X-ray atomic orbital analysis of 4f and 5d electron configuration of SmB₆ at 100, 165, 230 and 298 K

Accurate electron-density measurement of SmB₆ at 100, 165, 230 and 298 K, and X-ray atomic orbital (XAO) analysis were carried out. The 4f-electron density around Sm and 5d electron density at ∼ 1 Å from Sm were analysed by XAO analysis. The 5d electron density is due to the electrons of the 5d_{J = 5/2}Γ₈ orbitals which stem from the e_g orbitals in the strong field approximation. The change in electron populations of the 5d_5/2Γ₈ orbitals with temperature is similar to that of the resistivity. Since the conduction band consists of 5d_5/2Γ₈ and B-2p orbitals according to band theory, this indicates that the larger populations of the 5d_5/2Γ₈ orbitals correspond to the larger number of localized electrons and are correlated to the resistivity of SmB₆. The occupation of the bulky 5d_5/2Γ₈ orbitals may be the reason for the elongation of the lattice parameter below 150 K. The 4f_7/2Γ₆ orbitals are obviously occupied except at 100 K, which seems to be caused by the energy gap between 4f_5/2 and 4f_7/2 states, which begins to exist between 100 and 150 K, and may represent one of the properties of a Kondo insulator.

Computing details

For all structures, 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).

samarium hexaboride (100K)

Crystal data

B6·Sm	Dx = 5.064 Mg m^−3
Mr = 215.23	Mo Kα radiation, λ = 0.71073 Å
Cubic, Pm3m	Cell parameters from 29 reflections
Hall symbol: -P 4 2 3	θ = 36.5–39.1°
a = 4.1327 (2) Å	µ = 20.50 mm^−1
V = 70.58 (1) Å^3	T = 100 K
Z = 1	Sphere, metallic dark blue
F(000) = 92	0.08 × 0.08 × 0.08 × 0.04 (radius) mm

Data collection

Four-circle diffractometer	187 independent reflections
Radiation source: fine-focus rotating anode	182 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.011
Detector resolution: 5.46x5.46 mm pixels mm^-1	θmax = 74.9°, 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 = 0.356, Tmax = 0.418	l = −5→9
598 measured reflections

Refinement

Refinement on F	12 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.009	(Δ/σ)max = 0.001
wR(F^2) = 0.010	Δρmax = 0.61 e Å^−3
S = 0.86	Δρmin = −0.29 e Å^−3
593 reflections	Extinction correction: B-C type 1 Gaussian anisotropic
35 parameters	Extinction coefficient: 0.208 (4) E04
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 Sm 4f orbitals. B—C anisotropic type1 extinction parameters B—C anisoropic extinction parameters are as follows 45.7 (78) 21.6 (30) 21.1 (15) -5.0 (28) 1.4 (18) 1.2 (11)

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

	x	y	z	Uiso*/Ueq
Sm	0.5	0.5	0.5	0.00305 (1)
B	0.0	0.0	0.2994 (3)	0.00341 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sm	0.00304 (3)	0.00304 (3)	0.00304 (3)	0.0	0.0	0.0
B	0.00388 (10)	0.00388 (10)	0.00244 (15)	0.0	0.0	0.0

Geometric parameters (Å, º)

Sm—B	3.0376 (3)	B—B^ii	1.658 (2)
B—B^i	1.750 (1)
B—Sm—B^ii	31.674 (8)	B—Sm—B^i	33.483 (15)

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

samarium hexaboride (165K)

Crystal data

B6^3^−·Sm^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 215.23	Cell parameters from 30 reflections
Cubic, Pm3m	θ = 36.5–39.1°
a = 4.1325 (2) Å	µ = 20.51 mm^−1
V = 70.57 (1) Å^3	T = 165 K
Z = 1	Sphere, metallic dark blue
F(000) = 92	0.08 × 0.08 × 0.08 × 0.04 (radius) mm
Dx = 5.064 Mg m^−3

Data collection

Four-circle diffractometer	182 independent reflections
Radiation source: fine-focus rotating anode	182 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.013
Detector resolution: 5.46x5.46 mm pixels mm^-1	θmax = 74.9°, 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 = −10→11
Tmin = 0.356, Tmax = 0.418	l = −6→9
593 measured reflections

Refinement

Refinement on F	12 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.008	(Δ/σ)max = 0.001
wR(F^2) = 0.012	Δρmax = 0.39 e Å^−3
S = 1.11	Δρmin = −0.41 e Å^−3
582 reflections	Extinction correction: B-C type 1 Gaussian anisotropic
36 parameters	Extinction coefficient: 0.194 (4) E04
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 Sm 4f orbitals. B—C anisotropic type1 extinction parameters B—C anisoropic extinction parameters are as follows 43.5 (51) 17.3 (45) 25.5 (14) -1.40 (328) 0.40 (163) 0.32 (19)

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

	x	y	z	Uiso*/Ueq
Sm	0.5	0.5	0.5	0.00427 (2)
B	0.0	0.0	0.2967 (2)	0.00385 (6)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sm	0.00421 (1)	0.00421 (1)	0.00421 (1)	0.0	0.0	0.0
B	0.00431 (8)	0.00431 (8)	0.00274 (12)	0.0	0.0	0.0

Geometric parameters (Å, º)

Sm—B	3.0408 (3)	B—B^ii	1.6803 (12)
B—B^i	1.7340 (8)
B—Sm—B^ii	32.08 (2)	B—Sm—B^i	33.14 (2)

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

samarium hexaboride (230K)

Crystal data

B6^3^−·Sm^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 215.23	Cell parameters from 34 reflections
Cubic, Pm3m	θ = 36.5–39.1°
a = 4.1338 (2) Å	µ = 20.49 mm^−1
V = 70.64 (1) Å^3	T = 230 K
Z = 1	Sphere, metallic dark blue
F(000) = 92	0.08 × 0.08 × 0.08 × 0.04 (radius) mm
Dx = 5.059 Mg m^−3

Data collection

Four-circle diffractometer	187 independent reflections
Radiation source: fine-focus rotating anode	187 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.011
Detector resolution: 5.46x5.46 mm pixels mm^-1	θmax = 74.8°, θmin = 4.9°
integrated intensities data fom ω/2θ scans	h = −9→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 = 0.356, Tmax = 0.418	l = −7→10
664 measured reflections

Refinement

Refinement on F	12 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.010	(Δ/σ)max = 0.001
wR(F^2) = 0.140	Δρmax = 0.68 e Å^−3
S = 1.04	Δρmin = −0.70 e Å^−3
648 reflections	Extinction correction: B-C type 1 Gaussian anisotropic
33 parameters	Extinction coefficient: 0.162 (4) E04
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 Sm 4f orbitals. B—C anisotropic type1 extinction parameters B—C anisoropic extinction parameters are as follows 22.5 (62) 25.3 (52) 43.2 (36) -12.0 (53) 20.0 (30) 1.75 (250)

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

	x	y	z	Uiso*/Ueq
Sm	0.5	0.5	0.5	0.00565 (2)
B	0.0	0.0	0.29890 (19)	0.00392 (7)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sm	0.00561 (1)	0.00561 (1)	0.00561 (1)	0.0	0.0	0.0
B	0.00471 (10)	0.00471 (10)	0.00268 (16)	0.0	0.0	0.0

Geometric parameters (Å, º)

Sm—B	3.0389 (2)	B—B^ii	1.6627 (11)
B—B^i	1.7474 (11)
B—Sm—B^ii	31.739 (5)	B—Sm—B^i	33.427 (10)

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

samarium hexaboride (298K)

Crystal data

B6^3^−·Sm^3+	Mo Kα radiation, λ = 0.71073 Å
Mr = 215.22	Cell parameters from 24 reflections
Cubic, Pm3m	θ = 39.1–39.1°
a = 4.1346 (2) Å	µ = 20.43 mm^−1
V = 70.68 (1) Å^3	T = 298 K
Z = 1	Sphere, metallic dark blue
F(000) = 92	0.08 × 0.08 × 0.08 × 0.04 (radius) mm
Dx = 5.057 Mg m^−3

Data collection

Four-circle diffractometer	191 independent reflections
Radiation source: fine-focus rotating anode	191 reflections with F > 3.0σ(F)
Graphite monochromator	Rint = 0.044
Detector resolution: 5.46x5.46 mm pixels mm^-1	θmax = 74.8°, 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 = −9→10
Tmin = 0.356, Tmax = 0.418	l = −11→11
2162 measured reflections

Refinement

Refinement on F	12 constraints
Least-squares matrix: full	Weighting scheme based on measured s.u.'s
R[F^2 > 2σ(F^2)] = 0.008	(Δ/σ)max = 0.001
wR(F^2) = 0.011	Δρmax = 0.41 e Å^−3
S = 0.98	Δρmin = −0.25 e Å^−3
2149 reflections	Extinction correction: B-C type 1 Gaussian anisotropic
35 parameters	Extinction coefficient: 0.172 (1) E04
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 Sm 4f orbitals. B—C anisotropic type1 extinction parameters B—C anisoropic extinction parameters are as follows 23.6 (9) 28.4 (7) 47.9 (17) 2.4 (5) -4.2 (7) -0.3 (6)

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

	x	y	z	Uiso*/Ueq
Sm	0.5	0.5	0.5	0.00778 (1)
B	0.0	0.0	0.29823 (10)	0.00478 (4)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Sm	0.00779 (1)	0.00779 (1)	0.00779 (1)	0.0	0.0	0.0
B	0.00540 (5)	0.00450 (5)	0.00354 (8)	0.0	0.0	0.0

Geometric parameters (Å, º)

Sm—B	3.0403 (1)	B—B^ii	1.6685 (6)
B—B^i	1.7438 (4)
B—Sm—B^ii	31.852 (3)	B—Sm—B^i	33.331 (6)

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