Redetermination of the crystal structure of yttrium chromium tetra­boride, YCrB4, from single-crystal X-ray diffraction data

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

doi:10.1107/S2056989023008952

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ISSN: 2056-9890

Volume 79| Part 11| November 2023| Pages 1072-1075

https://doi.org/10.1107/S2056989023008952

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Redetermination of the crystal structure of yttrium chromium tetraboride, YCrB₄, from single-crystal X-ray diffraction data

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

^aInstitute of Industrial Nano Materials, Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-8555, Japan, ^bDepartment of Applied Quantum Physics and Nuclear Engineering, Kyushu University, Fukuoka 819-0395, Japan, and ^cInstitute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
^*Correspondence e-mail: tokuda@nech.kumamoto-u.ac.jp

Edited by S. Parkin, University of Kentucky, USA (Received 7 September 2023; accepted 12 October 2023; online 26 October 2023)

The structural parameters of yttrium chromium tetraboride YCrB₄ were refined based on single-crystal X-ray diffraction data. YCrB₄ is orthorhombic, having a space group of type Pbam (No. 55) and with lattice parameters of a = 5.9425 (2), b = 11.4831 (4), c = 3.4643 (1) Å. The Y and Cr atoms are located at Wyckoff 4h sites (x, y, 0) and B atoms at the Wyckoff 4g sites (x, y, 1/2). The first structural investigation of YCrB₄ was performed using a single crystalline sample [Kuz'ma, (1970 ). Kristallografiya. 15, 372–374]. The present study successfully refined all the positional and atomic displacement parameters of the Y, Cr, and B atoms.

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

CCDC reference: 2300781

1. Chemical context

The investigation of AlB₂-type-analogous intermetallic compounds (RB₂, MB₂, RMB₄, and R₂MB₆; R = rare-earth, M = aluminium or transition metal) has been pursued using various experimental and theoretical methods. Recently, hydrogenated monolayer boron sheets (borophene) have attracted attention because of their topological Dirac nodal loops, with the AlB₂-type-analogous compounds expected to be the parent materials (Cuong et al., 2020 ; Niibe et al., 2021 ; Tateishi et al., 2022 ). YCrB₄ is a parent material candidate for the synthesis of (5-7)-α-borophene sheets (i.e., boron networks with five- and seven-membered rings), for which detailed structural data are currently required (Zhang et al., 2022 , 2023 ). YCrB₄ is a promising semiconductor material with good thermoelectric properties and a good power factor of 6.0 µW cm⁻¹ K⁻² at 500 K (Simonson & Poon, 2010 ; Flipo et al., 2021 ). The YCrB₄ compound is also expected to be a super-hard material (Akopov et al., 2018 ) and a narrow bandgap semiconductor (Medvedeva et al., 2002 ). A theoretically calculated Debye temperature θ_D for YCrB₄ of 965 K was given by Candan et al. (2019 ). Notably, Kuz'ma (1970) conducted the first structural analysis of YCrB₄.

2. Structural commentary

The AlB₂-type-analogous compounds are composed of borophene layers stacked with other metal atomic layers. The boron network is composed of six-membered rings (honeycomb layer), with R or M atoms located at the center of a hexagonal prism formed by twelve boron atoms (Fig. 1a). YCrB₄ exhibits an ordered and rearranged crystal structure derived from the AlB₂-type structure of YB₂ or CrB₂ (Kuz'ma, 1970). The six-membered rings are rearranged into five- and seven-membered rings [(5-7)-α-borophene layer] due to the ordering of Cr and Y (Fig. 1b). These (5-7)-α-borophene layers are accumulated along the c axis in an αα stacking sequence with the metal atomic layers. The Cr and Y atoms are located at the centers of the CrB₁₀ pentagonal and YB₁₄ heptagonal prisms, respectively (Fig. 2). With different arrangements of the MB₁₀ pentagonal prism and RB₁₄ heptagonal prism, three distinct structural types have been reported for the AlB₂-type-analogous compounds: (5-7)-α-type (YCrB₄-type: Rogl, 1978 ; Sobczak & Rogl, 1979 ), (5-7)-β-type (ThMoB₄-type: Rogl & Nowotny 1974 ; Veremchuk et al., 2008 ), and (5-6-7)-γ-type (Y₂ReB₆-type: Kuz'ma & Svarichevskaya, 1972 ; Okada et al., 2006 ).

Figure 1
Crystal structure of boron-metal-layered compounds. Honeycomb borophene layer in AlB₂ (b) and (5–7)-α-borophene layer in YCrB₄ (a) viewed along the c-axis and illustrated using VESTA (Momma & Izumi, 2011

Figure 2
Cr and Y atoms settle in the center of the pentagonal CrB₁₀ and heptagonal YB₁₄ prisms, respectively.

The Cr—B and Y—B interatomic distances are in the range of 2.2677 (15)–2.3254 (10) and 2.6177 (16)–2.7478 (14) Å, respectively (Table 1), which are close to the sums of the respective Goldschmidt radii (r_B = 0.97 Å, r_Cr = 1.36 Å, and r_Y = 1.81 Å; Brandes & Brook, 1992 ). The interplanar Cr—Cr distance is 2.3745 (4) Å, indicating a strong correlation between the Cr atoms. The intra- and interplanar Y—Y distances are 3.7446 (3)–3.7653 (5) and 3.46425 (12) Å, respectively (the latter simply corresponding to the c-axis length). The interplanar Y—Y distance is much smaller than the sum of radii of the Y atoms. A short intraplanar R—R distance can be observed in various R–M–B systems with layered structures (Higashi et al., 1988 ; Tokuda et al., 2022 ). The B—B interatomic distances within the pentagons and heptagons in YCrB₄ are in the ranges 1.724 (4)–1.828 (2) and 1.741 (3)–1.832 (2) Å, respectively, similar to the average B—B covalent bonding distances of 1.77 Å in α-rhombohedral boron (Donohue, 1974 ).

Table 1
Selected bond lengths (Å) in YCrB₄

CrB₁₀ Pentagonal prism		Five-membered ring
Cr—B3×2	2.2677 (15)	B3–B3^viii	1.724 (4)
Cr—B3×2	2.2723 (9)	B2ⁱ–B3^viii	1.741 (4)
Cr—B1×2	2.2962 (11)	B3–B4	1.742 (2)
Cr—B2×2	2.3081 (16)	B1ⁱ–B2ⁱ	1.807 (2)
Cr—B4×6	2.3254 (10)	B1ⁱ–B4	1.828 (2)

YB₁₄ Heptagonal prism		Seven-membered ring
Y—B3×2	2.6177 (16)	B2^v–B3ⁱ	1.741 (3)
Y—B4×2	2.6582 (11)	B3ⁱ–B4ⁱ	1.742 (2)
Y—B2×2	2.6959 (15)	B2–B2^v	1.788 (4)
Y—B1×2	2.7003 (12)	B1–B2	1.807 (2)
Y—B2×6	2.7241 (11)	B1ⁱ–B4	1.828 (2)
Y—B1×2	2.7350 (13)	B1–B4	1.832 (2)
Y—B4×6	2.7478 (14)	B1ⁱ–B4ⁱ	1.832 (2)

Interplanar atomic distances
Crⁱ—Cr^x	2.3745 (4)	Yⁱ—Y	3.7446 (3)
Yⁱ—Crⁱⁱⁱ	3.0517 (4)	Yⁱ—Y^ix	3.7446 (3)
Yⁱ—Cr^ix	3.0760 (3)	Yⁱ—Yⁱⁱ	3.7653 (5)
Yⁱ—Cr	3.0789 (3)
Yⁱ—Crⁱ	3.0803 (4)
Symmetry codes: (i) x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ , z; (ii) −x + $[{1\over 2}]$ , y + $[{1\over 2}]$ , −z; (iii) 1 − x, 1 − y, −z; (v) 1 − x, 1 − y, 1 − z; (viii) 1 − x, −y, 1 − z; (ix) 1 + x, y, z; (x) −x + $[{1\over 2}]$ , y − $[{1\over 2}]$ , −z]

A covalently bonded boron network in boride compounds plays an important role for thermal conductivity and mechanical and lattice dynamical properties. The Debye temperature θ_D was used to characterize these physical properties. Previous studies on intermetallic boride compounds have also proposed that the bulk θ_D is associated with the rigidity of the boron network (Korsukova et al., 1987 ; Levchenko et al., 2006 ; Singh et al., 2010 ). Using the isotropic atomic displacement parameter U_iso and Debye approximation (Willis & Pryor, 1975 ), the θ_D were derived using the following equation: <U_iso²> = (3h² T) /(4π² m k_B θ_D²), where h is Planck's constant, m is the mass of the atom, and k_B is the Boltzmann constant. The mean square <U_iso²> for B atoms was calculated using the average U_iso for the boron sites. The anisotropic displacement parameters (ADPs) for each atom are listed in Table 2, with no significant anisotropy being observed in the ADPs of any atom (Fig. 3). The estimated θ_D for Y, Cr, and B were 413 (2), 524 (3), and 996 (25) K, respectively. Candan et al. (2019) studied the lattice-dynamical properties of YCrB₄ using density functional theory and gave a calculated θ_D of 965 K that corresponds well with our estimated θ_D for the B atoms. This result indicates that the bulk θ_D of the AlB₂-type-analogous compounds can be estimated from the ADPs for the B atom.

Table 2
Atomic coordinates and anisotropic displacement parameters (10 ³Å²) for YCrB₄

The Y and Cr atoms lie on the Wyckoff sites 4h (x, y, 0), and the B atoms occupy the 4g (x, y, 1/2) site. The anisotropic displacement factor exponent takes the form: −2π²[(ha*)²U₁₁ + ⋯ + 2hka*b*U₁₂]. U_iso is defined as a third of the trace of the orthogonalized U_ij tensor. U₁₂ = U₂₃ = 0.

Atom	x	y	U₁₁	U₂₂	U₃₃	U₁₂	U_iso
Y	0.12446 (2)	0.15077 (2)	0.00298 (4)	0.00275 (4)	0.00284 (4)	0.00027 (4)	0.00285 (3)
Cr	0.12421 (4)	0.41902 (2)	0.00262 (6)	0.00241 (6)	0.00297 (6)	0.00007 (6)	0.00267 (3)
B1	0.2818 (3)	0.31614 (15)	0.0045 (5)	0.0035 (4)	0.0047 (5)	0.0007 (4)	0.0042 (2)
B2	0.3630 (4)	0.46779 (13)	0.0037 (6)	0.0035 (4)	0.0053 (5)	0.0001 (5)	0.0042 (2)
B3	0.3869 (4)	0.04697 (12)	0.0029 (5)	0.0034 (4)	0.0043 (4)	−0.0001 (5)	0.0036 (2)
B4	0.4746 (3)	0.19170 (13)	0.0041 (5)	0.0028 (5)	0.0054 (5)	−0.0001 (4)	0.0041 (2)

Figure 3
Displacement ellipsoids of each atom in YCrB₄. Displacement ellipsoids are drawn at the 99% probability level. [Symmetry codes: (i) x + $[{1\over 2}]$ , −y + $[{1\over 2}]$ , z; (ii) −x + $[{1\over 2}]$ , y + $[{1\over 2}]$ , −z; (iii) 1 − x, 1 − y, −z; (iv) x − $[{1\over 2}]$ , −y + $[{1\over 2}]$ , z; (v) 1 − x, 1 − y, 1 − z; (vi) −x + $[{1\over 2}]$ , y + $[{1\over 2}]$ , 1 − z; (vii) −x + $[{3\over 2}]$ , y + $[{1\over 2}]$ , 1 - z; (viii) 1 − x, −y, 1 − z; (ix) 1 + x, y, z; (x) −x + $[{1\over 2}]$ , y − $[{1\over 2}]$ , −z].

3. Synthesis and crystallization

The starting materials were Y (99.9%), Cr (99.95%), and B (99.5%). They were weighed in an atomic ratio Y:Cr:B = 1:1:4. The mixture was melted in an argon-arc melting furnace (ACM-01, Diavac). The product was then turned over and remelted three times to improve its chemical homogeneity. Homogeneous YCrB₄ crystals were obtained.

4. Refinement details

Refinement was conducted using a space group of type Pbam, as reported by Kuz'ma, 1970. A correction for isotropic extinction was applied during the least-squares refinement. Final refinements were performed with inclusion of anisotropic ADPs to each atom. The final refinement results are listed in Table 3. The refinement was successful, with the R factor converging without any problems and no noticeable residuals.

Table 3
Experimental details

Crystal data
Chemical formula	YCrB₄
M_r	184.15
Crystal system, space group	Orthorhombic, Pbam
Temperature (K)	294
a, b, c (Å)	5.9425 (2), 11.4831 (4), 3.46425 (12)
V (Å³)	236.40 (1)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	28.57
Crystal size (mm)	0.05 × 0.03 × 0.03

Data collection
Diffractometer	XtaLAB Synergy, HyPix
Absorption correction	Numerical (CrysAlis PRO; Rigaku OD, 2021 )
T_min, T_max	0.367, 0.655
No. of measured, independent and observed [I > 2σ(I)] reflections	13376, 1074, 865
R_int	0.036
(sin θ/λ)_max (Å⁻¹)	0.992

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.015, 0.029, 1.11
No. of reflections	1074
No. of parameters	38
Δρ_max, Δρ_min (e Å⁻³)	0.58, −0.71
Computer programs: CrysAlis PRO (Rigaku OD, 2021), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ), and VESTA (Momma & Izumi, 2011 ).

Supporting information

CCDC reference: 2300781

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2056989023008952/pk2696sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989023008952/pk2696Isup2.hkl

checkCIF report

Computing details top

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).

Yttrium chromium tetraboride top

Crystal data top

YCrB₄	D_x = 5.174 Mg m⁻³
M_r = 184.15	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pbam	Cell parameters from 6090 reflections
a = 5.9425 (2) Å	θ = 3.5–44.9°
b = 11.4831 (4) Å	µ = 28.57 mm⁻¹
c = 3.46425 (12) Å	T = 294 K
V = 236.40 (1) Å³	Block, metallic
Z = 4	0.05 × 0.03 × 0.03 mm
F(000) = 332

Data collection top

XtaLAB Synergy, HyPix diffractometer	1074 independent reflections
Radiation source: micro-focus sealed X-ray tube, PhotonJet (Mo) X-ray Source	865 reflections with I > 2σ(I)
Mirror monochromator	R_int = 0.036
Detector resolution: 10.0000 pixels mm^-1	θ_max = 44.9°, θ_min = 3.6°
ω scans	h = −11→11
Absorption correction: numerical (CrysAlisPro; Rigaku OD, 2021)	k = −22→22
T_min = 0.367, T_max = 0.655	l = −6→6
13376 measured reflections

Refinement top

Refinement on F²	0 restraints
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.0074P)² + 0.1807P] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.015	(Δ/σ)_max = 0.020
wR(F²) = 0.029	Δρ_max = 0.58 e Å⁻³
S = 1.11	Δρ_min = −0.71 e Å⁻³
1074 reflections	Extinction correction: SHELXL (Sheldrick, 2015b), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
38 parameters	Extinction coefficient: 0.0111 (7)

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
Y	0.12446 (2)	0.15077 (2)	0.000000	0.00285 (3)
Cr	0.12421 (4)	0.41902 (2)	0.000000	0.00267 (3)
B1	0.2818 (3)	0.31614 (15)	0.500000	0.0042 (2)
B2	0.3630 (4)	0.46779 (13)	0.500000	0.0042 (2)
B3	0.3869 (4)	0.04697 (12)	0.500000	0.0036 (2)
B4	0.4746 (3)	0.19170 (13)	0.500000	0.0041 (2)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Y	0.00298 (4)	0.00275 (4)	0.00284 (4)	0.00027 (4)	0.000	0.000
Cr	0.00262 (6)	0.00241 (6)	0.00297 (6)	0.00007 (6)	0.000	0.000
B1	0.0045 (5)	0.0035 (4)	0.0047 (5)	0.0007 (4)	0.000	0.000
B2	0.0037 (6)	0.0035 (4)	0.0053 (5)	0.0001 (5)	0.000	0.000
B3	0.0029 (5)	0.0034 (4)	0.0043 (4)	0.0000 (5)	0.000	0.000
B4	0.0041 (5)	0.0028 (5)	0.0054 (5)	−0.0001 (4)	0.000	0.000

Geometric parameters (Å, º) top

Y—B3	2.6177 (16)	Cr—B3^vii	2.2723 (9)
Y—B3ⁱ	2.6177 (16)	Cr—B1ⁱ	2.2962 (11)
Y—B4ⁱⁱ	2.6582 (11)	Cr—B1	2.2962 (11)
Y—B4ⁱⁱⁱ	2.6582 (11)	Cr—B2ⁱ	2.3081 (16)
Y—B2ⁱⁱⁱ	2.6959 (15)	Cr—B2	2.3081 (16)
Y—B2ⁱⁱ	2.6959 (15)	Cr—B4ⁱⁱⁱ	2.3254 (10)
Y—B1ⁱⁱⁱ	2.7003 (12)	Cr—B4ⁱⁱ	2.3254 (10)
Y—B1ⁱⁱ	2.7003 (12)	Cr—Cr^viii	2.3745 (4)
Y—B2^iv	2.7241 (11)	B1—B2	1.807 (2)
Y—B2^v	2.7241 (11)	B1—B4ⁱⁱ	1.828 (2)
Y—B1	2.7350 (13)	B1—B4	1.832 (2)
Y—B1ⁱ	2.7350 (13)	B2—B3^vi	1.741 (4)
Cr—B3ⁱⁱⁱ	2.2677 (15)	B2—B2^ix	1.789 (5)
Cr—B3ⁱⁱ	2.2677 (15)	B3—B3^x	1.724 (4)
Cr—B3^vi	2.2723 (9)	B3—B4	1.742 (2)

B3—Y—B3ⁱ	82.86 (6)	B2—B1—Cr^xi	67.24 (6)
B3—Y—B4ⁱⁱ	94.49 (3)	B4ⁱⁱ—B1—Cr^xi	67.55 (5)
B3ⁱ—Y—B4ⁱⁱ	160.16 (5)	B4—B1—Cr^xi	131.03 (3)
B3—Y—B4ⁱⁱⁱ	160.16 (5)	Cr—B1—Cr^xi	97.93 (6)
B3ⁱ—Y—B4ⁱⁱⁱ	94.49 (3)	B2—B1—Y^xii	70.31 (7)
B4ⁱⁱ—Y—B4ⁱⁱⁱ	81.33 (4)	B4ⁱⁱ—B1—Y^xii	139.48 (3)
B3—Y—B2ⁱⁱⁱ	122.58 (4)	B4—B1—Y^xii	68.78 (5)
B3ⁱ—Y—B2ⁱⁱⁱ	71.84 (4)	Cr—B1—Y^xii	135.97 (7)
B4ⁱⁱ—Y—B2ⁱⁱⁱ	124.69 (6)	Cr^xi—B1—Y^xii	75.60 (2)
B4ⁱⁱⁱ—Y—B2ⁱⁱⁱ	74.45 (4)	B2—B1—Y^xiii	70.31 (7)
B3—Y—B2ⁱⁱ	71.84 (4)	B4ⁱⁱ—B1—Y^xiii	139.48 (3)
B3ⁱ—Y—B2ⁱⁱ	122.58 (4)	B4—B1—Y^xiii	68.78 (5)
B4ⁱⁱ—Y—B2ⁱⁱ	74.45 (4)	Cr—B1—Y^xiii	75.60 (2)
B4ⁱⁱⁱ—Y—B2ⁱⁱ	124.69 (5)	Cr^xi—B1—Y^xiii	135.97 (7)
B2ⁱⁱⁱ—Y—B2ⁱⁱ	79.96 (5)	Y^xii—B1—Y^xiii	79.80 (4)
B3—Y—B1ⁱⁱⁱ	159.68 (5)	B2—B1—Y^xi	139.50 (3)
B3ⁱ—Y—B1ⁱⁱⁱ	95.10 (4)	B4ⁱⁱ—B1—Y^xi	67.94 (6)
B4ⁱⁱ—Y—B1ⁱⁱⁱ	93.99 (4)	B4—B1—Y^xi	70.86 (5)
B4ⁱⁱⁱ—Y—B1ⁱⁱⁱ	39.96 (4)	Cr—B1—Y^xi	134.07 (6)
B2ⁱⁱⁱ—Y—B1ⁱⁱⁱ	39.13 (5)	Cr^xi—B1—Y^xi	74.94 (2)
B2ⁱⁱ—Y—B1ⁱⁱⁱ	92.78 (5)	Y^xii—B1—Y^xi	87.09 (2)
B3—Y—B1ⁱⁱ	95.10 (4)	Y^xiii—B1—Y^xi	139.62 (6)
B3ⁱ—Y—B1ⁱⁱ	159.68 (5)	B2—B1—Y	139.50 (3)
B4ⁱⁱ—Y—B1ⁱⁱ	39.96 (4)	B4ⁱⁱ—B1—Y	67.94 (6)
B4ⁱⁱⁱ—Y—B1ⁱⁱ	93.99 (4)	B4—B1—Y	70.86 (5)
B2ⁱⁱⁱ—Y—B1ⁱⁱ	92.78 (5)	Cr—B1—Y	74.94 (2)
B2ⁱⁱ—Y—B1ⁱⁱ	39.13 (5)	Cr^xi—B1—Y	134.07 (6)
B1ⁱⁱⁱ—Y—B1ⁱⁱ	79.80 (4)	Y^xii—B1—Y	139.62 (6)
B3—Y—B2^iv	93.05 (4)	Y^xiii—B1—Y	87.09 (2)
B3ⁱ—Y—B2^iv	37.98 (7)	Y^xi—B1—Y	78.59 (4)
B4ⁱⁱ—Y—B2^iv	161.52 (6)	B3^vi—B2—B2^ix	124.09 (14)
B4ⁱⁱⁱ—Y—B2^iv	96.88 (3)	B3^vi—B2—B1	105.99 (17)
B2ⁱⁱⁱ—Y—B2^iv	38.53 (9)	B2^ix—B2—B1	129.92 (17)
B2ⁱⁱ—Y—B2^iv	92.00 (3)	B3^vi—B2—Cr	66.58 (9)
B1ⁱⁱⁱ—Y—B2^iv	73.82 (5)	B2^ix—B2—Cr	131.30 (4)
B1ⁱⁱ—Y—B2^iv	122.48 (5)	B1—B2—Cr	66.55 (6)
B3—Y—B2^v	37.98 (7)	B3^vi—B2—Cr^xi	66.58 (9)
B3ⁱ—Y—B2^v	93.05 (4)	B2^ix—B2—Cr^xi	131.30 (4)
B4ⁱⁱ—Y—B2^v	96.88 (3)	B1—B2—Cr^xi	66.55 (6)
B4ⁱⁱⁱ—Y—B2^v	161.52 (6)	Cr—B2—Cr^xi	97.26 (9)
B2ⁱⁱⁱ—Y—B2^v	92.00 (3)	B3^vi—B2—Y^xii	139.05 (5)
B2ⁱⁱ—Y—B2^v	38.53 (9)	B2^ix—B2—Y^xii	71.58 (9)
B1ⁱⁱⁱ—Y—B2^v	122.48 (5)	B1—B2—Y^xii	70.56 (6)
B1ⁱⁱ—Y—B2^v	73.82 (5)	Cr—B2—Y^xii	135.56 (6)
B2^iv—Y—B2^v	78.97 (4)	Cr^xi—B2—Y^xii	75.50 (2)
B3—Y—B1	72.15 (4)	B3^vi—B2—Y^xiii	139.05 (5)
B3ⁱ—Y—B1	122.11 (5)	B2^ix—B2—Y^xiii	71.58 (9)
B4ⁱⁱ—Y—B1	39.59 (4)	B1—B2—Y^xiii	70.56 (6)
B4ⁱⁱⁱ—Y—B1	93.14 (3)	Cr—B2—Y^xiii	75.50 (2)
B2ⁱⁱⁱ—Y—B1	162.65 (5)	Cr^xi—B2—Y^xiii	135.56 (6)
B2ⁱⁱ—Y—B1	98.09 (3)	Y^xii—B2—Y^xiii	79.95 (5)
B1ⁱⁱⁱ—Y—B1	124.49 (3)	B3^vi—B2—Y^vi	67.70 (5)
B1ⁱⁱ—Y—B1	75.75 (3)	B2^ix—B2—Y^vi	69.88 (7)
B2^iv—Y—B1	158.26 (6)	B1—B2—Y^vi	138.64 (4)
B2^v—Y—B1	97.09 (4)	Cr—B2—Y^vi	132.94 (8)
B3—Y—B1ⁱ	122.11 (5)	Cr^xi—B2—Y^vi	74.15 (3)
B3ⁱ—Y—B1ⁱ	72.15 (4)	Y^xii—B2—Y^vi	88.01 (3)
B4ⁱⁱ—Y—B1ⁱ	93.14 (3)	Y^xiii—B2—Y^vi	141.47 (9)
B4ⁱⁱⁱ—Y—B1ⁱ	39.59 (4)	B3^vi—B2—Y^vii	67.70 (5)
B2ⁱⁱⁱ—Y—B1ⁱ	98.09 (3)	B2^ix—B2—Y^vii	69.88 (7)
B2ⁱⁱ—Y—B1ⁱ	162.65 (5)	B1—B2—Y^vii	138.64 (4)
B1ⁱⁱⁱ—Y—B1ⁱ	75.75 (3)	Cr—B2—Y^vii	74.15 (3)
B1ⁱⁱ—Y—B1ⁱ	124.49 (3)	Cr^xi—B2—Y^vii	132.94 (8)
B2^iv—Y—B1ⁱ	97.09 (4)	Y^xii—B2—Y^vii	141.47 (9)
B2^v—Y—B1ⁱ	158.26 (6)	Y^xiii—B2—Y^vii	88.01 (3)
B1—Y—B1ⁱ	78.59 (4)	Y^vi—B2—Y^vii	78.97 (4)
B3ⁱⁱⁱ—Cr—B3ⁱⁱ	99.61 (9)	B3^x—B3—B2^v	109.78 (13)
B3ⁱⁱⁱ—Cr—B3^vi	116.93 (3)	B3^x—B3—B4	111.32 (18)
B3ⁱⁱ—Cr—B3^vi	44.63 (10)	B2^v—B3—B4	138.90 (18)
B3ⁱⁱⁱ—Cr—B3^vii	44.63 (10)	B3^x—B3—Cr^xii	67.83 (9)
B3ⁱⁱ—Cr—B3^vii	116.93 (3)	B2^v—B3—Cr^xii	128.34 (4)
B3^vi—Cr—B3^vii	99.33 (5)	B4—B3—Cr^xii	69.48 (6)
B3ⁱⁱⁱ—Cr—B1ⁱ	76.47 (5)	B3^x—B3—Cr^xiii	67.83 (9)
B3ⁱⁱ—Cr—B1ⁱ	156.70 (6)	B2^v—B3—Cr^xiii	128.34 (4)
B3^vi—Cr—B1ⁱ	156.85 (7)	B4—B3—Cr^xiii	69.48 (6)
B3^vii—Cr—B1ⁱ	76.67 (5)	Cr^xii—B3—Cr^xiii	99.61 (9)
B3ⁱⁱⁱ—Cr—B1	156.70 (6)	B3^x—B3—Cr^iv	67.54 (6)
B3ⁱⁱ—Cr—B1	76.47 (5)	B2^v—B3—Cr^iv	68.75 (5)
B3^vi—Cr—B1	76.67 (5)	B4—B3—Cr^iv	128.73 (4)
B3^vii—Cr—B1	156.85 (7)	Cr^xii—B3—Cr^iv	135.37 (10)
B1ⁱ—Cr—B1	97.94 (6)	Cr^xiii—B3—Cr^iv	63.07 (3)
B3ⁱⁱⁱ—Cr—B2ⁱ	76.55 (4)	B3^x—B3—Cr^v	67.54 (6)
B3ⁱⁱ—Cr—B2ⁱ	156.04 (5)	B2^v—B3—Cr^v	68.75 (5)
B3^vi—Cr—B2ⁱ	115.66 (5)	B4—B3—Cr^v	128.73 (4)
B3^vii—Cr—B2ⁱ	44.67 (8)	Cr^xii—B3—Cr^v	63.07 (3)
B1ⁱ—Cr—B2ⁱ	46.21 (5)	Cr^xiii—B3—Cr^v	135.37 (10)
B1—Cr—B2ⁱ	116.12 (6)	Cr^iv—B3—Cr^v	99.33 (5)
B3ⁱⁱⁱ—Cr—B2	156.04 (5)	B3^x—B3—Y	138.55 (3)
B3ⁱⁱ—Cr—B2	76.55 (4)	B2^v—B3—Y	74.33 (10)
B3^vi—Cr—B2	44.67 (8)	B4—B3—Y	75.16 (6)
B3^vii—Cr—B2	115.66 (5)	Cr^xii—B3—Y	142.90 (6)
B1ⁱ—Cr—B2	116.12 (6)	Cr^xiii—B3—Y	77.682 (19)
B1—Cr—B2	46.22 (5)	Cr^iv—B3—Y	76.87 (3)
B2ⁱ—Cr—B2	97.26 (9)	Cr^v—B3—Y	141.41 (10)
B3ⁱⁱⁱ—Cr—B4ⁱⁱⁱ	44.55 (5)	B3^x—B3—Y^xi	138.55 (3)
B3ⁱⁱ—Cr—B4ⁱⁱⁱ	115.17 (6)	B2^v—B3—Y^xi	74.33 (10)
B3^vi—Cr—B4ⁱⁱⁱ	155.54 (7)	B4—B3—Y^xi	75.15 (6)
B3^vii—Cr—B4ⁱⁱⁱ	76.98 (5)	Cr^xii—B3—Y^xi	77.682 (19)
B1ⁱ—Cr—B4ⁱⁱⁱ	46.59 (5)	Cr^xiii—B3—Y^xi	142.89 (6)
B1—Cr—B4ⁱⁱⁱ	115.88 (4)	Cr^iv—B3—Y^xi	141.41 (10)
B2ⁱ—Cr—B4ⁱⁱⁱ	78.97 (5)	Cr^v—B3—Y^xi	76.87 (3)
B2—Cr—B4ⁱⁱⁱ	157.93 (6)	Y—B3—Y^xi	82.86 (6)
B3ⁱⁱⁱ—Cr—B4ⁱⁱ	115.17 (6)	B3—B4—B1^xiii	104.59 (12)
B3ⁱⁱ—Cr—B4ⁱⁱ	44.55 (5)	B3—B4—B1	123.87 (12)
B3^vi—Cr—B4ⁱⁱ	76.98 (5)	B1^xiii—B4—B1	131.54 (10)
B3^vii—Cr—B4ⁱⁱ	155.54 (7)	B3—B4—Cr^xiii	65.97 (6)
B1ⁱ—Cr—B4ⁱⁱ	115.88 (4)	B1^xiii—B4—Cr^xiii	65.87 (5)
B1—Cr—B4ⁱⁱ	46.59 (5)	B1—B4—Cr^xiii	131.74 (3)
B2ⁱ—Cr—B4ⁱⁱ	157.93 (6)	B3—B4—Cr^xii	65.97 (6)
B2—Cr—B4ⁱⁱ	78.97 (5)	B1^xiii—B4—Cr^xii	65.87 (5)
B4ⁱⁱⁱ—Cr—B4ⁱⁱ	96.30 (6)	B1—B4—Cr^xii	131.74 (3)
B3ⁱⁱⁱ—Cr—Cr^viii	58.56 (3)	Cr^xiii—B4—Cr^xii	96.30 (6)
B3ⁱⁱ—Cr—Cr^viii	58.56 (3)	B3—B4—Y^xii	138.56 (3)
B3^vi—Cr—Cr^viii	58.37 (4)	B1^xiii—B4—Y^xii	72.47 (6)
B3^vii—Cr—Cr^viii	58.37 (4)	B1—B4—Y^xii	71.26 (5)
B1ⁱ—Cr—Cr^viii	131.03 (3)	Cr^xiii—B4—Y^xii	136.83 (7)
B1—Cr—Cr^viii	131.03 (3)	Cr^xii—B4—Y^xii	76.03 (2)
B2ⁱ—Cr—Cr^viii	101.08 (4)	B3—B4—Y^xiii	138.56 (3)
B2—Cr—Cr^viii	101.08 (4)	B1^xiii—B4—Y^xiii	72.47 (6)
B4ⁱⁱⁱ—Cr—Cr^viii	100.98 (4)	B1—B4—Y^xiii	71.26 (5)
B4ⁱⁱ—Cr—Cr^viii	100.98 (4)	Cr^xiii—B4—Y^xiii	76.03 (2)
B3ⁱⁱⁱ—Cr—Y^vii	98.87 (4)	Cr^xii—B4—Y^xiii	136.83 (7)
B3ⁱⁱ—Cr—Y^vii	98.87 (4)	Y^xii—B4—Y^xiii	81.33 (4)
B3^vi—Cr—Y^vii	56.65 (4)	B3—B4—Y^xi	67.06 (7)
B3^vii—Cr—Y^vii	56.65 (4)	B1^xiii—B4—Y^xi	138.40 (4)
B1ⁱ—Cr—Y^vii	104.42 (4)	B1—B4—Y^xi	70.11 (5)
B1—Cr—Y^vii	104.42 (4)	Cr^xiii—B4—Y^xi	131.73 (6)
B2ⁱ—Cr—Y^vii	59.17 (4)	Cr^xii—B4—Y^xi	74.13 (2)
B2—Cr—Y^vii	59.17 (4)	Y^xii—B4—Y^xi	87.67 (2)
B4ⁱⁱⁱ—Cr—Y^vii	131.60 (3)	Y^xiii—B4—Y^xi	141.34 (6)
B4ⁱⁱ—Cr—Y^vii	131.60 (3)	B3—B4—Y	67.06 (7)
Cr^viii—Cr—Y^vii	67.744 (10)	B1^xiii—B4—Y	138.40 (4)
B2—B1—B4ⁱⁱ	108.31 (12)	B1—B4—Y	70.11 (5)
B2—B1—B4	125.79 (12)	Cr^xiii—B4—Y	74.13 (2)
B4ⁱⁱ—B1—B4	125.90 (10)	Cr^xii—B4—Y	131.73 (6)
B2—B1—Cr	67.24 (6)	Y^xii—B4—Y	141.34 (6)
B4ⁱⁱ—B1—Cr	67.55 (5)	Y^xiii—B4—Y	87.67 (2)
B4—B1—Cr	131.03 (3)	Y^xi—B4—Y	78.16 (4)

Symmetry codes: (i) x, y, z−1; (ii) x−1/2, −y+1/2, z; (iii) x−1/2, −y+1/2, z−1; (iv) −x+1/2, y−1/2, −z; (v) −x+1/2, y−1/2, −z+1; (vi) −x+1/2, y+1/2, −z+1; (vii) −x+1/2, y+1/2, −z; (viii) −x, −y+1, −z; (ix) −x+1, −y+1, −z+1; (x) −x+1, −y, −z+1; (xi) x, y, z+1; (xii) x+1/2, −y+1/2, z+1; (xiii) x+1/2, −y+1/2, z.

Selected bond lengths (Å) in YCrB₄ top

CrB₁₀ Pentagonal prism		Five-membered ring
Cr—B3×2	2.2677 (15)	B3–B3^viii	1.724 (4)
Cr—B3×2	2.2723 (9)	B2ⁱ–B3^viii	1.741 (4)
Cr—B1×2	2.2962 (11)	B3–B4	1.742 (2)
Cr—B2×2	2.3081 (16)	B1ⁱ–B2ⁱ	1.807 (2)
Cr—B4×6	2.3254 (10)	B1ⁱ–B4	1.828 (2)

YB₁₄ Heptagonal prism		Seven-membered ring
Y—B3×2	2.6177 (16)	B2^v–B3ⁱ	1.741 (3)
Y—B4×2	2.6582 (11)	B3ⁱ–B4ⁱ	1.742 (2)
Y—B2×2	2.6959 (15)	B2–B2^v	1.788 (4)
Y—B1×2	2.7003 (12)	B1–B2	1.807 (2)
Y—B2×6	2.7241 (11)	B1ⁱ–B4	1.828 (2)
Y—B1×2	2.7350 (13)	B1–B4	1.832 (2)
Y—B4×6	2.7478 (14)	B1ⁱ–B4ⁱ	1.832 (2)

Interplanar atomic distances
Crⁱ—Cr^x	2.3745 (4)	Yⁱ—Y	3.7446 (3)
Yⁱ—Crⁱⁱⁱ	3.0517 (4)	Yⁱ—Y^ix	3.7446 (3)
Yⁱ—Cr^ix	3.0760 (3)	Yⁱ—Yⁱⁱ	3.7653 (5)
Yⁱ—Cr	3.0789 (3)
Yⁱ—Crⁱ	3.0803 (4)

Symmetry codes: (i) x + 1/2, -y + 1/2, z; (ii) -x + 1/2, y + 1/2, -z; (iii) 1 - x, 1 - y, -z; (v) 1 - x, 1 - y, 1 - z; (viii) 1 - x, -y, 1 - z; (ix) 1 + x, y, z; (x) -x + 1/2, y - 1/2, -z]

Atomic coordinates and anisotropic displacement parameters (10 ³Å²) for YCrB₄ top

The Y and Cr atoms lie on the Wyckoff sites 4h (x, y, 0), and the B atoms occupy the 4g (x, y, 1/2) site. The anisotropic displacement factor exponent takes the form: –2π²[(ha*)²U₁₁ + ··· + 2hka*b*U₁₂]. U_iso is defined as a third of the trace of the orthogonalized U_ij tensor. U₁₂ = U₂₃ = 0.

Atom	x	y	U₁₁	U₂₂	U₃₃	U₁₂	U_iso
Y	0.12446 (2)	0.15077 (2)	0.00298 (4)	0.00275 (4)	0.00284 (4)	0.00027 (4)	0.00285 (3)
Cr	0.12421 (4)	0.41902 (2)	0.00262 (6)	0.00241 (6)	0.00297 (6)	0.00007 (6)	0.00267 (3)
B1	0.2818 (3)	0.31614 (15)	0.0045 (5)	0.0035 (4)	0.0047 (5)	0.0007 (4)	0.0042 (2)
B2	0.3630 (4)	0.46779 (13)	0.0037 (6)	0.0035 (4)	0.0053 (5)	0.0001 (5)	0.0042 (2)
B3	0.3869 (4)	0.04697 (12)	0.0029 (5)	0.0034 (4)	0.0043 (4)	-0.0001 (5)	0.0036 (2)
B4	0.4746 (3)	0.19170 (13)	0.0041 (5)	0.0028 (5)	0.0054 (5)	-0.0001 (4)	0.0041 (2)

Funding information

We gratefully acknowledge the support from JSPS KAKENHI (grant Nos. JP19K05643, JP20H00189 and JP23K04373) and the GIMRT program (Nos. 202111-RDKGE-0002 and 202211-RDKGE-0008) at the Institute for Materials Research, Tohoku University, Japan.

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