Redetermination of the crystal structure of RhPb2 from single-crystal X-ray diffraction data, revealing a rhodium deficiency

Mochiku, T.; Matsushita, Y.; Subotić, N.; Kashiwagi, T.; Kadowaki, K.

doi:10.1107/S2056989021012275

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Volume 77| Part 12| December 2021| Pages 1327-1329

https://doi.org/10.1107/S2056989021012275

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Redetermination of the crystal structure of RhPb₂ from single-crystal X-ray diffraction data, revealing a rhodium deficiency

Takashi Mochiku,^a ^* Yoshitaka Matsushita,^a Nikola Subotić,^b Takanari Kashiwagi ^b and Kazuo Kadowaki ^b

^aNational Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan, and ^bUniversity of Tsukuba, 1-1-1 Tennouda, Tsukuba, Ibaraki 305-8573, Japan
^*Correspondence e-mail: mochiku.takashi@nims.go.jp

Edited by M. Weil, Vienna University of Technology, Austria (Received 18 October 2021; accepted 19 November 2021; online 25 November 2021)

RhPb₂ (rhodium dilead) is a superconductor crystallizing in the CuAl₂ structure type (space group I4/mcm). The Rh and Pb atoms are located at the 4a (site symmetry 422) and 8h (m.2m) sites, respectively. The crystal structure is composed of [RhPb₈] antiprisms, which share their square faces along the c axis and the edges in the direction perpendicular to the c axis. We have succeeded in growing single crystals of RhPb₂ and have re-determined the crystal structure on basis of single-crystal X-ray diffraction data. In comparison with the previous structure studies using powder X-ray diffraction data [Wallbaum (1943 ). Z. Metallkd. 35, 218–221; Havinga et al. (1972 ). J. Less-Common Met. 27, 169–186], the current structure analysis of RhPb₂ leads to more precise unit-cell parameters and fractional coordinates, together with anisotropic displacement parameters for the two atoms. In addition and likewise different from the previous studies, we have found a slight deficiency of Rh in RhPb₂, leading to a refined formula of Rh_0.950 (9)Pb₂.

Keywords: crystal structure; rhodium; lead; intermetallic compound; deficiency; superconductivity.

CCDC reference: 2123239

1. Chemical context

A large number of binary intermetallic compounds with the CuAl₂ structure type have been reported (Wallbaum, 1943; Havinga et al., 1972; Havinga, 1972 ), and several of them exhibit superconductivity (Gendron & Jones, 1962 ). RhPb₂ is one of them, with a superconducting transition temperature (T_c) of 2.66 K (Gendron & Jones, 1962). β-RhPb₂ adopting the β-PdBi₂ structure type (space group I4/mmm) has been reported as a candidate material for topological superconductors (Zhang et al., 2019 ), and RhPb₂ crystallizing in the CuAl₂ structure type has also attracted much attention. While the previous powder X-ray studies of RhPb₂ (Wallbaum, 1943; Havinga et al., 1972) used polycrystalline material prepared by a melting method, we have grown RhPb₂ single crystals by application of a vertical pulling mechanism using an infrared mirror furnace. Here we report on the redetermined crystal structure of RhPb₂ based on single-crystal X-ray data.

2. Structural commentary

The crystal structure of RhPb₂ refined from single-crystal data is essentially the same as determined previously (Wallbaum, 1943; Havinga et al., 1972). RhPb₂ is composed of [RhPb₈] antiprisms, which share the square faces along the c axis and the edges in the direction perpendicular to the c axis (Fig. 1). The Rh atom (site symmetry 422) is surrounded by eight Pb atoms occupying the edges of the [RhPb₈] antiprism, and two Rh atoms are spaced along the c axis at a distance of half of the unit-cell parameter c. The Pb—Pb distance in the adjacent [RhPb₈] antiprism is the shortest among the Pb—Pb distances (Table 1; Fig. 1b, Pb—Pb^ix); all Pb—Pb distances belonging to the shared square faces of the [RhPb₈] antiprism are equal (Fig. 1b, Pb—Pb^x), while the Pb—Pb distances belonging to the sides of the triangle of the [RhPb₈] antiprism are all different (Fig. 1c, Pb—Pb^x, Pb—Pb^xi and Pb^x-–Pb^xi).

Table 1
Comparison of unit-cell parameters and interatomic distances (Å) at room temperature in RhPb₂ determined in previous and the present studies

	Wallbaum (1943)	Havinga et al. (1972)	This work
a	6.651 (3)	6.674 (3)	6.7068 (4)
c	5.853 (3)	5.831 (3)	5.8623 (6)
Rh—Pb	2.902	2.885 (6)	2.9016 (2)
Pb—Pb^ix	2.972	3.134 (14)	3.1313 (13)
Pb—Pb^x	3.544	3.520 (10)	3.5416 (4)
Pb—Pb^xi	3.603	3.662 (9)	3.6734 (6)
Pb^x—Pb^xi	3.400	3.319 (7)	3.3448 (7)
Symmetry codes: (ix) −x + 1, −y, −z + 1; (x) −y + 1, x − 1, z; (xi) y + $[{1\over 2}]$ , −x + $[{1\over 2}]$ , −z + $[{1\over 2}]$ .

Figure 1
(a) The crystal structure of RhPb₂ in a view along the b axis showing the atoms in the asymmetric unit with displacement ellipsoids at the 99.9%; (b) the crystal structure of RhPb₂ in polyhedral representation in a view along the c axis; (c) details of the linkage of the [RhPb₈] antiprisms in the crystal structure of RhPb₂.

While RhPb₂ has been reported to be single phase only in a Pb-deficient sample (Havinga et al., 1972), we have found a deficiency of Rh rather than a deficiency of Pb in the grown single crystals. The chemical composition obtained from the analysis of the occupancy of Rh is Rh_0.950 (9)Pb₂. Hamilton's R-factor ratio test (Hamilton, 1965 ) was used to compare the R factors for the models with and without a deficiency of Rh. The result rejected the model without deficiency of Rh at a significance level of less than 0.005.

Table 1 shows the unit-cell parameters and interatomic distances obtained from the current and the previous studies (Wallbaum, 1943; Havinga et al., 1972). The unit-cell parameters are more precise and larger than those of the previous studies, and the free fractional coordinate of Rh was also obtained with higher precision. The resulting interatomic distances are slightly different from those in the previous studies. Anisotropic displacement parameters, which were not reported previously, were also obtained from the current redetermination.

3. Synthesis and crystallization

Single crystals of RhPb₂ were grown from the Pb-rich melt (molar ratio Rh:Pb = 1:8) by a slow cooling process in a steep temperature gradient infrared furnace according to the Pb–Rh binary phase diagram (El-Boragy et al., 1992 ), where RhPb₂ is shown to grow through the peritectic reaction incongruently melting between 593 and 913 K. The raw materials of Rh and Pb were of 99.9% purity in powder form (300 mesh) and 99.99% in shots, respectively, purchased from Furuuchi Chemical Co. Prior to crystal growth, Rh and Pb were melted together in an evacuated silica tube by heating with a flame torch. The obtained ingot was then put into a new silica tube and was vacuum sealed. The silica tube was hung in an infrared mirror furnace, which generally has a strong temperature gradient around the focal point. The sample silica tube was heated above 913 K, where the sample became completely liquid. Then, the silica tube was placed at the position where the temperature gradient is the highest. The silica tube was rotated slowly (∼10 r.p.m.) to promote single crystals to grow in a uniform temperature horizontally with a steep temperature gradient vertically. A silica tube with a cone-shaped bottom was used. The furnace temperature was slowly decreased with a constant rate of 0.5 K h⁻¹ until it reached the temperature well below 593 K, then it was lowered to room temperature.

After removing the silica tube carefully, the grown boule showed clearly the liquid–solid phase boundary as a horizontal line in the upper part of the boule, indicating that the single-crystal growth had progressed as planned according to the phase diagram (El-Boragy et al., 1992). More than half of the grown boule from the bottom appeared to have turned into a single crystal of RhPb₂. The latter cleaves easily, showing shiny reflection with a silvery luster from the cleaved surface. The single crystal was rather soft and could easily be scratched by tweezers. The product seems to be stable in air because the color of the cleaved surface did not change over time. In Fig. 2 photographs of the grown single crystals of RhPb₂ are shown.

Figure 2
(a) A photograph of two pieces of single crystals of RhPb₂ taken under an optical microscope; (b) an enlarged optical photograph of one of the single-crystals of RhPb₂.

4. Refinement

Crystal data, data collection and structure refinement details are summarized in Table 2. The equivalent isotropic atomic displacement parameter (U_eq) of the Rh sites for the model without deficiency of Rh was 0.0131 (5) Å², which was larger than that of Pb (0.0107 (3) Å²). We refined the occupancies of Rh and Pb. While the refined occupancy of Pb was very close to full occupation, the refined occupancy of Rh indicated a significant deficiency of this site. The final wR(F²) value for the model without deficiency of Rh was 0.047, and that for the model with deficiency of Rh was 0.042. In the final model [occupancy of Rh = 0.950 (9); full occupancy of Pb] the atomic displacement parameter (U_eq) of the Rh site is the same as that of the Pb site.

Table 2
Experimental details

Crystal data
Chemical formula	Rh_0.95Pb₂
M_r	512.14
Crystal system, space group	Tetragonal, I4/mcm
Temperature (K)	295
a, c (Å)	6.7068 (4), 5.8623 (6)
V (Å³)	263.69 (4)
Z	4
Radiation type	Mo Kα
μ (mm⁻¹)	132.87
Crystal size (mm)	0.11 × 0.05 × 0.03

Data collection
Diffractometer	XtaLAB Mini II
Absorption correction	Multi-scan (CrysAlis PRO; Rigaku OD, 2019 $[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]$ )
T_min, T_max	0.123, 1.000
No. of measured, independent and observed [I > 2σ(I)] reflections	461, 117, 88
R_int	0.033
(sin θ/λ)_max (Å⁻¹)	0.708

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.021, 0.042, 1.01
No. of reflections	117
No. of parameters	9
Δρ_max, Δρ_min (e Å⁻³)	1.96, −1.56
Computer programs: CrysAlis PRO (Rigaku OD, 2019 $[Rigaku OD (2019). CrysAlis PRO. Rigaku Oxford Diffraction, Yarnton, England.]$ ), SHELXT (Sheldrick, 2015a ), SHELXL (Sheldrick, 2015b ) and OLEX2 (Dolomanov et al., 2009 ).

Supporting information

CCDC reference: 2123239

Crystal structure: contains datablocks I, global. DOI: https://doi.org/10.1107/S2056989021012275/wm5626sup1.cif

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2056989021012275/wm5626Isup4.hkl

checkCIF report

Computing details top

Data collection: CrysAlis PRO (Rigaku OD, 2019); cell refinement: CrysAlis PRO (Rigaku OD, 2019); data reduction: CrysAlis PRO (Rigaku OD, 2019); program(s) used to solve structure: ShelXT (Sheldrick, 2015a); program(s) used to refine structure: SHELXL (Sheldrick, 2015b); molecular graphics: OLEX2 (Dolomanov et al., 2009); software used to prepare material for publication: OLEX2 (Dolomanov et al., 2009).

Rhodium dilead top

Crystal data top

Rh_0.95Pb₂	D_x = 12.900 Mg m⁻³
M_r = 512.14	Mo Kα radiation, λ = 0.71073 Å
Tetragonal, I4/mcm	Cell parameters from 295 reflections
a = 6.7068 (4) Å	θ = 6.1–30.2°
c = 5.8623 (6) Å	µ = 132.87 mm⁻¹
V = 263.69 (4) Å³	T = 295 K
Z = 4	Irregular, metallic dark grey
F(000) = 827	0.11 × 0.05 × 0.03 mm

Data collection top

XtaLAB Mini II diffractometer	88 reflections with I > 2σ(I)
Detector resolution: 10.0000 pixels mm^-1	R_int = 0.033
ω scans	θ_max = 30.2°, θ_min = 4.3°
Absorption correction: multi-scan (CrysAlisPro; Rigaku OD, 2019)	h = −9→8
T_min = 0.123, T_max = 1.000	k = −7→9
461 measured reflections	l = −8→7
117 independent reflections

Refinement top

Refinement on F²	Primary atom site location: iterative
Least-squares matrix: full	w = 1/[σ²(F_o²) + (0.013P)²] where P = (F_o² + 2F_c²)/3
R[F² > 2σ(F²)] = 0.021	(Δ/σ)_max < 0.001
wR(F²) = 0.042	Δρ_max = 1.96 e Å⁻³
S = 1.01	Δρ_min = −1.56 e Å⁻³
117 reflections	Extinction correction: SHELXL2018/3 (Sheldrick 2015b), Fc^*=kFc[1+0.001xFc²λ³/sin(2θ)]^-1/4
9 parameters	Extinction coefficient: 0.0030 (3)
0 restraints

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	Occ. (<1)
Rh	0.500000	0.500000	0.750000	0.0103 (7)	0.950 (9)
Pb	0.66507 (7)	0.16507 (7)	0.500000	0.0103 (3)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Rh	0.0111 (8)	0.0111 (8)	0.0088 (11)	0.000	0.000	0.000
Pb	0.0091 (3)	0.0091 (3)	0.0128 (4)	0.0013 (3)	0.000	0.000

Geometric parameters (Å, º) top

Rh—Rhⁱ	2.9312 (3)	Rh—Pb^viii	2.9016 (2)
Rh—Rhⁱⁱ	2.9312 (3)	Pb—Pb^ix	3.1313 (13)
Rh—Pbⁱⁱⁱ	2.9016 (2)	Pb—Pb^x	3.5416 (4)
Rh—Pb^iv	2.9016 (2)	Pb—Pb^xi	3.6734 (6)
Rh—Pbⁱⁱ	2.9016 (2)	Pb—Pb^xii	3.5416 (4)
Rh—Pb	2.9016 (2)	Pb—Pb^iv	3.5416 (4)
Rh—Pb^v	2.9016 (2)	Pb—Pb^vii	3.5416 (4)
Rh—Pb^vi	2.9016 (2)	Pb—Pb^xiii	3.3448 (7)
Rh—Pb^vii	2.9016 (2)	Pb—Pb^v	3.3448 (7)

Rhⁱⁱ—Rh—Rhⁱ	180.0	Rh^v—Pb—Pb^xi	99.966 (13)
Pbⁱⁱ—Rh—Rhⁱⁱ	59.663 (4)	Rh^xiv—Pb—Pb^x	52.390 (2)
Pb—Rh—Rhⁱ	120.337 (4)	Rhⁱⁱ—Pb—Pb^xii	96.44 (2)
Pbⁱⁱⁱ—Rh—Rhⁱ	59.663 (4)	Rh^xiv—Pb—Pb^iv	148.841 (9)
Pb^iv—Rh—Rhⁱ	120.337 (4)	Rh^v—Pb—Pb^xii	52.390 (2)
Pb^vi—Rh—Rhⁱ	59.663 (4)	Rh^xiv—Pb—Pb^xi	50.729 (10)
Pb^viii—Rh—Rhⁱ	59.663 (4)	Rh^v—Pb—Pb^vii	96.44 (2)
Pb^vii—Rh—Rhⁱⁱ	59.663 (4)	Rh—Pb—Pb^xii	96.44 (2)
Pb^vi—Rh—Rhⁱⁱ	120.337 (4)	Rh—Pb—Pb^x	148.842 (9)
Pbⁱⁱⁱ—Rh—Rhⁱⁱ	120.337 (4)	Rh^v—Pb—Pb^xiii	107.993 (18)
Pb—Rh—Rhⁱⁱ	59.663 (4)	Rhⁱⁱ—Pb—Pb^ix	106.118 (12)
Pb^vii—Rh—Rhⁱ	120.337 (4)	Rh—Pb—Pb^ix	106.118 (12)
Pb^v—Rh—Rhⁱⁱ	120.337 (4)	Rh^xiv—Pb—Pb^vii	96.44 (2)
Pb^v—Rh—Rhⁱ	59.663 (4)	Rh^v—Pb—Pb^ix	106.118 (12)
Pb^viii—Rh—Rhⁱⁱ	120.337 (4)	Rhⁱⁱ—Pb—Pb^x	148.841 (9)
Pb^iv—Rh—Rhⁱⁱ	59.663 (4)	Rh^xiv—Pb—Pb^ix	106.118 (12)
Pbⁱⁱ—Rh—Rhⁱ	120.337 (4)	Rhⁱⁱ—Pb—Pb^xi	93.646 (8)
Pb^vii—Rh—Pbⁱⁱⁱ	135.14 (2)	Rh^v—Pb—Pb^v	54.805 (6)
Pb^iv—Rh—Pb^vii	119.326 (8)	Rh—Pb—Pb^iv	52.390 (2)
Pb^iv—Rh—Pb^viii	70.390 (11)	Rh^xiv—Pb—Pb^v	107.993 (18)
Pbⁱⁱ—Rh—Pbⁱⁱⁱ	70.390 (11)	Rh—Pb—Pb^vii	52.390 (2)
Pb^iv—Rh—Pbⁱⁱ	75.220 (4)	Rh—Pb—Pb^xiii	107.993 (18)
Pb^iv—Rh—Pb^v	135.14 (2)	Rhⁱⁱ—Pb—Pb^v	107.993 (18)
Pb—Rh—Pb^viii	78.54 (2)	Rhⁱⁱ—Pb—Pb^xiii	54.805 (6)
Pb^vii—Rh—Pbⁱⁱ	75.220 (4)	Rhⁱⁱ—Pb—Pb^vii	52.390 (2)
Pb^vi—Rh—Pb	135.14 (2)	Rhⁱⁱ—Pb—Pb^iv	52.390 (2)
Pb^iv—Rh—Pbⁱⁱⁱ	78.54 (2)	Rh^xiv—Pb—Pb^xiii	54.805 (6)
Pb^vi—Rh—Pbⁱⁱⁱ	75.220 (4)	Pb^xiii—Pb—Pb^vii	64.40 (2)
Pb^viii—Rh—Pbⁱⁱ	135.14 (2)	Pb^v—Pb—Pb^xii	64.40 (2)
Pb—Rh—Pbⁱⁱⁱ	147.76 (2)	Pb^xii—Pb—Pb^xi	101.180 (5)
Pb^vi—Rh—Pb^viii	119.326 (8)	Pb^x—Pb—Pb^iv	127.53 (3)
Pb^viii—Rh—Pbⁱⁱⁱ	75.220 (3)	Pb^ix—Pb—Pb^xi	64.773 (7)
Pb^iv—Rh—Pb	75.220 (3)	Pb^vii—Pb—Pb^xi	124.800 (14)
Pb^iv—Rh—Pb^vi	147.76 (2)	Pb^xii—Pb—Pb^iv	142.47 (3)
Pb—Rh—Pb^vii	75.220 (3)	Pb^iv—Pb—Pb^xi	101.180 (5)
Pb—Rh—Pbⁱⁱ	119.326 (8)	Pb^vii—Pb—Pb^xii	52.47 (3)
Pb^viii—Rh—Pb^vii	147.76 (2)	Pb^ix—Pb—Pb^vii	153.764 (14)
Pb^v—Rh—Pb^viii	75.220 (4)	Pb^xiii—Pb—Pb^xi	60.398 (9)
Pb^vi—Rh—Pbⁱⁱ	78.54 (2)	Pb^ix—Pb—Pb^x	63.764 (14)
Pb—Rh—Pb^v	70.390 (12)	Pb^v—Pb—Pb^vii	64.40 (2)
Pb^vi—Rh—Pb^vii	70.390 (11)	Pb^vii—Pb—Pb^iv	90.0
Pb^v—Rh—Pbⁱⁱ	147.76 (2)	Pb^ix—Pb—Pb^v	118.80 (2)
Pb^v—Rh—Pbⁱⁱⁱ	119.326 (8)	Pb^v—Pb—Pb^x	102.295 (2)
Pb^v—Rh—Pb^vii	78.54 (2)	Pb^ix—Pb—Pb^xiii	118.80 (2)
Pb^vi—Rh—Pb^v	75.220 (3)	Pb^xiii—Pb—Pb^xii	64.40 (2)
Rh—Pb—Rh^v	109.610 (11)	Pb^v—Pb—Pb^xiii	122.41 (4)
Rh^v—Pb—Rhⁱⁱ	147.76 (2)	Pb^xiii—Pb—Pb^x	102.295 (2)
Rh—Pb—Rhⁱⁱ	60.674 (7)	Pb^ix—Pb—Pb^xii	153.764 (14)
Rhⁱⁱ—Pb—Rh^xiv	109.610 (12)	Pb^v—Pb—Pb^xi	154.764 (7)
Rh—Pb—Rh^xiv	147.76 (2)	Pb^ix—Pb—Pb^iv	63.764 (14)
Rh^v—Pb—Rh^xiv	60.674 (8)	Pb^vii—Pb—Pb^x	142.47 (3)
Rh^v—Pb—Pb^x	52.390 (2)	Pb^v—Pb—Pb^iv	102.295 (2)
Rh—Pb—Pb^xi	150.417 (3)	Pb^x—Pb—Pb^xi	55.200 (14)
Rh—Pb—Pb^v	54.805 (6)	Pb^xiii—Pb—Pb^iv	102.295 (2)
Rh^v—Pb—Pb^iv	148.841 (9)	Pb^xii—Pb—Pb^x	90.0
Rh^xiv—Pb—Pb^xii	52.390 (2)

Symmetry codes: (i) −x+1, −y+1, −z+2; (ii) −x+1, −y+1, −z+1; (iii) x−1/2, y+1/2, z+1/2; (iv) y, −x+1, −z+1; (v) −x+3/2, −y+1/2, −z+3/2; (vi) y+1/2, −x+3/2, −z+3/2; (vii) −y+1, x, z; (viii) −y+1/2, x−1/2, z+1/2; (ix) −x+1, −y, −z+1; (x) −y+1, x−1, z; (xi) y+1/2, −x+1/2, −z+1/2; (xii) y+1, −x+1, −z+1; (xiii) −x+3/2, −y+1/2, −z+1/2; (xiv) x+1/2, y−1/2, z−1/2.

Comparison of unit-cell parameters and interatomic distances (Å) at room temperature in RhPb₂ determined in previous and the present studies top

	Wallbaum (1943)	Havinga et al. (1972)	This work
a	6.651 (3)	6.674 (3)	6.7068 (4)
c	5.853 (3)	5.831 (3)	5.8628 (6)
Rh—Pb	2.902	2.885 (6)	2.9016 (2)
Pb—Pb^ix	2.972	3.134 (14)	3.1313 (13)
Pb—Pb^x	3.544	3.520 (10)	3.5416 (4)
Pb—Pb^xi	3.603	3.662 (9)	3.6734 (6)
Pb^x—Pb^xi	3.400	3.319 (7)	3.3448 (7)

Symmetry codes: (ix) -x + 1, -y, -z + 1; (x) -y + 1, x - 1, z; (xi) y + 1/2, -x + 1/2, -z + 1/2.

Funding information

Funding for this research was provided by: Japan Society for the Promotion of Science (grant No. JP19H05819).

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