nmc) and tetragonal (I41/a) for LiBH4, LiAlH4, NaBH4 and NaAlH4 respectively. The lattice constants are optimized by computing the total energy for various volumes. The volume corresponds to the minimum energy is called equilibrium volume. These data are then fitted to the universal second order Birch-Murnaghnan equation of state [33] to determine the bulk modulus B0 and its first derivative B0´ at normal pressure. At normal pressure LiBH4 crystallizes with an orthorhombic (space group Pnma) structure in which each [BH4]- anion is surrounded by 4

four lithium Li+ and each Li+ by four [BH4]- in tetrahedral geometry with Li-H distances of 1.213 Å. NaBH4 crystallizes with tetragonal (space group P42/nmc) structure in which each [BH4]anion is surrounded by four lithium Na+ in tetrahedral geometry with Na-H distances of 1.163 Å. LiAlH4 crystallizes in the monoclinic (space group P21/c) structure with the four formula units per unit cell. Four hydrogen atoms are arranged around aluminium in an almost regular tetrahedral configuration. The structure consists of [AlH4]- units well separated by Li+ ions with Li-H distances of 1.749 Å. At normal pressure, NaAlH4 crystallizes in the tetragonal (space group I41/a) structure. [AlH4]- anion has compressed tetrahedral geometry with Al-H distances of 1.741 Å. The Na+ cation has 8 nearest [H] neighbours. The cohesive energy (Ecoh) determines the strength of the binding between the constituent atoms in a solid. The cohesive energy of the solid is the difference between the total energy per atom of the bulk material at normal pressure and the atomic energies of the atoms belonging to the unit cell of the material:

E AMH4  [E A coh

atom

 EM

atom

 4E H

atom

 E AMH4 ]

(1)

total

where E AMH4 (A = Li, Na; M = B, Al) is the total energy of the compound at the equilibrium total

lattice constant and E A

atom

, EM

atom

and E H

atom

are the atomic energies of the pure constituent

atoms. The formation enthalpy is calculated using the formula

H  E AMH4  E A total

total

 E M  2E H2 total

total

(2)

The calculated cohesive energies and formation enthalpies for AMH4 (A = Li, Na; M = B, Al) are given in Table 1. It is observed that, NaBH4 is found to be the most stable one among the considered hydrides owing to its highest cohesive energy value. The negative formation enthalpies indicate that these hydrides can be easily synthesized at normal pressure. The 5

calculated ground state properties like cell volume V0 (Å3), lattice constants a, b and c (Å), angle β, valence electron density ρ (electrons/ Å3), cohesive energy Ecoh (eV), formation enthalpy ΔH (eV), bulk modulus B0 (GPa) and its derivative Bo´ for the considered phases of alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) using GGA are listed in Table 1 along with the experimental and other available theoretical results [3, 4, 10, 15, 17, 21, 24, 34-40]. The bond distance between metal and hydrogen of alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) for considered structures are given in Table 2. It is found that our calculated lattice constant and bond distance values are in good agreement with the available theoretical [4] and experimental data [34]. The calculated bulk modulus values of orthorhombic (Pnma) phase of LiBH4 and tetragonal (P42/nmc) phase of NaBH4 are in agreement with the result of Vajeeston et al. [10]. Similarly, the bulk modulus value of monoclinic (P21/c) phase of LiAlH4 and tetragonal (I41/a) phase of NaAlH4 are in agreement with the result of Vajeeston et al. [15]. 3.2 Structural phase transition. The enthalpy values are calculated for various pressures by using the formula H = E + PV

(3)

The computed enthalpy values are plotted against pressure in Fig. 3. A structural phase transition from orthorhombic (Pnma) to hexagonal (P63mc) phase is predicted at the pressure of 4 GPa in LiBH4, monoclinic (P21/c) to tetragonal (I41/a) phase is predicted at the pressure of 36.1 GPa in LiAlH4. On further increasing the pressure, tetragonal (I41/a) to orthorhombic (Pnma) phase transition is predicted at the pressure of 76 GPa for LiAlH4. In case of NaBH4, tetragonal (P42/nmc) to tetragonal (P-421c) phase transition is predicted at the pressure of 26.5 GPa and 6

tetragonal (I41/a) to orthorhombic (Pnma) phase transition is predicted at the pressure of 46 GPa in NaAlH4. The structural phase transition is also confirmed by plotting the pressure against cell volume for alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) in Fig. 4 and similar transition pressure values are observed. The pressure dependence of the A-H (A = Li, Na) and M-H (M = B, Al) bond distances for alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) and are given in Fig. 5. It is seen that, when pressure is applied the BH4 and AlH4 units remain essentially undistorted. Therefore, the reduction of the unit-cell size should be mainly associated to the compression of the A (A = Li, Na) cation. 3.3 Electronic structure The electronic structures of alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) are investigated by computing the total and partial density of states (DOS) with stable structures. The total and partial density of states (DOS) of AMH4 (A = Li, Na; M = B, Al) are given in Fig. 6. It is observed that all these compounds exhibit insulating behavior with band gap of 6.59 eV, 4.34 eV, 5.09 eV and 4.39 eV for LiBH4, LiAlH4, NaBH4 and NaAlH4 respectively. The peak emerging in the lower energy region of the DOS curve mainly originates from the s-state of M atoms (M = B, Al) with small contribution from H-s state. The valence state is mainly composed of strongly hybridized non-metal s and metal-s states, indicating a strong covalent interaction between metal and the hydrogen. The energy region just above the Fermi level is dominated by M-s, p (M= B, Al) state. Near the the Fermi level the broad peaks are due to the large contribution of H-s state electrons. Thus, hydrogen can be easily released without excessive heating and these materials can be used as hydrogen storage materials. 3.4 Mechanical properties 7

The elastic constants for alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) in their stable phases are determined using total energy method. The energy of a strained system [41] can be expressed in terms of the elastic constants Cij as:

 

6  V  6 E (V, ε i )  E (V0 , 0)  V0  σi ei  0   Cij ei e j   O e3i  2  i, j1 i 1 

(4)

where V0 is the volume of the unstrained lattice, E(V0, 0) is the total minimum energy at this unstrained volume of the crystal and V is the new volume of the lattice due to strain tensor. The elasticity tensor has six independent components (C11, C33, C44, C66, C12 and C13) for tetragonal crystals, nine (C11, C22, C33, C44, C55, C66, C12, C13 and C23) for orthorhombic crystals and thirteen (C11, C22, C33, C44, C55, C66, C12, C13, C23, C15, C25, C35 and C46) for monoclinic crystals. A proper choice of the set of strains {ei, i = 1, 2,.......,6}, in Eq. (4) leads to a parabolic relationship between ΔE/V0 and the chosen strain [42]. For each lattice structure of AMH4 (A = Li, Na; M = B, Al), the lattice was strained by 0%, ±1%, and ±2% to obtain their total minimum energies E (V). These energies and strains were fitted with the corresponding parabolic equations of ΔE/V0 to yield the required second-order elastic constants. The computed elastic constants Cij are given in Table 3. The Born-Huang elastic stability criteria [43] for different crystal structures are as given below: for tetragonal crystals: C11 > 0, C33 > 0, C44 > 0, C66 > 0, (C11 – 2C12) > 0, (C11 + C33 – 2C13) > 0, [2 (C11 + 2C12) + C33 + 4C13] > 0,

(5)

for orthorhombic crystals: C11 > 0, C22 > 0, C33 > 0, C44 > 0, C55 > 0, C66 > 0, 8

[C11 + C22 – C33 + 2 (C12 + C13 + C23)] > 0, (C11 + C22 – 2C12) > 0, (C11 + C33 – 2C13) > 0, (C22 + C33 – 2C23) > 0,

(6)

and for monoclinic crystals: C11 > 0, C22 > 0, C33 > 0, C44 > 0, C55 > 0, C66 > 0, 2 [C11 + C22 + C33 + 2 (C12 + C13 + C23)] > 0, (C33 C55 – C35 ) > 0, (C44 C66 – C246 ) > 0, 2 (C22 + C33 + 2C23) > 0, [(C22 (C33 C55 – C35 ) + 2C23 C25 C35 C223 – C55 – C225 C33] > 0,

{2 [C15 C25 (C33 C12 – C13 C23) + C15 C35 (C22 C13 – C12 C23) + C25 C35 (C11 C23 – C12 C13)] 2 2 2 2 – [ C15 (C22 C33 – C223 ) + C225 (C11 C33 – C13 ) + C35 (C11 C22 – C12 )] + C55 g} > 0.

(7)

where 2 2 g = C11 C22 C33 – C11 C223 – C22 C13 – C33 C12 + 2C12 C13 C23

(8)

From Table 3, it is clearly seen that the elastic constants for alkali metal hydrides LiBH4, LiAlH4, NaBH4 and NaAlH4 satisfy Born-Huang criteria suggesting that all are mechanically stable. From the calculated Cij values, the bulk modulus and shear modulus for the tetragonal, orthorhombic and monoclinic crystals are determined using the Voigt-Reuss-Hill (VRH) averaging scheme [44-46]. The computed bulk modulus (B), Young’s modulus (E), shear modulus (G), Poisson’s ratio (ν) and micro hardness parameter (H) [47] values of alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) using the elastic constants (Cij) are given in Table 4. From Table 1 and Table 4, it is found that the bulk modulus values obtained from the EOS fit are close to the values calculated using the elastic constants. Materials with high B and G are likely to be hard materials. The bulk modulus and rigidity modulus values of AMH4 (A = Li, Na; M = B, Al) are low and hence these materials are not hard materials. Young’s modulus is a measure of stiffness 9

of a solid, i.e., larger the value of Young’s modulus, stiffer is the material. The computed results indicate that NaBH4 is stiff among the four metal hydrides. The Poisson’s ratio is small (=0.1) for covalent materials, whereas it is greater than or equal to 0.25 [48] for ionic materials. Among these hydrides, the poisson’s ratio of LiAlH4 is the lowest, indicating that the Li-Al-H bonding is more directional in nature. The ratio of bulk modulus to shear modulus (B/G) is used to estimate the brittle or ductile behavior of materials. A high B/G value is associated with ductility, while a low B/G value corresponds to the brittle nature. The critical value which separates ductile and brittle materials is about 1.75. The calculated B/G values predict that AMH4 (A = Li, Na; M = B, Al) are brittle in nature. The relation between bulk and shear moduli for covalent and ionic materials are G ≈ 1.1B and G ≈ 0.8B, respectively [49]. Our calculated value of G/B is nearer to 0.8, this result strongly supports the ionic contribution to inter atomic bonding. The calculated H values indicate that NaBH4 is hard among the considered metal hydrides. The variation of elastic constants (Cij) with pressure for AMH4 (A = Li, Na; M = B, Al) is shown in Fig. 7. It is seen that the elastic constants C11, C13, C44 and C66 increase monotonically with increase in pressure. It is noticed that C33 and C12 increases rapidly with pressure. The elastic constant C11 represents the elasticity in length. A longitudinal strain produces a change in C11. The elastic constants C12 and C44 are related to the elasticity in shape, which is a shear constant. A transverse strain causes change in shape without change in volume. It is also observed that the pressure has an important influence on Young’s modulus, bulk modulus and shear modulus.

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3.5 Debye temperature The Debye temperature (θD) is an important parameter related to the thermal characteristics of materials, which correlates many physical properties of materials, such as specific heat, elastic constants and melting temperature [50]. The Debye temperature is defined in terms of the mean sound velocity vm and gives explicit information about the lattice vibrations and it is calculated using the equation [51]:

θD 

1/3   2 NA ρ  n vm 6π M  kB 

(9)

with  = h/2π, h is Planck’s constant, kB is Boltzman’s constant, NA is the Avogadro’s number, ρ is density, M is molecular weight, n is the number of atoms in the molecule and  1  2 1  v m       3  v3t v3l 

- 1/3

(10)

where 1/2   B  0.75 G     vl    ρ  

(11)

and

1/2 G    vt   ρ

(12)

are the velocities of longitudinal and transverse sound waves respectively. The computed density, velocities and Debye temperature for alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) at ambient condition are listed in Table 5. The high value of the Debye temperature for

11

LiBH4 implies that its thermal conductivity is more when compared with other hydrides considered. 3.6 volumetric and gravimetric hydrogen content in AMH4 (A = Li, Na; M = B, Al) Hydrogen fuel, which can be readily produced from renewable energy sources, contains at least three times larger chemical energy per mass 142 MJ Kg than any chemical fuel, thus making a hydrogen fuel cell an attractive alternative to the internal combustion engine for transportation [52]. The density of H/unit cell and the weight % of hydrogen for AMH4 (A = Li, Na; M = B, Al) are given in Table 6. It is seen that the weight percentage of hydrogen is higher in LiBH4 compared to other hydrides. 4. CONCLUSION The structural, electronic and mechanical properties of alkali metal hydrides AMH4 (A = Li, Na; M = B, Al) are investigated. The calculated ground state properties are in good agreement with the experimental and other available theoretical results. A pressure induced structural phase transition is predicted in LiBH4, LiAlH4, NaBH4 and NaAlH4 respectively. The density of states of AMH4 (A = Li, Na; M = B, Al) confirm that these metal hydrides are wide band gap insulators. The computed elastic constants obey the necessary mechanical stability condition suggesting that all these metal hydrides are mechanically stable. Acknowledgement The support received from the college management is greatly acknowledged.

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Figure 1. Crystal structures of (a) P63mc, (b) P42/nmc, (c) P-421c, (d) I41/a, (e) Pnma and (f) P21/c for AMH4 (A = Li, Na; M = B, Al). Figure 2. Total energy (in eV) versus cell volume (Å3) for the different structures of (a) LiBH4, (b) LiAlH4, (c) NaBH4 and (d) NaAlH4. Figure 3. Enthalpy versus pressure curve of (a) LiBH4, (b) LiAlH4, (c) NaBH4 and (d) NaAlH4. Figure 4. Cell volume versus pressure curve of (a) LiBH4, (b) LiAlH4, (c) NaBH4 and (d) NaAlH4. Figure 5. The pressure dependence of the A-H (A = Li, Na) and M-H (M = B, Al) distances for alkali metal hydrides Figure 6. Total and partial density of states (DOS) of (a) LiBH4, (b) LiAlH4, (c) NaBH4 and (d) NaAlH4. Figure 7. Variation of elastic constants Cij of (a) LiBH4, (b) LiAlH4, (c) NaBH4 and (d) NaAlH4 with pressures. Figure 1

16

Figure 2

17

Figure 3

18

Figure 4

19

Figure 5

Figure 6

Figure 7

20

Fig 7

TABLE CAPTIONS

21

Table 1 Calculated equilibrium volume V0 (Å3), lattice parameters a, b and c (Å), angle β, valence electron density ρ (electrons/ Å3), cohesive energy Ecoh(eV), formation enthalpy ΔH (eV), bulk modulus B0 (Gpa) and its derivative B0' for LiBH4, LiAlH4, NaBH4 and NaAlH4. Table 2 Calculated bond distance M-H1, M-H2 and M-H3 (M = B, Al) for considered phases of alkali metal hydrides. Table 3 Calculated elastic constants Cij (GPa) of AMH4 (A = Li, Na; M = B, Al) for their stable phases. Table 4 Calculated bulk modulus B (GPa), shear modulus G (GPa), Young’s modulus E (GPa), Poisson’s ratio ν, B/G ratio, G/B ratio and micro hardness parameter (H) of AMH4 (A = Li, Na; M = B, Al) for stable phases. Table 5 Calculated molecular mass M (g/mol), density ρ (g/cm3), longitudinal vl (m/s), transverse vt (m/s), average elastic wave velocity vm (m/s) and Debye temperature θD (K) of AMH4 (A = Li, Na; M = B, Al) for stable phases. Table 6 Calculated volumetric (g/cm3) and gravimetric hydrogen contents for AMH4 (A = Li, Na; M = B, Al).

Table 1 22

a b c β ρ Ecoh ΔH B0 4.262 4.262 6.916 0.1138 14.418 -1391.179 20.59 4.216b 4.216b 6.291b 20.8d c c c 4.267 4.267 6.922 4.1956d 4.1956d 6.6013d 4.2763e 4.2763e 6.9484e Pnma 208.90 7.3241 4.3961 6.5727 0.0777 13.367 -1289.719 15.19 b a a a 208.40 7.1785 4.4368 6.8031 15.3d 209.4c 7.328b 4.379b 6.494b c 7.121 4.406c 6.674c 7.3635d 4.3982d 6.5965d P42/nmc 67.73 4.1317 4.1317 5.5992 0.1181 16.986 -1638.899 8.51 d d d 4.1674 4.1674 5.6406 8.6d I41/a 64.54 3.853 3.853 8.697 0.1239 9.3832 -905.3409 13.62 Pnma 228.42 6.471 5.229 6.597 0.0350 7.4885 -722.5302 10.19 P21/c 254.96 4.8426 7.7981 7.9032 111.79 0.0314 9.3245 -899.6772 12.21 4.8535g 7.8259g 7.8419g 111.878g 12.95g 4.8174h 7.8020h 7.8214h 112.228h 4.79j 7.75j 7.79j 111.15j 4.845k 7.826k 7.917k 112.5k P42/nmc 72.12 4.3261 4.3261 5.9261 0.1109 17.847 -1721.981 21.14 d d d 4.3452 4.3452 5.8597 20.1d f f f 4.3320 4.3320 5.869 4.339m 4.339m 5.949m P421c 112.26 4.3516 4.3516 5.8891 0.0712 17.068 -1646.811 7.99 d d d 4.3464 4.3464 5.8620 7.8d P21/c 153.46 3.989 6.432 6.445 111.82 0.0521 16.275 -1570.298 12.29 I41/a 102.76 4.9971 4.9971 11.237 0.0778 10.149 -979.1933 19.02 4.9965g 4.9965g 11.0828g 19.31g i i i 4.9801 4.9801 11.1483 13.13n 4.99j 4.99j 11.22j l l 5.02 5.02 11.33l n n 5.442 5.442 12.661n Pnma 86.54 4.682 3.872 4.774 0.0924 6.519 -628.988 10.39 P21/c 217.59 4.482 7.226 7.241 112.01 0.0367 8.906 -859.298 8.72 a Ref [3] Theo, bRef [4] Theo, cRef [33] Exp, dRef [10] Theo, eRef [34] Exp, fRef [35] Exp, g Ref [15] Theo, hRef [36] Exp,, iRef [37] Theo, jRef [17] Theo, kRef [38] Exp, lRef [39] Exp, m Ref [21] Theo, nRef [24] Theo.

Hydrides Phase LiBH4 P63mc

LiAlH4

NaBH4

NaAlH4

Vo 108.9 96.8b 109.1c

Table 2 23

B0' 4.431 4.4d

3.862 3.9d

5.63 5.8d 4.63 5.356 4.432 4.10g

4.752 4.5d

5.536 5.4d 5.825 4.491 4.77g 5.06n

6.412 5.336

Hydrides Phase LiBH4 P63mc

M-H1 M-H2 0.969 1.031 0.962a 1.204a 1.220b 1.223b Pnma 1.213 1.226 a 1.213 1.224a 1.230b 1.233b P42/nmc 1.169 1.295 LiAlH4 I41/a 1.749 1.338 Pnma 1.219 1.246 P21/c 1.636 1.636 NaBH4 P42/nmc 1.163 1.291 P421c 1.227 1.227 P21/c 1.627 1.627 NaAlH4 I41/a 1.741 1.336 Pnma 1.220 1.243 P21/c 1.639 1.639 a Ref [34] Exp, bRef [4] Theo.

M-H3 1.031 1.204a 1.223b 1.207 1.208a 1.229b 2.374 1.338 1.211 1.648 2.296 2.163 1.636 1.336 1.209 1.649

Table 3 Hydrides LiBH4 LiAlH4 NaBH4 NaAlH4

Phase Pnma P21/c P42/nmc I41/a

C11 C22 42.02 20.99 8.78 10.56 48.25 46.83

C33 54.43 5.04 68.11 48.54

C44 C55 14.13 26.71 9.52 5.14 12.34 19.61

C66 16.96 5.74 11.83 16.88

C12 10.46 12.94 12.99 19.74

C13 C23 C15 C25 C35 C46 12.02 17.96 11.92 9.4 5.24 3.98 2.98 8.42 12.47 15.35

Table 4 Hydrides LiBH4 LiAlH4 NaBH4 NaAlH4

Phase Pnma P21/c P42/nmc I41/a

B 15.36 12.32 20.71 20.62

G 16.69 10.16 22.16 19.06

B/G 0.920 1.212 0.934 1.082

Table 5 24

G/B 1.087 0.824 1.070 0.924

E 39.97 22.94 52.21 44.19

ν 0.1975 0.1294 0.1750 0.1593

H 3.365 2.509 4.813 4.329

Hydrides LiBH4 LiAlH4 NaBH4 NaAlH4

M (g/mol) 21.784 37.955 37.833 54.001

ρ (g/cm3) 178.22 247.12 870.74 872.34

vl (m/s) 9861 9627 8037 7342

vt (m/s) 9677 6412 5044 4674

vm (m/s) 9968 7028 5554 5138

θD (K) 883 722 699 593

Table 6 Hydrides LiBH4 LiAlH4 NaBH4 NaAlH4

Volumetric H (g/cm3) 0.0925 0.0656 0.0826 0.0418

Gravimetric H (wt %) 18.39 10.55 10.58 7.41

Research Highlights ► Ground state properties of AMH4 (A = Li, Na; M = B, Al, Ga) are investigated. ► A structural stability is analyzed under high pressure. ► Electronic structure reveals that these materials exhibit insulating behavior. ► Computed elastic moduli obey traditional mechanical stability condition. ► Among these materials NaBH4 is found to be relatively hard material.

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