Xray 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)Γ_{8} orbitals are occupied partially, but 4f(j = 5/2)Γ_{8} orbitals are more populated than 4f(j = 5/2)Γ_{7} 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)Γ_{8} and Γ_{7} 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)Γ_{7} orbitals and the remaining one has a fully occupied 5d(j = 3/2)Γ_{8} orbital. Since the lobes of 5d(j = 3/2)Γ_{8} or 5d(j = 5/2)Γ_{7} orbitals do not overlap with the 4f(j = 5/2)Γ_{8} orbitals as well as the 5d(j = 5/2)Γ_{8} 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 sphericalatom 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)Γ_{8} orbitals seems to reduce the electron repulsion of the 5d(j = 5/2)Γ_{8} orbitals and helps the 4f(j = 5/2)Γ_{8} orbitals to remain as the ground state.
Supporting information
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, 246252 (1994)); cell refinement: RSLC3 UNICS system (Sakurai, T. & Kobayashi, K. (1979), Rep. Inst. Phys. Chem. Res. 55, 6977); data reduction: RDEDIT (K. Tanaka); program(s) used to refine structure: QNTAO (K. Tanaka, 2000).
(340K) cerium hexaboride
top
Crystal data top
B_{6}^{3}^{−}·Ce^{3+}  Mo Kα radiation, λ = 0.71073 Å 
M_{r} = 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) 
D_{x} = 4.787 Mg m^{−}^{3}  
Data collection top
Fourcircle diffractometer  180 independent reflections 
Radiation source: finefocus rotating anode  179 reflections with F > 3.0σ(F) 
Graphite monochromator  R_{int} = 0.006 
Detector resolution: 1.25x1.25 degrees pixels mm^{1}  θ_{max} = 74.4°, θ_{min} = 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 
T_{min} = 0.434, T_{max} = 0.483  l = −11→11 
902 measured reflections  
Refinement top
Refinement on F  24 constraints 
Leastsquares 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  Δρ_{max} = 0.70 e Å^{−}^{3} 
804 reflections  Δρ_{min} = −0.39 e Å^{−}^{3} 
38 parameters  Extinction correction: BC type 1 Gaussian anisotropic 
0 restraints  Extinction coefficient: 0.251 (2) times 10^{4} 
Crystal data top
B_{6}^{3}^{−}·Ce^{3+}  Z = 1 
M_{r} = 204.98  Mo Kα radiation 
Cubic, Pm3m  µ = 15.66 mm^{−}^{1} 
a = 4.14288 (3) Å  T = 338 K 
V = 71.11 (1) Å^{3}  0.04 mm (radius) 
Data collection top
Fourcircle diffractometer  180 independent reflections 
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)  179 reflections with F > 3.0σ(F) 
T_{min} = 0.434, T_{max} = 0.483  R_{int} = 0.006 
902 measured reflections  
Refinement top
R[F^{2} > 2σ(F^{2})] = 0.008  0 restraints 
S = 1.04  Δρ_{max} = 0.70 e Å^{−}^{3} 
804 reflections  Δρ_{min} = −0.39 e Å^{−}^{3} 
38 parameters  
Special details top
Experimental. Multiple diffraction was avoided by ψscan. Intensities was measured at equitemperature region of combinaion of angles ω and χ of fourcircle diffractometer 
Refinement. Spinorbit 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 (Å^{2}) top  x  y  z  U_{iso}*/U_{eq}  
Ce  0.5  0.5  0.5  0.5379 (4)  
B  0.0  0.0  0.2992 (15)  0.360 (2)  
Atomic displacement parameters (Å^{2}) top  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) top
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
top
Crystal data top
B_{6}^{3}^{−}·Ce^{3+}  Mo Kα radiation, λ = 0.71073 Å 
M_{r} = 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) 
D_{x} = 4.765 Mg m^{−}^{3}  
Data collection top
Fourcircle diffractometer  182 independent reflections 
Radiation source: finefocus rotating anode  171 reflections with F > 3.0σ(F) 
Graphite monochromator  R_{int} = 0.008 
Detector resolution: 1.25x1.25 degrees pixels mm^{1}  θ_{max} = 74.0°, θ_{min} = 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 
T_{min} = 0.435, T_{max} = 0.484  l = −9→9 
1066 measured reflections  
Refinement top
Refinement on F  24 constraints 
Leastsquares 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  Δρ_{max} = 0.55 e Å^{−}^{3} 
809 reflections  Δρ_{min} = −0.37 e Å^{−}^{3} 
38 parameters  Extinction correction: BC type 1 Gaussian anisotropic 
0 restraints  Extinction coefficient: 0.290 (2) times 10^{4} 
Crystal data top
B_{6}^{3}^{−}·Ce^{3+}  Z = 1 
M_{r} = 204.98  Mo Kα radiation 
Cubic, Pm3m  µ = 15.59 mm^{−}^{1} 
a = 4.14918 (4) Å  T = 535 K 
V = 71.43 (1) Å^{3}  0.04 mm (radius) 
Data collection top
Fourcircle diffractometer  182 independent reflections 
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)  171 reflections with F > 3.0σ(F) 
T_{min} = 0.435, T_{max} = 0.484  R_{int} = 0.008 
1066 measured reflections  
Refinement top
R[F^{2} > 2σ(F^{2})] = 0.009  0 restraints 
S = 1.30  Δρ_{max} = 0.55 e Å^{−}^{3} 
809 reflections  Δρ_{min} = −0.37 e Å^{−}^{3} 
38 parameters  
Special details top
Experimental. Multiple diffraction was avoided by ψscan. Intensities was measured at equitemperature region of combinaion of angles ω and χ of fourcircle diffractometer 
Refinement. Spinorbit 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 (Å^{2}) top  x  y  z  U_{iso}*/U_{eq}  
Ce  0.5  0.5  0.5  0.8521 (5)  
B  0.0  0.0  0.3019 (16)  0.495 (3)  
Atomic displacement parameters (Å^{2}) top  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) top
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. 
Experimental details
 (340K)  (535K) 
Crystal data 
Chemical formula  B_{6}^{3}^{−}·Ce^{3+}  B_{6}^{3}^{−}·Ce^{3+} 
M_{r}  204.98  204.98 
Crystal system, space group  Cubic, Pm3m  Cubic, Pm3m 
Temperature (K)  338  535 
a (Å)  4.14288 (3)  4.14918 (4) 
V (Å^{3})  71.11 (1)  71.43 (1) 
Z  1  1 
Radiation type  Mo Kα  Mo Kα 
µ (mm^{−}^{1})  15.66  15.59 
Crystal size (mm)  0.04 (radius)  0.04 (radius) 

Data collection 
Diffractometer  Fourcircle diffractometer  Fourcircle diffractometer 
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)  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) 
T_{min}, T_{max}  0.434, 0.483  0.435, 0.484 
No. of measured, independent and observed [F > 3.0σ(F)] reflections  902, 180, 179  1066, 182, 171 
R_{int}  0.006  0.008 
(sin θ/λ)_{max} (Å^{−}^{1})  1.355  1.353 

Refinement 
R[F^{2} > 2σ(F^{2})], wR(F^{2}), S  0.008, ?, 1.04  0.009, ?, 1.30 
No. of reflections  804  809 
No. of parameters  38  38 
Δρ_{max}, Δρ_{min} (e Å^{−}^{3})  0.70, −0.39  0.55, −0.37 
Selected geometric parameters (Å, º) for (340K) topCe—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. 
Selected geometric parameters (Å, º) for (535K) topCe—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. 