Inversion of 4f-states in CeB₆ thermally excited at 430 K

The 4f states of Ce in a typical Kondo crystal, CeB₆, are split into an excited state Γ₇ and the ground state Γ₈, with an excitation energy at 560 K. The electron-density distribution of the thermally excited state was measured at 430 K using a four-circle diffractometer equipped with a small furnace. In contrast to the previous results at lower temperature, electrons are transferred from B₆ to Ce at 430 K. X-ray atomic-orbital analysis revealed that the 5d-Γ₈ orbitals (the energy level of which is similar to that of the B-2p orbitals) are fully occupied and the 4f-Γ₇ orbitals are more populated than the 4f-Γ₈ orbitals. Fully occupied 5d-Γ₈ makes the 4f-Γ₈ states unstable and the energy levels of 4f-Γ₇ and 4f-Γ₈ are inverted.

Computing details

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); molecular graphics: ORTEP (Johnson, 1965).

cerium hexaboride

Crystal data

B6^3^−·Ce^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 204.98	Cell parameters from 39 reflections
Cubic, Pm3m	θ = 37.7–39.0°
a = 4.14586 (8) Å	µ = 15.63 mm^−1
V = 71.26 (1) Å^3	T = 430 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.777 Mg m^−3

Data collection

Four-circle diffractometer	181 independent reflections
Radiation source: fine-focus rotating anode	170 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.063
Detector resolution: 1.25x1.25 degrees pixels mm^-1	θmax = 74.2°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −9→8
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 = 0.482	l = −11→11
990 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)] = 0.012	(Δ/σ)max = 0.001
wR(F^2) = 0.015	Δρmax = 0.57 e Å^−3
S = 1.14	Δρmin = −0.70 e Å^−3
702 reflections	Extinction correction: B-C type 1 Gaussian anisotropic
38 parameters	Extinction coefficient: 0.334 (3) times 10^4
0 restraints

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 9.0 (4) 7.4 (8) 11.3 (8) -1.1 (4) 0.5 (3) 1.4 (6)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.6655 (2)
B	0.0	0.0	0.30090 (10)	0.417 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.008430 (10)	0.008430 (10)	0.008430 (10)	0.0	0.0	0.0
B	0.00607 (8)	0.00607 (8)	0.00370 (12)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0456 (2)	B—B^ii	1.6513 (6)
B—B^i	1.7640 (4)
B—Ce—B^ii	31.458 (3)	B—Ce—B^i	33.667 (3)

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