Boron carbide, B_13-xC_2-y (x = 0.12, y = 0.01)

Abstract

Boron carbide phases exist over a widely varying compos­itional range B_12+xC_3-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 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 B₁₂ 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 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 B_Eq (B2) thus rendering the formula B_0.87(B_0.98C_0.02)₁₂(B_0.13C_0.87)₂ for the current boron carbide crystal.

Related literature  

For X-ray/neutron diffraction studies on boron carbide, see: Yakel (1975 ▶); Will et al. (1979 ▶); Larson (1986 ▶); Kwei & Morosin (1996 ▶). For the boron carbide homogeneity field, see: Bouchacourt & Thevenot (1985 ▶); Gosset & Colin (1991 ▶). For electronic structure and bonding properties, see: Domnich et al. (2011 ▶); Balakrishnarajan et al. (2007 ▶). For electronic properties and charge transport, see: Werheit (2009 ▶).

Experimental  

Crystal data  

• C_1.99B_12.88

• M _r = 163.14

• Trigonal,

• a = 5.6530 (8) Å

• c = 12.156 (4) Å

• V = 336.42 (17) ų

• Z = 3

• Mo Kα radiation

• μ = 0.10 mm⁻¹

• T = 293 K

• 0.45 × 0.30 × 0.21 mm

Data collection  

• Rigaku AFC 7R diffractometer

• 1489 measured reflections

• 284 independent reflections

• 184 reflections with I > 2σ(I)

• R _int = 0.151

• 3 standard reflections every 150 reflections intensity decay: none

Refinement  

• R[F ² > 2σ(F ²)] = 0.046

• wR(F ²) = 0.109

• S = 1.03

• 284 reflections

• 22 parameters

• 1 restraint

• Δρ_max = 0.55 e Å⁻³

• Δρ_min = −0.37 e Å⁻³

Data collection: Rigaku/AFC Diffractometer Control Software (Rigaku, 1998 ▶); cell refinement: Rigaku/AFC Diffractometer Control Software; data reduction: TEXSAN (Molecular Structure Corporation, 1998 ▶); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008 ▶); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008 ▶); molecular graphics: ATOMS (Dowty, 1999 ▶); software used to prepare material for publication: SHELXL97 and WinGX (Farrugia, 1999 ▶).

Supplementary Material

Additional supplementary materials: crystallographic information; 3D view; checkCIF report

supplementary crystallographic information

Comment

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_28.5C₄ 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:

Figures

Fig. 1.

The idealized structure of boron carbide and the distances for B and C atoms of the C—B—C and B—B chains as obtained from structure refinement. Thermal ellipsoids depict the 80% probability level.

Fig. 2.

Observed Fourier maps projected onto xy plane at z=0; -1.5 e Å-3 < Δρ < 28.4 e Å-3.

Crystal data

C1.99B12.88	Dx = 2.416 Mg m−3
Mr = 163.14	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m	Cell parameters from 20 reflections
Hall symbol: -R 3 2"	θ = 8–50°
a = 5.6530 (8) Å	µ = 0.10 mm−1
c = 12.156 (4) Å	T = 293 K
V = 336.42 (17) Å3	Prism, black
Z = 3	0.45 × 0.3 × 0.21 mm
F(000) = 229

Data collection

Rigaku AFC 7R diffractometer	θmax = 39.8°, θmin = 4.5°
ω–2θ scans	h = −10→8
1489 measured reflections	k = 0→10
284 independent reflections	l = −21→21
184 reflections with I > 2σ(I)	3 standard reflections every 150 reflections
Rint = 0.151	intensity decay: none

Refinement

Refinement on F2	22 parameters
Least-squares matrix: full	1 restraint
R[F2 > 2σ(F2)] = 0.046	w = 1/[σ2(Fo2) + (0.0481P)2 + 0.3407P] where P = (Fo2 + 2Fc2)/3
wR(F2) = 0.109	(Δ/σ)max = 0.002
S = 1.03	Δρmax = 0.55 e Å−3
284 reflections	Δρmin = −0.37 e Å−3

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 F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
B1	0.44092 (16)	0.55908 (16)	0.05298 (12)	0.0053 (3)	0.958 (4)
C11	0.44092 (16)	0.55908 (16)	0.05298 (12)	0.0053 (3)	0.042 (4)
B2	0.50336 (16)	0.49664 (16)	0.19232 (11)	0.0054 (3)
B3	0	0	0	0.0118 (8)	0.87
C1	0	0	0.1177 (5)	0.0071 (8)	0.87 (2)
B11	0	0	0.079 (4)	0.0071 (8)	0.13 (2)

Atomic displacement parameters (Ų)

	U11	U22	U33	U12	U13	U23
B1	0.0056 (4)	0.0056 (4)	0.0047 (5)	0.0028 (5)	−0.0001 (2)	0.0001 (2)
C11	0.0056 (4)	0.0056 (4)	0.0047 (5)	0.0028 (5)	−0.0001 (2)	0.0001 (2)
B2	0.0046 (4)	0.0046 (4)	0.0059 (5)	0.0015 (4)	−0.0003 (2)	0.0003 (2)
B3	0.0099 (11)	0.0099 (11)	0.016 (2)	0.0049 (6)	0	0
C1	0.0041 (6)	0.0041 (6)	0.013 (2)	0.0021 (3)	0	0
B11	0.0041 (6)	0.0041 (6)	0.013 (2)	0.0021 (3)	0	0

Geometric parameters (Å, º)

B1—C11i	1.731 (3)	B2—B1ii	1.8091 (15)
B1—B1i	1.731 (3)	B2—C11iii	1.8091 (15)
B1—B2	1.801 (2)	B2—B1iii	1.8091 (15)
B1—B2ii	1.8091 (15)	B3—B11	0.96 (5)
B1—B2iii	1.8091 (15)	B3—B11vii	0.96 (5)
B1—B1iv	1.825 (3)	B3—C1vii	1.430 (6)
B1—C11iv	1.825 (3)	B3—C1	1.430 (6)
B1—C11v	1.825 (3)	C1—B2vi	1.6239 (19)
B1—B1v	1.825 (3)	C1—B2iii	1.6239 (19)
B2—C1vi	1.6239 (19)	C1—B2viii	1.6239 (19)
B2—B11vi	1.77 (2)	B11—B2vi	1.77 (2)
B2—B2iii	1.7778 (17)	B11—B2iii	1.77 (2)
B2—B2ii	1.7778 (17)	B11—B2viii	1.77 (2)
B2—C11ii	1.8091 (15)	B11—B11vii	1.92 (9)
C11i—B1—B1i	0.00 (8)	B11vi—B2—C11ii	108.5 (11)
C11i—B1—B2	118.22 (14)	B2iii—B2—C11ii	108.78 (7)
B1i—B1—B2	118.22 (14)	B2ii—B2—C11ii	60.26 (7)
C11i—B1—B2ii	121.45 (8)	B1—B2—C11ii	110.05 (9)
B1i—B1—B2ii	121.45 (8)	C1vi—B2—B1ii	121.07 (19)
B2—B1—B2ii	59.01 (5)	B11vi—B2—B1ii	108.5 (11)
C11i—B1—B2iii	121.45 (8)	B2iii—B2—B1ii	108.78 (7)
B1i—B1—B2iii	121.45 (8)	B2ii—B2—B1ii	60.26 (7)
B2—B1—B2iii	59.01 (5)	B1—B2—B1ii	110.05 (9)
B2ii—B1—B2iii	105.68 (11)	C11ii—B2—B1ii	0.00 (11)
C11i—B1—B1iv	125.36 (8)	C1vi—B2—C11iii	121.07 (19)
B1i—B1—B1iv	125.36 (8)	B11vi—B2—C11iii	108.5 (11)
B2—B1—B1iv	107.10 (6)	B2iii—B2—C11iii	60.26 (7)
B2ii—B1—B1iv	107.02 (6)	B2ii—B2—C11iii	108.78 (7)
B2iii—B1—B1iv	59.72 (5)	B1—B2—C11iii	110.05 (9)
C11i—B1—C11iv	125.36 (8)	C11ii—B2—C11iii	60.56 (11)
B1i—B1—C11iv	125.36 (8)	B1ii—B2—C11iii	60.56 (11)
B2—B1—C11iv	107.10 (6)	C1vi—B2—B1iii	121.07 (19)
B2ii—B1—C11iv	107.02 (6)	B11vi—B2—B1iii	108.5 (11)
B2iii—B1—C11iv	59.72 (5)	B2iii—B2—B1iii	60.26 (7)
B1iv—B1—C11iv	0.00 (9)	B2ii—B2—B1iii	108.78 (7)
C11i—B1—C11v	125.36 (8)	B1—B2—B1iii	110.05 (9)
B1i—B1—C11v	125.36 (8)	C11ii—B2—B1iii	60.56 (11)
B2—B1—C11v	107.10 (6)	B1ii—B2—B1iii	60.56 (11)
B2ii—B1—C11v	59.72 (5)	C11iii—B2—B1iii	0.00 (4)
B2iii—B1—C11v	107.02 (6)	B11—B3—B11vii	180.0000 (10)
B1iv—B1—C11v	60	B11—B3—C1vii	180.0000 (10)
C11iv—B1—C11v	60	B11vii—B3—C1vii	0.0000 (10)
C11i—B1—B1v	125.36 (8)	B11—B3—C1	0.0000 (10)
B1i—B1—B1v	125.36 (8)	B11vii—B3—C1	180.0000 (10)
B2—B1—B1v	107.10 (6)	C1vii—B3—C1	180
B2ii—B1—B1v	59.72 (5)	B3—C1—B2vi	100.1 (2)
B2iii—B1—B1v	107.02 (6)	B3—C1—B2iii	100.1 (2)
B1iv—B1—B1v	60	B2vi—C1—B2iii	117.01 (13)
C11iv—B1—B1v	60	B3—C1—B2viii	100.1 (2)
C11v—B1—B1v	0.00 (10)	B2vi—C1—B2viii	117.01 (13)
C1vi—B2—B11vi	15.1 (12)	B2iii—C1—B2viii	117.01 (13)
C1vi—B2—B2iii	121.49 (7)	B3—B11—B2vi	115.2 (13)
B11vi—B2—B2iii	125.0 (2)	B3—B11—B2iii	115.2 (13)
C1vi—B2—B2ii	121.49 (7)	B2vi—B11—B2iii	103.2 (16)
B11vi—B2—B2ii	125.0 (2)	B3—B11—B2viii	115.2 (13)
B2iii—B2—B2ii	108.39 (8)	B2vi—B11—B2viii	103.2 (16)
C1vi—B2—B1	119.9 (2)	B2iii—B11—B2viii	103.2 (16)
B11vi—B2—B1	135.0 (14)	B3—B11—B11vii	0.0000 (10)
B2iii—B2—B1	60.73 (7)	B2vi—B11—B11vii	115.2 (13)
B2ii—B2—B1	60.73 (7)	B2iii—B11—B11vii	115.2 (13)
C1vi—B2—C11ii	121.07 (19)	B2viii—B11—B11vii	115.2 (13)

Symmetry codes: (i) −x+1, −y+1, −z; (ii) x−y+2/3, x+1/3, −z+1/3; (iii) y−1/3, −x+y+1/3, −z+1/3; (iv) −x+y, −x+1, z; (v) −y+1, x−y+1, z; (vi) −x+2/3, −y+1/3, −z+1/3; (vii) −x, −y, −z; (viii) x−y−1/3, x−2/3, −z+1/3.