Ab initio studies of the electronic structure of the quaternary system LiBC4N4

Journal of Alloys and Compounds 427 (2007) 61–66

Ab initio studies of the electronic structure of the quaternary system LiBC4N4 S.F. Matar a,∗ , E. Betranhandy a , M. Nakhl b a

Institut de Chimie de la Mati`ere Condens´ee de Bordeaux-CNRS, Universit´e Bordeaux I, 87 ave Dr Albert Schweitzer, F-33608 Pessac, France b Faculty of Science and Engineering. University “Saint-Esprit” Kaslik, USEK, Jounieh, Lebanon Received 3 March 2006; accepted 20 March 2006 Available online 27 April 2006

Abstract Starting from experimental data on the synthesis of solid LiBC4 N4 , an ab initio study has been carried out within the DFT-LDA framework of its structure and completed by accounting for other potential cubic arrangements. The consideration of stabilization energies confirms the experimental phase as the most stable one but predicts some other potential arrangements. The system is found very compressible with a bulk modulus close to that of gypsum (B0 = 35 GPa). The electronic structure characteristics are provided allowing to confirm an ionic behavior involving complex anionic species (Li+ [B(CN)4 ]− ). The control of the crystal cell size by a stoichiometry modification, such as by a CN group substitution is also studied. The proposition of LiBX4 and LiBS4 N4 stoichiometries leads to predict new materials. © 2006 Elsevier B.V. All rights reserved. Keywords: DFT-LDA; ELF; ECOV ; Electronic structure; Ionic crystal; Geometry optimization

1. Introduction Several ways for the syntheses of various solid carbon nitrides are proposed since the prediction of such stoichiometries 20 years ago as potential ultra-hard materials [1]. Nevertheless, the solid binary carbon nitrides (CNx ) present positive magnitudes of formation enthalpies, which is a limiting factor for obtaining pure crystal compounds. Alternative (ternary) compositions were proposed – theoretically and experimentally – essentially with the addition of boron, in order to make these enthalpies negative on one hand, and to keep their exceptional mechanical properties on the other hand. One of the most interesting proposed stoichiometries is BC2 N—theoretically proposed by Mattesini and Matar [2] and synthesized by Solozhenko et al. [3]. Another ternary system, BC3 N3 was investigated by us in different 2D and 3D crystal structures (graphitic-like, ␤ or rhombohedral) [4], and a pathway for its synthesis was proposed by Kouvetakis et al. [5]. Simultaneously, a crystal quaternary carbon nitride, LiBC4 N4 was also obtained by this research team and “might provide a unique synthetic route to new hard materials with diamond-like or graphite-like structures by high-

pressure methods” (sic). Recent investigations were reported on the crystal structure determination of a similar lithium boron system with H− anion: LiBH4 [6]. The orthorhombic structure and the atomic arrangements are, however, quite different from those of LiBC4 N4 . Our purpose is to investigate and characterize the structure of LiBC4 N4 by ab initio methods based on the well-established density functional theory (DFT) in its local approximation (LDA). In a first step, two cubic theoretical structures are considered [LiB(CN)4 formula type] compared with the experimentally obtained cubic one (P−43m ). From this a first insight into the electronic structure influence on stability can be obtained. Then, the mechanical property of compressibility will be established through the calculation of the bulk moduli. The electronic behavior of such compounds will be also characterized. Moreover, considering that the cyanide ion CN− and a halogen ion X− carry the same charge, and that they are isoelectronic with each other, we have also compared LiBC4 N4 with hypothetical LiBX4 structures. Finally, we have taken into account another hypothetical way to control the cell parameter with the insertion of sulfur atoms in the tetrahedral central group. 2. Computational details

∗

Corresponding author. Tel.: +33 5 4000 2690; fax: +33 5 4000 2761. E-mail address: [email protected] (S.F. Matar).

0925-8388/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2006.03.033

Calculations of the electronic states were carried out in the framework of density functional theory (DFT) [7] using mainly

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the VASP package [8]. The interactions between the ions and the electrons are described by using ultra-soft Vanderbilt pseudo potentials (US-PP) [9] and the electron–electron interaction is treated within the LDA by the Ceperley–Alder exchangecorrelation potential [10]. In the plane wave pseudo potential approach, the rapid variation of the potential near the nuclei is avoided by substituting the all-electron Hamiltonian with a smoother pseudo-Hamiltonian, which reproduces the valence energy spectrum. The rapid variations of the wave functions near the nucleus, characterising the core states are removed. The socalled frozen core approximation. The PP allows a considerable reduction of the necessary number of plane waves per atom for transition metal and first row elements, thus force and full stress tensor can be easily calculated and used to relax atoms. In our computational scheme the conjugate-gradient algorithm [11] is used to relax the ions of the considered systems into their ground state. Optimization of the structural parameters is performed ˚ −1 and all until the forces on the atoms are less than 0.02 eV A −3 ˚ stress components made less than 0.003 eV A . The calculations were performed by using an energy cut-off of 434.8 eV for the plane wave basis set. The tetrahedron method with Bl¨ochl corrections [12] as well as a Methfessel–Paxton scheme for conducting systems was applied for both geometry relaxation and total energy calculations. Brillouin-zone integrals were approximated using the special k-point sampling of Monkhorst and Pack [13]. Furthermore, from US-PP calculations a qualitative picture of the electron localization can be obtained through real space electronic structure plots of the electron localization function ELF according to Becke and Edgecombe [14]. Besides its use of the DFT LDA, the augmented spherical wave (ASW) [15] method is based on the atomic sphere approximation (ASA). The ASA consists in dividing the cell into atomic spheres whose total volume is equal to the cell volume. The calculation being carried out in the atomic spheres space, empty spheres (pseudo-atoms) need to be introduced in low compactness structures, such as those in the systems studied here. Moreover, the supplementary approximation of a spherical average on potential and electronic density is introduced. In this work, ASW calculations are used in order to get electronic properties and chemical bonds characteristics. 3. Structural results Kouvetakis et al. [5] proposed a synthetic route for the preparation of crystalline LiBC4 N4 which is as follows: 4SiMe3 CN + LiBF4 → LiBC4 N4 + 4SiMe3 F Then, a heating of the obtained amorphous solid (250 ◦ C) allows crystallizing the product in a cubic structure. This last one is described as two interpenetrating diamond-like networks of BC4 and LiN4 tetrahedra linked by C N chemical bonds, as indicated by several experimental characterization techniques. They also indicated, with 7 Li, 11 B and 13 C NMR spectra, that this structure can be considered as a tetragonal complex anion B(CN)4 − with B C bonds and with the lithium cation as counter-ion (Fig. 1).

Fig. 1. LiBC4 N4 crystal structure from [5]. Boron is at the cell center and is bonded with C atoms. Li is at origin and N is between C and Li. Notice the “CN” entities.

We have considered in a first step that other types of LiBC4 N4 structures could be obtained in the presented reaction. One of them theoretically devised can be set up from the experimental one by a position exchange between Li and B, before geometry optimization. Such geometry allows studying another connection for CN pairs, particularly if we consider the existence of LiCN, used for several chemical reactions [16]. One can note that the theoretical study of the single isolated LiCN molecule and its isomerism was carried out on various bases, such as Hartree–Fock or DFT calculations, as, for example, in references [17]. The other configurations can be considered as intermediate between the experimentally described structure and the theoretical structure obtained by a Li/B inversion. As a matter of fact, three other structural types can be built where boron is linked with 3, 2 and 1 carbon atoms when lithium is, respectively, linked with 3, 2 and 1 nitrogen atoms. These so-called “mixed” structures are geometrically optimized with a full relaxation of the parameters. Such operation leads to obtain the relaxation energies, which are used to compare the relative stabilities of all the considered LiBC4 N4 structures. Concerning the calculations on the experimental structure, the first results point to a conservation of the initial geometry within the same P−43m space group, with stabilization energy of −84,937 eV per formula unit (f.u.). The calculated lattice ˚ which slightly underestimates the experiparameter is 5.369 A, ˚ This is explained by the use of the LDA, mental value (5.476 A). which is known for its underestimation of distances. Note that the calculations are at zero entropy (0 K). Li is located in the (1a) site while B is in (1b) site. C and N atoms are both in (4e) sites with xC = 0.3325 and xN = 0.2086. If we compare the interatomic distances with the experimental values [5], the underestimation due to using the LDA is found again, but the global agreement is still good, which enforces our computational results. It is set as a reference for the following calculations.

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Concerning the structure where Li and B are initially inverted before geometry optimization (inv.-LiBC4 N4 ), the obtained results show geometry conservation (P−43m space group) with stabilization energy of −83.391 eV/f.u. This energy difference (≈1.5 eV) clearly indicates that this hypothetical structure is thermodynamically disadvantaged in a synthesis process. The ˚ Li is located in the (1a) site lattice parameter is here 5.440 A. while B is in (1b) site. C and N atoms are both in (4e) sites with xC = 0.2181 and xN = 0.3416. The changes of distances in comparison with the experimental LiBC4 N4 can be attributed to a modification of the electronic structure in the crystal cell. This will be studied more accurately further in this article. The “mixed” structures are all less stable than the experimental LiBC4 N4 one: compared with the reference, their energies are higher. For a single B N bond in the cell, the loss of stability is shown with -84.058 eV/f.u. energy, and for two B N bonds, the energy is −84.470 eV/f.u. as examples. Concerning the last “mixed” structure – where B is bonded with three N atoms – several calculations were carried out either in LDA or in general gradient approximation GGA, but they all lead to positive energies (>40 eV in LDA) with a strong internal pressure parameter. This highlights a very strong instability of this hypothetical structure, which can be interpreted from an experimental point of view by a very weak probability to observe this phase. Moreover, the “mixed” phases are no more cubic after the geometry optimizations, and according to boron (respectively, lithium) atom bonding, they can be either rhombohedral (with three B C bonds) or monoclinic (with two B C bonds). These geometry modifications indicate that the electronic structures of such compounds are modified too. In the text hereafter, LiBC4 N4 will designate the experimental structure. 4. A mechanical characterization of LiBC4 N4 One of the ways to provide a characterization of a (crystal) material is to explore its mechanical properties. As a matter of fact, this is linked with the internal electronic structures and particularly to the nature of chemical bonds and the dimensionality of the crystal. This is underlined by the research

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on ultra-hard compounds for which a strongly covalent structure is needed to drastically decrease their compressibility and deformability [1,18]. These properties are measured by, respectively, the bulk (B0 ) and shear (G0 ) moduli. The higher their bulk magnitudes, the less the considered materials are compressible (respectively, deformable). We have calculated the bulk moduli for LiBC4 N4 and inv.-LiBC4 N4 : the energies for several fixed volumes around the equilibrium were computed (all other parameters were set free) and then the obtained curves were fitted with the Birch equation of state [19]. As it was expected for such voidempty crystal structures the magnitudes of bulk moduli are low: B0 (LiBC4 N4 ) = 35 GPa, B0 (inv.-LiBC4 N4 ) = 28 GPa. One can note that gypsum (CaSO4 ·2H2 O) exhibits a bulk modulus magnitude of 45 GPa [20]. Such a low bulk magnitude leads us to signal that a crystal structure determination by X-ray powder diffraction must be carried out carefully in order to keep a statistic distribution and to avoid privileged directions. These values clearly point to a very ductile material. Such a behavior is expected from a compound which exhibits ionic chemical bonds more than covalent ones as well as a low compactness. 5. Electronic structure study The electronic structure of LiBC4 N4 crystal is studied through the ASW method for band structure, density of states (DOS) function and ECOV function, and with the VASP code for obtaining the ELF function. The site projected DOS and the electronic band structure plots (Fig. 2) show that the crystal behavior is ionic, as it can be inferred from the narrow flat bands and the high localization of DOS for the different species in the valence band (VB). Moreover the system is found to be an insulator with an indirect large gap: RV –Γ C ∼5.5 eV. A detailed analysis of DOS shows that C and N, on one hand, and B and C, on other hand, are covalently bonded from the similarity of the respective DOS shapes. The Li DOS are less localized and are smeared all over the VB with different shape from the other species DOS. This leads to suggest perhaps a higher ionicity, in agreement with Kouvetakis et al. conclusions [5]. The use

Fig. 2. Site projected density of states (DOS) (on the left side) and electronic band structure (on the right side) of LiBC4 N4 crystal.

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of ECOV and ELF functions will help to better qualify both the nature and the role of the interactions in LiBC4 N4 structure. We can note that for inv.-LiBC4 N4 the DOS and band structure (not presented here) show a higher localization of states, that is to say a more ionic behavior of the atomic species. Information about the nature of the interaction between atomic constituents can be provided using overlap population (OP) leading to the so-called crystal orbital overlap population (COOP) [21] or alternatively introducing the Hamiltonian based population crystal orbital Hamiltonian population (COHP) [22]. Both approaches lead to a qualitative description of the chemical interactions between two atomic species by assigning a bonding, non-bonding or anti-bonding character. A slight refinement of the COHP was recently proposed in form of the “covalent bond energy” ECOV which combines both COHP and COOP so as to make the resulting quantity independent of the choice of the zero of potential [23]. The ECOV was recently implemented within the ASW method [24]. Our experience with both COOP and ECOV shows that they give similar general trends although COOP exaggerates the magnitude of anti-bonding states. This approach – which describes the role of the electronic interaction in the crystal cell stabilization – is completed, as specified before, by the use of the electron localization function (ELF) [25]. By this, one seeks the isolocalization surfaces (3D) or contour lines (2D section), in order to qualify the chemical interactions. ELF is a normalized function between 0 and 1 where 0 corresponds to nil localization and 1 to a localization maximum. A high localization (close to 1) between two atoms corresponds to a covalent bond, when a low or nil localization (close to 0) indicates no bonding. Both functions are plotted in Figs. 3 and 4 (ECOV ) and (ELF). The ECOV function indicates bonding interactions between C and N atoms on one hand and between C and B on the other hand, while there is a non-bonding interaction between N and Li. Moreover, the other types of interactions (not represented here) are either (at least) non-bonding ones or anti-bonding ones. It seems that there are B–C–N atomic chains (chemically bonded)

Fig. 4. ELF function for LiBC4 N4 crystal in [1 1 0] plane.

while Li is independent from N. The ELF was plotted for a [1 1 0] crystallographic plane. Strong electronic localizations are shown between B and C, C and N and close to N. If the first two can be attributed to covalent bonds (high localization and negative ECOV value), the last one is the fingerprint of the non-bonding electrons of N. This last assertion is deduced from the nil value of Li/N, ECOV which underlines the lack of interaction between the two considered species. We can note that the electron localization is essentially situated around the atomic chains. As a consequence, we have proved that the model of Kouvetakis et al. (as an ionic crystal [B(CN)4 ]− Li+ ) is effectively the one to be taken into account to describe the synthesized material. The ELF also allows observing an effective modification of the electronic structure when boron is connected with one or more N atom, particularly around the CN group (not presented here). The shape of electronic localization is quite cylindrical when CN is connected with B by a B C bond, but when the connection is a B N bond, the shape is two spheres stuck with each other and centered on C and N. This points to a more ionic character of C and N, and, as a consequence, explains the destabilization of crystal structures—C and N are more covalent than ionic. 6. Comparisons with hypothetical LiBX4 or LiBS4 C4 N4

Fig. 3. ECOV function for experimental LiBC4 N4 structure. Negative, positive and zero ECOV magnitudes are for bonding, antibonding and non-bonding interactions, respectively.

The CN group can be compared to halogen atoms if we consider their global valence: only one electron is available to build a chemical bond with another atom, while the other valence electrons are implied in the triple C N bond. Moreover, the cyanide group is isoelectronic to halogen atoms (same global number of p electrons). Nevertheless, a behavior difference is expected: as a matter of fact, the bonding character is given by the carbon atom (covalence) whereas halogen atoms generally present an ionic behavior. In terms of ELF representations, such a behavior can be illustrated by either a strong electronic localization between two atoms for covalence, or for ionicity by a strong localization centered on the ionic element and clearly isolated from other elements. This modification of the “central” element (atom or group between Li and B) can be used for experimentalist to control the Li–B distance, and as a matter of fact, the porosity of such (generic) structures.

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7. Conclusions

Fig. 5. ELF function for LiBBr4 crystal in [1 1 0] plane.

The structures where X is chlorine, bromine and iodine were investigated, because their atomic radii are closest to the CN length than the fluorine’s. After geometry optimizations, the symmetries are conserved (P−43m space group) and the result˚ for X = Br, ing cell parameters are: for X = Cl, a = 4.897 A, ˚ and for X = I, a = 5.758 A. ˚ As it can be inferred from a = 5.271 A these results, the substitution of the central group seems to be a medium to control the cell size, and then, the crystal sites size. As it could be supposed considering the ionicity of halogen atoms and the existence of molecular boron halides, such as BBr3 or BCl3 , the resulting electronic structures show that B is covalently bonded with the halogen atoms while Li is ionic. They can be presented as a complex [BX4 ]− anion with Li+ as counter ion (represented for bromine in Fig. 5). Another type of substitution is considered, which is supposed to increase the cell parameter. It is based on the well-known K+ [S C N]− used as fungicide or pesticide. As a matter of fact, LiBC4 N4 could be considered also as the product of the following hypothetical ionic reaction: B(CN)3 + LiCN → LiBC4 N4 Boron tri-thiocyanate [26] and LiSCN, used in electrolytes [27], could be substituted in this process to obtain LiBS4 C4 N4 : B(SCN)3 + LiSCN → LiBS4 C4 N4 The coordination of boron is still four (sulfur is bivalent). This resulting stoichiometry was used to build a cubic model structure within the P−43m space group. After geometry optimization, ˚ the symmetry is conserved and the cell parameter is 9.364 A. As previously observed for LiBC4 N4 , Li is in (1a) crystallographic site and B in (1b) site while the other atomic species are in (4e) sites. Such substitutions could be extended to other atoms or groups in order to get a specific cell parameter/to control the empty sites sizes, as for new zeolites-type crystals [28]. One can note that first preliminary theoretical attempts of hetero-elements insertions, such as rare gas (Ne) or molecules (H2 ) in chosen sites do not produce significant changes in optimized cell parameters values and symmetries. Other calculations are still carried out.

The LiBC4 N4 experimental structure was studied and compared with other LiBC4 N4 structural cubic arrangements, obtained by cyanide group spatial direction inversion. The calculated stabilization energies indicate that the experimental structure is effectively the most stable one. Its mechanical properties (bulk modulus) were also computed and point to a very compressible structure. This can be assigned to both large empty crystal sites, which do not offer resistance to a compression, and the strong ionic character of the structure as established through the study of electronic structure. The latter shows that the crystal is constituted (as inferred by Kouvetakis et al.) by [B(CN)4 ]− anions connected with each other by an ionic bonding with Li+ cation. The substitution of cyanide groups connected to boron either with halogen atoms or with thiocyanate groups ( S C N) were considered to bring an overview of a possible crystal cell parameter control. This can constitute a potential outcome for catalysis reactions or gas storage, for examples. As expected, the global symmetry was not changed after these substitutions, even if the cell parameter value depends on the substitutional atom or group. The prospective works are, for this type of structures, studies on the cation influence on both crystal stability and shape and on other CN substitutions, and their syntheses. As far as literature mentions the existence of LiGaC4 N4 , the synthesis of the intermediate compound, LiAlC4 N4 should be carried out. Theoretical tools, such as molecular dynamics could be used to study the various mechanisms of hetero species fit into vacant sites. Acknowledgements One of us (E.B.) acknowledges the Aquitaine Regional Council and the French National Centre of Scientific Research (CNRS) for its financial support and Dr. C. Desplanches (ICMCB-CNRS) for his kind help on organic compounds references. Calculations were done on the Regatta IBM p690 supercomputer of the “M3PEC M´esocentre R´egional” for intensive numerical computations facility of the University Bordeaux 1 financed by the Aquitaine Regional Council and the French Ministry of Research and Technology. References [1] A.Y. Liu, M.L. Cohen, Science 245 (1989) 841. [2] M. Mattesini, S.F. Matar, Int. J. Inorg. Mater. 3 (2001) 943. [3] V.L. Solozhenko, D. Andrault, G. Fiquet, M. Mezouar, D.C. Rubie, Appl. Phys. Lett. 78 (2001) 1385. [4] E. Betranhandy, S.F. Matar, Ch. El-Kfoury, R. Weihrich, J. Etourneau, Z. Anorg. Allg. Chem. 630 (2004) 2587. [5] D. Williams, B. Pleune, J. Kouvetakis, M.D. Williams, R.A. Andersen, J. Am. Chem. Soc. 122 (2000) 7735. [6] J-Ph. Souli´e, G. Renaudin, R. Cerny, K. Yvon, J. Alloys Compd. 346 (2002) 200. [7] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133; P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [8] G. Kresse, J. Hafner, Phys. Rev. B 47 (1993) 558; G. Kresse, J. Hafner, Phys. Rev. B 49 (1994) 14251; G. Kresse, J. Furthm¨uller, Comput. Mater. Sci. 6 (1996) 15; G. Kresse, J. Furthm¨uller, Phys. Rev. B 54 (1996) 11169.

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