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Pressure-induced structural transitions of LiNH2: A first-principle study
Journal of Alloys and Compounds 544 (2012) 129–133
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Pressure-induced structural transitions of LiNH2: A first-principle study Yan Zhong a, Huaiying Zhou a,b, Chaohao Hu b,c,⇑, Dianhui Wang b, Guanghui Rao b a
School of Materials Science and Engineering, Central South University, Changsha 410083, PR China School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China c International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, PR China b
a r t i c l e
i n f o
Article history: Received 23 May 2012 Received in revised form 26 July 2012 Accepted 27 July 2012 Available online 4 August 2012 Keywords: Lithium amide Pressure-induced structural transition First-principles method Evolutionary structure prediction
a b s t r a c t The pressure-induced phase transformations in LiNH2 have been studied by using ab initio total-energy calculations and evolutionary structure prediction simulations. Two stable high-pressure polymorphs of LiNH2 are found: b-LiNH2 (orthorhombic, NaNH2-type, Fddd) and c-LiNH2 (orthorhombic, P21212). The b ? c structural transition occurs at 10.7 GPa, which is in good agreement with experimental observation. Further analysis of the structural properties, charge density distribution, and calculated phonon density of states indicates that the possibility of the N–H N hydrogen bond occurring in the high-pressure c-LiNH2 is extremely high. The existence of hydrogen bond weakens the N–H polar covalent bonds within NH2 groups, which can facilitate the hydrogen desorption. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction To meet the requirements for efficient storage systems for the future vehicle applications powered by clean hydrogen energy, light metal complex hydrides have received considerable attention due to their high gravimetric hydrogen densities [1–5]. Among them, lithium amide (LiNH2) has been extensively studied as a promising hydrogen storage material since Chen et al. [3] first reported that Li3N can adsorb/desorb hydrogen in two-step reactions. At temperature below 300 °C, the reversible hydrogen capacity of LiNH2 reaches to 6.5 wt.% under 0.04 and 20 bar [3]. However, its dehydrogenation temperature and hydrogenation pressure are still relatively high for practical applications. On the one hand, much effort has been devoted to further improving the thermodynamics and kinetics of the Li–N–H systems [6–9]. Price et al. [7] investigated the effects of different transition metal halides (TiCl3, VCl3, ScCl3, and NiCl3) on the sorption properties of the 1:1 molar ratio of LiNH2 to MgH2 and found that the hydrogen desorption temperature can be significantly reduced after adding these halides, particularly TiCl3. Leng et al. [9] found that the additives of MgCl2 with different amount can improve the H-desorption properties of Li–N–H system through different mechanisms. On the other hand, high-pressure polymorphism of light metal complex hydrides offers new insights because of the higher hydrogen density in them. First-principles investigation into the high-pressure structures of LiBH4 ⇑ Corresponding author at: School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China. Tel.: +86 773 2291 680; fax: +86 773 2290 129. E-mail address: [email protected] (C. Hu). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.07.142
demonstrated that the pressure-induced structural changes in BH4 anions may decrease the activation energy for hydrogen desorption [10]. Chellappa et al. [11] found that during compressing and decompressing the ambient-pressure tetragonal LiNH2 structure a reversible structural transition occurred in the pressure range 8–14 GPa. However, no detailed experimental structural data are yet available for its high-pressure polymorph. As stressed in our previous work [12,13], the structural information of a great number of light metal complex hydrides, especially of their high-pressure phases, is still missing, mainly due to the difficulty in determining the atomic position of light elements like hydrogen from the poor X-ray data. Moreover, the question whether hydrogen bond appears in alkali metal amides like LiNH2 and NaNH2 is still open. Hydrogen bonding interactions in a solution or a compound generally cause the significant changes in their physical and chemical properties including frequency shifts of IR and Raman bands, dielectric constants, electrical conductivities, and altered freezing and boiling points [14]. The typical hydrogen-bonded systems like H2O, NH3, some organic molecules containing N–H groups, and related condensed phases have been extensively studied [15–17]. It is necessary to investigate the formation of hydrogen bond in inorganic amides due to the existence of special NH2 groups in these structures. Although the previous IR and Raman studies reported that hydrogen bonds could not be observed in LiNH2, NaNH2, and even in their high-pressure phases [11,18,19], we explore the possibility of hydrogen bond formation in the high-pressure amide systems due to the ordering induced by pressure on the oriented amide ions. This is also motivated by our work [20] on NaNH2 that has shown the presence of N–H N hydrogen bond under high
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pressure. In this paper, our effort is mainly devoted to investigating the energetically favorable high-pressure phases of LiNH2 in the different pressure ranges and their structural features in order to better understand its high-pressure behavior. 2. Computational details To find the stable high-pressure structures of LiNH2, an ab initio evolutionary algorithm (EA) as implemented in the USPEX (Universal Structure Predictor: Evolutionary Xtallography) code [21,22] was employed. Currently, many successful applications have indicated the EA simulations in USPEX are an effective way to search for the structures with the lowest free energy without requiring any experimental information [23,24]. In our present work, variable-cell structure simulations for LiNH2 with one to four formula units (f.u.) at 0, 10, 20, and 40 GPa were performed to detect the lowest-enthalpy phases at different pressure ranges. Following the first generation of structure produced randomly, each subsequent generation was obtained from the lowest-enthalpy 60% structures of the preceding generation. The variation operators including heredity (65% structures), lattice mutation (25%), and atomic permutation (10%) were used for generating offspring. The underlying ab initio calculations were carried out by using a plane-wave method within the PBE exchange-correlation [25] as implemented in the Vienna Abinitio Simulation Package (VASP) [26]. The electron-ion interaction was described by the all-electron projector augmented wave (PAW) scheme [27] and the electron configurations of 1s22s1, 2s22p3, and 1s1 were treated as valence for Li, N, and H, respectively. During structural relaxation an energy cutoff of 600 eV was used for the plane wave basis sets, and the k-point resolution smaller than 2p⁄0.03 Å 1 in the reciprocal space was used for all structures in order to minimize the error from the k-point meshes. The atomic positions, lattice parameters, and cell volume were fully optimized with an iterative matrix diagonalization scheme until the total energy is converged to 0.1 meV/cell in the self-consistent loop and the force on each atom is less than 1 meV/Å. Phonon calculations were carried out by the supercell method [28] as implemented in the FROPHO code [29], where the force constant matrices are obtained by displacing the atom inside the supercell and the phonon frequencies are directly derived from these matrices. In our work, the 2 2 1, 2 1 2, and 2 2 2 supercells for a-, b-, and c-LiNH2 were constructed and the ±0.01 Å atomic displacements were used in all cases. For detailed comparisons with the experiments, the Raman spectra of high-pressure phases of LiNH2 were calculated using the Quantum–Espresso (QE) package [30]. In our calculations, the norm-conserving pseudopotentials with local density approximation in Troullier–Martins type, a planewave cutoff energy of 80 Ry, and a 10 10 10 Monkhorst-Pack mesh of k-points in the BZ integration were used.
3. Results and discussion At 0 GPa, the ground-state tetragonal phase with space group I4 (hereafter a-LiNH2) and a metastable NaNH2-type structure with space group Fddd (hereafter b-LiNH2) are identified from our EA search for the system with 16 atoms in unit cell, which is a correct result and confirms the robustness of EA for crystal structure prediction. In a higher pressure range from 10 to 40 GPa, an energetically favorable structure with space group P21212 (hereafter c-LiNH2) is predicted from the EA simulations for systems with 8 and 16 atoms. The corresponding crystal structures of a-, b-, and c-LiNH2 are presented in Fig. 1. For the EA searches for systems 4 and 12 atoms in unit cell, two structures with the same space group C2 (for clarity, noted as C2⁄ and C2⁄⁄, respectively) are detected.
By comparing the Gibbs free energies of any two phases, one can determine when the structural phase transition occurs. The Gibbs free energy G = E + PV TS becomes equal to the enthalpy H = E + PV, since all calculations in our work are performed at T = 0 K. Therefore, the high-pressure behavior of LiNH2 can be well understood by comparing the static enthalpies of the above model structures as a function of pressure. As shown in Fig. 2, a-LiNH2 is the most stable polymorph for pressures up to 4.6 GPa, at which it will transform into b-LiNH2. However, it must be noted that the enthalpy difference between a-and b-LiNH2 is tiny, only 1.2– 3.2 meV/f.u. at pressures in the range of 0–4.6 GPa. Further increasing pressure to 10.7 GPa, c-LiNH2 becomes more stable than b-LiNH2. A reversible structural transition for LiNH2 detected from high-pressure Raman spectroscopy study [11] occurs in the pressure range from 8 to 14 GPa, which agrees well with our prediction. Crystal structure information of high-pressure phase of LiNH2, however, is not available from the previous experiment. The identified c-LiNH2 with space group P21212 is first reported in the present work. In addition, we must stress that it may be difficult to detect the structural transition from a- to b-LiNH2 only depending on the present experimental techniques due to the tiny energy difference between a- and b-LiNH2 as mentioned above. In fact, the small energy difference of only a few meV between two competing structures has also been thought to be beyond the accuracy of the present DFT-based calculations. The optimized structural parameters for a-(0 GPa), b-(4.6 GPa), and c-LiNH2 (10.7 GPa) are compiled in Table 1 and the available experimental parameters for a-LiNH2 [31] are also listed for comparison. The calculated volume–pressure relation (see Fig. 3) shows that the changes in volume accompanying with the a ? b and b ? c transitions are about 0.9% and 4.5%. Considering the structural relationship and lower energy barrier between a and b phases, the a ? b transition can be easily implemented by slightly adjusting the atomic position of Li ions and orientation of NH2 amide groups, which belongs to be a displacive transition. However, the transition from orientionally disordered b to ordered c phase generally needs substantial structural modifications (i.e. breaking and reforming Li–N bonds), and should be reconstructive. A structural similarity can be found in these competing crystal structures in which Li atoms are tetrahedrally coordinated by four NH2 groups. Considering the pressure effect, however, a pronounced structural difference in the arrangement of the NH2 groups and Li atoms can be found. As shown in Fig. 1a, the variation in the Li–N bond length in tetragonal a-LiNH2 ranges from 2.064 to 2.220 Å and in the N–Li–N bond angles from 101.96° to 113.23°. The two N–H bond lengths in NH2 group are slightly different from each other, about 1.027 and 1.028 Å. These results are in good agreement with the previous experimental data [31]. For b-LiNH2 displayed in Fig. 1b, Li atoms and amide ions occupy Wyckoff positions of 16f and 16g. The N–H bond lengths in the NH2 groups are exactly equal and about 1.026 Å at 4.6 GPa. The c-LiNH2 phase shown in Fig. 1c and d adopts a pronounced
Fig. 1. Top view of stable crystal structures of LiNH2 at different pressures: (a) a-LiNH2 (I-4) at 0 GPa, (b) b-LiNH2 (Fddd, NaNH2-type) at 4.6 GPa, (c) and (d) c-LiNH2 (P21212) at 10.7 GPa. The dashed lines depicted in (d) indicate hydrogen bond between [NH2] ions in c-LiNH2.
Y. Zhong et al. / Journal of Alloys and Compounds 544 (2012) 129–133
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Fig. 2. Calculated enthalpy differences (DH, in eV/f.u.), relative to a-LiNH2, as a function of pressure for various structures. For clarity the DH between a- and b-LiNH2 at low pressure range below 10 GPa is shown in the inset.
Fig. 3. Calculated volume-pressure relationship for LiNH2 at ambient temperature. The changes in volume accompanying with the I-4 ? Fddd and Fddd ? P21212 transitions are about 0.9% and 4.5%, respectively.
two-dimensional packing in which every two NH2 layers are intercalated by a Li ions layer. The arrangement of every NH2 groups within each NH2 layer is aligned in one direction and the two
neighboring NH2 anion layers are perpendicular to each other. The connection between the N atom on a NH2 group and the N–H bond in its two neighboring NH2 groups is approximately linear and the corresponding N–H N bond angle is about 175.6° at 10.7 GPa. It may be easy to think of the existence of N–H N hydrogen bond in c-LiNH2 considering its specific structural orientation. In fact, the inter-molecular N H distance in c-LiNH2 (2.105 Å at 10.7 GPa) is substantially shorter than the sum of Van der Waals radii of N and H (2.75 Å) where hydrogen bond is approved [32]. In a-and b-LiNH2, the orientation of amide ions is disordered and the average N H distances are about 2.915 and 3.032 Å, respectively. The two lower-pressure phases do not seem possess any significant hydrogen bonding, which is consistent with the previous experimental observations [18]. Additionally, compared to a- and b-LiNH2, the N–H bond lengths in each NH2 group of c-LiNH2 is 1.032 Å and distinctly elongated at 10.7 GPa, which is a good indicator of the emergence of hydrogen bond and would be further discussed in detail from the latter lattice dynamical calculations. Calculated charge density distribution (CDD) presented in Fig. 4 reveals the chemical bonding characteristics of the competing polymorphs of LiNH2. Spherical charge distribution around Li atoms shows the ionic bonding interaction between Li and NH2 groups. Strong polarized covalent bond exists between N and H
Fig. 4. Charge density distribution of LiNH2 in the range of 0–0.1 e/Å3 in the various slices (a) across the N–H bond and a neighboring NH2 group for a-LiNH2 at 0 GPa, (b) across the NH2 group and a neighboring N atom for b-LiNH2 at 4.6 GPa, and (c) across the NH2 groups and neighboring N atoms for c-LiNH2 at 10.7 GPa. The hydrogen bond path in c-LiNH2 is denoted by a dotted line.
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Fig. 5. Predicted phonon densities of states (PDOS) for a-(at equilibrium), b-(at 4.6 GPa), and c-LiNH2 (at 10.7 GPa). For clarity a fragment of N–H N hydrogen bond path is schematically illustrated in the top panel of this figure.
atoms owing to the directional feature of CDD around each NH2 group. Charge density analysis is also an effective way to probe the existence of hydrogen bond. According to the topological properties of charge density (q) at the bond critical points (bcp), hydrogen bond can be confirmed. Generally, about 0.01–0.03 electrons are transferred from the proton acceptor to the donor when hydrogen bond exists [33]. As shown in Fig. 4c, the calculated qbcp is in the range of 0.02–0.03 eÅ 3 along the N–H N bond path, clearly reflecting the existence of hydrogen bond in c-LiNH2. The similar feature cannot be found in a-and b-LiNH2 (see Fig. 4a and b). The phonon density of states (PDOS) for a- (at equilibrium), b- (at 4.6 GPa), and c-LiNH2 (at 10.7 GPa) presented in Fig. 5 are calculated using the direct force constant approach [28]. No imaginary phonon frequencies are found in the whole Brillouin zone, indicating that these structures are dynamically stable. The basic features of the PDOSs are rather similar for all structures – all phonon modes can be clearly divided into three frequencies ranges: (i) the low-frequency modes which are assigned to translational and librational motions and associated with the displacements of both Li+ cations and [NH2] anions; (ii) the medium-frequency modes arising from the H–N–H bending deformation; and (iii) the high-frequency modes mainly being ascribed to the N–H symmetric and asymmetric stretching. In a-LiNH2, our calculated N–H stretching modes at 3337 and 3400 cm 1, which are consistent with the previous Raman spectra experiment (3269 and 3332 cm 1) [11]. Considering the different local arrangements of Li ions and NH2 groups, however, some significant differences in the PDOSs of the three structures can also be found. First, the librational modes shift to higher frequency with increasing pressure. This means an enhancement of the vibronic coupling of N and H atoms in [NH2] ions. Second, the medium-frequency bending modes broaden evidently and also shift to higher frequency, especially in c-LiNH2. This originates from the smaller H–N–H bond angles (102.3°, 99.4°) in b- and c-LiNH2, compared to bond angle of 102.5° for a-LiNH2. Finally, it can be seen that the changes in the high-frequency N–H stretching modes in b- and c-LiNH2 is different entirely from each other with increasing pressure. In b-LiNH2, the N–H stretching modes shift slightly to higher frequency, which is a typical bond compression resulting from pressure effect. In c-LiNH2, however, the corresponding stretching modes shifts distinctly to lower frequency, which should be attributed to the equally strong N–H N hydrogen bond as illustrated in Fig. 5. The emergence of hydrogen bond undoubtedly elongates the N–H bond length and softens the N–H stretching modes. As pointed out by Li et al. [34], the estimation of relative hydrogen
bond strength from shifts in the X–H stretching frequencies can be thought of a simple and widely used measure. Unfortunately, as suggested by Chellappa et al. [11], hydrogen bond cannot be identified from their high-pressure Raman spectroscopic experiment. In fact, we have found that Raman spectra under compression in reference [11] have definitely indicated a high-frequency shift in the range from 7.6 to 10.1 GPa and a low-frequency shift above 12.5 GPa. The reason why the past conclusion that hydrogen bond does not emerge in LiNH2 or other amides is made may be perhaps due to the lack of detailed high-pressure crystal information. The existence of hydrogen bonding weakens the covalent N–H, which possibly facilitates the hydrogen release from c-LiNH2. Finally, the Raman spectra of c-LiNH2 at 14.8 GPa is calculated using the Quantum-Espresso (QE) package [30]. For c-LiNH2 with space group P21212, the zone-center optical modes can be classified as the following irreducible representations: Copt = 5A + 5B1 + 7B2 + 7B3, where B1, B2, and B3 are infrared and Raman active and A is only Raman active. The calculated Raman-active modes due to the N–H symmetric and asymmetric stretching are at 3138 and 3206 cm 1, respectively, which can be comparable to the experimental values (3253 and 3340 cm 1) [11]. The calculated librational modes are at 493, 564, 617 cm 1, which is also consistent with the experimental observations (524, 610, and 658 cm 1) [11]. The error between our calculated values and experimental data is about 4–7% and mainly attributed to the use of LDA functional in our present work. 4. Conclusions In conclusion, a detailed study of the high-pressure structural stability in LiNH2 has been investigated by ab initio total-energy calculations and evolutionary structure searches. Two high-pressure polymorphs, b-LiNH2 (orthorhombic, Fddd) and c-LiNH2 (orthorhombic, P21212), are found to be more stable than the ground-state a-LiNH2 with increasing pressure. Static enthalpy calculations reveal that a-LiNH2 first transforms into b-LiNH2 at 4.6 GPa, then into c-LiNH2 above 10.7 GPa. Under compression, transformation into a higher-pressure stable structure with lower symmetry and pressure-induced ordering are consistent with the experimental observations. Further analysis on the structural properties, charge density distribution, and the calculated phonon densities of states for all the competing structures shows the N–H N hydrogen bond emerges in c-LiNH2. It is worth mentioning that hydrogen bonds in c-LiNH2 and shorter N–H N contacts undoubtedly weaken the covalent N–H bonds in amide ions and may be beneficial to the hydrogen release from c-LiNH2. Acknowledgments This research is supported by the National Natural Science Foundation of China (Grant Nos. 50901023, 50971049, 11164005, 51161004), the Guangxi Natural Science Foundation of China (Grant Nos. 2010GXNSFD013009, 2012GXNSFGA060002), the Research Foundation of Guangxi Key Laboratory of Information, and the Project-sponsored by SRF for ROCS, SEM. References [1] B. Bogdanovic, M. Schwickardi, J. Alloys Compd. 253 (1997) 1. [2] A. Züttel, P. Wenger, S. Rentsch, P. Sudan, P. Mauron, C. Emmenegger, J. Power Sources 118 (2003) 1. [3] P. Chen, Z.T. Xiong, J.Z. Luo, J.Y. Lin, K.L. Tan, Nature 420 (2002) 302. [4] C. Liang, Y.F. Liu, H.L. Fu, Y.F. Ding, M.X. Gao, H.G. Pan, J. Alloys Compd. 509 (2011) 7844. [5] Y.F. Zhou, Y.F. Liu, W. Wu, Y. Zhang, M.X. Gao, H.G. Pan, J. Phys. Chem. C 116 (2012) 1588. [6] D. Pottmaier, F. Dolci, M. Orlova, G. Vaughan, M. Fichtner, W. Lohstroh, M. Baricco, J. Alloys Compd. 509S (2011) S719. [7] C. Price, J. Gray, R.L. Jr, D.L. Anton, Int. J. Hydrogen Energy 37 (2012) 2742.
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Contents lists available at SciVerse ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Pressure-induced structural transitions of LiNH2: A first-principle study Yan Zhong a, Huaiying Zhou a,b, Chaohao Hu b,c,⇑, Dianhui Wang b, Guanghui Rao b a
School of Materials Science and Engineering, Central South University, Changsha 410083, PR China School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China c International Center for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, PR China b
a r t i c l e
i n f o
Article history: Received 23 May 2012 Received in revised form 26 July 2012 Accepted 27 July 2012 Available online 4 August 2012 Keywords: Lithium amide Pressure-induced structural transition First-principles method Evolutionary structure prediction
a b s t r a c t The pressure-induced phase transformations in LiNH2 have been studied by using ab initio total-energy calculations and evolutionary structure prediction simulations. Two stable high-pressure polymorphs of LiNH2 are found: b-LiNH2 (orthorhombic, NaNH2-type, Fddd) and c-LiNH2 (orthorhombic, P21212). The b ? c structural transition occurs at 10.7 GPa, which is in good agreement with experimental observation. Further analysis of the structural properties, charge density distribution, and calculated phonon density of states indicates that the possibility of the N–H N hydrogen bond occurring in the high-pressure c-LiNH2 is extremely high. The existence of hydrogen bond weakens the N–H polar covalent bonds within NH2 groups, which can facilitate the hydrogen desorption. Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction To meet the requirements for efficient storage systems for the future vehicle applications powered by clean hydrogen energy, light metal complex hydrides have received considerable attention due to their high gravimetric hydrogen densities [1–5]. Among them, lithium amide (LiNH2) has been extensively studied as a promising hydrogen storage material since Chen et al. [3] first reported that Li3N can adsorb/desorb hydrogen in two-step reactions. At temperature below 300 °C, the reversible hydrogen capacity of LiNH2 reaches to 6.5 wt.% under 0.04 and 20 bar [3]. However, its dehydrogenation temperature and hydrogenation pressure are still relatively high for practical applications. On the one hand, much effort has been devoted to further improving the thermodynamics and kinetics of the Li–N–H systems [6–9]. Price et al. [7] investigated the effects of different transition metal halides (TiCl3, VCl3, ScCl3, and NiCl3) on the sorption properties of the 1:1 molar ratio of LiNH2 to MgH2 and found that the hydrogen desorption temperature can be significantly reduced after adding these halides, particularly TiCl3. Leng et al. [9] found that the additives of MgCl2 with different amount can improve the H-desorption properties of Li–N–H system through different mechanisms. On the other hand, high-pressure polymorphism of light metal complex hydrides offers new insights because of the higher hydrogen density in them. First-principles investigation into the high-pressure structures of LiBH4 ⇑ Corresponding author at: School of Materials Science and Engineering, Guilin University of Electronic Technology, Guilin 541004, PR China. Tel.: +86 773 2291 680; fax: +86 773 2290 129. E-mail address: [email protected] (C. Hu). 0925-8388/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2012.07.142
demonstrated that the pressure-induced structural changes in BH4 anions may decrease the activation energy for hydrogen desorption [10]. Chellappa et al. [11] found that during compressing and decompressing the ambient-pressure tetragonal LiNH2 structure a reversible structural transition occurred in the pressure range 8–14 GPa. However, no detailed experimental structural data are yet available for its high-pressure polymorph. As stressed in our previous work [12,13], the structural information of a great number of light metal complex hydrides, especially of their high-pressure phases, is still missing, mainly due to the difficulty in determining the atomic position of light elements like hydrogen from the poor X-ray data. Moreover, the question whether hydrogen bond appears in alkali metal amides like LiNH2 and NaNH2 is still open. Hydrogen bonding interactions in a solution or a compound generally cause the significant changes in their physical and chemical properties including frequency shifts of IR and Raman bands, dielectric constants, electrical conductivities, and altered freezing and boiling points [14]. The typical hydrogen-bonded systems like H2O, NH3, some organic molecules containing N–H groups, and related condensed phases have been extensively studied [15–17]. It is necessary to investigate the formation of hydrogen bond in inorganic amides due to the existence of special NH2 groups in these structures. Although the previous IR and Raman studies reported that hydrogen bonds could not be observed in LiNH2, NaNH2, and even in their high-pressure phases [11,18,19], we explore the possibility of hydrogen bond formation in the high-pressure amide systems due to the ordering induced by pressure on the oriented amide ions. This is also motivated by our work [20] on NaNH2 that has shown the presence of N–H N hydrogen bond under high
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pressure. In this paper, our effort is mainly devoted to investigating the energetically favorable high-pressure phases of LiNH2 in the different pressure ranges and their structural features in order to better understand its high-pressure behavior. 2. Computational details To find the stable high-pressure structures of LiNH2, an ab initio evolutionary algorithm (EA) as implemented in the USPEX (Universal Structure Predictor: Evolutionary Xtallography) code [21,22] was employed. Currently, many successful applications have indicated the EA simulations in USPEX are an effective way to search for the structures with the lowest free energy without requiring any experimental information [23,24]. In our present work, variable-cell structure simulations for LiNH2 with one to four formula units (f.u.) at 0, 10, 20, and 40 GPa were performed to detect the lowest-enthalpy phases at different pressure ranges. Following the first generation of structure produced randomly, each subsequent generation was obtained from the lowest-enthalpy 60% structures of the preceding generation. The variation operators including heredity (65% structures), lattice mutation (25%), and atomic permutation (10%) were used for generating offspring. The underlying ab initio calculations were carried out by using a plane-wave method within the PBE exchange-correlation [25] as implemented in the Vienna Abinitio Simulation Package (VASP) [26]. The electron-ion interaction was described by the all-electron projector augmented wave (PAW) scheme [27] and the electron configurations of 1s22s1, 2s22p3, and 1s1 were treated as valence for Li, N, and H, respectively. During structural relaxation an energy cutoff of 600 eV was used for the plane wave basis sets, and the k-point resolution smaller than 2p⁄0.03 Å 1 in the reciprocal space was used for all structures in order to minimize the error from the k-point meshes. The atomic positions, lattice parameters, and cell volume were fully optimized with an iterative matrix diagonalization scheme until the total energy is converged to 0.1 meV/cell in the self-consistent loop and the force on each atom is less than 1 meV/Å. Phonon calculations were carried out by the supercell method [28] as implemented in the FROPHO code [29], where the force constant matrices are obtained by displacing the atom inside the supercell and the phonon frequencies are directly derived from these matrices. In our work, the 2 2 1, 2 1 2, and 2 2 2 supercells for a-, b-, and c-LiNH2 were constructed and the ±0.01 Å atomic displacements were used in all cases. For detailed comparisons with the experiments, the Raman spectra of high-pressure phases of LiNH2 were calculated using the Quantum–Espresso (QE) package [30]. In our calculations, the norm-conserving pseudopotentials with local density approximation in Troullier–Martins type, a planewave cutoff energy of 80 Ry, and a 10 10 10 Monkhorst-Pack mesh of k-points in the BZ integration were used.
3. Results and discussion At 0 GPa, the ground-state tetragonal phase with space group I4 (hereafter a-LiNH2) and a metastable NaNH2-type structure with space group Fddd (hereafter b-LiNH2) are identified from our EA search for the system with 16 atoms in unit cell, which is a correct result and confirms the robustness of EA for crystal structure prediction. In a higher pressure range from 10 to 40 GPa, an energetically favorable structure with space group P21212 (hereafter c-LiNH2) is predicted from the EA simulations for systems with 8 and 16 atoms. The corresponding crystal structures of a-, b-, and c-LiNH2 are presented in Fig. 1. For the EA searches for systems 4 and 12 atoms in unit cell, two structures with the same space group C2 (for clarity, noted as C2⁄ and C2⁄⁄, respectively) are detected.
By comparing the Gibbs free energies of any two phases, one can determine when the structural phase transition occurs. The Gibbs free energy G = E + PV TS becomes equal to the enthalpy H = E + PV, since all calculations in our work are performed at T = 0 K. Therefore, the high-pressure behavior of LiNH2 can be well understood by comparing the static enthalpies of the above model structures as a function of pressure. As shown in Fig. 2, a-LiNH2 is the most stable polymorph for pressures up to 4.6 GPa, at which it will transform into b-LiNH2. However, it must be noted that the enthalpy difference between a-and b-LiNH2 is tiny, only 1.2– 3.2 meV/f.u. at pressures in the range of 0–4.6 GPa. Further increasing pressure to 10.7 GPa, c-LiNH2 becomes more stable than b-LiNH2. A reversible structural transition for LiNH2 detected from high-pressure Raman spectroscopy study [11] occurs in the pressure range from 8 to 14 GPa, which agrees well with our prediction. Crystal structure information of high-pressure phase of LiNH2, however, is not available from the previous experiment. The identified c-LiNH2 with space group P21212 is first reported in the present work. In addition, we must stress that it may be difficult to detect the structural transition from a- to b-LiNH2 only depending on the present experimental techniques due to the tiny energy difference between a- and b-LiNH2 as mentioned above. In fact, the small energy difference of only a few meV between two competing structures has also been thought to be beyond the accuracy of the present DFT-based calculations. The optimized structural parameters for a-(0 GPa), b-(4.6 GPa), and c-LiNH2 (10.7 GPa) are compiled in Table 1 and the available experimental parameters for a-LiNH2 [31] are also listed for comparison. The calculated volume–pressure relation (see Fig. 3) shows that the changes in volume accompanying with the a ? b and b ? c transitions are about 0.9% and 4.5%. Considering the structural relationship and lower energy barrier between a and b phases, the a ? b transition can be easily implemented by slightly adjusting the atomic position of Li ions and orientation of NH2 amide groups, which belongs to be a displacive transition. However, the transition from orientionally disordered b to ordered c phase generally needs substantial structural modifications (i.e. breaking and reforming Li–N bonds), and should be reconstructive. A structural similarity can be found in these competing crystal structures in which Li atoms are tetrahedrally coordinated by four NH2 groups. Considering the pressure effect, however, a pronounced structural difference in the arrangement of the NH2 groups and Li atoms can be found. As shown in Fig. 1a, the variation in the Li–N bond length in tetragonal a-LiNH2 ranges from 2.064 to 2.220 Å and in the N–Li–N bond angles from 101.96° to 113.23°. The two N–H bond lengths in NH2 group are slightly different from each other, about 1.027 and 1.028 Å. These results are in good agreement with the previous experimental data [31]. For b-LiNH2 displayed in Fig. 1b, Li atoms and amide ions occupy Wyckoff positions of 16f and 16g. The N–H bond lengths in the NH2 groups are exactly equal and about 1.026 Å at 4.6 GPa. The c-LiNH2 phase shown in Fig. 1c and d adopts a pronounced
Fig. 1. Top view of stable crystal structures of LiNH2 at different pressures: (a) a-LiNH2 (I-4) at 0 GPa, (b) b-LiNH2 (Fddd, NaNH2-type) at 4.6 GPa, (c) and (d) c-LiNH2 (P21212) at 10.7 GPa. The dashed lines depicted in (d) indicate hydrogen bond between [NH2] ions in c-LiNH2.
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Fig. 2. Calculated enthalpy differences (DH, in eV/f.u.), relative to a-LiNH2, as a function of pressure for various structures. For clarity the DH between a- and b-LiNH2 at low pressure range below 10 GPa is shown in the inset.
Fig. 3. Calculated volume-pressure relationship for LiNH2 at ambient temperature. The changes in volume accompanying with the I-4 ? Fddd and Fddd ? P21212 transitions are about 0.9% and 4.5%, respectively.
two-dimensional packing in which every two NH2 layers are intercalated by a Li ions layer. The arrangement of every NH2 groups within each NH2 layer is aligned in one direction and the two
neighboring NH2 anion layers are perpendicular to each other. The connection between the N atom on a NH2 group and the N–H bond in its two neighboring NH2 groups is approximately linear and the corresponding N–H N bond angle is about 175.6° at 10.7 GPa. It may be easy to think of the existence of N–H N hydrogen bond in c-LiNH2 considering its specific structural orientation. In fact, the inter-molecular N H distance in c-LiNH2 (2.105 Å at 10.7 GPa) is substantially shorter than the sum of Van der Waals radii of N and H (2.75 Å) where hydrogen bond is approved [32]. In a-and b-LiNH2, the orientation of amide ions is disordered and the average N H distances are about 2.915 and 3.032 Å, respectively. The two lower-pressure phases do not seem possess any significant hydrogen bonding, which is consistent with the previous experimental observations [18]. Additionally, compared to a- and b-LiNH2, the N–H bond lengths in each NH2 group of c-LiNH2 is 1.032 Å and distinctly elongated at 10.7 GPa, which is a good indicator of the emergence of hydrogen bond and would be further discussed in detail from the latter lattice dynamical calculations. Calculated charge density distribution (CDD) presented in Fig. 4 reveals the chemical bonding characteristics of the competing polymorphs of LiNH2. Spherical charge distribution around Li atoms shows the ionic bonding interaction between Li and NH2 groups. Strong polarized covalent bond exists between N and H
Fig. 4. Charge density distribution of LiNH2 in the range of 0–0.1 e/Å3 in the various slices (a) across the N–H bond and a neighboring NH2 group for a-LiNH2 at 0 GPa, (b) across the NH2 group and a neighboring N atom for b-LiNH2 at 4.6 GPa, and (c) across the NH2 groups and neighboring N atoms for c-LiNH2 at 10.7 GPa. The hydrogen bond path in c-LiNH2 is denoted by a dotted line.
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Fig. 5. Predicted phonon densities of states (PDOS) for a-(at equilibrium), b-(at 4.6 GPa), and c-LiNH2 (at 10.7 GPa). For clarity a fragment of N–H N hydrogen bond path is schematically illustrated in the top panel of this figure.
atoms owing to the directional feature of CDD around each NH2 group. Charge density analysis is also an effective way to probe the existence of hydrogen bond. According to the topological properties of charge density (q) at the bond critical points (bcp), hydrogen bond can be confirmed. Generally, about 0.01–0.03 electrons are transferred from the proton acceptor to the donor when hydrogen bond exists [33]. As shown in Fig. 4c, the calculated qbcp is in the range of 0.02–0.03 eÅ 3 along the N–H N bond path, clearly reflecting the existence of hydrogen bond in c-LiNH2. The similar feature cannot be found in a-and b-LiNH2 (see Fig. 4a and b). The phonon density of states (PDOS) for a- (at equilibrium), b- (at 4.6 GPa), and c-LiNH2 (at 10.7 GPa) presented in Fig. 5 are calculated using the direct force constant approach [28]. No imaginary phonon frequencies are found in the whole Brillouin zone, indicating that these structures are dynamically stable. The basic features of the PDOSs are rather similar for all structures – all phonon modes can be clearly divided into three frequencies ranges: (i) the low-frequency modes which are assigned to translational and librational motions and associated with the displacements of both Li+ cations and [NH2] anions; (ii) the medium-frequency modes arising from the H–N–H bending deformation; and (iii) the high-frequency modes mainly being ascribed to the N–H symmetric and asymmetric stretching. In a-LiNH2, our calculated N–H stretching modes at 3337 and 3400 cm 1, which are consistent with the previous Raman spectra experiment (3269 and 3332 cm 1) [11]. Considering the different local arrangements of Li ions and NH2 groups, however, some significant differences in the PDOSs of the three structures can also be found. First, the librational modes shift to higher frequency with increasing pressure. This means an enhancement of the vibronic coupling of N and H atoms in [NH2] ions. Second, the medium-frequency bending modes broaden evidently and also shift to higher frequency, especially in c-LiNH2. This originates from the smaller H–N–H bond angles (102.3°, 99.4°) in b- and c-LiNH2, compared to bond angle of 102.5° for a-LiNH2. Finally, it can be seen that the changes in the high-frequency N–H stretching modes in b- and c-LiNH2 is different entirely from each other with increasing pressure. In b-LiNH2, the N–H stretching modes shift slightly to higher frequency, which is a typical bond compression resulting from pressure effect. In c-LiNH2, however, the corresponding stretching modes shifts distinctly to lower frequency, which should be attributed to the equally strong N–H N hydrogen bond as illustrated in Fig. 5. The emergence of hydrogen bond undoubtedly elongates the N–H bond length and softens the N–H stretching modes. As pointed out by Li et al. [34], the estimation of relative hydrogen
bond strength from shifts in the X–H stretching frequencies can be thought of a simple and widely used measure. Unfortunately, as suggested by Chellappa et al. [11], hydrogen bond cannot be identified from their high-pressure Raman spectroscopic experiment. In fact, we have found that Raman spectra under compression in reference [11] have definitely indicated a high-frequency shift in the range from 7.6 to 10.1 GPa and a low-frequency shift above 12.5 GPa. The reason why the past conclusion that hydrogen bond does not emerge in LiNH2 or other amides is made may be perhaps due to the lack of detailed high-pressure crystal information. The existence of hydrogen bonding weakens the covalent N–H, which possibly facilitates the hydrogen release from c-LiNH2. Finally, the Raman spectra of c-LiNH2 at 14.8 GPa is calculated using the Quantum-Espresso (QE) package [30]. For c-LiNH2 with space group P21212, the zone-center optical modes can be classified as the following irreducible representations: Copt = 5A + 5B1 + 7B2 + 7B3, where B1, B2, and B3 are infrared and Raman active and A is only Raman active. The calculated Raman-active modes due to the N–H symmetric and asymmetric stretching are at 3138 and 3206 cm 1, respectively, which can be comparable to the experimental values (3253 and 3340 cm 1) [11]. The calculated librational modes are at 493, 564, 617 cm 1, which is also consistent with the experimental observations (524, 610, and 658 cm 1) [11]. The error between our calculated values and experimental data is about 4–7% and mainly attributed to the use of LDA functional in our present work. 4. Conclusions In conclusion, a detailed study of the high-pressure structural stability in LiNH2 has been investigated by ab initio total-energy calculations and evolutionary structure searches. Two high-pressure polymorphs, b-LiNH2 (orthorhombic, Fddd) and c-LiNH2 (orthorhombic, P21212), are found to be more stable than the ground-state a-LiNH2 with increasing pressure. Static enthalpy calculations reveal that a-LiNH2 first transforms into b-LiNH2 at 4.6 GPa, then into c-LiNH2 above 10.7 GPa. Under compression, transformation into a higher-pressure stable structure with lower symmetry and pressure-induced ordering are consistent with the experimental observations. Further analysis on the structural properties, charge density distribution, and the calculated phonon densities of states for all the competing structures shows the N–H N hydrogen bond emerges in c-LiNH2. It is worth mentioning that hydrogen bonds in c-LiNH2 and shorter N–H N contacts undoubtedly weaken the covalent N–H bonds in amide ions and may be beneficial to the hydrogen release from c-LiNH2. Acknowledgments This research is supported by the National Natural Science Foundation of China (Grant Nos. 50901023, 50971049, 11164005, 51161004), the Guangxi Natural Science Foundation of China (Grant Nos. 2010GXNSFD013009, 2012GXNSFGA060002), the Research Foundation of Guangxi Key Laboratory of Information, and the Project-sponsored by SRF for ROCS, SEM. References [1] B. Bogdanovic, M. Schwickardi, J. Alloys Compd. 253 (1997) 1. [2] A. Züttel, P. Wenger, S. Rentsch, P. Sudan, P. Mauron, C. Emmenegger, J. Power Sources 118 (2003) 1. [3] P. Chen, Z.T. Xiong, J.Z. Luo, J.Y. Lin, K.L. Tan, Nature 420 (2002) 302. [4] C. Liang, Y.F. Liu, H.L. Fu, Y.F. Ding, M.X. Gao, H.G. Pan, J. Alloys Compd. 509 (2011) 7844. [5] Y.F. Zhou, Y.F. Liu, W. Wu, Y. Zhang, M.X. Gao, H.G. Pan, J. Phys. Chem. C 116 (2012) 1588. [6] D. Pottmaier, F. Dolci, M. Orlova, G. Vaughan, M. Fichtner, W. Lohstroh, M. Baricco, J. Alloys Compd. 509S (2011) S719. [7] C. Price, J. Gray, R.L. Jr, D.L. Anton, Int. J. Hydrogen Energy 37 (2012) 2742.
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