Hexagonal YbMnO₃ revisited

The crystal structure of hexagonal ytterbium manganese oxide, YbMnO₃, has been refined at room temperature. It is isomorphous with YMnO₃. The Mn ions lie near the centre of a trigonal bipyramid. Although the Yb ions lie on threefold axes, the apical oxy­gen ions are at dissimilar distances, leading to ferroelectric behaviour. The sample studied was composed of almost an equal volume of inversion twins.

Key indicators

• Single-crystal X-ray study
• T = 293 K
• Mean [sigma](Mn-O) = 0.004 Å
• R factor = 0.030
• wR factor = 0.072
• Data-to-parameter ratio = 26.1

checkCIF results

No syntax errors found


 Alert Level A:



PLAT_211  Alert A ADP of atom  O2     is non-positive-definite .          ?

Author response: ... Our calculations show that although the smallest principal mean square displacement of O2 is very small, 0.0001, it is not zero or negative. Note that oxygen compared with ytterbium has only very few electrons, 8 versus 70. However using isotropic atomic displacement for all oxygen positions, yields a very similar model. All atomic positions stay equal within the error of the refinement. The isotropic a.d.p.'s for the oxygen range between 0.0051(14) and 0.0071(11).

PLAT_211  Alert A ADP of atom  O4     is non-positive-definite .          ?

Author response: ... Our calculations show that although the smallest principal mean square displacement of O2 is very small, 0.0001, it is not zero or negative. Note that oxygen compared with ytterbium has only very few electrons, 8 versus 70. However using isotropic atomic displacement for all oxygen positions, yields a very similar model. All atomic positions stay equal within the error of the refinement. The isotropic a.d.p.'s for the oxygen range between 0.0051(14) and 0.0071(11).

 Alert Level B:



DIFMN_02  Alert B The minimum difference density is < -0.1*ZMAX*1.00
          _refine_diff_density_min given =     -7.300
          Test value =     -7.000

Author response: ... The differences in final electron density between calculation and observation are well known and appear to be present in most lanthanide manganese oxides.

PLAT_111  Alert B ADDSYM detects (pseudo) centre of symmetry ...        100 Perc Fit

Author response: ... Attempts to fit the data on a crystal structure with a space group that contains higher symmetry, like P63/mcm, where unsuccessful. A.d.p.'s indicated that the atoms at the mirror plane ought to be split in two on each side of the mirror plane. For instance an inversion symmetry on z //simeq 0.252 forces the two inequivalent Yb positions to have identical values for their z parameter. As the z parameter is free on all P63cm positions and the current refinement separates the z parameters by as much as 0.04, equivalent to 0.25 \%A, it is very unlikely that additional symmetry is missed.

PLAT_111  Alert B ADDSYM detects (pseudo) centre of symmetry ...        100 Perc Fit

Author response: ... Attempts to fit the data on a crystal structure with a space group that contains higher symmetry, like P63/mcm, where unsuccessful. A.d.p.'s indicated that the atoms at the mirror plane ought to be split in two on each side of the mirror plane. For instance an inversion symmetry on z //simeq 0.252 forces the two inequivalent Yb positions to have identical values for their z parameter. As the z parameter is free on all P63cm positions and the current refinement separates the z parameters by as much as 0.04, equivalent to 0.25 \%A, it is very unlikely that additional symmetry is missed.

 Alert Level C:



DIFMN_03  Alert C The minimum difference density is < -0.1*ZMAX*0.75
          The relevant atom site should be identified.

General Notes



ABSTM_02  The ratio of expected to reported Tmax/Tmin(RR) is > 2.00
          Tmin and Tmax reported:      0.059     0.577
          Tmin and Tmax expected:      0.011     0.568
          RR =      5.193
          Please check that your absorption correction is appropriate.

REFLT_03
         From the CIF: _diffrn_reflns_theta_max           39.90
         From the CIF: _reflns_number_total                835
         Count of symmetry unique reflns          434
         Completeness (_total/calc)            192.40%
         TEST3: Check Friedels for noncentro structure
         Estimate of Friedel pairs measured       401
         Fraction of Friedel pairs measured     0.924
         Are heavy atom types Z>Si present          yes
          Please check that the estimate of the number of Friedel pairs is
          correct. If it is not, please give the correct count in the
          _publ_section_exptl_refinement section of the submitted CIF.


 2 Alert Level A = Potentially serious problem

 3 Alert Level B = Potential problem

 1 Alert Level C = Please check

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S1. Comment

As part of a program to investigate the origin of the ferroelectric behaviour in the hexagonal LnMnO₃ family, we have determined accurate structural parameters for several members of this series (van Aken et al., 2001a,b,c). Here we report the structure of YbMnO₃. Single-crystal growth of YbMnO₃ has frequently been described (Yakel et al., 1963; Bertaut et al., 1963), but the structure was first reported by Isobe et al. (1991). Our refinement shows small but significant differences from the work of Isobe et al. (1991), as discussed below.

The hexagonal LnMnO₃ family has been described in great detail previously (van Aken et al., 2001a,b,c). The lattice parameter c of 11.5575 (5) Å reported by Isobe et al. (1991) is exceptionally long when compared with other LnMnO₃ compounds. However, the value we measured of 11.3561 (7) Å is likely more reliable, as it lies within the range observed for other isostructural compounds, i.e. 11.36–11.42 Å (Yakel et al., 1963; van Aken et al., 2001a,b,c).

The metal–oxygen bond lengths are given in Table 1. In contrast to the report of Isobe et al. (1991), the equatorial Mn—O distances are the same within the measured s.u.'s. More important, the apical Mn—O distances in our report are also the same within the accuracy. They differ by only 0.001 (7) Å, whereas Isobe reports a difference of 0.058 (10) Å. As a result, the Mn is approximately in the centre of its oxygen environment. Likewise, the differences between the apical bond distances of Yb1 and Yb2, 1.140 (18) and 0.876 (10) Å, respectively, are significantly larger than those reported by Isobe et al. (1991), viz. 1.071 and 0.707 Å.

Isobe et al. (1991) only measured reflections of one asymmetric hkl set and therefore included no Bijvoet pairs, meaning that they could obtain no information about the non-centrosymmetry of their sample. Our experiments included over 90% of the Friedel pairs, allowing us to calculate the Flack (1983) parameter. The refinement indicated that our sample contained roughly equal volumes of inversion twins as was also found for YMnO₃ (van Aken et al., 2001a). Our results show the significance of a full data set, for twinned non-centrosymmetric samples.

S2. Experimental

Single crystals of YbMnO₃ were obtained using a flux method by weighing appropriate amounts of Yb₂O₃ and MnO₂ with Bi₂O₃ in a 1:12 ratio (Yakel et al., 1963). The powders were thoroughly mixed and heated for 48 h at 1523 K in a Pt crucible. The crystals were separated from the flux by increasing the temperature to 1723 K and evaporating the Bi₂O₃ flux (Bertaut et al., 1963).

S3. Refinement

The space group is determined to be P6₃cm, taking into consideration the unit-cell parameters, statistical analyses of intensity distributions and, where appropriate, systematic extinctions (h-hl: l ≠ 2n; 00 l: l ≠ 2n). Attempts to fit the data in the space group P6₃/mcm were unsuccessful with wR² = 0.45 and R = 0.18. Anisotropic displacement parameters and SHELXL97 (Sheldrick, 1997) indicated that the Yb ions should be shifted away from the mirror plane perpendicular to the c axis. The structure was solved by using initial coordinates which are taken from a previous reported hexagonal manganite, YMnO₃ (van Aken et al., 2001a). The positional and anisotropic displacement parameters were refined. The final difference Fourier map showed a peak of 2.5 (10) e Å^-3 near the Yb1 position and a hole of 7.3 (10) e Å^-3 also near the Yb1 position. No other significant peaks having chemical meaning above the general background 1.0 e Å^-3 were observed in the final difference Fourier map. The Flack parameter (Flack, 1983) of an initial refinement indicated that the crystal was twinned. The model without a twin yielded a Flack parameter of x = 0.34 (3) and x = 0.57 (3) for the inverse structure. The R values are wR² = 0.0789 and R = 0.0305, and wR² = 0.086 and R = 0.0318, respectively. Therefore an inversion twin was added to the structure model, similar to the one reported for YMnO₃ (van Aken et al., 2001a). The final refinement gave a twin fraction near 50%. We expect a 50/50% istribution because this yields no net electrical polarization (Rao & Gopalakrishnan, 1997). Fixing the twin fraction at 50% had no significant influence on any other parameter.

Computing details

Data collection: CAD-4-UNIX Software (Enraf-Nonius, 1994); cell refinement: SET4 (de Boer & Duisenberg, 1984); data reduction: HELENA (Spek, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 (Farrugia, 2000); software used to prepare material for publication: PLATON (Spek, 2001).

Figures

Fig. 1. Schematic view of the crystallographic structure of YbMnO3. (a) A view along the basal plane. Er is represented by blue spheres, and the MnO5 clusters are represented by red trigonal bipyramids. This panel highlights the two-dimensional nature of the structure. (b) A view along the c axis of two layers to show the stacking of the bipyramids. The bipyramids below the Er layer are shown in red, with those above in green.

Ytterbium Manganese Oxide

Crystal data

YbMnO3	Unit cell parameters (Duisenberg, 1992) and orientation matrix were determined from a least-squares treatment of SET4 (de Boer & Duisenberg, 1984) setting. Reduced cell calculations did not indicate any higher metric lattice symmetry and examination of the final atomic coordinates of the structure did not yield extra symmetry elements (Spek, 1988; Le Page 1987, 1988)
Mr = 275.88	Dx = 7.617 Mg m^−3
Hexagonal, P63cm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 6c -2	Cell parameters from 22 reflections
a = 6.0584 (6) Å	θ = 15.0–27.9°
c = 11.3561 (7) Å	µ = 43.58 mm^−1
V = 360.97 (6) Å^3	T = 293 K
Z = 6	Platelet, black
F(000) = 714	0.15 × 0.10 × 0.01 mm

Data collection

Enraf Nonius CAD-4F diffractometer	636 reflections with F > 4σ(F)
Radiation source: fine focus sealed Philips Mo tube	Rint = 0.037
Perpendicular mounted graphite monochromator	θmax = 39.9°, θmin = 3.6°
ω/2θ scans	h = −10→0
Absorption correction: gaussian (Spek, 1983)	k = 0→10
Tmin = 0.059, Tmax = 0.577	l = −20→20
3264 measured reflections	3 standard reflections every 180 min
835 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: none
R[F^2 > 2σ(F^2)] = 0.030	w = 1/[σ^2(Fo^2) + (0.0494P)^2] where P = (Fo^2 + 2Fc^2)/3
wR(F^2) = 0.072	(Δ/σ)max < 0.001
S = 1.08	Δρmax = 2.5 (10) e Å^−3
835 reflections	Δρmin = −7.3 (10) e Å^−3
32 parameters	Extinction correction: SHELXL97, Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
0 restraints	Extinction coefficient: 0.0121 (7)
0 constraints

Special details

Geometry. Bond distances, angles etc. have been calculated using the rounded fractional coordinates. All e.s.d.'s are estimated from the variances of the (full) variance-covariance matrix. The cell e.s.d.'s are taken into account in the estimation of distances, angles and torsion angles

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 > 2σ(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
Yb1	0.00000	0.00000	0.27336 (5)	0.00427 (11)
Yb2	0.33333	−0.33333	0.23061 (3)	0.00472 (7)
Mn	0.3333 (5)	0.00000	−0.00194 (14)	0.0054 (2)
O1	0.3030 (12)	0.00000	0.1617 (6)	0.0039 (10)
O2	0.3610 (15)	0.00000	−0.1658 (6)	0.0074 (11)
O3	0.00000	0.00000	−0.0268 (16)	0.004 (2)
O4	0.33333	−0.33333	0.0192 (9)	0.0059 (17)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Yb1	0.0047 (2)	0.0047 (2)	0.0035 (2)	0.0023 (1)	0.0000	0.0000
Yb2	0.0035 (1)	0.0036 (1)	0.0071 (2)	0.0018 (1)	0.0000	0.0000
Mn	0.0069 (4)	0.0048 (4)	0.0039 (2)	0.0024 (6)	0.0002 (3)	0.0000
O1	0.0050 (14)	0.0017 (18)	0.0041 (19)	0.0009 (9)	−0.0019 (15)	0.0000
O2	0.014 (2)	0.0001 (18)	0.0033 (17)	0.0000 (9)	0.0002 (19)	0.0000
O3	0.003 (2)	0.003 (2)	0.005 (6)	0.0016 (10)	0.0000	0.0000
O4	0.009 (3)	0.009 (3)	0.000 (3)	0.0047 (13)	0.0000	0.0000

Geometric parameters (Å, º)

Yb1—Yb2	3.5313 (4)	Yb2—O1	2.257 (5)
Yb1—O1	2.231 (7)	Yb2—O4	2.401 (10)
Yb1—Yb2^i	3.5313 (4)	Yb2—O4^xi	3.277 (10)
Yb1—Yb2^ii	3.5313 (4)	Yb2—O2^xii	2.270 (8)
Yb1—Mn^iii	3.254 (3)	Yb2—O1^xiii	2.257 (6)
Yb1—O2^iii	2.294 (8)	Yb2—O2^xiv	2.270 (5)
Yb1—O3^iii	2.269 (18)	Yb2—O1^xv	2.257 (8)
Yb1—O3	3.409 (18)	Yb2—O2^vii	2.270 (5)
Yb1—O1^iv	2.231 (6)	Yb2—Yb2^viii	3.4978 (3)
Yb1—Mn^v	3.254 (3)	Yb2—Yb2^xvi	3.4978 (3)
Yb1—O2^v	2.294 (9)	Yb2—Yb2^x	3.4978 (3)
Yb1—O1^vi	2.231 (7)	Mn—O1	1.867 (7)
Yb1—Mn^vii	3.254 (3)	Mn—O2	1.868 (7)
Yb1—O2^vii	2.294 (7)	Mn—O3	2.039 (4)
Yb1—Yb2^viii	3.5313 (4)	Mn—O4	2.034 (4)
Yb1—Yb2^ix	3.5313 (4)	Mn—O4^x	2.034 (4)
Yb1—Yb2^x	3.5313 (4)
O1—Yb1—O2^iii	77.2 (2)	O1^xiii—Yb2—O2^vii	77.2 (2)
O1—Yb1—O3^iii	124.64 (18)	O1^xv—Yb2—O2^xiv	77.2 (3)
O1—Yb1—O1^iv	90.89 (18)	O2^xiv—Yb2—O2^vii	95.6 (3)
O1—Yb1—O2^v	162.9 (3)	O1^xv—Yb2—O2^vii	169.1 (2)
O1—Yb1—O1^vi	90.9 (2)	O1—Mn—O2	179.5 (4)
O1—Yb1—O2^vii	77.23 (17)	O1—Mn—O3	92.3 (6)
O2^iii—Yb1—O3^iii	72.47 (18)	O1—Mn—O4	86.1 (3)
O1^iv—Yb1—O2^iii	77.2 (3)	O1—Mn—O4^x	86.1 (3)
O2^iii—Yb1—O2^v	111.3 (2)	O2—Mn—O3	87.2 (6)
O1^vi—Yb1—O2^iii	162.9 (2)	O2—Mn—O4	94.2 (3)
O2^iii—Yb1—O2^vii	111.3 (3)	O2—Mn—O4^x	94.2 (3)
O1^iv—Yb1—O3^iii	124.64 (17)	O3—Mn—O4	120.54 (8)
O2^v—Yb1—O3^iii	72.47 (18)	O3—Mn—O4^x	120.54 (18)
O1^vi—Yb1—O3^iii	124.64 (18)	O4—Mn—O4^x	118.62 (19)
O2^vii—Yb1—O3^iii	72.47 (17)	Yb1—O1—Yb2	103.8 (2)
O1^iv—Yb1—O2^v	77.23 (17)	Yb1—O1—Mn	130.3 (4)
O1^iv—Yb1—O1^vi	90.9 (2)	Yb1—O1—Yb2^x	103.8 (2)
O1^iv—Yb1—O2^vii	162.9 (2)	Yb2—O1—Mn	107.0 (3)
O1^vi—Yb1—O2^v	77.2 (2)	Yb2—O1—Yb2^x	101.6 (3)
O2^v—Yb1—O2^vii	111.34 (16)	Yb2^x—O1—Mn	107.0 (3)
O1^vi—Yb1—O2^vii	77.2 (2)	Yb1^xvii—O2—Mn	102.4 (4)
O1—Yb2—O4	69.72 (17)	Yb2^xvii—O2—Mn	123.3 (2)
O1—Yb2—O2^xii	169.1 (3)	Yb2^xviii—O2—Mn	123.3 (2)
O1—Yb2—O1^xiii	108.65 (19)	Yb1^xvii—O2—Yb2^xvii	101.4 (2)
O1—Yb2—O2^xiv	77.2 (2)	Yb1^xvii—O2—Yb2^xvii	101.4 (2)
O1—Yb2—O1^xv	108.6 (2)	Yb2^xvii—O2—Yb2^xviii	100.8 (3)
O1—Yb2—O2^vii	77.2 (3)	Yb1^xvii—O3—Mn	98.0 (5)
O2^xii—Yb2—O4	121.22 (19)	Mn—O3—Mn^iv	118.1 (3)
O1^xiii—Yb2—O4	69.72 (17)	Mn—O3—Mn^vi	118.1 (3)
O2^xiv—Yb2—O4	121.22 (16)	Yb1^xvii—O3—Mn^iv	98.0 (5)
O1^xv—Yb2—O4	69.72 (18)	Yb1^xvii—O3—Mn^vi	98.0 (5)
O2^vii—Yb2—O4	121.22 (16)	Mn^iv—O3—Mn^vi	118.1 (3)
O1^xiii—Yb2—O2^xii	77.2 (3)	Yb2—O4—Mn	96.8 (3)
O2^xii—Yb2—O2^xiv	95.6 (3)	Yb2—O4—Mn^xiii	96.8 (3)
O1^xv—Yb2—O2^xii	77.2 (3)	Yb2—O4—Mn^xv	96.8 (3)
O2^xii—Yb2—O2^vii	95.6 (3)	Mn—O4—Mn^xiii	118.6 (2)
O1^xiii—Yb2—O2^xiv	169.1 (2)	Mn—O4—Mn^xv	118.63 (17)
O1^xiii—Yb2—O1^xv	108.6 (2)	Mn^xiii—O4—Mn^xv	118.63 (19)

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