Redetermination of the crystal structures of rare-earth trirhodium diboride RERh3B2 (RE = Pr, Nd and Sm) from single-crystal X-ray data

Tokuda, M.; Yubuta, K.; Shishido, T.; Sugiyama, K.

doi:10.1107/S2056989021013311

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Volume 78| Part 1| January 2022| Pages 76-79

https://doi.org/10.1107/S2056989021013311

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Redetermination of the crystal structures of rare-earth trirhodium diboride RERh₃B₂ (RE = Pr, Nd and Sm) from single-crystal X-ray data

Makoto Tokuda,^a ^* Kunio Yubuta,^a Toetsu Shishido ^a and Kazumasa Sugiyama ^a

^aInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
^*Correspondence e-mail: makoto.tokuda.b7@tohoku.ac.jp

Edited by M. Weil, Vienna University of Technology, Austria (Received 28 October 2021; accepted 15 December 2021; online 1 January 2022)

The crystal structures of the rare-earth (RE) trirhodium diborides praseodymium trirhodium diboride, PrRh₃B₂, neodymium trirhodium diboride, NdRh₃B₂, and samarium trirhodium diboride, SmRh₃B₂, were refined on the basis of single-crystal X-ray diffraction data. The crystal chemistry of RERh₃B₂ (RE: Pr, Nd, and Sm) compounds has previously been analyzed mainly on the basis of powder samples [Ku et al. (1980 ). Solid State Commun. 35, 91–96], and no structural investigation by single-crystal X-ray diffraction has been reported so far. The crystal structures of the three hexagonal RERh₃B₂ compounds are isotypic with that of CeRh₃B₂; RE, Rh and B sites are situated on special positions with site symmetry 6/mmm (Wyckoff position 1a), mmm (3g) and $[\overline{6}]$ m2 (2c), respectively. In comparison with the previous powder X-ray study of hexagonal RERh₃B₂, the present redetermination against single-crystal X-ray data has allowed for the modeling of all atoms with anisotropic displacement parameters (ADPs). The ADPs of the Rh atom in each of the structures result in an elongated displacement ellipsoid in the direction of the stacking of the Rh kagomé-type layer. The features of obtained ADPs of atoms are discussed in relation to RERh₃B₂-type and analogous structures.

Keywords: single-crystal diffraction; crystal structure; boride; isotypism.

CCDC references: 2128890; 2128891; 2128892

1. Chemical context

CeCo₃B₂-type RERh₃B₂ (RE = rare-earth element) compounds exhibit anomalous ferromagnetic properties (Malik et al., 1983 ; Yamada et al., 2004 ), and the unit-cell parameters of these compounds have been reported using powder X-ray diffraction (XRD) data (Ku et al., 1980; Ku & Meisner, 1981 ). Higashi et al. (1987 ) analyzed the crystal structure of CeRh₃B₂ by using single-crystal XRD data and discussed the characteristics of the anisotropic atomic displacement parameters (ADP) of atoms in CeRh₃B₂ in relation to the structure. We report here the results of structural refinements using single crystals of RERh₃B₂ (RE = Pr, Nd, and Sm) grown by the arc-melting method.

2. Structural commentary

The crystal structures of hexagonal RERh₃B₂ (RE; La–Gd) compounds are isotypic with CeCo₃B₂ and crystallize in space-group type P6/mmm (Kuz'ma et al., 1969 ). The CeCo₃B₂ type of structure is ordered and can be derived from the CaCu₅ type of structure, whereby two distinct atoms (Rh and B) occupy the corresponding Cu sites. Each B atom is surrounded by six Rh atoms, forming a trigonal prism. Such [BRh₆] trigonal prisms constitute a honeycomb structure and RE atoms are accommodated at the centers of the twelve [RERh₁₂] hexagonal prisms, as shown in Fig. 1. The RERh₃B₂ type of structure can also be described as being built up of kagomé layers of Rh atoms stacked along the c axis with an αα stacking sequence and with B and RE atoms at the centers of the Rh triangular and hexagonal prisms, respectively.

Figure 1
Structure of RERh₃B₂ compounds (space group: P6/mmm) as viewed along the c axis. B and RE atoms settle in the center of the trigonal and hexagonal prisms, respectively.

The unit-cell parameters a and c and the unit-cell volume V of RERh₃B₂ (RE = La–Sm) compounds are shown in Fig. 2. The decrease in unit-cell volume results from the lanthanide contraction. The lattice parameters a and c decrease and increase, respectively. These anisotropic changes in the unit-cell parameters are consistent with those of a previous report using powder XRD analysis (Malik et al., 1983).

Figure 2
Unit-cell parameters a (circles), c (squares) and unit-cell volume (triangles) of RERh₃B₂ compounds. Closed and open marks refer to this study and previous work (Malik et al., 1983

), respectively.

The anisotropic change in the unit-cell parameters can be explained by the change in interatomic distances due to the lanthanide contraction. The ranges of B—Rh and RE—Rh distances are 2.2129 (1)–2.2151 (1) Å and 3.1370 (1)–3.1447 (1) Å (Table 1), respectively, which are close to the values of the sums of the atomic radii (r_Rh = 1.35 Å, r_B = 0.85 Å, r_Pr = 1.84 Å, r_Nd = 1.83 Å, and r_Sm = 1.81 Å; Daane et al., 1954 ; Spedding et al., 1956 ; Zachariasen, 1973 ). The RE—Rh interatomic distances decrease due to the effect of the lanthanoid contraction. Rh—Rh interatomic distances in the ab plane also decrease with a decrease in RE—Rh distances. By contrast, the Rh—Rh interatomic distances along the c axis increase. This causes the [RERh₁₂] hexagonal and [BRh₆] trigonal prisms to shrink horizontally and stretch vertically, resulting in decreases of the volumes of the hexagonal and trigonal prisms. Therefore, the unit-cells of RERh₃B₂ compounds change anisotropically, suggesting that the unit-cell changes elastically in response to the substitution of elements of different sizes at the RE site.

Table 1
Selected bond lengths (Å) in RERh₃B₂ (RE = Pr, Nd and Sm)

	PrRh₃B₂	NdRh₃B₂	SmRh₃B₂
RE—RE ×2	3.1084 (1)	3.1107 (1)	3.1190 (1)
RE—RE ×6	5.4676 (4)	5.4527 (3)	5.4438 (3)
RE—Rh ×12	3.1447 (1)	3.1388 (1)	3.1370 (1)
RE—B ×6	3.1557 (2)	3.1481 (1)	3.1430 (1)
B—Rh ×6	2.2151 (1)	2.2129 (1)	2.2140 (1)
B—B ×3	3.1084 (1)	3.1107 (1)	3.1190 (1)
B—B ×3	3.1567 (2)	3.1481 (1)	3.1430 (1)
Rh—Rh ×4	2.7338 (2)	2.7264 (1)	2.7219 (1)
Rh—Rh ×2	3.1084 (1)	3.1107 (1)	3.1190 (1)

The obtained ADPs for each atom are summarized in Table 2. The displacement ellipsoid of the Rh atom shows a larger anisotropy than those of the B and RE atoms, as shown in Fig. 3. The U₃₃ of Rh atoms is approximately 2.1–2.6 times larger than U₁₁, which means that the displacement ellipsoids of Rh atoms are elongated along the c axis. The displacement ellipsoids of Rh atoms with large anisotropy correspond to the anisotropic electric resistivity of RERh₃B₂ compounds (Yamada et al., 2004; Obiraki et al., 2006 ). The ADPs of RE atoms are described as displacement ellipsoids suppressed in the c axis (U₁₁ < U₃₃). The feature of displacement ellipsoids of Rh and RE atoms is attributed to the unusually short RE—RE interatomic distances of 3.1084 (1)–3.1190 (1) Å, which are much shorter (15%) than the distance in the metal Pr, Nd, and Sm with hexagonal close-packed structures, (i.e., 3.67, 3.66, and 3.62 Å, respectively). The short RE—RE interatomic distance is a common feature of the CeCo₃B₂ type of structure. Anisotropy of electric or thermal conductivity is also expected to be observed in CeRh₃B₂ compounds.

Table 2
Atomic displacement parameters of RE, Rh, and B atoms in RERh₃B₂ (RE = Pr, Nd, and Sm)

Atom	U₁₁ (Å²)	U₂₂ (Å²)	U₃₃ (Å²)	U₁₂ (Å²)	U_eq (10 ³Å²)
PrRh₃B₂
Pr	0.00861 (18)	0.00861	0.00780 (20)	0.00430 (9)	8.35 (1)
Rh	0.00495 (16)	0.00386 (18)	0.01040 (20)	0.00193 (9)	6.53 (1)
B	0.0095 (16)	0.0095	0.009 (2)	0.0048 (8)	9.3 (10)
NdRh₃B₂
Nd	0.00896 (10)	0.00896	0.00662 (12)	0.00448 (5)	8.18 (9)
Rh	0.00492 (9)	0.00390 (11)	0.01104 (12)	0.00195 (5)	6.74 (8)
B	0.0100 (9)	0.0100	0.0079 (12)	0.0050 (4)	9.3 (6)
SmRh₃B₂
Sm	0.00841 (12)	0.00841	0.00658 (14)	0.00420 (6)	7.80 (10)
Rh	0.00502 (11)	0.00389 (13)	0.01287 (14)	0.00194 (6)	7.39 (10)
B	0.0085 (10)	0.0085	0.0102 (15)	0.0043 (5)	9.1 (7)

Figure 3
Displacement ellipsoids of each atom in NdRh₃B₂, with displacement ellipsoids drawn at the 99% probability level.

The obtained anisotropic ADPs of each atom in the structures of RERh₃B₂ compounds can be discussed in terms of the nucleation of interstitial atoms or layers in PrRh_4.8B₂ (Higashi et al., 1988 ). Higashi et al. (1988) discovered a new layered structure, namely, PrRh_4.8B₂, which is regarded as a stacking variant of a modified PrRh₃B₂ structure. The interstitial single Rh layer is positioned between the Rh kagomé layers of the modified PrRh₃B₂ blocks. The displacement ellipsoid in the stacking direction of the Rh atom in the PrRh₃B₂ structure implies that the Rh kagomé layer in PrRh₃B₂ could be a base for the nucleation of interstitial atoms or layers. The appearance of disordered La_1–xRh₃B₂ type and/or Nd_1–xRh_xRh₃B₂ type of structures (Ohtani et al., 1983 ; Vlasse et al., 1983 ; Ku et al., 1985 ) might be associated with the anisotropic ADPs of Rh and RE atoms.

3. Synthesis and crystallization

RERh₃B₂ (RE = Pr, Nd, and Sm) single crystals were grown using the arc-melting method. The starting materials used were RE elements (99.9%), along with Rh (99.95%), and B (99.5%). They were weighed at an atomic ratio of (RE+3Rh+2B), and the mixtures of the starting materials were placed in an argon-arc melting furnace (ACM-01, Diavac). Each product was remelted three times to improve homogeneity. The grown crystals were composed of homogeneous RERh₃B₂, and the atomic ratio Rh/RE was confirmed to be 3.00 by energy dispersive X-ray spectroscopy.

4. Refinement details

Crystal data, data collection and structure refinement details are summarized in Table 3. A reciprocal space plot using all reflection data was in good agreement with the hexagonal lattice (a ≃ 5 Å and c ≃ 3 Å), and there was no evidence of superstructure reflections. The refinement was conducted under the assumption that the space group type was P6/mmm, as reported by Ku et al. (1980). Based on structural reports of La_1–xRh₃B₂ and Nd_1–xRh_xRh₃B₂, we determined whether Rh substitution and vacancies at the RE site were possible; however, the results were negative. Therefore, we concluded that the RE sites were completely occupied by RE elements. A correction for isotropic extinction was applied during the least-squares refinements. The final refinements were performed by applying anisotropic ADPs to each atom. The remaining electron densities located 0.7–0.6 Å around rhodium and RE heavy elements are censoring effects caused by the finite Fourier series.

Table 3
Experimental details

	PrRh₃B₂	NdRh₃B₂	SmRh₃B₂
Crystal data
M_r	471.26	474.59	480.70
Crystal system, space group	Hexagonal, P6/mmm	Hexagonal, P6/mmm	Hexagonal, P6/mmm
Temperature (K)	293	293	293
a, c (Å)	5.4676 (3), 3.10837 (16)	5.4527 (2), 3.11066 (13)	5.4438 (2), 3.11901 (12)
V (Å³)	80.47 (1)	80.10 (1)	80.05 (1)
Z	1	1	1
Radiation type	Mo Kα	Mo Kα	Mo Kα
μ (mm⁻¹)	29.43	30.57	32.61
Crystal size (mm)	0.05 × 0.03 × 0.03	0.05 × 0.05 × 0.02	0.06 × 0.05 × 0.02

Data collection
Diffractometer	XtaLAB Synergy, Dualflex, HyPix	XtaLAB Synergy, Dualflex, HyPix	XtaLAB Synergy, Dualflex, HyPix
Absorption correction	Numerical (CrysAlis PRO; Rigaku OD, 2021 )	Numerical (CrysAlis PRO; Rigaku OD, 2021)	Numerical (CrysAlis PRO; Rigaku OD, 2021)
T_min, T_max	0.423, 0.601	0.424, 0.611	0.324, 0.542
No. of measured, independent and observed [I > 2σ(I)] reflections	733, 131, 126	827, 131, 130	696, 129, 128
R_int	0.017	0.010	0.011
(sin θ/λ)_max (Å⁻¹)	0.909	0.908	0.907

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.018, 0.053, 1.21	0.012, 0.032, 1.15	0.012, 0.032, 1.13
No. of reflections	131	131	129
No. of parameters	8	8	9
Δρ_max, Δρ_min (e Å⁻³)	1.80, −1.18	0.97, −2.46	1.76, −0.97
Computer programs: CrysAlis PRO (Rigaku OD, 2021), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ), VESTA (Momma & Izumi, 2011 ) and publCIF (Westrip, 2010 ).

Supporting information

CCDC references: 2128890; 2128891; 2128892

Crystal structure: contains datablocks global, I, II, III. DOI: https://doi.org/10.1107/S2056989021013311/wm5627sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989021013311/wm5627Isup5.hkl

Structure factors: contains datablock II. DOI: https://doi.org/10.1107/S2056989021013311/wm5627IIsup6.hkl

Structure factors: contains datablock III. DOI: https://doi.org/10.1107/S2056989021013311/wm5627IIIsup7.hkl

checkCIF report

Computing details top

For all structures, data collection: CrysAlis PRO (Rigaku OD, 2021); cell refinement: CrysAlis PRO (Rigaku OD, 2021); data reduction: CrysAlis PRO (Rigaku OD, 2021); program(s) used to solve structure: SHELXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: VESTA (Momma & Izumi, 2011); software used to prepare material for publication: publCIF (Westrip, 2010).

Praseodymium trirhodium diboride (I) top

Crystal data top

PrRh₃B₂	D_x = 9.724 Mg m⁻³
M_r = 471.26	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P6/mmm	Cell parameters from 623 reflections
a = 5.4676 (3) Å	θ = 4.3–39.9°
c = 3.10837 (16) Å	µ = 29.43 mm⁻¹
V = 80.47 (1) Å³	T = 293 K
Z = 1	Block, metallic
F(000) = 204	0.05 × 0.03 × 0.03 mm

Data collection top

XtaLAB Synergy, Dualflex, HyPix diffractometer	131 independent reflections
Radiation source: micro-focus sealed X-ray tube, PhotonJet (Mo) X-ray Source	126 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.017
Detector resolution: 10.0000 pixels mm^-1	θ_max = 40.3°, θ_min = 4.3°
ω scans	h = −9→7
Absorption correction: numerical (CrysAlisPro; Rigaku OD, 2021)	k = −9→9
T_min = 0.423, T_max = 0.601	l = −3→5
733 measured reflections

Refinement top

Refinement on F²	8 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.018	w = 1/[σ²(F_o²) + (0.0347P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.053	(Δ/σ)_max < 0.001
S = 1.21	Δρ_max = 1.80 e Å⁻³
131 reflections	Δρ_min = −1.18 e Å⁻³

Special details top

Geometry. All esds (except the esd in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell esds are taken into account individually in the estimation of esds in distances, angles and torsion angles; correlations between esds in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell esds is used for estimating esds involving l.s. planes.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Pr1	0.000000	0.000000	0.000000	0.00835 (14)
Rh1	0.500000	0.000000	0.500000	0.00653 (13)
B1	0.333333	0.666667	0.000000	0.0093 (10)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Pr1	0.00861 (18)	0.00861 (18)	0.0078 (2)	0.00430 (9)	0.000	0.000
Rh1	0.00495 (16)	0.00386 (18)	0.0104 (2)	0.00193 (9)	0.000	0.000
B1	0.0095 (16)	0.0095 (16)	0.009 (2)	0.0048 (8)	0.000	0.000

Geometric parameters (Å, º) top

Pr1—Pr1ⁱ	3.1084 (2)	Pr1—Rh1^x	3.1447 (1)
Pr1—Pr1ⁱⁱ	3.1084 (2)	Rh1—B1^xi	2.2151 (1)
Pr1—Rh1ⁱⁱⁱ	3.1447 (1)	Rh1—B1^xii	2.2151 (1)
Pr1—Rh1^iv	3.1447 (1)	Rh1—B1^xiii	2.2151 (1)
Pr1—Rh1	3.1447 (1)	Rh1—B1^xiv	2.2151 (1)
Pr1—Rh1^v	3.1447 (1)	Rh1—Rh1^xv	2.7338 (2)
Pr1—Rh1^vi	3.1447 (1)	Rh1—Rh1^xvi	2.7338 (2)
Pr1—Rh1^vii	3.1447 (1)	Rh1—Rh1ⁱⁱⁱ	2.7338 (2)
Pr1—Rh1^viii	3.1447 (1)	Rh1—Rh1^xvii	2.7338 (2)
Pr1—Rh1^ix	3.1447 (1)	Rh1—Rh1ⁱ	3.1084 (2)
Pr1—Rh1ⁱⁱ	3.1447 (1)	Rh1—Rh1ⁱⁱ	3.1084 (2)

Pr1ⁱ—Pr1—Pr1ⁱⁱ	180.0	B1^xiii—Rh1—Rh1^xv	51.897 (2)
Pr1ⁱ—Pr1—Rh1ⁱⁱⁱ	60.381 (1)	B1^xiv—Rh1—Rh1^xv	128.103 (2)
Pr1ⁱⁱ—Pr1—Rh1ⁱⁱⁱ	119.619 (1)	B1^xi—Rh1—Rh1^xvi	128.103 (1)
Pr1ⁱ—Pr1—Rh1^iv	119.619 (1)	B1^xii—Rh1—Rh1^xvi	51.897 (1)
Pr1ⁱⁱ—Pr1—Rh1^iv	60.381 (1)	B1^xiii—Rh1—Rh1^xvi	128.103 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1^iv	180.0	B1^xiv—Rh1—Rh1^xvi	51.897 (2)
Pr1ⁱ—Pr1—Rh1	60.381 (2)	Rh1^xv—Rh1—Rh1^xvi	180.0
Pr1ⁱⁱ—Pr1—Rh1	119.619 (2)	B1^xi—Rh1—Rh1ⁱⁱⁱ	51.896 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1	51.528 (1)	B1^xii—Rh1—Rh1ⁱⁱⁱ	128.104 (2)
Rh1^iv—Pr1—Rh1	128.472 (1)	B1^xiii—Rh1—Rh1ⁱⁱⁱ	51.896 (2)
Pr1ⁱ—Pr1—Rh1^v	119.619 (2)	B1^xiv—Rh1—Rh1ⁱⁱⁱ	128.104 (1)
Pr1ⁱⁱ—Pr1—Rh1^v	60.381 (2)	Rh1^xv—Rh1—Rh1ⁱⁱⁱ	60.0
Rh1ⁱⁱⁱ—Pr1—Rh1^v	128.472 (1)	Rh1^xvi—Rh1—Rh1ⁱⁱⁱ	120.0
Rh1^iv—Pr1—Rh1^v	51.528 (1)	B1^xi—Rh1—Rh1^xvii	128.104 (2)
Rh1—Pr1—Rh1^v	180.0	B1^xii—Rh1—Rh1^xvii	51.896 (2)
Pr1ⁱ—Pr1—Rh1^vi	60.381 (2)	B1^xiii—Rh1—Rh1^xvii	128.104 (2)
Pr1ⁱⁱ—Pr1—Rh1^vi	119.619 (2)	B1^xiv—Rh1—Rh1^xvii	51.896 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1^vi	51.528 (1)	Rh1^xv—Rh1—Rh1^xvii	120.0
Rh1^iv—Pr1—Rh1^vi	128.472 (1)	Rh1^xvi—Rh1—Rh1^xvii	60.0
Rh1—Pr1—Rh1^vi	97.678 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1^xvii	180.0
Rh1^v—Pr1—Rh1^vi	82.322 (2)	B1^xi—Rh1—Rh1ⁱ	45.442 (2)
Pr1ⁱ—Pr1—Rh1^vii	119.619 (2)	B1^xii—Rh1—Rh1ⁱ	134.558 (2)
Pr1ⁱⁱ—Pr1—Rh1^vii	60.381 (2)	B1^xiii—Rh1—Rh1ⁱ	134.558 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1^vii	128.472 (1)	B1^xiv—Rh1—Rh1ⁱ	45.442 (2)
Rh1^iv—Pr1—Rh1^vii	51.528 (1)	Rh1^xv—Rh1—Rh1ⁱ	90.0
Rh1—Pr1—Rh1^vii	82.322 (2)	Rh1^xvi—Rh1—Rh1ⁱ	90.0
Rh1^v—Pr1—Rh1^vii	97.678 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1ⁱ	90.0
Rh1^vi—Pr1—Rh1^vii	180.0	Rh1^xvii—Rh1—Rh1ⁱ	90.0
Pr1ⁱ—Pr1—Rh1^viii	60.381 (2)	B1^xi—Rh1—Rh1ⁱⁱ	134.558 (2)
Pr1ⁱⁱ—Pr1—Rh1^viii	119.619 (2)	B1^xii—Rh1—Rh1ⁱⁱ	45.442 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1^viii	120.763 (4)	B1^xiii—Rh1—Rh1ⁱⁱ	45.442 (2)
Rh1^iv—Pr1—Rh1^viii	59.238 (4)	B1^xiv—Rh1—Rh1ⁱⁱ	134.558 (2)
Rh1—Pr1—Rh1^viii	97.678 (3)	Rh1^xv—Rh1—Rh1ⁱⁱ	90.0
Rh1^v—Pr1—Rh1^viii	82.322 (3)	Rh1^xvi—Rh1—Rh1ⁱⁱ	90.0
Rh1^vi—Pr1—Rh1^viii	97.678 (3)	Rh1ⁱⁱⁱ—Rh1—Rh1ⁱⁱ	90.0
Rh1^vii—Pr1—Rh1^viii	82.322 (3)	Rh1^xvii—Rh1—Rh1ⁱⁱ	90.0
Pr1ⁱ—Pr1—Rh1^ix	119.619 (2)	Rh1ⁱ—Rh1—Rh1ⁱⁱ	180.0
Pr1ⁱⁱ—Pr1—Rh1^ix	60.381 (2)	B1^xi—Rh1—Pr1	110.289 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1^ix	59.238 (4)	B1^xii—Rh1—Pr1	69.711 (3)
Rh1^iv—Pr1—Rh1^ix	120.763 (4)	B1^xiii—Rh1—Pr1	69.710 (2)
Rh1—Pr1—Rh1^ix	82.322 (3)	B1^xiv—Rh1—Pr1	110.290 (2)
Rh1^v—Pr1—Rh1^ix	97.678 (3)	Rh1^xv—Rh1—Pr1	115.764 (1)
Rh1^vi—Pr1—Rh1^ix	82.322 (3)	Rh1^xvi—Rh1—Pr1	64.236 (1)
Rh1^vii—Pr1—Rh1^ix	97.678 (3)	Rh1ⁱⁱⁱ—Rh1—Pr1	64.236 (1)
Rh1^viii—Pr1—Rh1^ix	180.0	Rh1^xvii—Rh1—Pr1	115.764 (1)
Pr1ⁱ—Pr1—Rh1ⁱⁱ	119.619 (2)	Rh1ⁱ—Rh1—Pr1	119.619 (1)
Pr1ⁱⁱ—Pr1—Rh1ⁱⁱ	60.381 (2)	Rh1ⁱⁱ—Rh1—Pr1	60.381 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1ⁱⁱ	82.322 (3)	B1^xi—Rh1—Pr1^xviii	69.711 (2)
Rh1^iv—Pr1—Rh1ⁱⁱ	97.678 (3)	B1^xii—Rh1—Pr1^xviii	110.289 (3)
Rh1—Pr1—Rh1ⁱⁱ	59.238 (4)	B1^xiii—Rh1—Pr1^xviii	110.290 (2)
Rh1^v—Pr1—Rh1ⁱⁱ	120.762 (4)	B1^xiv—Rh1—Pr1^xviii	69.710 (2)
Rh1^vi—Pr1—Rh1ⁱⁱ	128.472 (1)	Rh1^xv—Rh1—Pr1^xviii	64.236 (1)
Rh1^vii—Pr1—Rh1ⁱⁱ	51.528 (1)	Rh1^xvi—Rh1—Pr1^xviii	115.764 (1)
Rh1^viii—Pr1—Rh1ⁱⁱ	128.472 (1)	Rh1ⁱⁱⁱ—Rh1—Pr1^xviii	115.764 (1)
Rh1^ix—Pr1—Rh1ⁱⁱ	51.528 (1)	Rh1^xvii—Rh1—Pr1^xviii	64.236 (1)
Pr1ⁱ—Pr1—Rh1^x	60.381 (2)	Rh1ⁱ—Rh1—Pr1^xviii	60.381 (2)
Pr1ⁱⁱ—Pr1—Rh1^x	119.619 (2)	Rh1ⁱⁱ—Rh1—Pr1^xviii	119.619 (2)
Rh1ⁱⁱⁱ—Pr1—Rh1^x	97.678 (3)	Pr1—Rh1—Pr1^xviii	180.0
Rh1^iv—Pr1—Rh1^x	82.322 (3)	Rh1^xix—B1—Rh1^xx	138.257 (2)
Rh1—Pr1—Rh1^x	120.762 (4)	Rh1^xix—B1—Rh1^vi	89.116 (4)
Rh1^v—Pr1—Rh1^x	59.238 (4)	Rh1^xx—B1—Rh1^vi	76.206 (4)
Rh1^vi—Pr1—Rh1^x	51.528 (1)	Rh1^xix—B1—Rh1^xxi	76.206 (4)
Rh1^vii—Pr1—Rh1^x	128.472 (1)	Rh1^xx—B1—Rh1^xxi	89.116 (4)
Rh1^viii—Pr1—Rh1^x	51.528 (1)	Rh1^vi—B1—Rh1^xxi	138.257 (2)
Rh1^ix—Pr1—Rh1^x	128.472 (1)	Rh1^xix—B1—Rh1ⁱⁱⁱ	138.257 (2)
Rh1ⁱⁱ—Pr1—Rh1^x	180.0	Rh1^xx—B1—Rh1ⁱⁱⁱ	76.206 (4)
B1^xi—Rh1—B1^xii	180.0	Rh1^vi—B1—Rh1ⁱⁱⁱ	76.206 (4)
B1^xi—Rh1—B1^xiii	89.116 (4)	Rh1^xxi—B1—Rh1ⁱⁱⁱ	138.257 (2)
B1^xii—Rh1—B1^xiii	90.884 (4)	Rh1^xix—B1—Rh1^ix	76.206 (4)
B1^xi—Rh1—B1^xiv	90.884 (4)	Rh1^xx—B1—Rh1^ix	138.257 (2)
B1^xii—Rh1—B1^xiv	89.116 (4)	Rh1^vi—B1—Rh1^ix	138.257 (2)
B1^xiii—Rh1—B1^xiv	180.0	Rh1^xxi—B1—Rh1^ix	76.206 (4)
B1^xi—Rh1—Rh1^xv	51.897 (1)	Rh1ⁱⁱⁱ—B1—Rh1^ix	89.116 (4)
B1^xii—Rh1—Rh1^xv	128.103 (1)

Symmetry codes: (i) x, y, z+1; (ii) x, y, z−1; (iii) −x+y+1, −x+1, z; (iv) −x+y, −x, z−1; (v) x−1, y, z−1; (vi) −y, x−y, z; (vii) −y, x−y−1, z−1; (viii) −x+y, −x, z; (ix) −x+y+1, −x+1, z−1; (x) x−1, y, z; (xi) −x+1, −y+1, −z+1; (xii) x, y−1, z; (xiii) −x+1, −y+1, −z; (xiv) x, y−1, z+1; (xv) −y+1, x−y, z; (xvi) −y, x−y−1, z; (xvii) −x+y+1, −x, z; (xviii) x+1, y, z+1; (xix) −y, x−y, z−1; (xx) x, y+1, z; (xxi) x, y+1, z−1.

Neodymium trirhodium diboride (II) top

Crystal data top

NdRh₃B₂	D_x = 9.839 Mg m⁻³
M_r = 474.59	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P6/mmm	Cell parameters from 729 reflections
a = 5.4527 (2) Å	θ = 4.3–40.7°
c = 3.11066 (13) Å	µ = 30.57 mm⁻¹
V = 80.10 (1) Å³	T = 293 K
Z = 1	Block, metallic
F(000) = 205	0.05 × 0.05 × 0.02 mm

Data collection top

XtaLAB Synergy, Dualflex, HyPix diffractometer	131 independent reflections
Radiation source: micro-focus sealed X-ray tube, PhotonJet (Mo) X-ray Source	130 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.010
Detector resolution: 10.0000 pixels mm^-1	θ_max = 40.2°, θ_min = 4.3°
ω scans	h = −9→8
Absorption correction: numerical (CrysAlisPro; Rigaku OD, 2021)	k = −7→9
T_min = 0.424, T_max = 0.611	l = −3→5
827 measured reflections

Refinement top

Refinement on F²	8 parameters
Least-squares matrix: full	0 restraints
R[F² > 2σ(F²)] = 0.012	w = 1/[σ²(F_o²) + (0.022P)²] where P = (F_o² + 2F_c²)/3
wR(F²) = 0.032	(Δ/σ)_max < 0.001
S = 1.15	Δρ_max = 0.97 e Å⁻³
131 reflections	Δρ_min = −2.46 e Å⁻³

Special details top

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Nd1	0.000000	0.000000	0.000000	0.00818 (9)
Rh1	0.500000	0.000000	0.500000	0.00674 (8)
B1	0.333333	0.666667	0.000000	0.0093 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Nd1	0.00896 (10)	0.00896 (10)	0.00662 (12)	0.00448 (5)	0.000	0.000
Rh1	0.00492 (9)	0.00390 (11)	0.01104 (12)	0.00195 (5)	0.000	0.000
B1	0.0100 (9)	0.0100 (9)	0.0079 (12)	0.0050 (4)	0.000	0.000

Geometric parameters (Å, º) top

Nd1—Nd1ⁱ	3.1107 (1)	Nd1—Rh1ⁱⁱ	3.1388 (1)
Nd1—Nd1ⁱⁱ	3.1107 (1)	Rh1—B1^xi	2.2129 (1)
Nd1—Rh1ⁱⁱⁱ	3.1388 (1)	Rh1—B1^xii	2.2129 (1)
Nd1—Rh1^iv	3.1388 (1)	Rh1—B1^xiii	2.2129 (1)
Nd1—Rh1^v	3.1388 (1)	Rh1—B1^xiv	2.2129 (1)
Nd1—Rh1^vi	3.1388 (1)	Rh1—Rh1^xv	2.7264 (1)
Nd1—Rh1	3.1388 (1)	Rh1—Rh1^xvi	2.7264 (1)
Nd1—Rh1^vii	3.1388 (1)	Rh1—Rh1ⁱⁱⁱ	2.7264 (1)
Nd1—Rh1^viii	3.1388 (1)	Rh1—Rh1^xvii	2.7264 (1)
Nd1—Rh1^ix	3.1388 (1)	Rh1—Rh1ⁱ	3.1107 (1)
Nd1—Rh1^x	3.1388 (1)	Rh1—Rh1ⁱⁱ	3.1107 (1)

Nd1ⁱ—Nd1—Nd1ⁱⁱ	180.0	B1^xiii—Rh1—Rh1^xv	51.974 (1)
Nd1ⁱ—Nd1—Rh1ⁱⁱⁱ	60.296 (1)	B1^xiv—Rh1—Rh1^xv	128.026 (1)
Nd1ⁱⁱ—Nd1—Rh1ⁱⁱⁱ	119.704 (1)	B1^xi—Rh1—Rh1^xvi	128.026 (1)
Nd1ⁱ—Nd1—Rh1^iv	119.704 (1)	B1^xii—Rh1—Rh1^xvi	51.974 (1)
Nd1ⁱⁱ—Nd1—Rh1^iv	60.296 (1)	B1^xiii—Rh1—Rh1^xvi	128.026 (2)
Rh1ⁱⁱⁱ—Nd1—Rh1^iv	180.0	B1^xiv—Rh1—Rh1^xvi	51.974 (1)
Nd1ⁱ—Nd1—Rh1^v	60.296 (1)	Rh1^xv—Rh1—Rh1^xvi	180.0
Nd1ⁱⁱ—Nd1—Rh1^v	119.704 (1)	B1^xi—Rh1—Rh1ⁱⁱⁱ	51.973 (1)
Rh1ⁱⁱⁱ—Nd1—Rh1^v	51.481 (1)	B1^xii—Rh1—Rh1ⁱⁱⁱ	128.027 (1)
Rh1^iv—Nd1—Rh1^v	128.519 (1)	B1^xiii—Rh1—Rh1ⁱⁱⁱ	51.973 (1)
Nd1ⁱ—Nd1—Rh1^vi	119.704 (1)	B1^xiv—Rh1—Rh1ⁱⁱⁱ	128.027 (1)
Nd1ⁱⁱ—Nd1—Rh1^vi	60.296 (1)	Rh1^xv—Rh1—Rh1ⁱⁱⁱ	60.0
Rh1ⁱⁱⁱ—Nd1—Rh1^vi	128.519 (1)	Rh1^xvi—Rh1—Rh1ⁱⁱⁱ	120.0
Rh1^iv—Nd1—Rh1^vi	51.481 (1)	B1^xi—Rh1—Rh1^xvii	128.027 (2)
Rh1^v—Nd1—Rh1^vi	180.0	B1^xii—Rh1—Rh1^xvii	51.973 (1)
Nd1ⁱ—Nd1—Rh1	60.296 (1)	B1^xiii—Rh1—Rh1^xvii	128.027 (1)
Nd1ⁱⁱ—Nd1—Rh1	119.704 (1)	B1^xiv—Rh1—Rh1^xvii	51.973 (1)
Rh1ⁱⁱⁱ—Nd1—Rh1	51.481 (1)	Rh1^xv—Rh1—Rh1^xvii	120.0
Rh1^iv—Nd1—Rh1	128.519 (1)	Rh1^xvi—Rh1—Rh1^xvii	60.0
Rh1^v—Nd1—Rh1	97.568 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1^xvii	180.0
Rh1^vi—Nd1—Rh1	82.432 (2)	B1^xi—Rh1—Rh1ⁱ	45.343 (2)
Nd1ⁱ—Nd1—Rh1^vii	119.704 (1)	B1^xii—Rh1—Rh1ⁱ	134.657 (1)
Nd1ⁱⁱ—Nd1—Rh1^vii	60.296 (1)	B1^xiii—Rh1—Rh1ⁱ	134.657 (2)
Rh1ⁱⁱⁱ—Nd1—Rh1^vii	128.519 (1)	B1^xiv—Rh1—Rh1ⁱ	45.343 (2)
Rh1^iv—Nd1—Rh1^vii	51.481 (1)	Rh1^xv—Rh1—Rh1ⁱ	90.0
Rh1^v—Nd1—Rh1^vii	82.432 (2)	Rh1^xvi—Rh1—Rh1ⁱ	90.0
Rh1^vi—Nd1—Rh1^vii	97.568 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1ⁱ	90.0
Rh1—Nd1—Rh1^vii	180.0	Rh1^xvii—Rh1—Rh1ⁱ	90.0
Nd1ⁱ—Nd1—Rh1^viii	60.296 (2)	B1^xi—Rh1—Rh1ⁱⁱ	134.657 (2)
Nd1ⁱⁱ—Nd1—Rh1^viii	119.704 (2)	B1^xii—Rh1—Rh1ⁱⁱ	45.343 (2)
Rh1ⁱⁱⁱ—Nd1—Rh1^viii	120.592 (3)	B1^xiii—Rh1—Rh1ⁱⁱ	45.343 (2)
Rh1^iv—Nd1—Rh1^viii	59.408 (3)	B1^xiv—Rh1—Rh1ⁱⁱ	134.657 (2)
Rh1^v—Nd1—Rh1^viii	97.568 (2)	Rh1^xv—Rh1—Rh1ⁱⁱ	90.0
Rh1^vi—Nd1—Rh1^viii	82.432 (2)	Rh1^xvi—Rh1—Rh1ⁱⁱ	90.0
Rh1—Nd1—Rh1^viii	97.568 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1ⁱⁱ	90.0
Rh1^vii—Nd1—Rh1^viii	82.432 (2)	Rh1^xvii—Rh1—Rh1ⁱⁱ	90.0
Nd1ⁱ—Nd1—Rh1^ix	119.704 (2)	Rh1ⁱ—Rh1—Rh1ⁱⁱ	180.0
Nd1ⁱⁱ—Nd1—Rh1^ix	60.296 (2)	B1^xi—Rh1—Nd1	110.381 (2)
Rh1ⁱⁱⁱ—Nd1—Rh1^ix	59.408 (3)	B1^xii—Rh1—Nd1	69.619 (2)
Rh1^iv—Nd1—Rh1^ix	120.592 (3)	B1^xiii—Rh1—Nd1	69.617 (2)
Rh1^v—Nd1—Rh1^ix	82.432 (2)	B1^xiv—Rh1—Nd1	110.383 (2)
Rh1^vi—Nd1—Rh1^ix	97.568 (2)	Rh1^xv—Rh1—Nd1	115.7
Rh1—Nd1—Rh1^ix	82.432 (2)	Rh1^xvi—Rh1—Nd1	64.3
Rh1^vii—Nd1—Rh1^ix	97.568 (2)	Rh1ⁱⁱⁱ—Rh1—Nd1	64.259 (1)
Rh1^viii—Nd1—Rh1^ix	180.0	Rh1^xvii—Rh1—Nd1	115.741 (1)
Nd1ⁱ—Nd1—Rh1^x	60.296 (1)	Rh1ⁱ—Rh1—Nd1	119.704 (1)
Nd1ⁱⁱ—Nd1—Rh1^x	119.704 (1)	Rh1ⁱⁱ—Rh1—Nd1	60.296 (1)
Rh1ⁱⁱⁱ—Nd1—Rh1^x	97.568 (3)	B1^xi—Rh1—Nd1^xviii	69.619 (2)
Rh1^iv—Nd1—Rh1^x	82.432 (3)	B1^xii—Rh1—Nd1^xviii	110.381 (2)
Rh1^v—Nd1—Rh1^x	51.481 (1)	B1^xiii—Rh1—Nd1^xviii	110.383 (2)
Rh1^vi—Nd1—Rh1^x	128.519 (1)	B1^xiv—Rh1—Nd1^xviii	69.617 (2)
Rh1—Nd1—Rh1^x	120.592 (3)	Rh1^xv—Rh1—Nd1^xviii	64.3
Rh1^vii—Nd1—Rh1^x	59.408 (3)	Rh1^xvi—Rh1—Nd1^xviii	115.7
Rh1^viii—Nd1—Rh1^x	51.481 (1)	Rh1ⁱⁱⁱ—Rh1—Nd1^xviii	115.741 (1)
Rh1^ix—Nd1—Rh1^x	128.519 (1)	Rh1^xvii—Rh1—Nd1^xviii	64.259 (1)
Nd1ⁱ—Nd1—Rh1ⁱⁱ	119.704 (1)	Rh1ⁱ—Rh1—Nd1^xviii	60.296 (1)
Nd1ⁱⁱ—Nd1—Rh1ⁱⁱ	60.296 (1)	Rh1ⁱⁱ—Rh1—Nd1^xviii	119.704 (1)
Rh1ⁱⁱⁱ—Nd1—Rh1ⁱⁱ	82.432 (3)	Nd1—Rh1—Nd1^xviii	180.0
Rh1^iv—Nd1—Rh1ⁱⁱ	97.568 (3)	Rh1^xix—B1—Rh1^xx	138.332 (1)
Rh1^v—Nd1—Rh1ⁱⁱ	128.519 (1)	Rh1^xix—B1—Rh1^v	89.314 (4)
Rh1^vi—Nd1—Rh1ⁱⁱ	51.481 (1)	Rh1^xx—B1—Rh1^v	76.053 (3)
Rh1—Nd1—Rh1ⁱⁱ	59.408 (3)	Rh1^xix—B1—Rh1^xxi	76.053 (3)
Rh1^vii—Nd1—Rh1ⁱⁱ	120.592 (3)	Rh1^xx—B1—Rh1^xxi	89.314 (4)
Rh1^viii—Nd1—Rh1ⁱⁱ	128.519 (1)	Rh1^v—B1—Rh1^xxi	138.332 (1)
Rh1^ix—Nd1—Rh1ⁱⁱ	51.481 (1)	Rh1^xix—B1—Rh1ⁱⁱⁱ	138.332 (1)
Rh1^x—Nd1—Rh1ⁱⁱ	180.0	Rh1^xx—B1—Rh1ⁱⁱⁱ	76.053 (2)
B1^xi—Rh1—B1^xii	180.0	Rh1^v—B1—Rh1ⁱⁱⁱ	76.053 (3)
B1^xi—Rh1—B1^xiii	89.314 (4)	Rh1^xxi—B1—Rh1ⁱⁱⁱ	138.332 (1)
B1^xii—Rh1—B1^xiii	90.686 (4)	Rh1^xix—B1—Rh1^ix	76.053 (3)
B1^xi—Rh1—B1^xiv	90.686 (4)	Rh1^xx—B1—Rh1^ix	138.332 (1)
B1^xii—Rh1—B1^xiv	89.314 (4)	Rh1^v—B1—Rh1^ix	138.332 (2)
B1^xiii—Rh1—B1^xiv	180.0	Rh1^xxi—B1—Rh1^ix	76.053 (3)
B1^xi—Rh1—Rh1^xv	51.974 (1)	Rh1ⁱⁱⁱ—B1—Rh1^ix	89.314 (4)
B1^xii—Rh1—Rh1^xv	128.026 (1)

Symmetry codes: (i) x, y, z+1; (ii) x, y, z−1; (iii) −x+y+1, −x+1, z; (iv) −x+y, −x, z−1; (v) −y, x−y, z; (vi) −y, x−y−1, z−1; (vii) x−1, y, z−1; (viii) −x+y, −x, z; (ix) −x+y+1, −x+1, z−1; (x) x−1, y, z; (xi) −x+1, −y+1, −z+1; (xii) x, y−1, z; (xiii) −x+1, −y+1, −z; (xiv) x, y−1, z+1; (xv) −y+1, x−y, z; (xvi) −y, x−y−1, z; (xvii) −x+y+1, −x, z; (xviii) x+1, y, z+1; (xix) −y, x−y, z−1; (xx) x, y+1, z; (xxi) x, y+1, z−1.

Samarium trirhodium diboride (III) top

Crystal data top

SmRh₃B₂	D_x = 9.972 Mg m⁻³
M_r = 480.70	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P6/mmm	Cell parameters from 649 reflections
a = 5.4438 (2) Å	θ = 4.3–40.1°
c = 3.11901 (12) Å	µ = 32.61 mm⁻¹
V = 80.05 (1) Å³	T = 293 K
Z = 1	Block, metallic
F(000) = 207	0.06 × 0.05 × 0.02 mm

Data collection top

XtaLAB Synergy, Dualflex, HyPix diffractometer	129 independent reflections
Radiation source: micro-focus sealed X-ray tube, PhotonJet (Mo) X-ray Source	128 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.011
Detector resolution: 10.0000 pixels mm^-1	θ_max = 40.1°, θ_min = 4.3°
ω scans	h = −8→9
Absorption correction: numerical (CrysAlisPro; Rigaku OD, 2021)	k = −7→7
T_min = 0.324, T_max = 0.542	l = −3→5
696 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0213P)² + 0.0484P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.012	(Δ/σ)_max < 0.001
wR(F²) = 0.032	Δρ_max = 1.76 e Å⁻³
S = 1.13	Δρ_min = −0.97 e Å⁻³
129 reflections	Extinction correction: SHELXL-2016/6 (Sheldrick 2016), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
9 parameters	Extinction coefficient: 0.034 (3)

Special details top

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq
Sm1	0.000000	0.000000	0.000000	0.00780 (10)
Rh1	0.500000	0.000000	0.500000	0.00739 (10)
B1	0.333333	0.666667	0.000000	0.0091 (7)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Sm1	0.00841 (12)	0.00841 (12)	0.00658 (14)	0.00420 (6)	0.000	0.000
Rh1	0.00502 (11)	0.00389 (13)	0.01287 (14)	0.00194 (6)	0.000	0.000
B1	0.0085 (10)	0.0085 (10)	0.0102 (15)	0.0043 (5)	0.000	0.000

Geometric parameters (Å, º) top

Sm1—Sm1ⁱ	3.1190 (1)	Sm1—Rh1^x	3.1370 (1)
Sm1—Sm1ⁱⁱ	3.1190 (1)	Rh1—B1^xi	2.2140 (1)
Sm1—Rh1ⁱⁱⁱ	3.1370 (1)	Rh1—B1^xii	2.2140 (1)
Sm1—Rh1^iv	3.1370 (1)	Rh1—B1^xiii	2.2140 (1)
Sm1—Rh1	3.1370 (1)	Rh1—B1^xiv	2.2140 (1)
Sm1—Rh1^v	3.1370 (1)	Rh1—Rh1^xv	2.7219 (1)
Sm1—Rh1^vi	3.1370 (1)	Rh1—Rh1^xvi	2.7219 (1)
Sm1—Rh1^vii	3.1370 (1)	Rh1—Rh1ⁱⁱⁱ	2.7219 (1)
Sm1—Rh1^viii	3.1370 (1)	Rh1—Rh1^xvii	2.7219 (1)
Sm1—Rh1^ix	3.1370 (1)	Rh1—Rh1ⁱ	3.1190 (1)
Sm1—Rh1ⁱⁱ	3.1370 (1)	Rh1—Rh1ⁱⁱ	3.1190 (1)

Sm1ⁱ—Sm1—Sm1ⁱⁱ	180.0	B1^xiii—Rh1—Rh1^xv	52.069 (1)
Sm1ⁱ—Sm1—Rh1ⁱⁱⁱ	60.189 (1)	B1^xiv—Rh1—Rh1^xv	127.931 (1)
Sm1ⁱⁱ—Sm1—Rh1ⁱⁱⁱ	119.811 (1)	B1^xi—Rh1—Rh1^xvi	127.931 (1)
Sm1ⁱ—Sm1—Rh1^iv	119.811 (1)	B1^xii—Rh1—Rh1^xvi	52.069 (1)
Sm1ⁱⁱ—Sm1—Rh1^iv	60.189 (1)	B1^xiii—Rh1—Rh1^xvi	127.931 (1)
Rh1ⁱⁱⁱ—Sm1—Rh1^iv	180.0	B1^xiv—Rh1—Rh1^xvi	52.069 (1)
Sm1ⁱ—Sm1—Rh1	60.189 (2)	Rh1^xv—Rh1—Rh1^xvi	180.0
Sm1ⁱⁱ—Sm1—Rh1	119.811 (1)	B1^xi—Rh1—Rh1ⁱⁱⁱ	52.069 (1)
Rh1ⁱⁱⁱ—Sm1—Rh1	51.423 (1)	B1^xii—Rh1—Rh1ⁱⁱⁱ	127.931 (1)
Rh1^iv—Sm1—Rh1	128.6	B1^xiii—Rh1—Rh1ⁱⁱⁱ	52.069 (1)
Sm1ⁱ—Sm1—Rh1^v	119.811 (1)	B1^xiv—Rh1—Rh1ⁱⁱⁱ	127.931 (1)
Sm1ⁱⁱ—Sm1—Rh1^v	60.189 (2)	Rh1^xv—Rh1—Rh1ⁱⁱⁱ	60.0
Rh1ⁱⁱⁱ—Sm1—Rh1^v	128.6	Rh1^xvi—Rh1—Rh1ⁱⁱⁱ	120.0
Rh1^iv—Sm1—Rh1^v	51.423 (1)	B1^xi—Rh1—Rh1^xvii	127.931 (1)
Rh1—Sm1—Rh1^v	180.0	B1^xii—Rh1—Rh1^xvii	52.069 (1)
Sm1ⁱ—Sm1—Rh1^vi	60.189 (2)	B1^xiii—Rh1—Rh1^xvii	127.931 (1)
Sm1ⁱⁱ—Sm1—Rh1^vi	119.811 (1)	B1^xiv—Rh1—Rh1^xvii	52.069 (1)
Rh1ⁱⁱⁱ—Sm1—Rh1^vi	51.423 (1)	Rh1^xv—Rh1—Rh1^xvii	120.0
Rh1^iv—Sm1—Rh1^vi	128.577 (1)	Rh1^xvi—Rh1—Rh1^xvii	60.0
Rh1—Sm1—Rh1^vi	97.428 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1^xvii	180.0
Rh1^v—Sm1—Rh1^vi	82.572 (2)	B1^xi—Rh1—Rh1ⁱ	45.219 (1)
Sm1ⁱ—Sm1—Rh1^vii	119.811 (1)	B1^xii—Rh1—Rh1ⁱ	134.781 (2)
Sm1ⁱⁱ—Sm1—Rh1^vii	60.189 (2)	B1^xiii—Rh1—Rh1ⁱ	134.781 (1)
Rh1ⁱⁱⁱ—Sm1—Rh1^vii	128.577 (1)	B1^xiv—Rh1—Rh1ⁱ	45.219 (1)
Rh1^iv—Sm1—Rh1^vii	51.423 (1)	Rh1^xv—Rh1—Rh1ⁱ	90.0
Rh1—Sm1—Rh1^vii	82.572 (2)	Rh1^xvi—Rh1—Rh1ⁱ	90.0
Rh1^v—Sm1—Rh1^vii	97.428 (2)	Rh1ⁱⁱⁱ—Rh1—Rh1ⁱ	90.0
Rh1^vi—Sm1—Rh1^vii	180.0	Rh1^xvii—Rh1—Rh1ⁱ	90.0
Sm1ⁱ—Sm1—Rh1^viii	60.189 (1)	B1^xi—Rh1—Rh1ⁱⁱ	134.781 (2)
Sm1ⁱⁱ—Sm1—Rh1^viii	119.811 (1)	B1^xii—Rh1—Rh1ⁱⁱ	45.219 (2)
Rh1ⁱⁱⁱ—Sm1—Rh1^viii	120.379 (3)	B1^xiii—Rh1—Rh1ⁱⁱ	45.219 (1)
Rh1^iv—Sm1—Rh1^viii	59.621 (3)	B1^xiv—Rh1—Rh1ⁱⁱ	134.781 (1)
Rh1—Sm1—Rh1^viii	97.428 (2)	Rh1^xv—Rh1—Rh1ⁱⁱ	90.0
Rh1^v—Sm1—Rh1^viii	82.572 (2)	Rh1^xvi—Rh1—Rh1ⁱⁱ	90.0
Rh1^vi—Sm1—Rh1^viii	97.428 (1)	Rh1ⁱⁱⁱ—Rh1—Rh1ⁱⁱ	90.0
Rh1^vii—Sm1—Rh1^viii	82.572 (1)	Rh1^xvii—Rh1—Rh1ⁱⁱ	90.0
Sm1ⁱ—Sm1—Rh1^ix	119.811 (1)	Rh1ⁱ—Rh1—Rh1ⁱⁱ	180.0
Sm1ⁱⁱ—Sm1—Rh1^ix	60.189 (1)	B1^xi—Rh1—Sm1	110.498 (2)
Rh1ⁱⁱⁱ—Sm1—Rh1^ix	59.621 (3)	B1^xii—Rh1—Sm1	69.502 (1)
Rh1^iv—Sm1—Rh1^ix	120.379 (3)	B1^xiii—Rh1—Sm1	69.501 (1)
Rh1—Sm1—Rh1^ix	82.572 (2)	B1^xiv—Rh1—Sm1	110.499 (1)
Rh1^v—Sm1—Rh1^ix	97.428 (2)	Rh1^xv—Rh1—Sm1	115.711 (1)
Rh1^vi—Sm1—Rh1^ix	82.572 (1)	Rh1^xvi—Rh1—Sm1	64.3
Rh1^vii—Sm1—Rh1^ix	97.428 (1)	Rh1ⁱⁱⁱ—Rh1—Sm1	64.289 (1)
Rh1^viii—Sm1—Rh1^ix	180.0	Rh1^xvii—Rh1—Sm1	115.7
Sm1ⁱ—Sm1—Rh1ⁱⁱ	119.811 (1)	Rh1ⁱ—Rh1—Sm1	119.811 (2)
Sm1ⁱⁱ—Sm1—Rh1ⁱⁱ	60.189 (1)	Rh1ⁱⁱ—Rh1—Sm1	60.189 (2)
Rh1ⁱⁱⁱ—Sm1—Rh1ⁱⁱ	82.572 (2)	B1^xi—Rh1—Sm1^xviii	69.502 (2)
Rh1^iv—Sm1—Rh1ⁱⁱ	97.428 (2)	B1^xii—Rh1—Sm1^xviii	110.498 (1)
Rh1—Sm1—Rh1ⁱⁱ	59.621 (3)	B1^xiii—Rh1—Sm1^xviii	110.499 (1)
Rh1^v—Sm1—Rh1ⁱⁱ	120.379 (4)	B1^xiv—Rh1—Sm1^xviii	69.501 (1)
Rh1^vi—Sm1—Rh1ⁱⁱ	128.577 (1)	Rh1^xv—Rh1—Sm1^xviii	64.3
Rh1^vii—Sm1—Rh1ⁱⁱ	51.423 (1)	Rh1^xvi—Rh1—Sm1^xviii	115.7
Rh1^viii—Sm1—Rh1ⁱⁱ	128.577 (1)	Rh1ⁱⁱⁱ—Rh1—Sm1^xviii	115.7
Rh1^ix—Sm1—Rh1ⁱⁱ	51.423 (1)	Rh1^xvii—Rh1—Sm1^xviii	64.3
Sm1ⁱ—Sm1—Rh1^x	60.189 (1)	Rh1ⁱ—Rh1—Sm1^xviii	60.189 (1)
Sm1ⁱⁱ—Sm1—Rh1^x	119.811 (1)	Rh1ⁱⁱ—Rh1—Sm1^xviii	119.811 (1)
Rh1ⁱⁱⁱ—Sm1—Rh1^x	97.428 (2)	Sm1—Rh1—Sm1^xviii	180.0
Rh1^iv—Sm1—Rh1^x	82.572 (2)	Rh1^xix—B1—Rh1^xx	138.425 (1)
Rh1—Sm1—Rh1^x	120.379 (4)	Rh1^xix—B1—Rh1^xxi	75.862 (3)
Rh1^v—Sm1—Rh1^x	59.621 (3)	Rh1^xx—B1—Rh1^xxi	89.562 (4)
Rh1^vi—Sm1—Rh1^x	51.423 (1)	Rh1^xix—B1—Rh1^vi	89.562 (4)
Rh1^vii—Sm1—Rh1^x	128.577 (1)	Rh1^xx—B1—Rh1^vi	75.862 (3)
Rh1^viii—Sm1—Rh1^x	51.423 (1)	Rh1^xxi—B1—Rh1^vi	138.425 (1)
Rh1^ix—Sm1—Rh1^x	128.577 (1)	Rh1^xix—B1—Rh1ⁱⁱⁱ	138.425 (1)
Rh1ⁱⁱ—Sm1—Rh1^x	180.0	Rh1^xx—B1—Rh1ⁱⁱⁱ	75.862 (3)
B1^xi—Rh1—B1^xii	180.0	Rh1^xxi—B1—Rh1ⁱⁱⁱ	138.425 (1)
B1^xi—Rh1—B1^xiii	89.561 (4)	Rh1^vi—B1—Rh1ⁱⁱⁱ	75.862 (3)
B1^xii—Rh1—B1^xiii	90.439 (4)	Rh1^xix—B1—Rh1^ix	75.862 (2)
B1^xi—Rh1—B1^xiv	90.439 (4)	Rh1^xx—B1—Rh1^ix	138.425 (1)
B1^xii—Rh1—B1^xiv	89.561 (4)	Rh1^xxi—B1—Rh1^ix	75.862 (3)
B1^xiii—Rh1—B1^xiv	180.0	Rh1^vi—B1—Rh1^ix	138.425 (1)
B1^xi—Rh1—Rh1^xv	52.069 (1)	Rh1ⁱⁱⁱ—B1—Rh1^ix	89.562 (4)
B1^xii—Rh1—Rh1^xv	127.931 (1)

Selected bond lengths (Å) in RERh₃B₂ (RE = Pr, Nd and Sm) top

	PrRh₃B₂	NdRh₃B₂	SmRh₃B₂
RE—RE ×2	3.1084 (1)	3.1107 (1)	3.1190 (1)
RE—RE ×6	5.4676 (4)	5.4527 (3)	5.4438 (3)
RE—Rh ×12	3.1447 (1)	3.1388 (1)	3.1370 (1)
RE—B ×6	3.1557 (2)	3.1481 (1)	3.1430 (1)
B—Rh ×6	2.2151 (1)	2.2129 (1)	2.2140 (1)
B—B ×3	3.1084 (1)	3.1107 (1)	3.1190 (1)
B—B ×3	3.1567 (2)	3.1481 (1)	3.1430 (1)
Rh—Rh ×4	2.7338 (2)	2.7264 (1)	2.7219 (1)
Rh—Rh ×2	3.1084 (1)	3.1107 (1)	3.1190 (1)

Atomic displacement parameters of RE, Rh, and B atoms in RERh₃B₂ (RE = Pr, Nd, and Sm) top

Atom	U₁₁ (Å²)	U₂₂ (Å²)	U₃₃ (Å²)	U₁₂ (Å²)	U_eq (10 ³Å²)
PrRh₃B₂
Pr	0.00861 (18)	0.00861	0.00780 (20)	0.00430 (9)	8.35 (1)
Rh	0.00495 (16)	0.00386 (18)	0.01040 (20)	0.00193 (9)	6.53 (1)
B	0.0095 (16)	0.0095	0.009 (2)	0.0048 (8)	9.3 (10)
NdRh₃B₂
Nd	0.00896 (10)	0.00896	0.00662 (12)	0.00448 (5)	8.18 (9)
Rh	0.00492 (9)	0.00390 (11)	0.01104 (12)	0.00195 (5)	6.74 (8)
B	0.0100 (9)	0.0100	0.0079 (12)	0.0050 (4)	9.3 (6)
SmRh₃B₂
Sm	0.00841 (12)	0.00841	0.00658 (14)	0.00420 (6)	7.80 (10)
Rh	0.00502 (11)	0.00389 (13)	0.01287 (14)	0.00194 (6)	7.39 (10)
B	0.0085 (10)	0.0085	0.0102 (15)	0.0043 (5)	9.1 (7)

Funding information

We gratefully acknowledge the support from JSPS KAKENHI grant Nos. JP19K05643 (KY) and JP20H05258 (KY).

References

Daane, A. H., Rundle, R. E., Smith, H. G. & Spedding, F. H. (1954). Acta Cryst. 7, 532–535. CrossRef ICSD IUCr Journals Google Scholar
Higashi, I., Kasaya, M., Okabe, A. & Kasuya, T. (1987). J. Solid State Chem. 69, 376–379. CrossRef CAS Google Scholar
Higashi, I., Shishido, T., Takei, H. & Kobayashi, T. (1988). J. Less-Common Met. 139, 211–220. CrossRef ICSD CAS Google Scholar
Ku, H. C., Ma, L. J., Tai, M. F., Wang, Y. & Horng, H. E. (1985). J. Less-Common Met. 109, 219–228. CrossRef ICSD CAS Google Scholar
Ku, H. C. & Meisner, G. P. (1981). J. Less-Common Met. 78, 99–107. CrossRef ICSD CAS Google Scholar
Ku, H. C., Meisner, G. P., Acker, F. & Johnston, D. C. (1980). Solid State Commun. 35, 91–96. CrossRef ICSD CAS Google Scholar
Kuz'ma, Y. B., Krypyakevych, P. I. & Bilonizhko, N. S. (1969). Dopov. Akad. Nauk Ukr. RSR Ser. A, pp. 939–941. Google Scholar
Malik, S. K., Vijayaraghavan, R., Wallace, W. E. & Dhar, S. K. (1983). J. Magn. Magn. Mater. 37, 303–308. CrossRef ICSD CAS Google Scholar
Momma, K. & Izumi, F. (2011). J. Appl. Cryst. 44, 1272–1276. Web of Science CrossRef CAS IUCr Journals Google Scholar
Obiraki, Y., Nakashima, H., Galatanu, A., Matsuda, T. D., Haga, Y., Takeuchi, T., Sugiyama, K., Kindo, K., Hagiwara, M., Settai, R., Harima, H. & Ōnuki, Y. (2006). J. Phys. Soc. Jpn, 75, 064702. CrossRef Google Scholar
Ohtani, T., Chevalier, B., Lejay, P., Etourneau, J., Vlasse, M. & Hagenmuller, P. (1983). J. Appl. Phys. 54, 5928–5934. CrossRef ICSD CAS Google Scholar
Rigaku OD (2021). CrysAlis PRO, Rigaku Corporation, Oxford, England. Google Scholar
Sheldrick, G. M. (2015a). Acta Cryst. A71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Sheldrick, G. M. (2015b). Acta Cryst. C71, 3–8. Web of Science CrossRef IUCr Journals Google Scholar
Spedding, F. H., Daane, A. H. & Herrmann, K. W. (1956). Acta Cryst. 9, 559–563. CrossRef ICSD IUCr Journals Google Scholar
Vlasse, M., Ohtani, T., Chevalier, B. & Etourneau, J. (1983). J. Solid State Chem. 46, 188–192. CrossRef ICSD CAS Google Scholar
Westrip, S. P. (2010). J. Appl. Cryst. 43, 920–925. Web of Science CrossRef CAS IUCr Journals Google Scholar
Yamada, M., Obiraki, Y., Okubo, T., Shiromoto, T., Kida, Y., Shiimoto, M., Kohara, H., Yamamoto, T., Honda, D., Galatanu, A., Haga, Y., Takeuchi, T., Sugiyama, K., Settai, R., Kindo, K., Dhar, S. K., Harima, H. & Ōnuki, Y. (2004). J. Phys. Soc. Jpn, 73, 2266–2275. CrossRef CAS Google Scholar
Zachariasen, W. H. (1973). J. Inorg. Nucl. Chem. 35, 3487–3497. CrossRef CAS Google Scholar

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Volume 78| Part 1| January 2022| Pages 76-79

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