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THE JOURNAL OF CHEMICAL PHYSICS 132, 114504 共2010兲

Structural investigation and thermodynamical properties of alkali calcium trihydrides P. Vajeeston,a兲 P. Ravindran, and H. Fjellvåg Department of Chemistry, Center for Materials Sciences and Nanotechnology, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway

共Received 6 August 2008; accepted 6 January 2010; published online 16 March 2010兲 The ground-state structure, equilibrium structural parameters, electronic structure, and thermodynamical properties of MCaH3 共M = Li, Na, K, Rb, and Cs兲 phases have been investigated. From the 104 structural models used as inputs for structural optimization calculations, the ground-state crystal structures of MCaH3 phases have been predicted. At ambient condition, LiCaH3, NaCaH3, and KCaH3 crystallize in hexagonal, monoclinic, and orthorhombic structures, respectively. The remaining phases RbCaH3 and CsCaH3 crystallize in a cubic structure. The calculated phonon spectra indicate that all the predicted phases are dynamically stable. The formation energy for the MCaH3 phases have been calculated along different reaction pathways. The electronic structures reveal that all these phases are insulators with an estimated band gap varying between 2.5 and 3.3 eV. © 2010 American Institute of Physics. 关doi:10.1063/1.3299732兴 I. INTRODUCTION

Crystallization plays an important role in various industries as a large-scale technique for separation, purification, and structure determination. Most of the compounds crystallize at some point during their production process. Knowledge about the crystal structures is a prerequisite for the rational understanding of the solid-state properties of new materials. The current interest in the development of novel metal hydrides stems from their potential use as reversible hydrogen storage devices at low and medium temperatures. The crystal structure, shape, size, and surface composition of materials are major factors that control the hydrogen sorption properties for energy storage applications. To act as an efficient energy carrier, hydrogen should be absorbed and desorbed in materials easily and in high quantities. Also, in order to use them in practical applications, the materials involved in such compounds should be easily available in large quantities with cheaper price. Alkali- and alkalineearth-based complex hydrides are expected to have a potential as viable modes for storing hydrogen at moderate temperatures and pressures.1–7 These hydrides 共e.g., LiAlH4, NaAlH4, etc.1–7兲 have higher hydrogen storage capacity at moderate temperatures than conventional hydride systems based on intermetallic compounds. The disadvantage for the use of these materials for practical applications is the lack of reversibility and poor kinetics. Recent experimental findings have shown that the decomposition temperature for certain complex hydrides can be modified by introduction of additives3,4 and/or reduction in particle size.8–11 This has opened up research activities on identification of appropriate admixtures for known or hitherto unexplored hydrides. Density functional theory has proven to be very useful for prea兲

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dicting the reaction thermodynamics of metal hydrides with known structures,12–24 but reliable prediction of unknown crystal structures is much more challenging. As proposed in our earlier communications,25 it should be possible to form several series of hydrides with alkali and alkaline-earth metals in combination with group III elements of the Periodic Table. In this article we will present results from structural study of the phases MCaH3 共M = Li, Na, K, Rb, and Cs兲 based on density-functional total energy calculations. In LiCaH3 and NaCaH3 phases, one can store H up to 6 and 4.6 wt %, respectively. The rest of the considered phases have relatively low weight percent H content. However, these phases may have potential application in electronic industry, as we proposed in our earlier studies on these type of hydrides.26,27 In addition, these phases may coexist as by-products/mixed-phases of the multiphase lightweight hydrides during synthesis. Hence, the understanding about the structural phase stability of these phases is very important. It should be noted that the structural properties of the MCaH3 phases are not yet known experimentally except that for RbCaH3 and CsCaH3.28,29 The formation of KCaH3 has also been reported in Ref. 30. One of the motivations for this study is to investigate in detail the ground-state atomic arrangements, electronic structures, and the chemical bonding behavior within the MCaH3 series, in order to check the stability of these materials for hydrogen storage and other electronic applications. The structural phase stability at high pressures for the MCaH3 phases are under examination and the results will be published in a forthcoming article.

II. COMPUTATIONAL DETAILS

It is well known that the generalized-gradient approximation 共GGA兲31 usually gives better equilibrium structural parameters as well as energetics for different phases and hence we have used GGA for all the present calculations.

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© 2010 American Institute of Physics

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The structures are fully relaxed for all volumes considered using force as well as stress minimization. The projectedaugmented-wave 共PAW兲32 implementation of the Vienna ab initio simulation package 共VASP兲33 was used for the total energy calculations to establish phase stability and transition pressures. In order to avoid ambiguities regarding the freeenergy results, the same energy cutoff and a similar k-grid density for convergence were always used. In all calculations, 500 k points in the whole Brillouin zone were used for KMnF3-type structure and a similar density of k points was used for all structural arrangements. A criterion of 0.01 meV atom−1 was placed on the self-consistent convergence of the total energy, and all calculations used a planewave cutoff of 500 eV. The formation energies 共⌬E兲 have been calculated according to the reaction equations: MH + CaH2 → MCaH3 ,

共1兲

M + CaH2 + 21 H2 → MCaH3 ,

共2兲

M + Ca + 23 H2 → MCaH3 ,

共3兲

MH + Ca + H2 → MCaH3 .

共4兲

The total energies of M, MH, and CaH2 have been computed for the ground-state structures, viz., in space group ¯ m for M, Fm3 ¯ m for MH, and Pnma for CaH , all with Im3 2 full geometry optimization. The energy of a free hydrogen molecule was computed via a hydrogen dimer in a larger cubic unit cell. Convergence at the 10−4 eV level was achieved with Ecut = 700 eV in a cell of length 9 Å using the Fermi smearing technique. The calculated corresponding value is ⫺6.794 eV/f.u. which is well agrees well with another theoretical simulation.34 The calculated H bond length in our work is 0.752 Å; the corresponding experimental value is 0.741 Å,35 as the plane-wave technique of VASP is better suited to solids rather than atoms and molecules. However, it was proven that use of the same PAW potential and the same methodology in computing reactance and product makes for greater accuracy in ⌬H due to cancelation of errors.34 The Phonon program developed by Parlinski36 was used for lattice dynamic calculations. The force calculations were made using the VASP code with the supercell approach and the resulting data were imported into the Phonon program. Thereafter the full Hessian was determined and the phonon density of states 共DOS兲 was calculated. The 2 ⫻ 2 ⫻ 1 共for LiCaH3 and NaCaH3兲 and 2 ⫻ 2 ⫻ 2 共for KCaH3, RbCaH3, and CsCaH3兲 supercells were constructed from the optimized structures for the force calculations. The Hessian 共harmonic approximation兲 was determined through numerical derivation using steps of 0.03 Å in both positive and negative directions of each coordinate to estimate the harmonic potentials. The sampling of the phonon band structure for the calculation of phonon DOS was set to “large” in the Phonon program36 with a point spacing of 0.005 THz. To gauge the bond strength, we have used the bond overlap population 共BOP兲 values on the basis of the Mulliken population implemented in the CASTEP code.37 For the

CASTEP computation we used the optimized VASP structures as input with norm-conserving pseudopotentials and the GGA exchange correlation functional proposed by Perdew, Burke, and Ernzerhof were used.31

III. RESULTS AND DISCUSSION

Thirty potentially applicable structure types 共ABX3; A and B represent the first and second elements in the following structures and X is either O, F, or H兲 have been used as starting inputs in the structural optimization calculations for the MCaH3 compounds 共Pearson structure classification notation in parenthesis兲: KMnF3 共tP20兲, GdFeO3 关NaCoF3共oP20兲兴, KCuF3 共tI20兲, BaTiO3 关RbNiF3共hP30兲兴, CsCoF3 共hR45兲, CaTiO3 关CsHgF3共cP5兲兴, PCF3 共tP40兲, KCuF3 共tP5兲, KCaF3 共mP40兲, NaCuF3 共aP20兲, SnTlF3 共mC80兲, KCaF3 共mB40兲, LiTaO3 共hR30兲, KCuF3 共oP40兲, PbGeS3 共mP20兲, CaKF3 共mP20兲, KNbO3 共tP5兲, KNbO3 共oA10兲, KNbO3 共hR5兲, LaNiO3 共hR30兲, CaTiO3 共oC10兲, FeTiO3 共hR30兲, SrZrO3 共oC40兲, BaRuO3 共hR45兲, ␣-CsMgH3 共Pmmm兲, CaSiO3 共mP60兲; CaSiO3 共aP30兲, MgSiO3 共mS40兲, YBO3 共oS60兲 USPEX-1 共C2; evolutionary search38兲, and USPEX-2 共P1; evolutionary search38兲.38–40 The present type of theoretical investigations are highly successful to predict the ground-state structure of hydrides24,41 and other materials.42,43 The reliability of the calculations depends upon the number of input structures considered in the calculations. Though it is a tedious process to select input structures from the 2545 entries for the ABX3 composition in the Inorganic Crystal Structure Database 共ICSD兲,39 which also involves tremendous computations, several compounds/ phases have the same structure type, and in some cases, have only small variations in the positional parameters 共of certain atoms兲. These possibilities are omitted because during the full geometry optimization, in spite of using different positional parameters, the structures mostly are converted to similar type of structural arrangements. In this particular composition, only 28 structure types have unique structural arrangements. In order to cover a wide range of structural modification from the above structural starting points we have made the computation in the following way: the first step is to obtain equilibrium volume for this particular chemical composition in different modifications we have made symmetry constrained stress minimization for all these modifications. The lattice parameters optimized starting structure models have been divided into four class of structure models 共in total of 4 ⫻ 30= 120 structure models兲: 共1兲 the original starting structures 共i.e., ABX3兲; 共2兲 the original starting structures have been transformed into P1 symmetry considered as P1-ABX3 model; 共3兲 the A and B element have been interchanged 共BAX3 model兲; and 共4兲 BAX3 model structures have been further transferred into P1 symmetry 共P1-BAX3 model兲. All the above mentioned structure models have been fully relaxed 共minimization of force and stress兲 without any constrains on the atomic positions and unit-cell parameters. It should be noted that, during the structural optimization, some of the initial structures are converted into other high/low symmetry structure types which are not included in the above models. The calculated total energy as a

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Structure of alkali calcium tri-hydrides

H Na

Ca

(a)

(b)

(c)

(d)

FIG. 1. Theoretically predicted crystal structures for 共a兲 LiCaH3, 共b兲 NaCaH3, 共c兲, KCaH3 共d兲 RbCaH3, and CsCaH3.

function of volume has been fitted to the so-called universal equation of state 共EOS兲44 to calculate the bulk modulus and its pressure derivative. 1. Structural features of the MCaH3 phases

Among the considered structure models for LiCaH3, a PbGeS3 derived model 1–4 atomic arrangements occur at the lowest total energy and all these phases are having exactly the same total energy. Our symmetry analysis shows that, during the structural relaxation processes, the low symmetry triclinic and monoclinic structural modifications of PbGeS3 transform into the somewhat high symmetry hexagonal 关Fig. ¯ c兴 phase. Such a situation arises often when we per1共a兲; R3 form full geometry optimization. It is often observed that, instead of relaxing to the local minimum, the system relaxes to the global minimum, as it is the case here. The LiCaH3 structure consists of corner-sharing LiH6 octahedra. From the interatomic Li–H distances 共1.843 Å兲 and H–Li–H angles 共ranging between 88.4 and 91.6°兲, it is evident that the LiH6 octahedra are slightly distorted. Ca is surrounded by 9 H atoms, the Ca–H distances vary from 2.32 to 2.57 Å. The shortest H–H separation in the LiCaH3 structure exceeds 2.57 Å, and is consistent with the H–H separation found in other complex/metal hydrides. According to the structural optimization calculations for the NaCaH3 phase, USPEX-1-derived models 1–4 atomic arrangements have the lowest total energy. After the structure relaxation the high symmetry monoclinic structure 共C2 trans¯ ; Table I, Fig. forms into low symmetry triclinic phase 关P1 1共b兲; hereafter ␣-NaCaH3兴. In addition with the USPEX-1derived models PbGeS3-derived models 1–4 共during the

structure relaxation, PbGeS3-derived models 1–4 transform into R3c rhombohedral phase; hereafter meta-NaCaH3兲 are energetically closer to the USPEX-1-derived models 共the involved energy difference is 0.06eV兲 and both structure models are also having almost similar equilibrium volume. In the ␣-NaCaH3 phase Na and Ca is surrounded by 5 and 7 hydrogen atoms, respectively. The calculated average Ca–H and Na–H distances are 2.33 and 2.30 Å, respectively. The bond angle between H–Ca–H vary from 70.7 to 105.8° and H–Na–H vary from 74.5 to 105.5°. In the meta-NaCaH3 phase, both Na and Ca are surrounded by six H in cornersharing octahedral coordination, with NaH6 octahedra highly distorted and CaH6 octahedra slightly distorted. The calculated average Ca–H and Na–H distances are 2.35 and 2.53 Å, respectively. Each H is surrounded by two Ca and two Na, and the shortest H–H separation is above 2.51 Å. The results obtained from structural optimizations for KCaH3 phase shows that the GdFeO3-derived 1, 3, and 4 model structures proved to have the lowest total energy. It is interesting to note that during the theoretical simulations, many of the initially assumed different trial structures relaxed toward the GdFeO3-type structure 共viz. strongly emphasizing that this particular atomic arrangement is energetically more favorable for KCaH3兲. This phase consists of slightly distorted CaH6 corner-sharing octahedra 关Fig. 1共c兲兴. The calculated Ca–H distances within the octahedra are 2.26 Å and the H–Ca–H bond angles vary from 89° to 91°. The K atom is surrounded by 8 H atoms and the calculated K–H distance varies between 2.83 and 3.15 Å. The structural optimizations for RbCaH3 phase show that the KCuF3-derived input structure model has the lowest total energy. The symmetry analysis for the RbCaH3 phase shows that the tetragonal structure is transformed into cubic modification 关Fig. 1共d兲兴. For the CsCaH3 phase, CaTiO3-type atomic arrangement has the lowest energy than the considered structure types consistent with the experimental findings. The calculated unit-cell dimensions and positional parameters for both RbCaH3 and CsCaH3 at 0 K and ambient pressure are in good agreement with the room temperature experimental findings 共see Table I兲.28,29 In RbCaH3 and CsCaH3, Rb/Cs is surrounded by 12 H in cuboctahedral coordination at a distance of 3.21 and 3.27 Å, respectively. Ca is octahedrally coordinated to six H at a distance of 2.27 Å in RbCaH3, and 2.31 Å in CsCaH3. Similarly, in both cases, H is surrounded by two Ca and four Rb/Cs, and the shortest H–H separation is 3.21 Å in RbCaH3, and 3.27 Å in CsCaH3. Although these compounds have isoelectronic configurations for all involved constituents, they stabilize in rather different crystal structures. The broad features of the structural arrangement vary from hexagonal-orthorhombic-cubic on moving from Li to Cs along the series. It is worthy to note that the rotation of CaH6 along 共110兲 and 共111兲 directions bring orthorhombic and rhombohedral distortion into the lattice. Generally, the variation in the crystal structures of ABX3 compounds can be rationalized in terms of the Goldschmidt tolerance factor 共t兲. The value of t may be used as an indicator of the tendency for structural transitions and for the deformation in the octahedral coordination at the B site in a given perovskite family member.45 The range of 0.8–0.89

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TABLE I. Optimized equilibrium structural parameters, bulk modulus 共B0兲, and pressure derivative of bulk modulus 共B⬘0兲 for the MCaH3 共M = Li, Na, K, Rb, or Cs兲 series. The experimental values are given in the parenthesis. Compound 共structure type; space group兲

Lattice parameters 共Å兲

B0 共GPa兲

B⬘0

¯ c , 167兲 LiCaH3 共R3

a = 5.2240 c = 12.4814

Li共6b兲:0.0, 0.0, 0.5 Ca共6a兲: 0.0, 0.0, 0.25 H共18e兲: 0.2197, 0.3333, 0.5833

36

3.9

¯兲 NaCaH3 共P1

a = 6.8555 b = 7.1940 c = 6.8040 ␣ = 118.59° ␤ = 117.01° ␥ = 29.78°

Na共2i兲: 0.7257, 0.0131, 0.2737 Ca共2i兲: 0.1609, 0.6291, 0.7517 H1共2i兲: 0.9004, 0.5172, 0.6503 H2共2i兲: 0.3627, 0.8224, 0.0155 H3共2i兲: 0.2330, 0.8404, 0.3466

27

2.6

meta-NaCaH3 共R3c兲

a = 5.8632 c = 15.2174

Na共6a兲: 0.0, 0.0, 0.7826 Ca共6a兲: 0.0, 0.0, 0.0014 H共18b兲: 0.9878, 0.2819, 0.3980

25

2.3

KCaH3 共Pnma兲

a = 6.3219 b = 8.9293 c = 6.3073

K共4c兲: 0.0165, 0.25, 0.9966 Ca共4b兲: 0.0, 0.0, 0.5 H1共4c兲: 0.9860, 0.25, 0.4439 H2共8d兲: 0.2219, 0.9705, 0.2218

24

3.9

¯ m ; CaTiO 兲 RbCaH3 共Pm3 3

a = 4.5427 共4.547兲a

Rb共1a兲: 0.0, 0.0, 0.0 共0.0, 0.0, 0.0兲a Ca共1b兲: 0.5, 0.5, 0.5 共0.5, 0.5, 0.5兲a H共3c兲: 0.5, 0.5, 0.0 共0.5, 0.5, 0.0兲a

24

3.8

¯ m ; CaTiO 兲 CsCaH3 共Pm3 3

a = 4.6297 共4.609兲b

Cs共1a兲: 0.0, 0.0, 0.0 共0.0, 0.0, 0.0兲b Ca共1b兲: 0.5, 0.5, 0.5 共0.5, 0.5, 0.5兲b H1共3c兲: 0.5, 0.5, 0.0 共0.5, 0.5, 0.0兲b

23

3.8

Positional parameters

a

Experimental values from Ref. 28. Experimental values from Ref. 29.

b

should be an indicator of tetragonal or orthorhombic distortion of the cubic symmetry, for cubic arrangement t should be in the range of 0.89–1.00, and t above 1 should single out hexagonal 共trigonal兲 stacking variants of the perovskite family. The t values for the compounds under investigation varies from 0.59 to 0.97 关0.59 共LiCaH3兲, 0.78 共NaCaH3兲, 0.86 共KCaH3兲, 0.92 共RbCaH3兲, and 0.97 共CsCaH3兲兴. Consistent with the Goldschmidt empirical rule, t takes a value close to one for cubic RbCaH3 and CsCaH3 where undistorted perovskite arrangements contain perfect octahedra. For the KCaH3 with t = 0.86, distorted octahedra occur within the orthorhombic structure. Even though LiCaH3 and NaCaH3 have smaller t value than the defined t factor, their ground-state structures are still perovskitelike frameworks. It indicates that either the Goldschmidt tolerance factor may not be suitable to describe the structure of hydrides or the assumed value of the H− radii 共1.4 Å for 6 coordination兲 may be wrong. It should be noted that this t factor was successfully used to explain the structural modifications along the MBeH3 and MMgH3 共M = Li, Na. K, Rb, and Cs兲 series.46,47 This indicates that the predicted LiCaH3 and NaCaH3 phases may have different bonding nature, and in particular, they may not be pure ionic compounds 共see the bonding analysis below兲. By fitting the total energy as a function of cell volume using the so-called universal EOS 共Ref. 44兲 the bulk modulus 共B0兲 and its pressure derivative 共B0⬘兲 are obtained 共Table

I兲, but no experimental data are yet available for comparison. The bulk modulus decreases monotonically when we move from Li to Cs and on the other hand its pressure derivative is almost constant 共except for NaCaH3兲. The variations in B0 is accordingly correlated with variations in the size of M and consequently also with the cell volume. Compared to intermetallic-based hydrides, these compounds have low B0 values, implying that they are soft and easily compressible. The soft character of the MCaH3 materials arises from the weaker bonding interaction between M and Ca. Also due to the soft nature, one may expect that destabilization of some of the hydrogen atoms from the matrix may be feasible. However, the Ca–H bonds are likely to be strong. From this point of view, one can expect that the MCaH3 phases also release hydrogen at elevated temperature only. Hence, these materials may not be suitable for on-board transportation applications. However, additive substitution/共particle size control兲 may reduce the decomposition temperature considerably as it was observed in alanates. Further research is needed in this direction. B. Formation-energy considerations

Formation enthalpy is the best aid to establish whether theoretically predicted phases are likely to be stable and also such data may serve as guides for possible synthesis routes.

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Structure of alkali calcium tri-hydrides

TABLE II. Calculated hydride formation energy 共⌬H; in kJ mol−1兲 according to Eqs. 共1兲–共4兲 for the MCaH3 series.

CsCaH3

0.10 0.05

Compound

⌬H1

⌬H2

⌬H3

⌬H4

RbCaH3

LiCaH3 NaCaH3 KCaH3 RbCaH3 CsCaH3

17.74 34.45 17.03 10.32 12.84

⫺70.01 ⫺10.55 ⫺25.62 ⫺24.67 ⫺24.26

⫺237.25 ⫺177.79 ⫺192.86 ⫺191.91 ⫺191.50

⫺149.51 ⫺132.79 ⫺150.21 ⫺156.93 ⫺154.4

Density of States (1/THz)

0.10 0.05

KCaH3

0.10 0.05

meta-NaCaH3 α− NaCaH3

0.10 0.05

In this study, we have considered four possible reaction pathways 关Eqs. 共1兲–共4兲兴, and the associated formation enthalpy listed in Table II are estimated from the calculated total energies without temperature effect. In general, synthesis of MCaH3 compounds from an equiatomic MCa matrix is not possible as the alkali metals and calcium are immiscible in the solid and liquid state.48 Schumacher and Weiss49 have suggested that the ternary MMgH3 hydrides can be synthesized directly by a reaction between M and Mg in hydrogen atmosphere at elevated temperatures. A similar approach may also be valid for the MCaH3 series. However, most of the MMgH3 compounds have also been synthesized from the appropriate combination of binary hydrides.29,50–52 This shows that, among the considered reaction pathways, tracks 1 and 3 are experimentally verified for MMgH3 series,29,50–52 but for the MCaH3 phases, reaction path 1 is not possible and the path 3 may be a possible route. On the other hand, tracks 2 and 4 are not yet verified for any of the MM ⬘H3 phases 共M ⬘ = any alkali-earth atom兲 and they are open for verification or rejections. The results show that reaction pathways 2–4 give rise to an endothermic reaction for the MCaH3 compounds. Hence, preparation of MCaH3 from MH and CaH2 共pathway 1兲 is not likely to be successful. It should be noted that CsCaH3 has been synthesized from its binary hydrides under 200 bar H2 pressure.29 All MCaH3 compounds are seen to exhibit high formation energies according to pathway 3. Hence, for all the studied phases, pathway 3 is energetically more favorable than other paths and we suggest that it should be possible to synthesize/stabilize these compounds using CaH2 and M by passing H2. One can easily verify the validity of the proposed reaction pathways 关Eqs. 共1兲–共4兲兴. The difference in ⌬H4 − ⌬H1 = ⌬H3 − ⌬H2 corresponds to the formation energy of CaH2 which amounts to −167.25 kJ mol−1, in good agreement with the measured value of −181.521⫾ 9.2 kJ mol−1.53 Temperature effect has not been included in the present calculations 共but note that one can reliably reproduce the formation energy of H2 without including thermal vibrations兲. In order to understand the stability of the predicted phases, we have calculated phonon DOS for the equilibrium structures for these phases, which are shown in Fig. 2. For all these compounds, no imaginary frequency was observed indicating that all the predicted structures are ground-state structures for these systems, or at least they are dynamically stable.54 It should be noted that, for the NaCaH3 phase, both ␣ and metamodifications are dynamically stable, hence we have displayed total phonon DOS for both phases in Fig. 2.

LiCaH3

0.10 0.05 0

10

20 Frequency (THz)

30

40

FIG. 2. Calculated total phonon DOS for MCaH3 compounds.

The structure of CsCaH3 is already known, but that for the other phases are not yet identified experimentally. As the predicted phases are expected to be stable, we need experimental verification. Both LiCaH3 and NaCaH3 have almost similar phonon DOS. Similarly the remaining phases KCaH3, RbCaH3, and CsCaH3 also exhibit almost similar phonon DOS. Hence we have displayed in Fig. 3 only the partial phonon DOS for LiCaH3 and CsCaH3. In both cases the partial phonon DOS is plotted along three directions, x, y, and z. For Li/Cs and Ca atoms, the vibrational modes along the x, y, and z directions are identical. On the other hand, the

FIG. 3. Calculated partial phonon DOS for 共a兲 LiCaH3 and 共b兲 CsCaH3 phases.

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J. Chem. Phys. 132, 114504 共2010兲

Vajeeston, Ravindran, and Fjellvåg

TABLE III. Calculated standard hydride formation energy 共⌬H; in kJ mol−1兲 according to Eq. 共1兲 for the MCaH3 series. The vibrational energies are given at 300 K. ⌬HZPE refers ZPE correction to the net reaction, ⌬HZPE+vib refers to the corrections due to ZPE plus vibrational contributions, and ⌬H1 refers electronic contributions to the reaction Eq. 共1兲. For calculation of standard enthalpy of formation 共⌬H兲 the following corresponding binary hydride values 共in kJ mol−1兲 were utilized: LiH= −90.621; NaH= −56.421; KH= −57.821; RbH= −47.421; CsH= −49.9; MgH2 = −76.2; and CaH2 = −181.521. Experimentally known formation energy is given in the parenthesis. Compound LiCaH3 ␣-NaCaH3 KCaH3 RbCaH3 CsCaH3 NaMgH3

⌬HZPE ⫺0.48 ⫺6.9 ⫺3.6 ⫺3.5 ⫺1.97 ⫺0.41

⌬HZPE+vib 0.37 ⫺4.8 ⫺1.5 ⫺1.6 ⫺1.4 ⫺0.18

⌬H1 17.74 34.45 17.03 10.32 12.84 ⫺10.71

⌬H ⫺271.77 ⫺242.74 ⫺240.84 ⫺230.54 ⫺232.82 ⫺143.4 共⫺144兲

modes along x direction in the H site in LiCaH3 is slightly different from those along the y and z directions 关see Fig. 3共a兲兴. In contrast, the H modes along the x and y are identical for CsCaH3 and that along the z direction is much different from the x and y directions 关see Fig. 3共b兲兴. Since the mass of H atom is much smaller than that of M or Ca atom, Fig. 2 shows that the high frequency modes above 10 THz are dominated by H atom, and the low frequency modes below 10 THz are mainly dominated by M 共except Li兲 and Ca atoms. The center of the Ca mode frequency in all these cases is always present around 5 THz. If one moves from Li to Cs due to the mass difference between the M atoms, the vibrational mode frequencies from M are systematically shifted toward low frequency region. The standard hydride formation energy 共⌬H兲 is calculated according to Eq. 共1兲 with the use of the ⌬H for the following corresponding binary hydrides 共all values are in kJ mol−1兲: LiH: ⫺90.621; NaH: ⫺56.421; KH: ⫺57.821; RbH: ⫺47.421; CsH: ⫺49.9; and CaH2: ⫺181.521.53 The vibrational energies are given at 300 K and the calculated net zero point energy 共ZPE兲 for the reaction Eq. 共1兲 are listed in Table III. The vibrational contribution to the formation energy is clearly shown to be smaller than that from the ZPE. Also, for all these phases, the vibrational contribution to the formation energy is negligible compared to that from electronic contribution 共⌬H1兲. In order to compare the numerical values, we have also included the values for NaMgH3 phase, for which the formation energy is already known experimentally.53 The calculated formation energy for NaMgH3 according to Eq. 共3兲 is −119.80 kJ mol−1. This value is considerably smaller than the experimentally known value of −144 kJ mol−1.53 In order to have reasonably good standard formation energy, we have adopted the following empirical method where the formation energy is estimated from the sum of the experimental formation energy of the constituent binary hydrides+ electronic contribution + ⌬HZPE+vib. Using this empirical method we obtained ⌬H value of −143.4 kJ mol−1 for NaMgH3 which is in very good agreement with the experimentally observed value. In order to establish the validity of this empirical method, we have made systematic estimation of ⌬H using this approach not

2.0

EF

CsCaH3

1.0

2.0 DOS (states/e.V f.u.)

114504-6

RbCaH3

1.0

2.0

KCaH3

1.0

2.0

NaCaH3

1.0

2.0

LiCaH3

1.0 -7.5

-5

-2.5

0 2.5 Energy (eV)

5

7.5

FIG. 4. Calculated total electronic DOS for MCaH3 phases. The Fermi level is set at zero energy and marked by the vertical dotted line.

only for the NaMgH3 phase, but also for several known ternary saline, as well as complex hydrides.55 Hence, one can expect that the MCaH3 series may also have the tabulated ⌬H values, and their magnitude indicates that these phases are quite stable. Further experimental investigations are needed to verify this prediction. C. Chemical bonding

In previous studies47,56,57 on hydrides we have demonstrated that several theoretical tools are needed in order to draw more assured conclusions regarding the nature of the chemical bonding. From the bonding analysis of MBeH3 and MMgH3 series we found46,47 that all these phases are basically saline hydrides similar to the parent alkali-/alkalineearth mono-/dihydrides. Generally one may expect that the MCaH3 phases may also have similar bonding behavior. The total electronic DOS at the equilibrium volumes for the ground-state structures of the MCaH3 compounds are displayed in Fig. 4 and site projected DOSs for LiCaH3 and CsCaH3 are shown in Fig. 5. All MCaH3 compounds have finite energy gap 共Eg; varying between 2.5 and 3.3 eV兲 between the valence band 共VB兲 and the conduction band and hence they can be considered as insulators. It is commonly recognized that the theoretically calculated Eg for semiconductors and insulators are strongly dependent on the approximations used and in particular on the exchange and correlation terms of the potential. In general, the Eg values obtained from the density-functional calculations are always underestimated compared to the experimentally measured values. From the band structure 共not given in the manuscript兲 we found that these materials having indirect band gap 共except KCaH3兲. According to pure ionic picture, the insulating behavior of these materials can be explained as follows: in each formula unit, one electron from M fills one of the three originally half-filled H-s orbitals and the other two are filled by electrons from Ca resulting in a completely filled VB and accordingly an insulating behavior. A similar feature was found in most of the complex hydrides 关e.g., MAlH5 共M

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J. Chem. Phys. 132, 114504 共2010兲

Structure of alkali calcium tri-hydrides EF 0.10

H H

0.05

Ca

Ca

DOS (states/eV f.u.)

H

H

0.10

H

H H H

H

Ca

1.00

Li H

-5

-2.5

(a)

0

2.5

5

7.5

Energy (eV)

Cs

H Cs

H

H

H (b)

Ca

Ca (d)

FIG. 6. Calculated 关共a兲 and 共b兲兴 valence-electron-charge density and 关共c兲 and 共d兲兴 ELF plots for LiCaH3 and CsCaH3, respectively.

H

0.10 0.05

DOS (states/eV f.u.)

Cs H

EF

0.15

Ca

0.15 0.10 0.05

Cs 0.15 0.10 0.05

Total

1.50 1.00 0.50 -10

Ca

Ca

Total

2.00

(b)

(c)

H

0.025

H Cs Ca

Ca

(a)

0.075 0.050

Cs

H

H Li

-7.5

Cs H

Li H

0.05

Ca

Ca

-5

0

Energy (eV)

5

10

FIG. 5. Calculated partial DOS for 共a兲 LiCaH3 and 共b兲 CsCaH3 phases. The Fermi level is set at zero energy and marked by the vertical dotted line; s states are shaded and p states are marked by continuous line.

= Mg, Ba兲 M 3AlH6 共M = Li, Na, K兲,58,59 and MAH4 共A = B , Al, Ga兲兴.60,61 On moving from LiCaH3 to CsCaH3, the calculated DOSs are significantly changing. In LiCaH3 the VB region is relatively broad and it systematically narrows when one moves to NaCaH3, KCaH3, RbCaH3, and CsCaH3 共Fig. 4兲. This may be due to the variation in the coordination number of Ca and also the increase in Ca–H bond length. A similar feature was also observed in MBeH3 and MMgH3 phases.46,47 It should be noted that the electronic structure of LiCaH3 has been investigated along with several light weight hydrides by Khowash et al.62 Because of the different crystal structure the estimated Eg value for the LiCaH3 phase is 共around 3.5 eV兲 much higher than the present investigation. In order to elucidate the bonding situation more properly, we have calculated the partial electronic DOS 共PDOS兲 for MCaH3. As seen from Fig. 5共a兲, the PDOSs for Li and Ca show very small contributions from s and p states in the VB. This demonstrates that valence electrons are transferred from the Li and Ca sites to the H sites. The small Li- and Ca-s states present at the VB are energetically degenerate with the H-s states. Compared with LiCaH3, a significant change in

the VB feature can be found in KCaH3, RbCaH3, and CsCaH3. As the VB features are almost having close similarity, we have displayed the PDOS for CsCaH3 only. In all phases Ca-p and H-s states are present in the vicinity of the Fermi level at the VB. In KCaH3, RbCaH3, and CsCaH3, the Ca-s and −p states are well-separated. In contrast, these states for LiCaH3 and NaCaH3 are energetically degenerate almost in the whole VB region, indicating hybridization interaction. In order to gain further understanding about the bonding situation in MCaH3 compounds, we turn our attention to charge density and electron-localization-function 共ELF兲 plots. Again the different members of the series exhibit similar features and in view of that we have only documented such plots for LiCaH3 and CsCaH3. Figures 6共a兲 and 6共b兲 show the charge-density distribution at the Li, Cs, Ca, and H sites, from which it is evident that the highest charge density resides in the immediate vicinity of the nuclei. Further, the spherical charge distribution shows that the bonding between Cs–H and Ca–H have predominantly ionic character. On the other hand, in the case of LiCaH3 关Fig. 6共a兲兴, the interaction between Li–H is almost ionic 共spherical charge distribution兲 with noticeable directional character. The nature of charge distribution seen in Fig. 6共b兲 appears to be typical for ionic compounds.25 A common distinction between the bonding in MCaH3 series and the situation in the MAlH4 and M 3AlH6 series is that the interaction between Ca and H has more ionic character than that between Al and H.57 In KCaH3, RbCaH3, and CsCaH3 the electron population between M and the CaH6 units is almost zero 共viz., charges are depleted from this region兲, which reconfirms that the interaction between M and CaH6 units is virtually purely ionic in these compounds. The calculated ELF plot 关Fig. 6共b兲; for more details about ELF see Refs. 63–65兴 shows a maximum of ca. 1 at the H site and these electrons have a paired character. The ELF values at the M and Ca sites are very low. The inference from this observation is that charges are transferred from the

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114504-8

J. Chem. Phys. 132, 114504 共2010兲

Vajeeston, Ravindran, and Fjellvåg

TABLE IV. Calculated 共BC 共given in terms of e兲 and energy band gap 共Eg in electron volts兲 for the MCaH3 series.

LiCaH3

␣-NaCaH3

KCaH3

RbCaH3

CsCaH3

Atom

BC

Eg

Li Ca H Na Ca H K Ca H Rb Ca H Cs Ca H

+0.79 +1.45 ⫺0.75 +0.83 +1.41 ⫺0.84 +0.84 +1.56 ⫺0.80 +0.76 +1.51 ⫺0.75 +0.67 +1.53 ⫺0.73

2.5

BOP

0.4

Compounds

Ca-H M-H

0.3 0.2 0.1

3.2 LiCaH3

NaCaH3

KCaH3

RbCaH3

CsCaH3

Compound

3.0 FIG. 7. Variation in the Ca–H and M – H 共M = Li, Na, K, Rb, and Cs兲 BOP along the MCaH3 series. 3.2

3.1

M and Ca sites to the H sites and there are certainly very few paired valence electrons left at the M and Ca sites. A certain polarized character is found in the ELF distribution at the H sites in all the complex hydrides we have investigated earlier.57 Similarly, in the MCaH3 phases, the ELF distribution is not spherically symmetric at the H site. But the polarization is considerably lower in MCaH3 phases than the aluminum based hydrides. In an effort to quantify the bonding and estimate the amount of electrons on and between the participating atoms, we have made Bader topological analysis. Although there is no unique definition to identify how many electrons are associated with an atom in a molecule or an atomic grouping in a solid, it has nevertheless proved useful in many cases to perform Bader analyses.66–68 In the Bader charge 共BC兲 analysis, each atom of a compound is surrounded by a surface 共called Bader regions兲 that run through minima of the charge density and total charge of an atom is determined by integration within the Bader region. The calculated BC for the MCaH3 series is given in Table IV. The BC for M and H in the MCaH3 compounds indicate that the interaction between M and H is almost ionic 共in all cases around one electron is transferred from M to H兲. This finding is consistent with the DOS and charge density analyses. Within the CaH6 units, Ca donates nearly 1.5 electrons in KCaH3, RbCaH3, and CsCaH3 and around 1.4 electrons in LiCaH3 and NaCaH3 phases to the H site, which is much smaller than in a pure ionic picture. This is partly associated with the small covalency present between Ca and H and also may be due to the artifact of making boundaries to integrate charges in each atomic basin using Bader’s “atoms in molecule” approach. However, consistent with the charge and DOS analysis, the BC analysis always qualitatively shows that M and Ca atoms donate electrons to the H site. To get a better understanding of the interaction between the constituents, the BOP values are calculated on the basis of the Mulliken population. The BOP can provide useful information about the bonding property between the two atoms. A high BOP value indicates a strong covalent bond,

while a low BOP value indicates an ionic interaction. The calculated BOP values for the Ca–H and M – H results are displayed in Fig. 7. From Fig. 7, it is seen that the BOP values for the Ca–H bonds in all the five hydrides vary between 0.15 and 0.49. Similarly, the calculated BOP values for the M – H vary between 0.01 and 0.16. It should be noted that the Ca–H BOP values are close to that for ionic 共0.39兲 Na–H bond in NaH, but lower than that for the covalent C–C bond in diamond 共1.08兲 and H–Al bonds in NaAlH4 共0.88兲 and Na3AlH6 共0.62–0.64兲. Therefore, the Ca–H bonds in these hydrides have dominant ionic character, and M – H interactions are much weaker. Figure 7 clearly indicates that where one goes from LiCaH3 to CsCaH3, the Ca–H interaction becomes stronger, on the other hand, the M – H interaction gets weaker. This is one of the reasons why the Ca–H distance is reduced on going from LiCaH3 to CsCaH3.69

IV. CONCLUSION

The crystal, electronic structure, and thermodynamical properties of the MCaH3 共M = Li, Na, K, Rb, and Cs兲 series have been studied by state-of-the-art density-functional calculations. For the experimentally known CsCaH3 phase, the ground-state structure has been successfully reproduced within the accuracy of the density-functional approach. The ground-state crystal structures for MCaH3 共M = Li, Na, K, Rb, and Cs兲 phases have been predicted by performing structural optimization of a number of different structure types using force as well as stress minimizations. The predicted crystal structures for LiCaH3 and NaCaH3 are found to have rhombohedral and triclinic structures, respectively, with insulating behavior. KCaH3 stabilizes in orthorhombic and RbCaH3 and KCaH3 stabilize in cubic structures. Formation energies for the MCaH3 series are calculated for different possible reaction pathways. For all these phases, we propose that synthesis from elemental M and Ca in hydrogen atmosphere should be a more feasible route. The phonon DOS of the lattices are calculated by using a direct force constant method and it shows that all the predicted phases are dynamically stable. A semiempirical method for estimation of standard enthalpy of formation for MCaH3 hydrides is proposed, which gives the best value for the known NaMgH3 phase. All the studied phases are wide-band-gap insulators and the insulating behavior is associated with well localized, paired s-electron configuration at the H site. The chemical

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114504-9

Structure of alkali calcium tri-hydrides

bonding character of these compounds is predominantly ionic according to analyses of DOS, charge density, ELF, BCs, and BOP. ACKNOWLEDGMENTS

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