Theoretical study of the structure of boron carbideB13C2

Abstract

We have resolved long-standing discrepancies between the theoretical and experimental crystal structures of boron carbide B 13 C 2 . Theoretical studies predict that B 13 C 2 should be stoichiometric and have the highest symmetry of the boron carbides. Experimentally, B 13 C 2 is a semiconductor and many defect states have been reported, particularly in the CBC chain. Reconciling the disordered states of the chain, the chemical composition, and the lowest-energy state is problematic. We have solved this problem by constructing a structural model where approximately three-quarters of the unit cells contain (B 11 C)(CBC) and one-quarter of them contain (B 12 ) (B 4 ). This structural model explains many experimental results, such as the large thermal factors in x-ray diffraction and the broadening of the Raman spectra, without introducing unstable CBB chains. The model also solves the energy-gap problem. We show that there are many arrangements of these two types of unit cells, which are energetically almost degenerate. This demonstrates that boron carbides are well described by a geometrically frustrated system, similar to that proposed for β-rhombohedral boron.

Configurational order-disorder induced metal-nonmetal transition inB13C2studied with first-principles superatom-special quasirandom structure method

“…As the carbon concentration decreases, approaching * anekt@ifm.liu.se B 13 C 2 , the replacement of carbon by boron can take place either within the icosahedra or in the chains, resulting in two different models: B 12 (CBC) or B 11 C(BBC), respectively, for B 13 C 2 . The former model is evident mainly by ab initio calculations [16][17][18], where it is shown to have considerably lower energy as compared to B 11 C(BBC) [16,19]. Meanwhile, the latter model is consistent with the analyses of structural data from x-ray diffraction [20] and Raman spectra [21][22][23] of boron carbide at different at.% C in its single-phase region.…”

“…We underline that the negative values of E in Table IV (CBC). This is also inspired by the suggestion of Shirai et al [19], but in contrast to that work, our larger supercell contains the exact stoichometry of B 13 C 2 . As shown in Fig.…”

“…Recently, Shirai et al [19] proposed an alternative structural model for B 13 C 2 , consisting of 3 different types of structural units, i.e., B 11 C p (CBC), B 12 (CBC), and B 12 (B 4 ) with a 4-atom rhombic (B 4 ) chain (see Fig. 8).…”

“…We were thus inspired, with a use of SA-SQS, to examine the model II in Ref. [19] a fairly good agreement. In fact, the total energies of the SA-SQS model II are somewhat lower due to the removal of cell constraints.…”

“…However, there are no detailed suggestions or calculations demonstrating how such effects should be realized if present. A recent theoretical study conducted by Shirai et al [19] proposed structural models for B 13 C 2 , consisting of B 11 C p (CBC), B 12 (CBC), and B 12 (B 4 ) units. According to their models, the presence of the B 12 (B 4 ) units can partially solve the band-gap problem and the hole density reduces to 0.25 holes/unit-cell, indicating less metallic character.…”