Crystal structure and charge distribution of YbFeMnO₄

The structure of synthetic YbFeMnO₄ has been refined by single-crystal X-ray diffraction. Space group Rm, a = 3.4580 (1), c = 25.647 (3) Å, V = 265.59 (3) Å³, Z = 3. Yb is in octahedral coordination, whereas Fe and Mn are disordered on a single crystallographic type of trigonal bipyramid, in which the cation is off-centred from the basal plane. Assuming perfect stoichiometry, R₁ = 0.0195, but the charge distribution (CD) analysis suggests incomplete occupation of the Yb site. Refinement of the occupancy lowers R₁ to 0.0175, resulting in s.o.f.(Yb) = 0.963 (3), with a significant improvement of the Fourier difference. The electroneutrality is likely preserved through incomplete occupancy of one of the two oxygen sites: the compound is thus non-stoichiometric, with the formula Yb_0.963FeMnO_3.945. Another mechanism for preserving the electroneutrality is the oxidation of a small amount of Mn²⁺ to Mn³⁺, which is, however, less probable because of the reduction conditions in which the sample was synthesized. Both models give a satisfactorily CD result, but they cannot be definitively distinguished by X-ray data.

Computing details

Data collection: CAD-4 EXPRESS; cell refinement: CAD-4 EXPRESS; data reduction: XCAD4 (Harms, 1996); program(s) used to solve structure: SHELXS97 (Sheldrick, 1990); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997).

Figures

Fig. 1.

(I)

Crystal data

Yb0.963FeMnO3.945	Dx = 6.405 Mg m^−3
Mr = 341.49	Mo Kα radiation, λ = 0.71073 Å
Hexagonal, R3m	Cell parameters from 18 reflections
Hall symbol: -R 3 2"	θ = 41.0–45.3°
a = 3.4580 (1) Å	µ = 32.64 mm^−1
c = 25.647 (3) Å	T = 293 K
V = 265.59 (3) Å^3	Sphere, black
Z = 3	0.06 × 0.06 × 0.06 × 0.06 (radius) mm
F(000) = 451

Data collection

Enraf Nonius CAD4 diffractometer	528 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tube	Rint = 0.020
Graphite monochromator	θmax = 59.8°, θmin = 2.4°
ω–θ scans	h = 0→7
Absorption correction: for a sphere PLATON	k = 0→4
Tmin = 0.086, Tmax = 0.166	l = −60→61
655 measured reflections	3 standard reflections every 240 min
577 independent reflections	intensity decay: none

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)] = 0.018	w = 1/[σ^2(Fo^2) + (0.0192P)^2 + 1.2133P] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.044	(Δ/σ)max = 0.001
S = 1.18	Δρmax = 2.55 e Å^−3
577 reflections	Δρmin = −4.88 e Å^−3
14 parameters	Extinction correction: SHELXL, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0290 (11)

Special details

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

Refinement. 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 > σ(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	Occ. (<1)
Yb	0.0000	0.0000	0.0000	0.01184 (5)	0.963 (3)
Fe	0.0000	0.0000	0.215706 (14)	0.00728 (7)	0.50
Mn	0.0000	0.0000	0.215706 (14)	0.00728 (7)	0.50
O1	0.0000	0.0000	0.12826 (13)	0.0208 (5)	0.97
O2	0.0000	0.0000	0.29345 (8)	0.0098 (2)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Yb	0.00345 (4)	0.00345 (4)	0.02863 (11)	0.00172 (2)	0.000	0.000
Fe	0.00660 (8)	0.00660 (8)	0.00865 (12)	0.00330 (4)	0.000	0.000
Mn	0.00660 (8)	0.00660 (8)	0.00865 (12)	0.00330 (4)	0.000	0.000
O1	0.0217 (8)	0.0217 (8)	0.0192 (10)	0.0108 (4)	0.000	0.000
O2	0.0095 (3)	0.0095 (3)	0.0106 (5)	0.00474 (17)	0.000	0.000

Geometric parameters (Å, º)

Yb—O2^i	2.2432 (10)	Fe—O1^v	2.0150 (5)
Yb—O2^ii	2.2432 (10)	Fe—O1	2.243 (3)
Yb—O2^iii	2.2432 (10)	Fe—Yb^xiii	3.6176 (4)
Yb—O2^iv	2.2432 (10)	Fe—Yb^xiv	3.6176 (4)
Yb—O2^v	2.2433 (10)	Fe—Yb^xv	3.6176 (4)
Yb—O2^vi	2.2433 (10)	O1—Mn^iii	2.0150 (5)
Yb—Yb^vii	3.4580	O1—Fe^iii	2.0150 (5)
Yb—Yb^viii	3.4580	O1—Mn^i	2.0150 (5)
Yb—Yb^ix	3.4580	O1—Fe^i	2.0150 (5)
Yb—Yb^x	3.4580	O1—Mn^v	2.0150 (5)
Yb—Yb^xi	3.4580	O1—Fe^v	2.0150 (5)
Yb—Yb^xii	3.4580	O2—Yb^xiii	2.2432 (10)
Fe—O2	1.994 (2)	O2—Yb^xiv	2.2432 (10)
Fe—O1^iii	2.0150 (4)	O2—Yb^xv	2.2433 (10)
Fe—O1^i	2.0150 (5)
O2^i—Yb—O2^ii	180.00 (10)	Yb^vii—Yb—Yb^xii	60.0
O2^i—Yb—O2^iii	100.84 (6)	Yb^viii—Yb—Yb^xii	120.0
O2^ii—Yb—O2^iii	79.16 (6)	Yb^ix—Yb—Yb^xii	180.0
O2^i—Yb—O2^iv	79.16 (6)	Yb^x—Yb—Yb^xii	120.0
O2^ii—Yb—O2^iv	100.84 (6)	Yb^xi—Yb—Yb^xii	60.0
O2^iii—Yb—O2^iv	180.00 (10)	O2—Fe—O1^iii	97.77 (9)
O2^i—Yb—O2^v	100.84 (6)	O2—Fe—O1^i	97.77 (9)
O2^ii—Yb—O2^v	79.16 (6)	O1^iii—Fe—O1^i	118.20 (4)
O2^iii—Yb—O2^v	100.84 (6)	O2—Fe—O1^v	97.77 (9)
O2^iv—Yb—O2^v	79.16 (6)	O1^iii—Fe—O1^v	118.20 (4)
O2^i—Yb—O2^vi	79.16 (6)	O1^i—Fe—O1^v	118.20 (4)
O2^ii—Yb—O2^vi	100.84 (6)	O2—Fe—O1	180.0
O2^iii—Yb—O2^vi	79.16 (6)	O1^iii—Fe—O1	82.23 (9)
O2^iv—Yb—O2^vi	100.84 (6)	O1^i—Fe—O1	82.23 (9)
O2^v—Yb—O2^vi	180.00 (10)	O1^v—Fe—O1	82.23 (9)
O2^i—Yb—Yb^vii	140.42 (3)	O2—Fe—Yb^xiii	33.496 (5)
O2^ii—Yb—Yb^vii	39.58 (3)	O1^iii—Fe—Yb^xiii	112.72 (8)
O2^iii—Yb—Yb^vii	39.58 (3)	O1^i—Fe—Yb^xiii	64.28 (9)
O2^iv—Yb—Yb^vii	140.42 (3)	O1^v—Fe—Yb^xiii	112.72 (8)
O2^v—Yb—Yb^vii	90.0	O1—Fe—Yb^xiii	146.504 (4)
O2^vi—Yb—Yb^vii	90.0	O2—Fe—Yb^xiv	33.496 (4)
O2^i—Yb—Yb^viii	39.58 (3)	O1^iii—Fe—Yb^xiv	64.28 (9)
O2^ii—Yb—Yb^viii	140.42 (3)	O1^i—Fe—Yb^xiv	112.72 (8)
O2^iii—Yb—Yb^viii	140.42 (3)	O1^v—Fe—Yb^xiv	112.72 (8)
O2^iv—Yb—Yb^viii	39.58 (3)	O1—Fe—Yb^xiv	146.504 (4)
O2^v—Yb—Yb^viii	90.0	Yb^xiii—Fe—Yb^xiv	57.102 (7)
O2^vi—Yb—Yb^viii	90.0	O2—Fe—Yb^xv	33.496 (4)
Yb^vii—Yb—Yb^viii	180.0	O1^iii—Fe—Yb^xv	112.72 (8)
O2^i—Yb—Yb^ix	90.0	O1^i—Fe—Yb^xv	112.72 (8)
O2^ii—Yb—Yb^ix	90.0	O1^v—Fe—Yb^xv	64.28 (9)
O2^iii—Yb—Yb^ix	140.42 (3)	O1—Fe—Yb^xv	146.504 (4)
O2^iv—Yb—Yb^ix	39.58 (3)	Yb^xiii—Fe—Yb^xv	57.102 (7)
O2^v—Yb—Yb^ix	39.58 (3)	Yb^xiv—Fe—Yb^xv	57.102 (7)
O2^vi—Yb—Yb^ix	140.42 (3)	Mn^iii—O1—Fe^iii	0.00 (2)
Yb^vii—Yb—Yb^ix	120.0	Mn^iii—O1—Mn^i	118.20 (4)
Yb^viii—Yb—Yb^ix	60.0	Fe^iii—O1—Mn^i	118.20 (4)
O2^i—Yb—Yb^x	140.42 (3)	Mn^iii—O1—Fe^i	118.20 (4)
O2^ii—Yb—Yb^x	39.58 (3)	Fe^iii—O1—Fe^i	118.20 (4)
O2^iii—Yb—Yb^x	90.0	Mn^i—O1—Fe^i	0.00 (2)
O2^iv—Yb—Yb^x	90.0	Mn^iii—O1—Mn^v	118.20 (4)
O2^v—Yb—Yb^x	39.58 (3)	Fe^iii—O1—Mn^v	118.20 (4)
O2^vi—Yb—Yb^x	140.42 (3)	Mn^i—O1—Mn^v	118.20 (4)
Yb^vii—Yb—Yb^x	60.0	Fe^i—O1—Mn^v	118.20 (4)
Yb^viii—Yb—Yb^x	120.0	Mn^iii—O1—Fe^v	118.20 (4)
Yb^ix—Yb—Yb^x	60.0	Fe^iii—O1—Fe^v	118.20 (4)
O2^i—Yb—Yb^xi	39.58 (3)	Mn^i—O1—Fe^v	118.20 (4)
O2^ii—Yb—Yb^xi	140.42 (3)	Fe^i—O1—Fe^v	118.20 (4)
O2^iii—Yb—Yb^xi	90.0	Mn^v—O1—Fe^v	0.00 (2)
O2^iv—Yb—Yb^xi	90.0	Mn^iii—O1—Fe	97.77 (9)
O2^v—Yb—Yb^xi	140.42 (3)	Fe^iii—O1—Fe	97.77 (9)
O2^vi—Yb—Yb^xi	39.58 (3)	Mn^i—O1—Fe	97.77 (9)
Yb^vii—Yb—Yb^xi	120.0	Fe^i—O1—Fe	97.77 (9)
Yb^viii—Yb—Yb^xi	60.0	Mn^v—O1—Fe	97.77 (9)
Yb^ix—Yb—Yb^xi	120.0	Fe^v—O1—Fe	97.77 (9)
Yb^x—Yb—Yb^xi	180.0	Fe—O2—Yb^xiii	117.13 (5)
O2^i—Yb—Yb^xii	90.0	Fe—O2—Yb^xiv	117.13 (5)
O2^ii—Yb—Yb^xii	90.0	Yb^xiii—O2—Yb^xiv	100.84 (6)
O2^iii—Yb—Yb^xii	39.58 (3)	Fe—O2—Yb^xv	117.13 (5)
O2^iv—Yb—Yb^xii	140.42 (3)	Yb^xiii—O2—Yb^xv	100.84 (6)
O2^v—Yb—Yb^xii	140.42 (3)	Yb^xiv—O2—Yb^xv	100.84 (6)
O2^vi—Yb—Yb^xii	39.58 (3)

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