5d and 4f electron configuration of CeB₆ at 340 and 535 K

X-ray atomic orbital (XAO) analysis revealed that at both temperatures the electrons are transferred from B 2p_x(= p_y) to Ce 5d and 4f orbitals. At 340 K 5d(j = 5/2)Γ₈ orbitals are occupied partially, but 4f(j = 5/2)Γ₈ orbitals are more populated than 4f(j = 5/2)Γ₇ orbitals, in contrast to our observation at 430 K [Makita et al. (2007). Acta Cryst. B63, 683–692]. At 535 K the XAO analysis revealed clearly that the order of the energy levels of 4f(j = 5/2)Γ₈ and Γ₇ states reversed again and is the same as that at room temperature. It also limited the possible 5d configurations to three models among the nine possible ones. However, the XAO analysis could not decide which of the three models was the best with the present accuracy of the measurement. Two of them have partially and fully occupied 5d(j = 5/2)Γ₇ orbitals and the remaining one has a fully occupied 5d(j = 3/2)Γ₈ orbital. Since the lobes of 5d(j = 3/2)Γ₈ or 5d(j = 5/2)Γ₇ orbitals do not overlap with the 4f(j = 5/2)Γ₈ orbitals as well as the 5d(j = 5/2)Γ₈ orbitals, the order of the energy levels of the 4f(j = 5/2) orbitals became the same as that at room temperature. These results indicate that the crystal field varies with temperature due to the electron transfer from B 2p to Ce 5d orbitals. The difference densities after the spherical-atom refinement at the three temperatures clearly revealed the different combinations of 4f and 5d orbitals which are occupied. In the present study positive peaks due to the 4f electrons appear near the Ce nucleus and those due to 5d orbitals are found in the area outside the 4f peaks. Between the two areas there is a negative area distributed spherically at 340 K. The negative area produced by the contraction of 4f(j = 5/2)Γ₈ orbitals seems to reduce the electron repulsion of the 5d(j = 5/2)Γ₈ orbitals and helps the 4f(j = 5/2)Γ₈ orbitals to remain as the ground state.

Computing details

For both compounds, data collection: MXC(MAC Science) and a program IUANGLE by Tanaka (Tanaka, K.,Kumazawa S., Tsubokawa, M., Maruno, S. & Shirotani, I. (Acta Cryst., A50, 246-252 (1994)); cell refinement: RSLC-3 UNICS system (Sakurai, T. & Kobayashi, K. (1979), Rep. Inst. Phys. Chem. Res. 55, 69-77); data reduction: RDEDIT (K. Tanaka); program(s) used to refine structure: QNTAO (K. Tanaka, 2000).

Figures

(340K) cerium hexaboride

Crystal data

B6^3^−·Ce^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 204.98	Cell parameters from 45 reflections
Cubic, Pm3m	θ = 36.4–39.0°
a = 4.14288 (3) Å	µ = 15.66 mm^−1
V = 71.11 (1) Å^3	T = 338 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.787 Mg m^−3

Data collection

Four-circle diffractometer	180 independent reflections
Radiation source: fine-focus rotating anode	179 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.006
Detector resolution: 1.25x1.25 degrees pixels mm^-1	θmax = 74.4°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −8→10
Absorption correction: for a sphere Transmission cefficient for spheres tabulated in International Table II(1972) Table 5.3.6B was interpolated with Lagrange's method (four point interpolation)	k = −11→11
Tmin = 0.434, Tmax = 0.483	l = −11→11
902 measured reflections

Refinement

Refinement on F	24 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.008	(Δ/σ)max = 0.00031
S = 1.04	Δρmax = 0.70 e Å^−3
804 reflections	Δρmin = −0.39 e Å^−3
38 parameters	Extinction correction: B-C type 1 Gaussian anisotropic
0 restraints	Extinction coefficient: 0.251 (2) times 10^4

Special details

Experimental. Multiple diffraction was avoided by ψ-scan. Intensities was measured at equi-temperature region of combinaion of angles ω and χ of four-circle diffractometer

Refinement. Spin-orbit interaction for Ce 4f orbitals. B—C anisotropic type1 extinction parameters B—C anisoropic extinction parameters are as follows 14.3 (5) 18.4 (11) 21.6 (12) −0.5 (4) −3.2 (5) −0.1 (6)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.5379 (4)
B	0.0	0.0	0.2992 (15)	0.360 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.006810 (10)	0.006810 (10)	0.006810 (10)	0.0	0.0	0.0
B	0.00518 (5)	0.00518 (5)	0.00331 (7)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0453 (16)	B—B^ii	1.664 (6)
B—B^i	1.753 (4)
B—Ce—B^ii	31.70 (3)	B—Ce—B^i	33.46 (3)

Symmetry codes: (i) z, x, y; (ii) x, −y, −z+1.

(535K) cerium hexaboride

Crystal data

B6^3^−·Ce^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 204.98	Cell parameters from 50 reflections
Cubic, Pm3m	θ = 36.3–38.9°
a = 4.14918 (4) Å	µ = 15.59 mm^−1
V = 71.43 (1) Å^3	T = 535 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.765 Mg m^−3

Data collection

Four-circle diffractometer	182 independent reflections
Radiation source: fine-focus rotating anode	171 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.008
Detector resolution: 1.25x1.25 degrees pixels mm^-1	θmax = 74.0°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −11→11
Absorption correction: for a sphere Transmission cefficient for spheres tabulated in International Table II(1972) Table 5.3.6B was interpolated with Lagrange's method (four point interpolation)	k = −11→11
Tmin = 0.435, Tmax = 0.484	l = −9→9
1066 measured reflections

Refinement

Refinement on F	24 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.009	(Δ/σ)max = 0.00005
S = 1.30	Δρmax = 0.55 e Å^−3
809 reflections	Δρmin = −0.37 e Å^−3
38 parameters	Extinction correction: B-C type 1 Gaussian anisotropic
0 restraints	Extinction coefficient: 0.290 (2) times 10^4

Special details

Experimental. Multiple diffraction was avoided by ψ-scan. Intensities was measured at equi-temperature region of combinaion of angles ω and χ of four-circle diffractometer

Refinement. Spin-orbit interaction for Ce 4f orbitals. B—C anisotropic type1 extinction parameters B—C anisoropic extinction parameters are as follows 15.8 (13) 13.7 (14) 8.2 (5) −0.8 (8) −1.6 (4) −2.3 (5)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.8521 (5)
B	0.0	0.0	0.3019 (16)	0.495 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.01079 (2)	0.01079 (2)	0.01079 (2)	0.0	0.0	0.0
B	0.00736 (6)	0.00736 (6)	0.00409 (9)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0469 (18)	B—B^ii	1.644 (7)
B—B^i	1.772 (5)
B—Ce—B^ii	31.30 (3)	B—Ce—B^i	33.80 (3)

Symmetry codes: (i) z, x, y; (ii) x, −y, −z+1.