Observation of 4f electron transfer from Ce to B₆ in the Kondo crystal CeB₆ and its mechanism by multi-temperature X-ray diffraction

Electron density distributions (EDD) in CeB₆ were measured by X-ray diffraction at 100, 165, 230 and 298 K. Analysis with a weak-field model, in which the spin-orbit interaction dominates the energy splitting of the 4f levels, revealed that more 4f electrons were donated from Ce to B₆ at the lower temperature. Donated electrons localize around the B—B bonds connecting B₆ octahedra. The localized electrons and an expansion of the outermost 5p orbitals change the effective atomic potentials and enhance the anharmonic vibration (AHV) of constituent atoms at lower temperature. Enhanced AHV increases the entropy and makes the electron donation inevitable. Changes in crystal structure, EDD, electron configuration and AHV are found to be closely correlated with one another and the mechanism of the electron transfer in the Kondo crystal CeB₆ in the studied temperature range was elucidated. This is, to the authors' knowledge, the first multi-temperature measurement of EDD that elucidates a mechanism of change from the temperature dependence of the EDD. Parameters change consistently at all the temperatures except 298 K, at which the excited states Γ₇ of the Ce 4f states have significant electron population. The thermal excitation to Γ₇ levels expands the B₆ octahedra, since Γ₇ has main lobes along 〈111〉 or from Ce to the centre of B₆ octahedra. The energy gap between the ground state Γ₈ and Γ₇ was calculated to be 470 K from the ratio of electron populations of both states. The present experiment opens the door to accurate X-ray EDD analyses of rare earth complexes.

Computing details

For all 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) for 100K, 165K, 230K; RSLC-3 UNICS system(Sakurai,T. & Kobayashi,K. (1979), Rep.Inst.Phys.Chem. Res.55,69-77) for 298K. For all compounds, data reduction: RDEDIT (K. Tanaka); program(s) used to refine structure: QNTAO (K. Tanaka, 1988); molecular graphics: ORTEP (Johnson, 1965).

(100K) 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(originatthecenterofB6octahedron)	θ = 36.5–39.1°
a = 4.1367 (1) Å	µ = 16.01 mm^−1
V = 70.79 (1) Å^3	T = 100 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.808 Mg m^−3

Data collection

Four-circle diffractometer	167 independent reflections
Radiation source: fine-focus rotating anode	1063 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.021
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.6°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −10→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 = −9→11
Tmin = 0.433, Tmax = 0.481	l = −9→10
1089 measured reflections

Refinement

Refinement on F	22 constraints
Least-squares matrix: full	Unit
R[F^2 > 2σ(F^2)] = 0.006	(Δ/σ)max = 0.018
wR(F^2) = 0.008	Δρmax = 0.38 e Å^−3
1063 reflections	Δρmin = −0.40 e Å^−3
24 parameters	Extinction correction: B-C type 1 Gaussian anisotropic
2 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 99 (12) 328 (42) 71 (7) 154 (20) -44 (7) -105 (14)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.179 (2)
B	0.0	0.0	0.2984 (3)	0.252 (5)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.00227 (5)	0.00227 (5)	0.00227 (5)	0.0	0.0	0.0
B	0.00365 (12)	0.00365 (12)	0.00228 (11)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0416 (3)	B—B^ii	1.6676 (17)
B—B^i	1.7459 (12)
B—Ce—B^ii	31.820 (9)	B—Ce—B^i	33.358 (9)

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

(165K)

Crystal data

B6^3^−·Ce^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 204.98	Cell parameters from 50 reflections
Cubic, Pm3m(originatthecenterofB6octahedron)	θ = 36.4–39.0°
a = 4.1381 (1) Å	µ = 16.00 mm^−1
V = 70.86 (1) Å^3	T = 165 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.803 Mg m^−3

Data collection

Four-circle diffractometer	187 independent reflections
Radiation source: fine-focus rotating anode	815 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.024
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.6°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −10→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 = −10→11
Tmin = 0.433, Tmax = 0.481	l = −9→8
857 measured reflections

Refinement

Refinement on F	22 constraints
Least-squares matrix: full	Unit
R[F^2 > 2σ(F^2)] = 0.007	(Δ/σ)max = 0.021
wR(F^2) = 0.008	Δρmax = 0.36 e Å^−3
815 reflections	Δρmin = −0.53 e Å^−3
23 parameters	Extinction correction: B-C type1 anisotropic
2 restraints

Special details

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

Refinement. Spin-orbit interaction for Ce 4f orbitals. B—C anisotropic type1 extinction parameters are as follows 86 (7) 230 (18) 44 (3) 109 (10) -26 (3) -61 (5)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.274 (2)
B	0.0	0.0	0.2972 (3)	0.275 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.00347 (5)	0.00347 (5)	0.00347 (5)	0.0	0.0	0.0
B	0.00397 (12)	0.00397 (12)	0.00253 (14)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0440 (4)	B—B^ii	1.678 (2)
B—B^i	1.7395 (16)
B—Ce—B^ii	32.002 (12)	B—Ce—B^i	33.203 (12)

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

(230K) 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(originatthecenterofB6octahedron)	θ = 36.5–39.1°
a = 4.1391 (1) Å	µ = 15.98 mm^−1
V = 70.91 (1) Å^3	T = 230 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.800 Mg m^−3

Data collection

Four-circle diffractometer	168 independent reflections
Radiation source: fine-focus rotating anode	788 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.007
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.5°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −10→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 = 0.433, Tmax = 0.482	l = −4→10
841 measured reflections

Refinement

Refinement on F	22 constraints
Least-squares matrix: full	Unit
R[F^2 > 2σ(F^2)] = 0.007	(Δ/σ)max = 0.030
wR(F^2) = 0.008	Δρmax = 0.50 e Å^−3
788 reflections	Δρmin = −0.49 e Å^−3
23 parameters	Extinction correction: B-C type1 anisotropic
2 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 are as follows 39 (3) 110 (10) 27 (2) 33 (4) -7(1) -21 (2)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.355 (2)
B	0.0	0.0	0.2963 (4)	0.286 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.00450 (5)	0.00450 (5)	0.00450 (5)	0.0	0.0	0.0
B	0.00421 (14)	0.00421 (14)	0.00245 (18)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0459 (7)	B—B^ii	1.687 (4)
B—B^i	1.734 (3)
B—Ce—B^ii	32.149 (18)	B—Ce—B^i	33.077 (18)

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

(298K)

Crystal data

B6^3^−·Ce^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 204.98	Cell parameters from 50 reflections
Cubic, Pm3m(originatthecenterofB6octahedron)	θ = 37.7–39.0°
a = 4.1407 (1) Å	µ = 15.97 mm^−1
V = 71.00 (1) Å^3	T = 298 K
Z = 1	Sphere, metallic dark purple
F(000) = 88	0.04 mm (radius)
Dx = 4.794 Mg m^−3

Data collection

Four-circle diffractometer	192 independent reflections
Radiation source: fine-focus rotating anode	983 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.045
Detector resolution: 1.5x1.5 degrees pixels mm^-1	θmax = 74.5°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −10→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 = −10→11
Tmin = 0.434, Tmax = 0.482	l = −7→10
1079 measured reflections

Refinement

Refinement on F	22 constraints
Least-squares matrix: full	Unit
R[F^2 > 2σ(F^2)] = 0.008	(Δ/σ)max = 0.010
wR(F^2) = 0.009	Δρmax = 0.51 e Å^−3
983 reflections	Δρmin = −0.41 e Å^−3
25 parameters	Extinction correction: B-C type1 anisotropic
2 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 are as follows 62 (4) 90 (7) 24 (1) 53 (4) 7(1) 11 (1)

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

	x	y	z	Uiso*/Ueq
Ce	0.5	0.5	0.5	0.456 (1)
B	0.0	0.0	0.2989 (4)	0.339 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ce	0.00577 (5)	0.00577 (5)	0.00577 (5)	0.0	0.0	0.0
B	0.00493 (13)	0.00493 (13)	0.0030 (2)	0.0	0.0	0.0

Geometric parameters (Å, º)

Ce—B	3.0439 (4)	B—B^ii	1.664 (2)
B—B^i	1.7511 (15)
B—Ce—B^ii	31.732 (11)	B—Ce—B^i	33.433 (11)

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