Site-different structures from dilithium hexaboride (Li2b6) to dimagnesium hexaboride (Mg2B6) by first-principles
Introduction
Boron represents structural complexity, unusual bonding situations, electron deficiency and wide variety of compounds [1]. As a result of unusual bonding characteristics, some boron and boron-rich compounds have special boron sub-lattice which is formed by structural units such as icosahedrons in α-boron [2], dodecahedrons in ZrB12 [3], octahedrons in UB4 and UB6 [4] and planar sheets in MgB2 [5], [6]. And, this boron sub-lattice undertakes important roles on material’s properties. On the other hand, light elements such as Li, B and C, and their compounds can present novel physical properties [7]. Especially, the compounds in Li–B system have attracted a constant interest over the past years, only a few compounds such as Li3B14 and Li2B6 could have been successfully characterized [7], [8]. Their structures contain complicated polyhedral B networks with Li sitting in the interstitial sites in order to overcome the electron deficiency originated from B [7]. And, their pressure-dependent properties have been explored, theoretically [9]. In addition to compounds in Li–B system, Li-doping into boron crystals have been also studied. For instance, Hayami et al. have investigated stability of lithium in α-boron [10], and they found that some sites can be stable, unstable or metastable with respect to Li concentration. And, Dekura et al. have presented an efficient method for Li doping of α-boron [11], and found that Li-doped α-boron can be characterized as an impurity system, and doping causes weakening of the bonding characters, softening in the elastic properties and a positive formation energy. In another study, Soga et al. have studied effects of Li- and Mg-doping into α- and β-boron [12]. And, Gunji and Kamimura have investigated metal-doped icosahedral B12 solids (metal is Li and Ca) [13]. They have predicted the existence of B12-based LixB12 (x = 1–4), and showed that CaxB12 (x = 1–4) is unstable. Furthermore, Gasior et al. have measured formation enthalpies of LiB13, Li3B14 and LiB3 (Li2B6) compounds by using reaction calorimetric method, experimentally [14], and found that LiB3 is the most stable compound due to the formation enthalpy of −43.6 kJ/mol.
As a special interest, dilithium hexaboride (Li2B6) which is a member of Li–B system [15] have been synthesized by Mair et al. [16]. Its crystal structure contains octahedral boron sub-lattice and lithium atoms sitting in the interstitial sites as mentioned above, and there is a small amount of information about it in the literature. Thus, in this study, the structural, mechanical and electronic properties of dilithium hexaboride are investigated by first-principles density functional calculations and limited information about this material is expanded. And, effects of Mg-substitution to different sites in the structure on the actual properties are studied with possible comparisons.
Section snippets
Calculation method
All calculations including geometry optimization, electronic structure and elastic constants in this study were performed by using first principles density functional plane-wave pseudopotential method as implemented in CASTEP code [17]. The PW91 form of generalized gradient approximation [18] were considered to describe exchange–correlation effects. In order to modeling the interactions between ionic core and valence electrons, the ultrasoft pseudopotentials were used [19]. The kinetic energy
Result and discussion
Experimental and optimized ground state geometries of Li2B6 (LiB3) are showed in Fig. 1a and b and calculated atomic coordinates are listed in Table 1 with experimental ones [16]. Its space group is P4/mbm (No: 127) and crystal system is tetragonal. There are 16 atoms in the structure: four Li atoms and 12 boron atoms. Boron octahedrons as a structural unit (B6) containing six boron atoms form boron sub-lattice and Li atoms place to spaces in this sub-lattice (as expressed in Ref. [7], see Fig.
Conclusion
All structures are thermodynamically stable and all new designed Mg-including structures have more negative formation enthalpies than LiB3. From calculated band structure and partial density of states, LiB3 and Mg-including structures are metallic, and fully magnesium including structure (MgB3) have the highest metallicity due to higher density of states of magnesium. It is observed from calculated Mulliken atomic charges and bond overlap populations that boron sub-lattice have negative-charged
Acknowledgement
This work was partly supported by the State of Planning Organization of Turkey under Grant No. 2011K120290. Some of calculations were performed in high performance computing center (HPCC) at Gazi University.
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