Structural, electronic and elastic properties of alkali hydrides (MH: M = Li, Na, K, Rb, Cs): Ab initio study

Computational Materials Science 84 (2014) 206–216

Contents lists available at ScienceDirect

Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci

Structural, electronic and elastic properties of alkali hydrides (MH: M = Li, Na, K, Rb, Cs): Ab initio study G. Sudha Priyanga a, A.T. Asvini Meenaatci a, R. Rajeswara Palanichamy a,⇑, K. Iyakutti b a b

Department of Physics, N.M.S.S.V.N. College, Madurai, Tamil Nadu 625019, India Department of Physics & Nanotechnology, SRM University, Chennai, Tamil Nadu 603203, India

a r t i c l e

i n f o

Article history: Received 1 August 2013 Received in revised form 27 November 2013 Accepted 3 December 2013 Available online 31 December 2013 Keywords: Ab initio calculations High pressure Structural phase transition Electronic structure Elastic property

a b s t r a c t The structural, electronic and elastic properties of alkali metal hydrides (MH: M = Li, Na, K, Rb, Cs) are investigated by first principles calculation using the Vienna ab initio simulation package. The lattice constants, bulk modulus and the density of states are obtained. The calculated lattice parameters are in good agreement with the available results. A structural phase transition from NaCl to CsCl phase is predicted under high pressure. The electronic structure reveals that these materials are non-metallic at normal pressure. The computed elastic constants indicate that these hydrides are mechanically stable at ambient pressure. The calculated Debye temperature values are in good agreement with experimental results. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction

2. Computational details

The metal-hydrogen systems have received wide attention due to their large number of technical applications [1]. The metal hydrides are potential materials for portable fuel cell applications [2]. Perrot [3] predicted a structural phase transition from NaCl (B1) to CsCl (B2) phase for LiH at a pressure of 200 GPa. Loubeyre [4] investigated the various physical properties of LiH and LiD under high pressure using single crystal X-ray diffraction method. With the development of the high pressure experimental techniques, investigations of structural phase transition, insulator–metal transition and superconducting transition under pressure were widely carried out [5,6]. The X-ray experimental study [7] showed that LiH, NaH, KH, RbH and CsH crystallize with the rock salt (B1) structure at room temperature. A structural phase transition from NaCl to CsCl phase was observed in CsH [8], NaH [9] and KH, RbH [10] at high pressure. To the best of our knowledge the electronic and elastic properties of the high pressure phase (CsCl) of alkali hydrides are not yet reported. In the present work, we have investigated the structural phase transition, density of states (DOS), and elastic properties of the alkali hydrides MH (M = Li, Na, K, Rb, Cs) in both NaCl and CsCl phases, under normal and high pressures.

The total energy calculations are performed in the frame work of density functional theory as implemented in the VASP code [11–13]. Both the local density approximation (LDA) [14] and generalized gradient approximation (GGA) [15–17], are used for the exchange and correlation. Ground state geometries are determined by minimizing stresses and Hellman–Feynman forces using the conjugate-gradient algorithm with force convergence less than 103eV Å1 and the Brillouin zone integration is performed with a Gaussian broadening of 0.1 eV. The cutoff energy for plane waves in our calculation is 400 eV. The valence electron configurations are Li 2s1, Na 3s1, K 4s1, Rb 5s1, Cs 6s1 and H 1s1 atoms. Brillouin zone integrations are performed on the Monkhorst–Pack K-point mesh [18] with a grid size of 12  12  12 for structural optimization and the total energy calculation. The unit cell structure of the proposed phases of alkali metal hydrides are shown in Fig. 1. The Murnaghan’s second order equation [19,20] is used to calculate accurate pressure corresponding to the desired volume and it is given as,

3 P ¼ B0 2

"  "  #)  5=3 # ( 7=3 2=3 V0 V0 3 0 V0  1 þ ðB0  4Þ  1 4 V V V ð1Þ

⇑ Corresponding author. Tel.: +91 0452 2459187; fax: +91 0452 2458358. E-mail address: [email protected] (R.R. Palanichamy). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.12.003

where P is the pressure, B0 and B00 are the bulk modulus and its first pressure derivative respectively. V/V0 = 1.0 is the primitive cell volume corresponding to normal pressure, where ‘V0’ is the volume

207

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

corresponding to normal pressure and ‘V’ is the volume for pressure P. This equation of state (EOS) has been found to give a good estimate of pressure values. Therefore, in this work, we have used the Murnaghan’s EOS formula for the pressure calculations. The total energy calculation is performed as a function of reduced volume (V/V0) which ranges from 1.0 to 0.4.

3. Results and discussion 3.1. Geometric properties of alkali hydrides The lattice constants for both NaCl and CsCl structures of alkali hydrides MH (M = Li, Na, K, Rb, Cs) are optimized and their total energies (per unit cell) are calculated. The calculated ground state properties like lattice constant a0 (Å), cell volume V0 (Å3), valence electron density q (electrons/ Å3), energy band gap Eg (eV), bond distance M–H (Å), bulk modulus B0 (GPa) and its derivative B00 for

Fig. 1. Unit cell for the NaCl and CsCl phases of alkali hydrides.

Table 1 Calculated lattice parameter a0 (Å), equilibrium volume V0 (Å3), valence electron density q (electrons/ Å3), energy gap Eg (eV), bond length M–H (Å), bulk modulus B0 (GPa), pressure derivative B00 for the alkali hydrides with NaCl structure. NaCl type a0

GGA LDA

V0

GGA LDA GGA LDA GGA LDA

q Eg

M–H B0

B00

a b

GGA LDA GGA LDA

GGA LDA

LiH

NaH

KH

RbH

CsH

4.0811 3.651 4.075[21]a, 4.084[22]a 4.069[23]a, 3.92[24]b 16.99 12.17 0.1177 0.164 4.6723 3.1 4.4[25]a, 9.2[26]a 3.31[27]a, 6.61[28]b 9.15[29]b, 4.92[32]b 4.99[30,31]a 4.64[32]b, 5.24[33]b 5.37[34]b 1.5801 1.5105 33 43.8 32.2[8]a, 32.3[37]b 40.5[38]b, 34.1[39]b 33.6[27]b, 40.5[40]b 34.24[23]a

4.8511 4.381 4.880[21]a 4.775[24]b 28.54 21.02 0.0700 0.0951 4.8560 4.501 1.52[28]b 3.46[35]b 5.68[34]b

5.7210 5.551 5.70[21]a 5.701[24]b 46.81 42.76 0.0427 0.0441 3.5992 3.21 3.203[35]b

5.9918 6.0611 6.037[21]a 6.199[24]b 53.78 55.67 0.0371 0.0359 3.0255 2.201 2.96[35]b

6.344 6.551 6.376[21]a, 6.38[8]a 6.407[24]b 63.83 70.29 0.0313 0.0284 2.4472 2.0 2.80[36]b

1.962 1.628 26 33.53 14.3[41]a, 19.4[9]a 29.6[24]b, 30.8[42]b 19.7[39]b, 27.4[38]b 23.5[36]b 22.8[32,34]b 3.62 3.81 4.40[9]a

1.9843 1.892 16 19.6 15.6[41]a 17.3[40]b 16.3[38]b

2.2004 1.95 14.1 15.34 10.0[41]a 14.7[40]b 14.1[39]b

2.01 1.92 12 11.18 7.6[41]a, 11.9[40]b 8.8[38]b, 8.0[8]a

2.955 3.61 4.00[10]a

2.8402 3.21

3.0365 2.95 4.00[44]a

4.9 4.2 3.95[43]a

Experimental estimates. Other theoretical findings.

Table 2 Calculated lattice parameter a0 (Å), equilibrium volume V0 (Å3), valence electron density q (electrons/Å3), energy gap Eg (eV), bond length M–H (Å), bulk modulus B0 (GPa), pressure derivative B00 for the alkali hydrides with CsCl structure. CsCl type

LiH

NaH

KH

RbH

CsH

a0

GGA LDA

2.458 2.316

3.520 3.398

3.81 3.68

3.84 4.088

V0

GGA LDA

14.87 12.44

43.62 39.23

55.35 49.35

56.72 68.32

q

GGA

0.1344

3.010 2.668 3.094[9]a,4.838[45]b 4.955[46]b 27.21 18.99 29.07[9]a 28.35[47]b 0.0735

0.0458

0.03613

0.03526 (continued on next page)

208

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

Table 2 (continued) CsCl type

Eg M–H B0

B00

a b

LiH

NaH

KH

RbH

LDA

0.1607

0.1054

0.0509

0.0405

GGA LDA GGA LDA GGA LDA

1.5 1.8 1.501 1.49 30.16 39.3

2.0 1.9 1.901 1.65 20 26.6

2.1 1.8 2.02 1.78 14.9 19.3

GGA LDA

4.05 4.17

1.0 1.1 1.856 1.52 28 35.9 19.4[9]a, 22.81[46]b 23.5[47]b 2.669 3.26 3.75[36]b, 4.4[9]a 3.16[47]b

3.0071 2.99

2.866 3.21

CsH 0.0292 continued on next page 2.5 2.1 2.15 1.82 14 15.9

4.675 4.61

Experimental estimates. Other theoretical findings.

alkali hydrides in NaCl and CsCl phases using both GGA and LDA are listed in Tables 1 and 2 along with the experimental and other theoretical works [21–47]. From Table 1, it is found that the

equilibrium lattice constant and energy band gap of all alkali hydrides calculated using GGA are in good agreement with the experimental values [21–23,8,25–27,30,31] and the other theoretical

Fig. 2. Total energy (eV) versus reduced volume (V/V0, V0 = equilibrium volume) for alkali hydrides with NaCl and CsCl crystal structures: (a) using GGA: (b) using LDA.

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

209

Fig. 2 (continued)

results [24,28,29,31–36], when compared to LDA. Valence electron density q (VED) which is defined as the total number of valence electrons per unit cell volume is an important factor for analyzing super hard materials. From our analysis, we predict that LiH (CsCl phase) is the hardest material. 3.2. Structural phase transition The total energies are calculated for lithium hydride (LiH), sodium hydride (NaH), potassium hydride (KH), rubidium hydride (RbH) and cesium hydride (CsH) in both NaCl and CsCl phases as a function of reduced volume using both GGA and LDA and their plots are given in Fig. 2(a and b). These plots show these alkali hydrides are stable in the NaCl phase at ambient pressure and a structural phase transition from NaCl to CsCl phase occurs at higher pressures. In order to determine these transition pressures accurately, enthalpy is calculated using the formula,

H ¼ E þ PV

ð2Þ

The transition pressure values are determined from the intersection of enthalpy versus pressure curves (Fig. 3(a and b)). The computed transition pressures for CsH, RbH, KH, NaH, and LiH along with the experimental data are given in Table 3. The calculated transition pressure value of NaH (37 GPa) based on GGA is in good agreement with the result obtained by Xiao et al. [48] using ab initio plane-wave pseudopotential density functional theory with generalised gradient approximation (GGA) and transition pressure value obtained using LDA deviates slightly (5%) from the above reference due to the different exchange correlation functional used. The calculated transition pressures of NaH, KH, RbH and CsH using both GGA and LDA are comparable with the results obtained by diamond anvil-cell high pressure experimental technique [9] and high pressure X-ray diffraction study [10,41]. The transition pressures value of NaH, KH, RbH and CsH using GGA differ by only about 4.7%, 13%, 24% and 40% respectively from the experiment [9,10,41], almost within error bars and similarly transition pressure of NaH, KH, RbH and CsH using LDA differ by an amount, about 2.05%, 19%, 18.6% and 41% respectively from the experiment [9,10,41].

210

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

Fig. 3. Enthalpy as a function of pressure for alkali hydrides: (a) using GGA; (b) using LDA.

3.3. Electronic properties of alkali hydride In order to understand the electronic structure of alkali hydrides, the total and partial density of states (DOS) of the alkali hydrides MH (M: Li, Na, K, Rb, Cs) at ambient pressure are computed using both GGA and LDA exchange correlation and it is found that all the hydrides exhibit non-metallic behavior at normal pressure. The lattice constants and band gap values calculated with GGA are closer to the experimental findings and therefore the electronic properties are analyzed using GGA only. The total and partial density of states (DOS) are given in Fig. 4. The Fermi level is indicated by a dotted horizontal line. From the total and partial DOS, it is observed that for LiH and NaH, the highest peak below the Fermi level is due to the s state electron of hydrogen atom along with small contributions from s and p state electrons of alkali metal atom, whereas in the case of KH, RbH and CsH the highest peak below the Fermi level is due to the s state electron of hydrogen atom with quite a large contribution from d state and small contributions from s and p state electrons of alkali metal atom.

The energy gap obtained for LiH, NaH, KH and RbH, CsH are 4.67 eV, 4.85 eV, 3.59 eV and 3.20 eV, 2.44 eV respectively, indicating that the alkali hydrides LiH, NaH and KH are insulators whereas RbH and CsH are wide band gap semiconductors. The estimated band gaps are in good agreement with the experimental [25–27,30,31] and the other available theoretical results [28,29,32–36]. From Fig. 5, it is observed that the heights of peaks are considerably reduced when the pressure is increased. A pressure induced insulator to metal transition is found in LiH at a pressure of 208 GPa and a semiconductor to metal transition is found in CsH at a pressure of 45 GPa. To analyze the ionic/covalent character of alkali hydrides, the charge density calculations are carried out. The computed charge density maps of cubic NaCl phase of alkali hydride contain M+ and H ions are shown in Fig. 6. It is clearly seen that charge strongly accumulates between alkali metal (M+) and H atoms indicates that a strong directional bonding exists between them. The bonding nature of these materials is found to be more ionic in nature than covalent.

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216 Table 3 Calculated transition pressure along with their experimental and theoretical data. Compound LiH NaH

KH

a b

NaCl ? CsCl PT (GPa) GGA LDA GGA LDA

GGA LDA

RbH

GGA LDA

CsH

GGA LDA

Experimental estimates. Other theoretical findings.

208 193 37 35 32[9,10,41]a 37[48]b 3.5 3.1 4.0[9,10,41]a 3.0 2.6 2.2[9,10,41]a 2.1 2.14 1.2[9,10,41]a

211

3.4. Elastic properties Elastic constants are the measure of resistance of a crystal to an externally applied stress. For small strains, Hooke’s law is valid and the crystal energy E is a quadratic function of strain [49]. Consider a symmetric 3  3 non rotating strain tensor e which has matrix elements eij (i, j = 1, 2 and 3) defined by the following equation,

0

e1

B e6

e¼B B e25 @

2

e6 2

e2 e6 2

e5 2 e4 2

1

C C C e3 A

ð3Þ

such a strain transforms the three lattice vectors to

a0K ¼ ðI þ eÞaK

ð4Þ

where I is defined by its elements, Iij = 1 for i = j and 0 for i – j and K = 1, 2 and 3; K0 = 1, 2 and 3.

Fig. 3 (continued)

212

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

Each lattice vector aK or a0K is a 3  1 matrix. The change in total energy due to the above strain (Eq. (3)) is,

!   6 X 6 Eðfei gÞ  E0 V 1 X PðV 0 Þ þ DE ¼ ¼ 1 C ij ei ej þ Oðfe3i gÞ V0 2 1 1 V0 ð5Þ where V0 is the volume of the unstrained lattice, E0 is the total minimum energy at this unstrained volume of the crystal, P(V0) is the pressure of the unstrained lattice, and V is the new volume of the lattice due to strain in Eq. (3). The elasticity tensor has three independent components (C11, C12, C44) for cubic crystals and five (C11, C12, C44, C13, C33) for hexagonal crystals. A proper choice of the set of strains {ei, i = 1, 2, . . ., 6}, in Eq. (5) leads to a parabolic relationship between DE/V0 (DE  E  E0) and the chosen strain. Such choices for the set {ei} and the corresponding form of DE are shown in Table 4 for cubic [50] lattice. The lattice is strained by 0%, ±1%, and ±2% to obtain the total minimum energies E (V) at these strains. These energies

and strains were fitted with the corresponding parabolic equations of DE/V0 as given in Table 4 to yield the required second-order elastic constants. While computing these energies all atoms are allowed to relax with the cell shape and volume fixed by the choice of strains {ei}. From the calculated Cij values, the bulk modulus and shear modulus for the cubic crystal are calculated using the Voigt– Reuss–Hill (VRH) averaging scheme [51–53]. The strain energy 1/2Cijeiej of a given crystal in Eq. (3) must always be positive for all possible values of the set {ei} for the crystal to be mechanically stable. The calculated elastic constants Cij (GPa), Young’s modulus E (GPa), shear modulus G (GPa), elastic anisotropy factor A and Poisson’s ratio (m) using GGA and LDA are given in Table 5 for NaCl phase and Table 6 for CsCl phase and it is found that these values are in good agreement with the available experimental [37,42,54] and theoretical results [37,38–40]. For a stable cubic structure, the three independent elastic constants Cij (C11, C12, C44) should satisfy the Born–Huang criteria [55],

C 44 > 0;

C 11 > jC 12 j;

C 11 þ 2C 12 > 0

Fig. 4. Total density of states for alkali hydrides in NaCl structure at normal pressure.

ð6Þ

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

213

Fig. 5. Total density of states for alkali hydrides in CsCl structure under high pressure.

The calculated elastic constants for cubic NaCl (Table 5) and CsCl (Table 6) phases of alkali hydrides satisfy Born–Huang criteria, suggesting that they are mechanically stable. Young’s modulus (E) and Poisson’s ratio (m) are the two important factors for technological and engineering applications. The Young’s modulus E is calculated using the expression,

E¼

9BG ð3B þ GÞ

m¼

ð8Þ

The Poisson’s ratio of the B1 phase of LiH is the least, indicating that the Li–H bonding is more directional in nature than the other M–H (M = Na, K, Rb and Cs) bonding. For cubic crystals, the anisotropy factor is defined as,

ð7Þ

The stiffness of the solid can be analyzed using the Young’s modulus (E) value. The larger the value of E, stiffer is the material. LiH is found to be the stiffest material among the five alkali hydrides. The Poisson’s ratio (v) is associated with the volume change during uniaxial deformation which also provides more information about the characteristics of the bonding forces and if v = 0.5, the material is incompressible. The Poisson’s ratio is calculated using the expression,

C 12 C 11 þ C 12

A¼

2C 44 C 11  C 12

ð9Þ

The value of A = 1 represents completely elastic isotropy, while the values smaller or larger than 1 measure the degree of elastic anisotropy. From Tables 5 and 6, it is seen that all the alkali hydrides are elastically anisotropic at ambient pressure. The ratio of bulk modulus (B) to shear modulus (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

214

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

Fig. 6. charge density distributions for alkali hydrides.

Table 4 Strain combinations in the strain tensor Eq. (3) for calculating the elastic constants of cubic structures (B1 and B2).

with  h = h/2p is the Avogadro’s number, q is density, M is molecular weight, n is the number of atoms in the molecule and

mm ¼

Strain

Parameters (unlisted ei = 0)

DE/V0

Cubic crystals 1 2 3

e1 = e2 = d, e3 = (1 + d)2  1 e1 = e2 = e3 = d e6 = d, e3 = d2(4  d2)1

3(C11  C12)d2 (3/2)(C11 + 2C12)d2 (1/2)C44d2

hD ¼

 1=3 h NA q 6p2 n mm kB M

ð10Þ

ð11Þ

where

ml ¼ to brittle nature. The critical value which separates ductile and brittle materials is about 1.75. The calculated values of B/G show that all the hydrides are brittle in nature for both NaCl and CsCl phases. The Debye temperature (hD) is an important parameter for determining the thermal characteristics of materials, which correlates many physical properties of materials, such as specific heat, elastic constants and their melting points. The Debye temperature is defined in terms of the mean sound velocity mm and gives explicit information about the lattice vibrations [56] and it is calculated using the equation [57],

  1=3 1 2 1 þ 3 m3t m3l

 1=2 B þ 0:75G

q

ð12Þ

and

mt ¼

 1=2 G

q

ð13Þ

are the velocities of longitudinal and transverse sound waves respectively. The calculated Debye temperature for alkali metal and their hydrides using GGA and LDA are listed in Table 7 along with the experimental results [58]. It is found that our calculated Debye temperature values of individual metals are in agreement with the experimental values. The predicted Debye temperature values for LiH, NaH, KH, RbH and CsH are: 1131 K, 549 K, 348 K, 215 K and 167 K respectively. The Debye temperature is thus found to decrease with the increase in atomic number of the alkali hydrides.

215

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216 Table 5 Calculated elastic constants for alkali hydrides with NaCl structure. Compound

a b c d e f

NaCl-type C11

C12

C44

G

E

m

A

B/G

LiH

GGA LDA

78.01 93 66.4a 82.7b 74.1c 67.2d 76.9e

10.5 19.2 15.6a 10.7 b 14.2c 14.8d 22.3e

43.3 54.6 45.8a 52.5 b 48.1c 46.1d 51.7e

39 47.52

83 105.2

0.11 0.17

1.28 1.47

0.8 0.91

NaH

GGA LDA

59.10 68 53.2 b 47.3c 43.8 e 56.9f

9.2 16.3 14.8 b 2.5c 19.2e 15.9f

22.02 35 22.7 b 22.5c 26.1e 24.7f

23 31.3

53 71.6

0.13 0.19

0.88 1.35

1.13 1.06

KH

GGA LDA

31.10 40 26.8 b 32.8e 39.4f

8.35 9.5 6.5 b 8.04e 6.3f

14.47 20.1 10.6 b 12.9e 10.4f

13 18.1

31 41.5

0.21 0.19

1.27 1.31

1.2 1.08

RbH

GGA LDA

26.46 29.6 24.6 b 28.2e 35.1f

7.93 8.22 6.5 b 7.11e 4.5f

10.97 11.8 10.6 b 12.5e 7.6f

10.2 11.3

25 27.2

0.23 0.21

1.18 1.10

1.37 1.35

CsH

GGA LDA

23.23 25.6 22.4 b 20.3e 33.4f

6.761 4.93 3.2 b 3.1e 1.2f

9.74 8.4 5.8 b 9.1e 4.7f

9.15 9.17

22 21.8

0.22 0.16

1.18 0.81

1.31 1.21

[54]-Expt. [24]-Other theo. [37]-Expt. [42]-Expt. [38]-Other theo. [40]-Other theo.

Table 6 Calculated elastic constants for alkali hydrides with CsCl structure.

Table 7 Density q (g/cm3), longitudinal velocity ml (m/s), transverse velocity mt (m/s), average velocity mm (m/s) and Debye temperature hD (K).

CsCl-type C11 LiH NaH H RbH CsH

GGA LDA GGA LDA GGA LDA GGA LDA GGA LDA

66.5 82 73.02 77.7 51 60.3 42 46.1 38 40.5

C12 12 18 11.9 15.1 4.5 9.8 1.4 5.9 3.2 3.6

C44 32 46 30.11 38.99 20 25 12 14.2 6.5 8.8

G 30 40.4 30.4 35.9 21 25.1 15 16.5 11 12.6

E 68 90.2 66 80.8 46 57.2 34 38.5 26 29.9

m 0.15 0.18 0.14 0.16 0.08 0.13 0.03 0.11 0.07 0.08

A 1.17 1.43 0.98 1.24 0.86 0.99 0.59 0.70 0.37 0.47

q

ml

mt

mm

hD

Li

GGA LDA

0.533 0.569

7210 7789

3296 3359

3715 3795

LiH

GGA LDA GGA LDA

0.776 1.060 0.968 0.829

10477 9783 4967 5819

7103 6633 2025 2533

7748 7235 2292 2860

GGA LDA GGA LDA

1.395 1.818 0.865 0.864

6382 6398 4381 5107

4072 4134 2000 2194

4475 4536 2254 2479

GGA LDA GGA LDA

1.422 1.584 1.621 1.640

4854 5240 2553 3326

3039 3364 1091 1535

3347 3695 1233 1729

GGA LDA GGA LDA

2.669 2.607 1.905 1.992

3225 3374 2073 2462

1959 2034 929 1076

2165 2249 1048 1215

GGA LDA

3.482 3.175

2634 2693

1618 1685

1786 1856

397 414 344[58]a 1131 930 200 237 157[58]a 549 617 149 173 91.1[58]a 348 398 82 116 56.5[58]a 215 222 64 75 40.5[58]a 167 169

Compound

B/G 1.0 0.97 0.86 1.01 0.95 1.05 0.99 1.16 1.27 1.26

Na

NaH K

KH

4. Conclusion

Rb

The structural, electronic and elastic properties of the alkali metal hydrides are investigated using ab initio calculations based on density functional theory as implemented in VASP code with both GGA and LDA exchange correlation. The computed equilibrium lattice parameters and bulk modulus values are consistent with the experimental and other available theoretical results. All the alkali hydrides are found to be stable in the NaCl phase at ambient pressure. A pressure-induced structural phase transition from NaCl to CsCl phase occurs in LiH at 208 GPa, NaH at 37 GPa, KH at 3.5 GPa, RbH at 3.0 GPa and CsH at 2.1 GPa respectively. The density of states of alkali metal hydrides confirms that they are non-metallic in nature at normal pressure. The elastic constants

RbH Cs

CsH a

Experimental estimate.

computed by both GGA and LDA obey the necessary mechanical stability conditions suggesting that all the hydrides are

216

G.S. Priyanga et al. / Computational Materials Science 84 (2014) 206–216

mechanically stable at ambient condition. Lithium hydride is found to be the hardest material among the alkali metal hydrides. Acknowledgements We thank our college management for their constant encouragement. The financial assistance from UGC, India is duly acknowledged with thanks. References [1] M.J. Latroche, Phys. Chem. Solids 65 (2004) 517. [2] R. Wiswall, in: G. Alefeld, J. Volkl (Eds.), Hydrogen storage in Metals II, Berlin, 1978, pp. 201–242. [3] F. Perrot, Phys. Stat. Sol. B 77 (1976) 517. [4] P. Loubeyre, Phys. Rev. B 57 (1998) 10403. [5] Ion Errea, Miguel Martinez-Canales, Aitor Bergara, Phys. Rev. B78 (2008) 172501. [6] Stephen A. Gramsch, Ronald E. Cohen, Sergej Yu Savrasov, Am. Mineral. 88 (2003) 257. [7] E. Zintl, A. Harder, Z. Phys. Chem. Abt. B 14 (1931) 265. [8] K. Ghandehari, H. Luo, A.L. Ruoff, Phys. Rev. Lett. 74 (1995) 2264. [9] S.J. Duclos, Y.K. Vohra, A.L. Ruoff, S. Filipek, B. Baronowski, Phys. Rev. B 36 (1987) 7664–7667. [10] H.D. Hochheimer, K. Strossner, W. Honle, B. Baronowski, Z. Phys, Chem. NeueFolge. 143 (1985) 139. [11] W. Kohn, L. Sham, Phys. Rev. 140 (1965) A1133. [12] G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251. [13] G. Kresse, J. Furthmuller, Comput. Mater. Sci. 6 (1996) 15. [14] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048. [15] P.E. Blochl, Phys. Rev. B50 (1994) 17953. [16] G. Kresse, D. Joubert, Phys. Rev. B59 (1999) 1758. [17] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [18] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [19] F.D. Murnaghan, Proc. Natl. Acad. Sci. 30 (1944) 244. [20] F. Birch, Phys. Rev. 71 (1947) 809. [21] G. Vidal valat, J.P. Vadal, K. Kurkisuonio, R. Kurkisuonio, Acta Crystallogr., A 48 (1992) 46. [22] R.W.G. Wyckoff, Crystal Structures, vol. 1, Interscience, New York, 1963. [23] P. Loubeyre, R. LeToullec, M. Hanfland, L. Ulivi, F. Datchi, D. Hausermann, Phys. Rev. B 45 (1998) 2613. [24] Jingyun Zhang, Lijun Zhang, Tian Lui, Yanming Ma, Phys. Rev. B. 75 (2007) 104115.

[25] T.A. Betenekova, S.O. Cholakh, I.M. Shabanova, V.A. Trapeznikov, F.F. Gavrilov, B.V. Shulgin, Phys-Solid States 20 (1978) 1426. [26] K. Ichikawa, N. Suzuki, K. Jsutsumi, J. Phys. Soc. Jpn. 50 (1981) 3650. [27] S. Lebeque, M. Alouani, B. Arnuad, W.E. Pickett, Euraphys. Lett. 63 (2003) 562. [28] A.B. Kunz, D.J. Mickish, Phys. Rev. B 11 (1975) 1700. [29] G. Grosso, G.P. Parravicini, Phys. Rev. B 20 (1979) 2366. [30] G.S. Zavt, K.A. Kalder, I.L. Kuusmann, C.B. Lushchik, V.G. Plekhanov, S.O. Cholakh, P.A. Evarestov, Sov. Phys.—Solid State 18 (1976) 1588. [31] V.G. Plekhanov, V.A. Pustovarov, A.A. O’Connel-Bronin, T.A. Betenekova, S.O. Cholakh, Sov. Phys.—Solid State 18 (1976) 1422. [32] S. Lebègue, B. Arnaud, M. Alouani, P.E. Bloechl, Phys. Rev. B 67 (2003) 155208. [33] E.L. Shirley, Phys. Rev. B 58 (1998) 9579. [34] S. Baroni, G.P. Parravicini, G. Pezzica, Phys. Rev. B 32 (1985) 4077. [35] V.I. Zinenko, A.S. Fedorov, Sov. Phys.-Solid State 36 (1994) 742. [36] P. Vajeeston, Theoretical Modeling of Hydrides, PhD thesis University of Oslo, 2004. [37] B.W. James, J. Kheyrandish, J. Phys. C: Solid State Phys. 15 (1982) 6321. [38] L. Engebretsen, Electronic Structure Calculations of the Elastic Properties of Alkali Hydrides Graduation Thesis, Royal Institute of Technology KTH, Stockholm. [39] D.Kh. Blat, J. Phys.: Condens. Matter 3 (1991) 5515. [40] G.D. Barrera, D. Colognesi, P.C.H. Mitchell, A.J. Ramirez-Cuesta, Chem. Phys. 317 (2005) 119. [41] H.D. Hochheimer, K. Strossner, W. Honle, J. Less, Comm. Met. 107 (1985) L13. [42] E. Haque, A.K.M.A. Islam, Phys. Status Solidi B 158 (1990) 457. [43] D. Gerlich, C.S. Smith, J. Phys. Chem. Solids 35 (1974) 1587. [44] W. Pearson, P. Villars, L.D. Calvere, Pesrson’s Handbook of Crystallographic Data for Intermetallic Phases, ASM, Metals Park, Ohio, 1985. [45] X.Z. Ke, I. Tanaka, Phys. Rev. B 71 (2005) 024117. [46] W. Yu, C. Q Jin, A. Kohlmeyer, J. Phys. Condens. Matter 19 (2007) 086209. [47] C.O. Rodriguez, M. Methfessel, Phys. Rev. B 45 (1992) 90. [48] Xiao-Wei, Qi-Feng Chen, Xiang-Rong Chen, Fu-Qjan Jing, J. Solid State Chem. 184 (2011) 427–431. [49] J.F. Nye, Physical Properties of Crystals, Oxford University Press, 1985. [50] M. Kalay, H.H. Kart, T. Çagin, J. Alloys Compd. 484 (2009) 431–438. [51] W. Voigt, LehrburchderKristallphysik, Teubner, Leipzig, 1928. [52] A. Reuss, Z. Angew, Math. Mech. 9 (1929) 49–58. [53] R. Hill, Phys. Soc. London 65 (1952) 350. [54] K.H. Hellege, R.F.S. Hearmon, The Elastic Constants of Non-Piezoelectric Crystals, vol. III of Landolt-Bornstein, New Series, Group III, vol. 2, SpringerVerlag, Berlin, 1969. [55] M. Born, K. Huang, Dynamical Theory of Crystal Lattices, Clarendon, Oxford, 1956. [56] A.M. Ibrahim, Nucl. Instrum. Methods B 34 (1988) 135. [57] O.L. Anderson, J. Phys. Chem. Solids 24 (1963) 909. [58] G.R. Stewart, Rev. Sci. Instrum. 54 (1983) 1–11.