Boron carbide, B13-xC2-y (x = 0.12, y = 0.01)

Boron carbide phases exist over a widely varying compositional range B12+xC3-x (0.06 < x < 1.7). One idealized structure corresponds to the B13C2 composition (space group R-3m) and contains one icosahedral B12 unit and one linear C—B—C chain. The B12 units are composed of crystallographically distinct B atoms BP (polar, B1) and BEq (equatorial, B2). Boron icosahedra are interconnected by C atoms via their BEq atoms, forming layers parallel to (001), while the B12 units of the adjacent layers are linked through intericosahedral BP—BP bonds. The unique B atom (BC) connects the two C atoms of adjacent layers, forming a C—B—C chain along [001]. Depending on the carbon concentration, the carbon and BP sites exhibit mixed B/C occupancies to varying degrees; besides, the BC site shows partial occupancy. The decrease in carbon content was reported to be realized via an increasing number of chainless unit cells. On the basis of X-ray single-crystal refinement, we have concluded that the unit cell of the given boron-rich crystal contains following structural units: [B12] and [B11C] icosahedra (about 96 and 4%, respectively) and C—B—C chains (87%). Besides, there is a fraction of unit cells (13%) with the B atom located against the triangular face of a neighboring icosahedron formed by BEq (B2) thus rendering the formula B0.87(B0.98C0.02)12(B0.13C0.87)2 for the current boron carbide crystal.

Boron carbide phases exist over a widely varying compositional range B 12+x C 3-x (0.06 < x < 1.7). One idealized structure corresponds to the B 13 C 2 composition (space group R3m) and contains one icosahedral B 12 unit and one linear C-B-C chain. The B 12 units are composed of crystallographically distinct B atoms B P (polar, B1) and B Eq (equatorial, B2). Boron icosahedra are interconnected by C atoms via their B Eq atoms, forming layers parallel to (001), while the B 12 units of the adjacent layers are linked through intericosahedral B P -B P bonds. The unique B atom (B C ) connects the two C atoms of adjacent layers, forming a C-B-C chain along [001]. Depending on the carbon concentration, the carbon and B P sites exhibit mixed B/C occupancies to varying degrees; besides, the B C site shows partial occupancy. The decrease in carbon content was reported to be realized via an increasing number of chainless unit cells. On the basis of X-ray singlecrystal refinement, we have concluded that the unit cell of the given boron-rich crystal contains following structural units: [B 12 ] and [B 11 C] icosahedra (about 96 and 4%, respectively) and C-B-C chains (87%). Besides, there is a fraction of unit cells (13%) with the B atom located against the triangular face of a neighboring icosahedron formed by B Eq (B2) thus rendering the formula B 0.87 (B 0.98 C 0.02 ) 12 (B 0.13 C 0.87 ) 2 for the current boron carbide crystal.
This work was partly supported by grants from the Thermal and Electric Energy Technology Foundation and AOARD. The positioning the C1 and B11 atoms on two adjacent 6c (0, 0, z) sites is in good agreement with observations reported from powder neutron diffraction studies of boron-rich boron carbides by Kwei and Morosin (1996). No atom in the 36i site claimed by Yakel (1975) has been found.

Experimental
Boron carbide single-crystal has been obtained as a co-product of the yttrium boron carbide phase synthesized via solid state reaction of yttrium tetraboride, amorphous boron and carbon. The reaction process was performed from compacted powders in the BN crucible inserted into a graphite susceptor using the RF furnace under a flow of Ar at a temperature of about 1973 K and holding time 8 h; afterwards the setup was cooled down in 1 h to room temperature. The sample contained crystals of the title compound, in the presence of YB 28.5 C 4 and binary yttrium borides, as revealed by powder X-ray diffraction analysis.

Refinement
The crystal structure refinement was performed starting from the atomic coordinates reported for α-rh B. The chain atoms were located from the difference Fourier synthesis. The refinement on boron icosahedral polar site-occupancy factors led to reliability factors R1=0.0517 and wR2=0.1519 revealing the remaining electron density of 1.42 e Å -3 in 6c Wyckoff position (0, 0, z; z=0.07) at close distance from chain atom C1. Further refinement on occupancy parameters of the B3 (B C ) chain atom and refining the C1/B11 in split 6c atom site reduced the highest Fourier difference peak to 0.55 e Å -3 at (0, 0, 0.1663) located 0.6 Å away from C1 and decreased the reliability factors to R1=0.0455 and wR2=0.1087. The ADPs of B1 and B2 have comparable values, while the thermal ellipsoids of C1/B11 chain atoms slightly extend parallel to the chain direction. The B3 in the center of a chain shows rather large ADP values. Data collection and cell refinement:

Special details
Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes. Refinement. Refinement of F 2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F 2 , conventional R-factors R are based on F, with F set to zero for negative F 2 . The threshold expression of F 2 > σ(F 2 ) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F 2 are statistically about twice as large as those based on F, and R-factors based on ALL data will be even larger.