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

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.

Computing details

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

Crystal data

Gd6FeBi2	Dx = 9.246 Mg m^−3
Mr = 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) Å^3	T = 150 K
Z = 1	Irregular, grey-silver
F(000) = 576	0.03 × 0.02 × 0.02 mm

Data collection

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

Refinement

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

Special details

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 (Ų)

	x	y	z	Uiso*/Ueq
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 (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
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)

Bi1—Gd1	3.2504 (17)	Gd1—Gd2^iv	3.6749 (19)
Bi1—Gd1^i	3.2504 (17)	Gd2—Bi1^xiii	3.3071 (12)
Bi1—Gd1^ii	3.2504 (17)	Gd2—Bi1^xiv	3.3071 (12)
Bi1—Gd2	3.3071 (12)	Gd2—Bi1^viii	3.3071 (12)
Bi1—Gd2^iii	3.3071 (12)	Gd2—Fe1	3.347 (2)
Bi1—Gd2^i	3.3071 (12)	Gd2—Gd1^xv	3.6015 (15)
Bi1—Gd2^iv	3.3071 (12)	Gd2—Gd1^ii	3.6015 (15)
Bi1—Gd2^v	3.3071 (12)	Gd2—Gd1^xvi	3.6015 (15)
Bi1—Gd2^ii	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—Gd1^ii	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—Gd2^iii	3.6015 (15)	Fe1—Gd1^xix	2.8993 (12)
Gd1—Gd2^xi	3.6015 (15)	Fe1—Gd1^xvi	2.8993 (12)
Gd1—Gd2^i	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—Gd1^i	120.0	Gd2^iii—Gd1—Gd2^iv	74.49 (2)
Gd1—Bi1—Gd1^ii	120.0	Gd2^xi—Gd1—Gd2^iv	114.09 (3)
Gd1^i—Bi1—Gd1^ii	120.0	Gd2^i—Gd1—Gd2^iv	114.09 (3)
Gd1—Bi1—Gd2	68.16 (2)	Gd2^xii—Gd1—Gd2^iv	74.49 (2)
Gd1^i—Bi1—Gd2	140.24 (2)	Gd2—Gd1—Gd2^iv	70.25 (5)
Gd1^ii—Bi1—Gd2	66.62 (2)	Bi1—Gd2—Bi1^xiii	79.49 (4)
Gd1—Bi1—Gd2^iii	66.62 (2)	Bi1—Gd2—Bi1^xiv	151.25 (4)
Gd1^i—Bi1—Gd2^iii	68.16 (2)	Bi1^xiii—Gd2—Bi1^xiv	93.39 (4)
Gd1^ii—Bi1—Gd2^iii	140.24 (2)	Bi1—Gd2—Bi1^viii	93.39 (4)
Gd2—Bi1—Gd2^iii	134.781 (13)	Bi1^xiii—Gd2—Bi1^viii	151.25 (4)
Gd1—Bi1—Gd2^i	66.62 (2)	Bi1^xiv—Gd2—Bi1^viii	79.49 (4)
Gd1^i—Bi1—Gd2^i	68.16 (2)	Bi1—Gd2—Fe1	104.37 (2)
Gd1^ii—Bi1—Gd2^i	140.24 (2)	Bi1^xiii—Gd2—Fe1	104.37 (2)
Gd2—Bi1—Gd2^i	83.50 (3)	Bi1^xiv—Gd2—Fe1	104.37 (2)
Gd2^iii—Bi1—Gd2^i	79.49 (4)	Bi1^viii—Gd2—Fe1	104.37 (2)
Gd1—Bi1—Gd2^iv	68.16 (2)	Bi1—Gd2—Gd1^xv	152.23 (4)
Gd1^i—Bi1—Gd2^iv	140.24 (2)	Bi1^xiii—Gd2—Gd1^xv	97.71 (4)
Gd1^ii—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)
Gd2^iii—Bi1—Gd2^iv	83.50 (3)	Fe1—Gd2—Gd1^xv	49.15 (2)
Gd2^i—Bi1—Gd2^iv	134.781 (14)	Bi1—Gd2—Gd1^ii	55.94 (2)
Gd1—Bi1—Gd2^v	140.24 (2)	Bi1^xiii—Gd2—Gd1^ii	100.99 (3)
Gd1^i—Bi1—Gd2^v	66.62 (2)	Bi1^xiv—Gd2—Gd1^ii	152.23 (4)
Gd1^ii—Bi1—Gd2^v	68.16 (2)	Bi1^viii—Gd2—Gd1^ii	97.71 (4)
Gd2—Bi1—Gd2^v	134.781 (14)	Fe1—Gd2—Gd1^ii	49.15 (2)
Gd2^iii—Bi1—Gd2^v	83.50 (3)	Gd1^xv—Gd2—Gd1^ii	98.30 (4)
Gd2^i—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—Gd2^ii	140.24 (2)	Bi1^xiv—Gd2—Gd1^xvi	100.99 (3)
Gd1^i—Bi1—Gd2^ii	66.62 (2)	Bi1^viii—Gd2—Gd1^xvi	55.94 (2)
Gd1^ii—Bi1—Gd2^ii	68.16 (2)	Fe1—Gd2—Gd1^xvi	49.15 (2)
Gd2—Bi1—Gd2^ii	83.50 (3)	Gd1^xv—Gd2—Gd1^xvi	71.90 (4)
Gd2^iii—Bi1—Gd2^ii	134.781 (14)	Gd1^ii—Gd2—Gd1^xvi	56.98 (4)
Gd2^i—Bi1—Gd2^ii	83.50 (3)	Bi1—Gd2—Gd1^xvii	100.99 (3)
Gd2^iv—Bi1—Gd2^ii	134.781 (14)	Bi1^xiii—Gd2—Gd1^xvii	55.93 (2)
Gd2^v—Bi1—Gd2^ii	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)	Gd1^ii—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)	Gd1^ii—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—Gd2^iii	60.85 (2)	Bi1^xiii—Gd2—Gd1^xiii	55.19 (2)
Fe1^vii—Gd1—Gd2^iii	111.67 (3)	Bi1^xiv—Gd2—Gd1^xiii	55.19 (2)
Bi1^viii—Gd1—Gd2^iii	130.83 (3)	Bi1^viii—Gd2—Gd1^xiii	99.49 (4)
Bi1—Gd1—Gd2^iii	57.443 (17)	Fe1—Gd2—Gd1^xiii	144.87 (2)
Gd1^ix—Gd1—Gd2^iii	61.511 (18)	Gd1^xv—Gd2—Gd1^xiii	101.37 (4)
Gd1^x—Gd1—Gd2^iii	109.14 (2)	Gd1^ii—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)	Gd1^ii—Fe1—Gd1^xv	139.991 (19)
Gd1^ix—Gd1—Gd2^xi	109.14 (2)	Gd1^ii—Fe1—Gd1^xviii	139.991 (19)
Gd1^x—Gd1—Gd2^xi	61.511 (18)	Gd1^xv—Fe1—Gd1^xviii	72.67 (4)
Gd2^iii—Gd1—Gd2^xi	170.13 (4)	Gd1^ii—Fe1—Gd1^xvii	93.66 (5)
Fe1^vi—Gd1—Gd2^i	111.67 (3)	Gd1^xv—Fe1—Gd1^xvii	72.67 (4)
Fe1^vii—Gd1—Gd2^i	60.85 (3)	Gd1^xviii—Fe1—Gd1^xvii	72.67 (4)
Bi1^viii—Gd1—Gd2^i	130.83 (3)	Gd1^ii—Fe1—Gd1^xix	72.67 (4)
Bi1—Gd1—Gd2^i	57.443 (17)	Gd1^xv—Fe1—Gd1^xix	139.991 (19)
Gd1^ix—Gd1—Gd2^i	61.511 (18)	Gd1^xviii—Fe1—Gd1^xix	93.66 (5)
Gd1^x—Gd1—Gd2^i	109.14 (2)	Gd1^xvii—Fe1—Gd1^xix	139.991 (19)
Gd2^iii—Gd1—Gd2^i	71.90 (4)	Gd1^ii—Fe1—Gd1^xvi	72.67 (4)
Gd2^xi—Gd1—Gd2^i	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)	Gd1^ii—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)
Gd2^iii—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)
Gd2^i—Gd1—Gd2^xii	170.13 (4)	Gd1^xvi—Fe1—Gd2^xx	69.995 (10)
Fe1^vi—Gd1—Gd2	168.30 (3)	Gd1^ii—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)
Gd2^iii—Gd1—Gd2	114.09 (3)	Gd2^xx—Fe1—Gd2^xxi	120.0
Gd2^xi—Gd1—Gd2	74.49 (2)	Gd1^ii—Fe1—Gd2	69.995 (10)
Gd2^i—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.