Structural analysis of Gd6FeBi2 from single-crystal X-ray diffraction methods and electronic structure calculations

Zhang, J.; Kang, Y.-M.; Shan, G.; Bobev, S.

doi:10.1107/S2053229619004868

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Structural analysis of Gd₆FeBi₂ from single-crystal X-ray diffraction methods and electronic structure calculations

J. Zhang, Y.-M. Kang, G. Shan and S. Bobev

The crystal structure of the gadolinium iron bismuthide Gd₆FeBi₂ has been characterized by single-crystal X-ray diffraction data and analyzed in detail using first-principles calculations. The structure is isotypic with the Zr₆CoAl₂ structure, which is a variant of the ZrNiAl structure and its binary prototype Fe₂P (Pearson code hP9, Wyckoff sequence g f d a). As such, the structure is best viewed as an array of tricapped trigonal prisms of Gd atoms centered alternately by Fe and Bi. The magnetic-ordering temperature of this compound (ca 350 K) is much higher than that of other rare-earth metal-rich phases with the same or related structures. It is also higher than the ordering temperature of many other Gd-rich ternary phases, where the magnetic exchange is typically governed by Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions. First-principles calculations reveal a larger than expected Gd magnetic moment, with the additional contribution arising from the Gd 5d electrons. The electronic structure analysis suggests strong Gd 5d–Fe 3d hybridization to be the cause of this effect, rather than weak interactions between Gd and Bi. These details are of importance for understanding the magnetic response and explaining the high ordering temperature in this material.

Keywords: rare-earth metals; gadolinium; electronic structure; ternary phase; high magnetic-ordering temperature; crystal structure.

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Supporting information

	Crystallographic Information File (CIF) https://doi.org/10.1107/S2053229619004868/fn3304sup1.cif Contains datablocks global, I
	Structure factor file (CIF format) https://doi.org/10.1107/S2053229619004868/fn3304Isup2.hkl Contains datablock I

CCDC reference: 1909048

Computing details top

Data collection: SMART (Bruker, 2014); cell refinement: SMART (Bruker, 2014); data reduction: SAINT (Bruker, 2014); program(s) used to solve structure: SHELXTL (Sheldrick, 2001); program(s) used to refine structure: SHELXTL (Sheldrick, 2001); molecular graphics: CrystalMaker (CrystalMaker, 2007); software used to prepare material for publication: publCIF (Westrip, 2010).

Hexagadolinium iron bismuthide top

Crystal data top

Gd₆FeBi₂	D_x = 9.246 Mg m⁻³
M_r = 1417.31	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, P62m	Cell parameters from 456 reflections
a = 8.337 (4) Å	θ = 4.8–27.3°
c = 4.229 (2) Å	µ = 74.21 mm⁻¹
V = 254.5 (2) Å³	T = 150 K
Z = 1	Irregular, grey-silver
F(000) = 576	0.03 × 0.02 × 0.02 mm

Data collection top

Bruker SMART CCD area detector diffractometer	297 independent reflections
Radiation source: fine-focus sealed tube	285 reflections with I > 2σ(I)
Graphite monochromator	R_int = 0.076
phi and ω scans	θ_max = 29.5°, θ_min = 2.8°
Absorption correction: multi-scan (SADABS; Bruker, 2014)	h = −11→11
T_min = 0.207, T_max = 0.365	k = −10→11
2709 measured reflections	l = −5→5

Refinement top

Refinement on F²	Primary atom site location: structure-invariant direct methods
Least-squares matrix: full	Secondary atom site location: difference Fourier map
R[F² > 2σ(F²)] = 0.023	w = 1/[σ²(F_o²)]
wR(F²) = 0.040	(Δ/σ)_max < 0.001
S = 1.04	Δρ_max = 1.51 e Å⁻³
297 reflections	Δρ_min = −1.71 e Å⁻³
14 parameters	Absolute structure: (Flack, 1983)
0 restraints	Absolute structure parameter: 0.014 (19)

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.

Refinement. The data were collected on a Bruker SMART APEX CCD diffractometer using monochromated Mo Kα radiation (λ = 0.71073 Å). The SAINT software (Bruker, 2014) was used for the raw data reduction and integration. Semi-empirical absorption correction was applied with SADABS (Bruker, 2014). The crystal structure was solved by direct methods and refined by full-matrix least squares methods on F² with SHELXL. The structure solution and refinement were straightforward. Direct methods provided the positions of all the atoms, and anisotropic refinement converged smoothly to low residuals and no unaccounted residual electron density. Trial refinements with freed occupations factors confirm that the structure is devoid of disorder.

Refinement of F² against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F², conventional R-factors R are based on F, with F set to zero for negative F². The threshold expression of F² > 2sigma(F²) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F² are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

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

	x	y	z	U_iso*/U_eq
Bi1	0.6667	0.3333	0.5000	0.0100 (2)
Gd1	0.76206 (13)	0.0000	0.5000	0.0116 (2)
Gd2	0.40153 (15)	0.0000	0.0000	0.0109 (2)
Fe1	0.0000	0.0000	0.0000	0.0156 (11)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Bi1	0.0095 (3)	0.0095 (3)	0.0108 (4)	0.00476 (15)	0.000	0.000
Gd1	0.0095 (4)	0.0081 (5)	0.0166 (5)	0.0041 (2)	0.000	0.000
Gd2	0.0116 (4)	0.0109 (5)	0.0099 (5)	0.0055 (3)	0.000	0.000
Fe1	0.0195 (18)	0.0195 (18)	0.008 (2)	0.0098 (9)	0.000	0.000

Geometric parameters (Å, º) top

Bi1—Gd1	3.2504 (17)	Gd1—Gd2^iv	3.6749 (19)
Bi1—Gd1ⁱ	3.2504 (17)	Gd2—Bi1^xiii	3.3071 (12)
Bi1—Gd1ⁱⁱ	3.2504 (17)	Gd2—Bi1^xiv	3.3071 (12)
Bi1—Gd2	3.3071 (12)	Gd2—Bi1^viii	3.3071 (12)
Bi1—Gd2ⁱⁱⁱ	3.3071 (12)	Gd2—Fe1	3.347 (2)
Bi1—Gd2ⁱ	3.3071 (12)	Gd2—Gd1^xv	3.6015 (15)
Bi1—Gd2^iv	3.3071 (12)	Gd2—Gd1ⁱⁱ	3.6015 (15)
Bi1—Gd2^v	3.3071 (12)	Gd2—Gd1^xvi	3.6015 (15)
Bi1—Gd2ⁱⁱ	3.3071 (12)	Gd2—Gd1^xvii	3.6015 (15)
Gd1—Fe1^vi	2.8993 (12)	Gd2—Gd1^xiii	3.6749 (19)
Gd1—Fe1^vii	2.8993 (12)	Fe1—Gd1ⁱⁱ	2.8993 (12)
Gd1—Bi1^viii	3.2504 (17)	Fe1—Gd1^xv	2.8993 (12)
Gd1—Gd1^ix	3.436 (2)	Fe1—Gd1^xviii	2.8993 (12)
Gd1—Gd1^x	3.436 (2)	Fe1—Gd1^xvii	2.8993 (12)
Gd1—Gd2ⁱⁱⁱ	3.6015 (15)	Fe1—Gd1^xix	2.8993 (12)
Gd1—Gd2^xi	3.6015 (15)	Fe1—Gd1^xvi	2.8993 (12)
Gd1—Gd2ⁱ	3.6015 (15)	Fe1—Gd2^xx	3.347 (2)
Gd1—Gd2^xii	3.6015 (15)	Fe1—Gd2^xxi	3.347 (2)
Gd1—Gd2	3.6749 (19)

Gd1—Bi1—Gd1ⁱ	120.0	Gd2ⁱⁱⁱ—Gd1—Gd2^iv	74.49 (2)
Gd1—Bi1—Gd1ⁱⁱ	120.0	Gd2^xi—Gd1—Gd2^iv	114.09 (3)
Gd1ⁱ—Bi1—Gd1ⁱⁱ	120.0	Gd2ⁱ—Gd1—Gd2^iv	114.09 (3)
Gd1—Bi1—Gd2	68.16 (2)	Gd2^xii—Gd1—Gd2^iv	74.49 (2)
Gd1ⁱ—Bi1—Gd2	140.24 (2)	Gd2—Gd1—Gd2^iv	70.25 (5)
Gd1ⁱⁱ—Bi1—Gd2	66.62 (2)	Bi1—Gd2—Bi1^xiii	79.49 (4)
Gd1—Bi1—Gd2ⁱⁱⁱ	66.62 (2)	Bi1—Gd2—Bi1^xiv	151.25 (4)
Gd1ⁱ—Bi1—Gd2ⁱⁱⁱ	68.16 (2)	Bi1^xiii—Gd2—Bi1^xiv	93.39 (4)
Gd1ⁱⁱ—Bi1—Gd2ⁱⁱⁱ	140.24 (2)	Bi1—Gd2—Bi1^viii	93.39 (4)
Gd2—Bi1—Gd2ⁱⁱⁱ	134.781 (13)	Bi1^xiii—Gd2—Bi1^viii	151.25 (4)
Gd1—Bi1—Gd2ⁱ	66.62 (2)	Bi1^xiv—Gd2—Bi1^viii	79.49 (4)
Gd1ⁱ—Bi1—Gd2ⁱ	68.16 (2)	Bi1—Gd2—Fe1	104.37 (2)
Gd1ⁱⁱ—Bi1—Gd2ⁱ	140.24 (2)	Bi1^xiii—Gd2—Fe1	104.37 (2)
Gd2—Bi1—Gd2ⁱ	83.50 (3)	Bi1^xiv—Gd2—Fe1	104.37 (2)
Gd2ⁱⁱⁱ—Bi1—Gd2ⁱ	79.49 (4)	Bi1^viii—Gd2—Fe1	104.37 (2)
Gd1—Bi1—Gd2^iv	68.16 (2)	Bi1—Gd2—Gd1^xv	152.23 (4)
Gd1ⁱ—Bi1—Gd2^iv	140.24 (2)	Bi1^xiii—Gd2—Gd1^xv	97.71 (4)
Gd1ⁱⁱ—Bi1—Gd2^iv	66.62 (2)	Bi1^xiv—Gd2—Gd1^xv	55.94 (2)
Gd2—Bi1—Gd2^iv	79.49 (4)	Bi1^viii—Gd2—Gd1^xv	100.99 (3)
Gd2ⁱⁱⁱ—Bi1—Gd2^iv	83.50 (3)	Fe1—Gd2—Gd1^xv	49.15 (2)
Gd2ⁱ—Bi1—Gd2^iv	134.781 (14)	Bi1—Gd2—Gd1ⁱⁱ	55.94 (2)
Gd1—Bi1—Gd2^v	140.24 (2)	Bi1^xiii—Gd2—Gd1ⁱⁱ	100.99 (3)
Gd1ⁱ—Bi1—Gd2^v	66.62 (2)	Bi1^xiv—Gd2—Gd1ⁱⁱ	152.23 (4)
Gd1ⁱⁱ—Bi1—Gd2^v	68.16 (2)	Bi1^viii—Gd2—Gd1ⁱⁱ	97.71 (4)
Gd2—Bi1—Gd2^v	134.781 (14)	Fe1—Gd2—Gd1ⁱⁱ	49.15 (2)
Gd2ⁱⁱⁱ—Bi1—Gd2^v	83.50 (3)	Gd1^xv—Gd2—Gd1ⁱⁱ	98.30 (4)
Gd2ⁱ—Bi1—Gd2^v	134.781 (14)	Bi1—Gd2—Gd1^xvi	97.71 (4)
Gd2^iv—Bi1—Gd2^v	83.50 (3)	Bi1^xiii—Gd2—Gd1^xvi	152.23 (4)
Gd1—Bi1—Gd2ⁱⁱ	140.24 (2)	Bi1^xiv—Gd2—Gd1^xvi	100.99 (3)
Gd1ⁱ—Bi1—Gd2ⁱⁱ	66.62 (2)	Bi1^viii—Gd2—Gd1^xvi	55.94 (2)
Gd1ⁱⁱ—Bi1—Gd2ⁱⁱ	68.16 (2)	Fe1—Gd2—Gd1^xvi	49.15 (2)
Gd2—Bi1—Gd2ⁱⁱ	83.50 (3)	Gd1^xv—Gd2—Gd1^xvi	71.90 (4)
Gd2ⁱⁱⁱ—Bi1—Gd2ⁱⁱ	134.781 (14)	Gd1ⁱⁱ—Gd2—Gd1^xvi	56.98 (4)
Gd2ⁱ—Bi1—Gd2ⁱⁱ	83.50 (3)	Bi1—Gd2—Gd1^xvii	100.99 (3)
Gd2^iv—Bi1—Gd2ⁱⁱ	134.781 (14)	Bi1^xiii—Gd2—Gd1^xvii	55.93 (2)
Gd2^v—Bi1—Gd2ⁱⁱ	79.49 (4)	Bi1^xiv—Gd2—Gd1^xvii	97.71 (4)
Fe1^vi—Gd1—Fe1^vii	93.66 (5)	Bi1^viii—Gd2—Gd1^xvii	152.23 (4)
Fe1^vi—Gd1—Bi1^viii	117.379 (11)	Fe1—Gd2—Gd1^xvii	49.15 (2)
Fe1^vii—Gd1—Bi1^viii	117.379 (11)	Gd1^xv—Gd2—Gd1^xvii	56.98 (4)
Fe1^vi—Gd1—Bi1	117.379 (11)	Gd1ⁱⁱ—Gd2—Gd1^xvii	71.90 (4)
Fe1^vii—Gd1—Bi1	117.379 (11)	Gd1^xvi—Gd2—Gd1^xvii	98.30 (4)
Bi1^viii—Gd1—Bi1	95.53 (3)	Bi1—Gd2—Gd1	55.19 (2)
Fe1^vi—Gd1—Gd1^ix	53.663 (19)	Bi1^xiii—Gd2—Gd1	99.49 (4)
Fe1^vii—Gd1—Gd1^ix	53.66 (2)	Bi1^xiv—Gd2—Gd1	99.49 (4)
Bi1^viii—Gd1—Gd1^ix	162.232 (14)	Bi1^viii—Gd2—Gd1	55.19 (2)
Bi1—Gd1—Gd1^ix	102.233 (14)	Fe1—Gd2—Gd1	144.87 (2)
Fe1^vi—Gd1—Gd1^x	53.66 (2)	Gd1^xv—Gd2—Gd1	150.78 (2)
Fe1^vii—Gd1—Gd1^x	53.663 (19)	Gd1ⁱⁱ—Gd2—Gd1	101.37 (4)
Bi1^viii—Gd1—Gd1^x	102.233 (14)	Gd1^xvi—Gd2—Gd1	101.37 (4)
Bi1—Gd1—Gd1^x	162.233 (14)	Gd1^xvii—Gd2—Gd1	150.78 (2)
Gd1^ix—Gd1—Gd1^x	60.0	Bi1—Gd2—Gd1^xiii	99.49 (4)
Fe1^vi—Gd1—Gd2ⁱⁱⁱ	60.85 (2)	Bi1^xiii—Gd2—Gd1^xiii	55.19 (2)
Fe1^vii—Gd1—Gd2ⁱⁱⁱ	111.67 (3)	Bi1^xiv—Gd2—Gd1^xiii	55.19 (2)
Bi1^viii—Gd1—Gd2ⁱⁱⁱ	130.83 (3)	Bi1^viii—Gd2—Gd1^xiii	99.49 (4)
Bi1—Gd1—Gd2ⁱⁱⁱ	57.443 (17)	Fe1—Gd2—Gd1^xiii	144.87 (2)
Gd1^ix—Gd1—Gd2ⁱⁱⁱ	61.511 (18)	Gd1^xv—Gd2—Gd1^xiii	101.37 (4)
Gd1^x—Gd1—Gd2ⁱⁱⁱ	109.14 (2)	Gd1ⁱⁱ—Gd2—Gd1^xiii	150.78 (2)
Fe1^vi—Gd1—Gd2^xi	111.67 (3)	Gd1^xvi—Gd2—Gd1^xiii	150.78 (2)
Fe1^vii—Gd1—Gd2^xi	60.85 (3)	Gd1^xvii—Gd2—Gd1^xiii	101.37 (4)
Bi1^viii—Gd1—Gd2^xi	57.442 (17)	Gd1—Gd2—Gd1^xiii	70.25 (5)
Bi1—Gd1—Gd2^xi	130.83 (3)	Gd1ⁱⁱ—Fe1—Gd1^xv	139.991 (19)
Gd1^ix—Gd1—Gd2^xi	109.14 (2)	Gd1ⁱⁱ—Fe1—Gd1^xviii	139.991 (19)
Gd1^x—Gd1—Gd2^xi	61.511 (18)	Gd1^xv—Fe1—Gd1^xviii	72.67 (4)
Gd2ⁱⁱⁱ—Gd1—Gd2^xi	170.13 (4)	Gd1ⁱⁱ—Fe1—Gd1^xvii	93.66 (5)
Fe1^vi—Gd1—Gd2ⁱ	111.67 (3)	Gd1^xv—Fe1—Gd1^xvii	72.67 (4)
Fe1^vii—Gd1—Gd2ⁱ	60.85 (3)	Gd1^xviii—Fe1—Gd1^xvii	72.67 (4)
Bi1^viii—Gd1—Gd2ⁱ	130.83 (3)	Gd1ⁱⁱ—Fe1—Gd1^xix	72.67 (4)
Bi1—Gd1—Gd2ⁱ	57.443 (17)	Gd1^xv—Fe1—Gd1^xix	139.991 (19)
Gd1^ix—Gd1—Gd2ⁱ	61.511 (18)	Gd1^xviii—Fe1—Gd1^xix	93.66 (5)
Gd1^x—Gd1—Gd2ⁱ	109.14 (2)	Gd1^xvii—Fe1—Gd1^xix	139.991 (19)
Gd2ⁱⁱⁱ—Gd1—Gd2ⁱ	71.90 (4)	Gd1ⁱⁱ—Fe1—Gd1^xvi	72.67 (4)
Gd2^xi—Gd1—Gd2ⁱ	107.21 (4)	Gd1^xv—Fe1—Gd1^xvi	93.66 (5)
Fe1^vi—Gd1—Gd2^xii	60.85 (3)	Gd1^xviii—Fe1—Gd1^xvi	139.991 (19)
Fe1^vii—Gd1—Gd2^xii	111.67 (3)	Gd1^xvii—Fe1—Gd1^xvi	139.991 (19)
Bi1^viii—Gd1—Gd2^xii	57.442 (17)	Gd1^xix—Fe1—Gd1^xvi	72.67 (4)
Bi1—Gd1—Gd2^xii	130.83 (3)	Gd1ⁱⁱ—Fe1—Gd2^xx	133.17 (3)
Gd1^ix—Gd1—Gd2^xii	109.14 (2)	Gd1^xv—Fe1—Gd2^xx	69.995 (10)
Gd1^x—Gd1—Gd2^xii	61.511 (18)	Gd1^xviii—Fe1—Gd2^xx	69.995 (10)
Gd2ⁱⁱⁱ—Gd1—Gd2^xii	107.21 (4)	Gd1^xvii—Fe1—Gd2^xx	133.17 (3)
Gd2^xi—Gd1—Gd2^xii	71.90 (4)	Gd1^xix—Fe1—Gd2^xx	69.995 (10)
Gd2ⁱ—Gd1—Gd2^xii	170.13 (4)	Gd1^xvi—Fe1—Gd2^xx	69.995 (10)
Fe1^vi—Gd1—Gd2	168.30 (3)	Gd1ⁱⁱ—Fe1—Gd2^xxi	69.995 (10)
Fe1^vii—Gd1—Gd2	98.05 (4)	Gd1^xv—Fe1—Gd2^xxi	133.17 (3)
Bi1^viii—Gd1—Gd2	56.651 (17)	Gd1^xviii—Fe1—Gd2^xxi	69.995 (10)
Bi1—Gd1—Gd2	56.651 (17)	Gd1^xvii—Fe1—Gd2^xxi	69.995 (10)
Gd1^ix—Gd1—Gd2	135.098 (17)	Gd1^xix—Fe1—Gd2^xxi	69.995 (10)
Gd1^x—Gd1—Gd2	135.098 (17)	Gd1^xvi—Fe1—Gd2^xxi	133.17 (3)
Gd2ⁱⁱⁱ—Gd1—Gd2	114.09 (3)	Gd2^xx—Fe1—Gd2^xxi	120.0
Gd2^xi—Gd1—Gd2	74.49 (2)	Gd1ⁱⁱ—Fe1—Gd2	69.995 (10)
Gd2ⁱ—Gd1—Gd2	74.49 (2)	Gd1^xv—Fe1—Gd2	69.995 (10)
Gd2^xii—Gd1—Gd2	114.09 (3)	Gd1^xviii—Fe1—Gd2	133.17 (3)
Fe1^vi—Gd1—Gd2^iv	98.05 (4)	Gd1^xvii—Fe1—Gd2	69.995 (10)
Fe1^vii—Gd1—Gd2^iv	168.30 (3)	Gd1^xix—Fe1—Gd2	133.17 (3)
Bi1^viii—Gd1—Gd2^iv	56.651 (18)	Gd1^xvi—Fe1—Gd2	69.995 (10)
Bi1—Gd1—Gd2^iv	56.650 (17)	Gd2^xx—Fe1—Gd2	120.0
Gd1^ix—Gd1—Gd2^iv	135.098 (17)	Gd2^xxi—Fe1—Gd2	120.0
Gd1^x—Gd1—Gd2^iv	135.098 (17)

Symmetry codes: (i) −y+1, x−y, z; (ii) −x+y+1, −x+1, z; (iii) −y+1, x−y, z+1; (iv) x, y, z+1; (v) −x+y+1, −x+1, z+1; (vi) x+1, y, z+1; (vii) x+1, y, z; (viii) y, x−1, −z+1; (ix) −x+y+2, −x+1, z; (x) −y+1, x−y−1, z; (xi) −x+y+1, −x, z; (xii) −x+y+1, −x, z+1; (xiii) x, y, z−1; (xiv) y, x−1, −z; (xv) −y, x−y−1, z−1; (xvi) −y, x−y−1, z; (xvii) −x+y+1, −x+1, z−1; (xviii) x−1, y, z−1; (xix) x−1, y, z; (xx) −x+y, −x, z; (xxi) −y, x−y, z.

Ordering temperature T_C of selected Gd-rich compounds top

Chemical Formula	T_C (K)	Reference
Gd₅Bi₃	110	Szade & Drzyzga (2000)
Gd₂In₃	187	McAlister (1984)
Gd₆CoTe₂	220	Morozkin et al. (2010)
Gd₄Sb₃	264	Niu et al. (2001)
Gd₄Sb_1.5Bi_1.5	288	Niu et al. (2001)
Gd₄Bi₃	332	Niu et al. (2001)
Gd (hcp)	292	Coey et al. (1999)
Gd₆FeBi₂	350	Zhang et al. (2016)

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