The nature of the chemical bonding in boron carbide. IV. Electronic band structure of boron carbide, B13C2, and three models of the structure B12C3

Armstrong, David R.; Bolland, John M.; Perkins, P. G.; Will, G.; Kirfel, Α.

doi:10.1107/s0108768183002487

Cited by 80 publications

(48 citation statements)

References 10 publications

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“…According to recent experiments [103], the band gap has been modified as 2.09 eV. On the other hand, all band calculations so far published show gaps as large as 3 eV [74,[105][106][107][108][109][110]. Let us look in more detail at the calculated energy gap of boron carbide.…”

Section: Gap Problemmentioning

confidence: 99%

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

Shirai

2010

J. Superhard Mater.

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Section: Gap Problemmentioning

confidence: 99%

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

Shirai

2010

J. Superhard Mater.

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“…Based on the explanation of Longuet-Higgins and Roberts [14], forty-eight electrons are required in order to complete the valence band of boron carbide and thus yielding a semiconducting character. This condition is somehow satisfied only for B 4 C, meanwhile [40,46,59]. Unlike B 13 C 2 , B 4 C does not suffer from the electron deficiency.…”

Section: Boron Carbidementioning

confidence: 99%

“…Later it was shown by nuclear magnetic resonance (NMR) studies [35][36][37], x-ray [1,38] and neutron [39] diffractions that rather than B 12 (CCC), the structure unit of B 4 C should be represented by B 11 C(CBC), in which one of the boron atoms in the icosahedron is substituted by the chain-center carbon atom, yielding a B 11 C icosahedron linking to a (CBC) chain. Demonstrated by first-principles-based theoretical calculations [40][41][42][43][44], the B 11 C p (CBC) unit is most energetically favorable over the other B 4 C units, i.e. B 11 C e (CBC), B 12 (CCC), and B 11 C(CCB), where the superscript p and e denote the polar and equatorial sites of the icosahedron, respectively.…”

Section: Boron Carbidementioning

confidence: 99%

“…To visualize the relevant energy scale, rather than the ground-state energy, which depending on the definition can vary with thousands of eV, the formation energy with respect to pure phases is used, when plotting a convex hull. In the case of boron carbide, the ground state of B 13 C 2 , determined by the first-principles-based energy minimization, can be given by B 12 (CBC) [46][47][48], meanwhile it is B 11 C p (CBC) for B 4 C [ [40][41][42][43][44]. The convex hull of boron carbide, constructed based only on the two mentioned stoichiometries, is shown in Fig.4.1.…”

Section: Convex Hull and Formation Energymentioning

confidence: 99%

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First-principles study of configurational disorder in icosahedral boron-rich solids

Ektarawong¹

2015

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This thesis is a theoretical study of configurationally disordered icosahedral boronrich solids, in particular boron carbides, using density functional theory and alloy theory. The goal is to resolve discrepancies, regarding the properties of boron carbides, between experiments and previous theoretical calculations which have been a controversial issue in the field of icosahedral boron-rich solids. For instance, B 13 C 2 is observed experimentally to be a semiconductor, meanwhile electronic band structure calculations reveal a metallic character of B 13 C 2 due to its electron deficiency. In B 4 C, on the other hand, the experimentally observed band gap is unexpectedly smaller, not the usual larger, than that of standard DFT calculations. Another example is given by the existence of a small structural distortion in B 4 C, as predicted in theoretical calculations, which reduces the crystal symmetry from the experimentally observed rhombohedral (R3m) to the based-centered monoclinic (Cm). Since boron carbide is stable as a single-phase over a broad composition range (∼8-20 at.% C), substitution of boron and carbon atoms for one another is conceivable. For this reason, the discrepancies have been speculated in the literature, without a proof, to originate from configurational disorder induced by substitutional defects. However, owing to its complex atomic structure, represented by 12-atom icosahedra and 3-atom intericosahedral chains, a practical alloy theory method for direct calculations of the properties of the relevant configurations of disordered boron carbides, as well as for a thermodynamic assessment of their stability has been missing.In this thesis, a new approach, the superatom-special quasirandom structure (SA-SQS), has been developed. The approach allows one to model configurational disorder in boron carbide, induced by high concentrations of low-energy B/C substitutional defects. B 13 C 2 and B 4 C are the two stoichiometries, mainly considered in this study, as they are of particular importance and have been in focus in the literature. The results demonstrate that, from thermodynamic considerations, both B 13 C 2 and B 4 C configurationally disorder at high temperature. In the case of B 13 C 2 , the configurational disorder splits off some valence states into the band gap that in turn compensates the electron deficiency in ordered B 13 C 2 , thus resulting in a semiconducting character. As for B 4 C, the configurational disorder eliminates the monoclinic distortion, thus resulting in the restoration of the higher rhombohedral symmetry. Configurational disorder can also account for an exceliii iv lent agreement on elastic moduli of boron carbide between theory and experiment. Thus, several of the previous discrepancies between theory and experiments are resolved.Inspired by attempts to enhance the mechanical properties of boron suboxide by fabricating boron suboxide-boron carbide composites, as recently suggested in the literature, the SA-SQS approach is used for modeling mixtures of boron sub...

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“…However, it was shown later by nuclear magnetic resonance (NMR) studies [48][49][50], x-ray [2,51] and neutron [52] diffractions that rather than B 12 (CCC), the basic unit of B 4 C should be represented by a B 11 C icosahedron as well as a (CBC) chain, in which one of the icosahedral boron atoms is swapped with the middle carbon atom in the chain. Further clarified by first-principles calculations [53][54][55][56][57], B 11 C p (CBC) is found to be the most energetically favorable basic unit over the other units, e.g., B 11 C e (CBC), B 12 (CCC), and B 11 C p (CCB), where the superscript p and e denote the polar and equatorial sites, respectively. However, swapping the middlechain carbon atom with the icosahedral boron atom to obtain the more favorable model of B 11 C p (CBC) introduces a distortion, reducing the crystal symmetry of boron carbide to base-centered monoclinic with the Cm space group [56,57].…”

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confidence: 89%

Disordered Icosahedral Boron-Rich Solids: A Theoretical Study of Thermodynamic Stability and Properties

Ektarawong¹

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The cover page illustrates the crystal structure of disordered boron carbide (B 4 C), projected on the (100) r crystal plane in rhombohedral symmetry.The cover image is visualized by the VESTA package. Red and white spheres represent boron and carbon atoms, respectively.During the course of research underlying this thesis, Annop Ektarawong was enrolled in Agora Materiae, a multidisciplinary doctoral program at Linköping University, Sweden.c Annop Ektarawong Printed by LiU-Tryck 2017 AbstractThis thesis is a theoretical study of configurational disorder in icosahedral boronrich solids, in particular boron carbide, including also the development of a methodological framework for treating configurational disorder in such materials, namely superatom-special quasirandom structure (SA-SQS). In terms of its practical implementations, the SA-SQS method is demonstrated to be capable of efficiently modeling configurational disorder in icosahedral boron-rich solids, whiles the thermodynamic stability as well as the properties of the configurationally disordered icosahedral boron-rich solids, modeled from the SA-SQS method, can be directly investigated, using the density functional theory (DFT).In case of boron carbide, especially B 4 C and B 13 C 2 compositions, the SA-SQS method is used for modeling configurational disorder, arising from a high concentration of low-energy B/C substitutional defects. The results, obtained from the DFT-based calculations, demonstrate that configurational disorder of B and C atoms in boron carbide is not only thermodynamically favored at high temperature, but it also plays an important role in altering the properties of boron carbide − for example, restoration of higher rhombohedral symmetry of B 4 C, a metal-tononmetal transition and a drastic increase in the elastic moduli of B 13 C 2 . The configurational disorder can also explain large discrepancies, regarding the properties of boron carbide, between experiments and previous theoretical calculations, having been a long standing controversial issue in the field of icosahedral boronrich solids, as the calculated properties of the disordered boron carbides are found to be in qualitatively good agreement with those, observed in experiments. In order to investigate the configurational evolution of B 4 C as a function of temperature, beyond the SA-SQS level, a brute-force cluster-expansion method in combination with Monte Carlo simulations is implemented. The results demonstrate that configurational disorder in B 4 C indeed essentially takes place within the icosahedra in a way that justifies the focus on low-energy defect patterns of the superatom picture.The investigation of the thermodynamic stability of icosahedral carbon-rich iii iv boron carbides beyond the believed solubility limit of carbon (20 at.% C) demonstrates that, apart from B 4 C generally addressed in the literature, B 2.5 C represented by B 10 C p 2 (CC) is predicted to be thermodynamically stable with respect to B 4 C as well as pure boron and carbon under high pressure...

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The nature of the chemical bonding in boron carbide. IV. Electronic band structure of boron carbide, B₁₃C₂, and three models of the structure B₁₂C₃

Cited by 80 publications

References 10 publications

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

Electronic structures and mechanical properties of boron and boron-rich crystals (Part I)

First-principles study of configurational disorder in icosahedral boron-rich solids

Disordered Icosahedral Boron-Rich Solids: A Theoretical Study of Thermodynamic Stability and Properties

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