Icosahedron  Helmut Werheit | Prof. Dr. rer. nat website:   http://www.werheit.mynetcologne.de/
e-mail:   helmut.werheit@koeln.de
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Structures of some boron-rich structures

Bauarbeiter (Mann mit Schaufel neben Sandhaufen)


Boron carbide

Symmetry type of the structure is (space group 166). Initially, the rhombohedral unit cell was assumed to be composed of B12 icosahedra at its vertices and a linear CCC chain on the main diagonal parallel to the crystallographic c-axis, leading to the chemical composition B12C3. After the central chain atom was proved to be solely boron, the structure formula (B12) CCC was modified to (B11C) CBC. This structure model is depicted in Fig. 1 using the program VESTA[i]. The apparently plausible formula B4C is long since proved to be incorrect 7, but nevertheless it has often been used as a synonym for boron carbide.

According to the present state of art, the chemical compound B4C or B12C3 does not exist, at least not, when it is prepared by the common high-temperature preparation methods melting or hot-pressing, typically exceeding 2300 K. Actual chemical compounds of boron carbide exist in the large homogeneity range extending from the carbon-rich limit B4.3C [ii] to the boron-rich limit B~10.8C [iii]. Various structure elements have been identified; their concentrations depend on the actual chemical composition, and the distribution is assumed to be statistical, as no superlattice has been identified so far:

 ·                B12 icosahedra

·                B11C icosahedra with the C atom accommodated in one of the 6 polar sites

·                CBC chains

·                CBB chains

·                B□B arrangements (□, vacancy)

 Thus, boron carbide has no real crystal structure characterized by a well defined unit cell, but exhibits at the most an elementary cell with a twelve-atom icosahedron and a mostly three-atom chain, both in varying compositions, which are randomly distributed.

Therefore, the most prominent methods of structure analysis, x-ray as well as neutron scattering and NMR, fail in determining the actual microstructure of boron carbide, indeed for different reasons. X-ray and neutron diffraction, averaging a large volume with differently composed elementary cells, yield the atomic sites correctly, but are unable to determine their individual occupancies. Moreover, these methods are decisively impeded by the difficulty of distinguishing B and C atoms because of their very similar scattering cross section.

NMR spectra of boron carbide contain the overlapping resonances of 11B and 13C isotopes respectively, whose local environments vary in the volume analyzed. This aggravates decisively the general problem of NMR, whose interpretation is unambiguous at most in neat structures. Otherwise, it depends on the more or less arbitrarily chosen structure models used for fitting the spectra. In the case of boron carbide, the random mixture of differently composed cells and structure elements makes a reliable analysis of the spectra nearly impossible.


Concentration of structure elements of boron carbide vs. carbon content

a, CBC, CBB and B□B (□, vacancy). Isotopically pure BxC: Full squares, CBC chains (derived from the stretching mode); open squares, CBB chains (derived from the stretching mode); triangles, CBC chains (derived from the Eu mode); dashed-dotted line, average of chainless elementary cells (see Fig. 4). natBxC: Full diamonds, CBC; open diamonds, CBB.

b. B11C and B12 icosahedra. Isotopically pure BxC: Squares. natBxC:  diamonds, this work;. Circles, results obtained from other natB4.3C spectra not shown here.

[i] K. Momma and F. Izumi, J. Appl. Crystallogr. 44, 1272 (2011).

[ii] K. A. Schwetz and P. Karduck, AIP Conf. Proc., 231, 405 (1990).

[iii] H. Werheit and S. Shalamberidze, J. Phys.: Condens. Matter., 24, 385406 (2012).