inorganic compounds
Redetermination of the perovskitetype compound YRh_{3}B revealing a Rh deficiency
^{a}Graduate School of Materials Science and Engineering, Nagoya Institute of Technology, Gokisocho, Showaku, Japan, and ^{b}Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Japan
^{*}Correspondence email: 14515020@stn.nitech.ac.jp
In contrast with previous structural studies of ytterbium trirhodium boride, YbRh_{3}B, that suggest a boron deficiency, the current redetermination of the of YbRh_{3}B revealed instead a rhodium deficiency with a refined composition of YbRh_{2.67 (2)}B. In the ABX_{3} perovskitetype structure, Yb, B and Rh are located on the A, B and X positions, respectively, with site symmetries of mm for the A and B sites, and 4/mm.m for the X site.
Related literature
For a previous powder diffraction study of YbRh_{3}B, see: Takei & Shishido (1984). For general background, see: Becker & Coppens (1975); Libermann et al. (1971); Mann (1968).
Experimental
Crystal data

Data collection
Refinement

Data collection: MXCSYS (MacScience, 1995) and IUANGLE (Tanaka et al., 1994); cell RSLC3 UNICS system (Sakurai & Kobayashi, 1979); data reduction: RDEDIT (Tanaka, 2008); program(s) used to solve structure: QNTAO (Tanaka & Ōnuki, 2002; Tanaka et al., 2008); program(s) used to refine structure: QNTAO; molecular graphics: ATOMS for Windows (Dowty, 2000); software used to prepare material for publication: RDEDIT.
Supporting information
10.1107/S1600536808030754/wm2195sup1.cif
contains datablocks global, I. DOI:Structure factors: contains datablock I. DOI: 10.1107/S1600536808030754/wm2195Isup2.hkl
Single crystals were grown using a
method with copper as the solvent. Stoichiometric quantities of Yb, Rh and B were mixed with copper in a ratio of about 1:8 by weight. The mixture was heated in a high purity alumina crucible by electric furnace under a purified He gas flow at a rate of about 400 Kh^{1}. The sample was kept at a temperature between 1523 and 1623 K for 10 h and cooled at a rate of 1 Kh^{1} to 353 K. Then the furnace was cooled rapidly to room temperature. The boride crystals were separated from the copper by treatment with hot nitric acid. The sample was cut into small pieces and was finally ground into a sphere with 41 µm radius by a wind pressure granulation machine with diamond paste.In the first stage of the ρ_{max}, ρ_{min}) values for Yb, Rh and B were (4.59, 8.48), (4.92, 9.06) and (4.91, 8.58) eÅ^{3}, respectively, with the Rfactor converging at 3.14%. After this stage we checked the results of Takei & Shishido (1984) for a deficiency of the boron site and refined the s.o.f. of boron. However, the Rfactor and the difference density map showed no noticeable improvement. Then the s.o.f. of both Yb and Rh were refined independently. Whereas the s.o.f. of Yb remained unchanged, that of Rh changed from 1 to 0.891 (6). Fig. 3 (a), (b) and (c) show the difference density map around Yb, Rh and B after the of the s.o.f. of Rh. The positive and negative peaks showed a significant improvement compared with the first with a constrained s.o.f. for Rh. The remaining electron densities (ρ_{max}, ρ_{min}) around Yb, Rh and B were (1.89, 1.79), (1.96, 1.86) and (1.98, 1.33) eÅ^{3}, respectively, and the Rfactor converged at 1.4%.
the site occupation factors (s.o.f.) of Yb, Rh and B were assumed to be 1. Fig. 2 (a), (b) and (c) show the difference density map at this stage of the around Yb, Rh and B, respectively. The center of the difference density map is the core of atom; the width and depth of the difference density map is 4.13 Å × 4.13 Å. The (Data collection: MXCSYS (MacScience, 1995) and IUANGLE (Tanaka et al., 1994).; cell
RSLC3 UNICS system (Sakurai & Kobayashi, 1979); data reduction: RDEDIT (Tanaka, 2008); program(s) used to solve structure: QNTAO (Tanaka & Ōnuki, 2002; Tanaka et al., 2008); program(s) used to refine structure: QNTAO (Tanaka & Ōnuki, 2002; Tanaka et al., 2008); molecular graphics: ATOMS for Windows (Dowty, 2000); software used to prepare material for publication: RDEDIT (Tanaka, 2008).YbRh_{2.67}B  D_{x} = 10.81 Mg m^{−}^{3} 
M_{r} = 458.61  Mo Kα radiation, λ = 0.71073 Å 
Cubic, Pm3m  Cell parameters from 30 reflections 
Hall symbol: P 4 2 3  θ = 36.5–38.3° 
a = 4.12992 (7) Å  µ = 47.90 mm^{−}^{1} 
V = 70.44 (1) Å^{3}  T = 109 K 
Z = 1  Sphere, black 
F(000) = 195.14  0.08 × 0.08 × 0.08 × 0.04 (radius) mm 
MacScience M06XHF22 fourcircle diffractometer  193 independent reflections 
Radiation source: finefocus rotating anode  193 reflections with F > 3σ(F) 
Graphite monochromator  R_{int} = 0.019 
Detector resolution: 1.25 x 1.25° pixels mm^{1}  θ_{max} = 74.9°, θ_{min} = 4.9° 
ω/2θ scans  h = −7→9 
Absorption correction: for a sphere [transmission coefficients for spheres tabulated in International Tables for Xray Crystallography (Vol. II, 1972, Table 5.3.6B) were interpolated with Lagrange's method (four point interpolation; Yamauchi et al., 1965)]  k = −11→11 
T_{min} = 0.069, T_{max} = 0.169  l = −11→11 
953 measured reflections 
Refinement on F  3 restraints 
Leastsquares matrix: full  Weighting scheme based on measured s.u.'s 
R[F^{2} > 2σ(F^{2})] = 0.014  (Δ/σ)_{max} = 0.00010 
wR(F^{2}) = 0.029  Δρ_{max} = 1.86 e Å^{−}^{3} 
S = 1.15  Δρ_{min} = −1.98 e Å^{−}^{3} 
193 reflections  Extinction correction: BC type 1 Gaussian anisotropic (Becker & Coppens, 1975) 
11 parameters  Extinction coefficient: 0.052 (2) times 10^{4} 
YbRh_{2.67}B  Z = 1 
M_{r} = 458.61  Mo Kα radiation 
Cubic, Pm3m  µ = 47.90 mm^{−}^{1} 
a = 4.12992 (7) Å  T = 109 K 
V = 70.44 (1) Å^{3}  0.08 × 0.08 × 0.08 × 0.04 (radius) mm 
MacScience M06XHF22 fourcircle diffractometer  193 independent reflections 
Absorption correction: for a sphere [transmission coefficients for spheres tabulated in International Tables for Xray Crystallography (Vol. II, 1972, Table 5.3.6B) were interpolated with Lagrange's method (four point interpolation; Yamauchi et al., 1965)]  193 reflections with F > 3σ(F) 
T_{min} = 0.069, T_{max} = 0.169  R_{int} = 0.019 
953 measured reflections 
R[F^{2} > 2σ(F^{2})] = 0.014  11 parameters 
wR(F^{2}) = 0.029  3 restraints 
S = 1.15  Δρ_{max} = 1.86 e Å^{−}^{3} 
193 reflections  Δρ_{min} = −1.98 e Å^{−}^{3} 
Experimental. Multiple diffraction was avoided by using ψscans. Intensities was measured at the equitemperature region of combinaion of angles ω and χ of a fourcircle diffractometer. 
x  y  z  U_{iso}*/U_{eq}  Occ. (<1)  
Yb  0.5000  0.5000  0.5000  0.212 (1)  
Rh  0.0000  0.0000  0.5000  0.143 (2)  0.891 (6) 
B  0.0000  0.0000  0.0000  0.291 (6) 
U^{11}  U^{22}  U^{33}  U^{12}  U^{13}  U^{23}  
Yb  0.00269 (4)  0.00269 (4)  0.00269 (4)  0  0  0 
Rh  0.00202 (6)  0.00202 (6)  0.00139 (6)  0  0  0 
B  0.0037 (2)  0.0037 (2)  0.0037 (2)  0  0  0 
Rh^{i}—Rh^{ii}  2.9203 (1)  B^{i}—Yb  3.5766 (1) 
B^{i}—Rh^{i}  2.0650 (1)  Rh^{i}—Yb  2.9203 (1) 
Rh^{i}—B^{i}—Rh^{ii}  90.000  Rh^{i}—Yb—B^{i}  35.264 
Rh^{i}—Yb—Rh^{ii}  60.000  Yb—B^{i}—Rh^{ii}  54.736 
Symmetry codes: (i) x+1, y, z; (ii) z, x, y. 
Experimental details
Crystal data  
Chemical formula  YbRh_{2.67}B 
M_{r}  458.61 
Crystal system, space group  Cubic, Pm3m 
Temperature (K)  109 
a (Å)  4.12992 (7) 
V (Å^{3})  70.44 (1) 
Z  1 
Radiation type  Mo Kα 
µ (mm^{−}^{1})  47.90 
Crystal size (mm)  0.08 × 0.08 × 0.08 × 0.04 (radius) 
Data collection  
Diffractometer  MacScience M06XHF22 fourcircle diffractometer 
Absorption correction  For a sphere [transmission coefficients for spheres tabulated in International Tables for Xray Crystallography (Vol. II, 1972, Table 5.3.6B) were interpolated with Lagrange's method (four point interpolation; Yamauchi et al., 1965)] 
T_{min}, T_{max}  0.069, 0.169 
No. of measured, independent and observed [F > 3σ(F)] reflections  953, 193, 193 
R_{int}  0.019 
(sin θ/λ)_{max} (Å^{−}^{1})  1.358 
Refinement  
R[F^{2} > 2σ(F^{2})], wR(F^{2}), S  0.014, 0.029, 1.15 
No. of reflections  193 
No. of parameters  11 
No. of restraints  3 
Δρ_{max}, Δρ_{min} (e Å^{−}^{3})  1.86, −1.98 
Computer programs: MXCSYS (MacScience, 1995) and IUANGLE (Tanaka et al., 1994)., RSLC3 UNICS system (Sakurai & Kobayashi, 1979), RDEDIT (Tanaka, 2008), QNTAO (Tanaka & Ōnuki, 2002; Tanaka et al., 2008), ATOMS for Windows (Dowty, 2000).
Rh^{i}—Rh^{ii}  2.9203 (1)  B^{i}—Yb  3.5766 (1) 
B^{i}—Rh^{i}  2.0650 (1)  Rh^{i}—Yb  2.9203 (1) 
Symmetry codes: (i) x+1, y, z; (ii) z, x, y. 
References
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Takei & Shishido (1984) reported various rare earth trirhodium borides with the perovskite structure (Fig. 1) and suggest a deficiency for the boron site. For a closer inspection of this assumption and since anisotropic displacement factors were not reported in the original study, we decided to redetermine the structure of YbRh_{3}B and present the results of the structure analysis in this communication.
In the ABX_{3} perovskitetype structure, Yb, B and the partly occupied Rh atoms are located on the A, B and X positions, respectively, with site symmetries of m3m for the A and B sites and 4/mm.m for the X site.