Hexagonal LuMnO₃ revisited

The crystal structure of hexagonal LuMnO₃ at room temperature is isomorphous with YMnO₃ and deviates in important details from the early work of Yakel et al. [Acta Cryst. (1963), 16, 957-962]. Mn is near the centre of its oxy­gen coordination environment. On the threefold axes, the apical O-Lu bonds have alternating long and short bond lengths, leading to ferroelectric behaviour. The sample studied was composed of almost equal volumes of inversion twins.

Key indicators

• Single-crystal X-ray study
• T = 293 K
• Mean [sigma](Mn-O) = 0.007 Å
• R factor = 0.027
• wR factor = 0.065
• Data-to-parameter ratio = 26.0

checkCIF results

No syntax errors found


 Alert Level B:



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 Lu 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 a centre of 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 Lu 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 a centre of symmetry is missed.

 Alert Level C:



DIFMN_02  Alert C The minimum difference density is < -0.1*ZMAX*0.75
          _refine_diff_density_min given =     -5.600
          Test value =     -5.325

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:      0.084     0.758
          Tmin and Tmax expected:      0.009     0.832
          RR =     10.210
          Please check that your absorption correction is appropriate.

REFLT_03
         From the CIF: _diffrn_reflns_theta_max           39.98
         From the CIF: _reflns_number_total                833
         Count of symmetry unique reflns          433
         Completeness (_total/calc)            192.38%
         TEST3: Check Friedels for noncentro structure
         Estimate of Friedel pairs measured       400
         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.


 0 Alert Level A = Potentially serious problem

 2 Alert Level B = Potential problem

 2 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 single crystals of this series (Van Aken et al., 2001a,b,c). Here we report the structure of LuMnO₃. Single crystal growth of LuMnO₃ has frequently been reported (Yakel et al., 1963; Bertaut et al., 1963) and the structure was reported by Yakel et al. Our refinement shows small but significant differences from the work of Yakel et al. as discussed below. The hexagonal LnMnO₃ family has been described in great detail previously (Van Aken et al., 2001 d).

The metal-oxygen bond lengths are given in Table 1. The non-equivalent Mn—O atomic distances, both within the basal plane and to the apices, have smaller differences than in previous reports on LuMnO₃ (Yakel et al., 1963). In-plane differences are 0.023 (7) Å (this work) and 0.09 Å (Yakel et al.), apical 0.031 (7) Å (this work) and 0.08 Å (Yakel et al.). As a result the Mn is approximately in the centre of its oxygen environment. Likewise, the equatorial Lu—O1 and Lu—O2 bond lengths show less variation than Yakel et al.'s result. Our data yield equatorial bond lengths of 2.227–2.294 Å, whereas Yakel et al. report 2.18–2.35 Å. The differences in apical bond distances of Lu1 and Lu2 are larger [1.192 (14) and 0.879 (10) Å] respectively, than those reported by Yakel et al. (0.84 and 0.96 Å).

Yakel et al. (1963) only measured reflections of one asymmetric hkl set, i.e. no Bijvoet pairs. Based on the observation of ferroelectricity (Bertaut et al., 1963) and systematic absences, the non-centrosymmetric space group P6₃cm was chosen. Our experiment included over 90% of the Friedel pairs and subsequent analysis confirmed this space group. Yakel et al. also discuss the possibility of the existence of domains with reversed polar direction. Our refinement indicated that our sample contained roughly equal volume of twin domains.

S2. Experimental

Single crystals LuMnO₃ were obtained using a flux method by weighing appropriate amounts of Lu₂O₃ 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 systematic extinctions (h-hl: l ≠ 2n; 00 l: l ≠ 2n). Attempts to fit the intensities with a crystal structure in space group P6₃/mcm, were unsuccessful. Anisotropic displacement parameters and SHELXL97 indicated that the Lu ions should be shifted away from the mirror plane perpendicular to the c axis.

The integrated intensities were measured in 'flat mode' as the absorption is very large. In 'flat mode' every reflection is measured in the orientation that minimizes the path length through the crystal and thus the absorption. The minimum transmission factor is therefore larger than expected from the crystal size.

The structure was solved by using initial co-ordinates which were 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 2.0 (4) e Å^-3 near the Lu position and a hole of 5.7 (4) e Å^-3 also near the Lu position. No other significant peaks having chemical meaning above the general background (0.9 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. Therefore an inversion twin was added to the structure model, similar to the one reported for YMnO₃ (Van Aken et al., 2001a). An initial attempt gave a twin fraction near 50%. We expect a 50%-50% distribution because this yields no net electrical polarization (Rao & Gopalakrishnan, 1997). We fixed the twin fraction at 50%, which had no significant influence on any other parameter.

Computing details

Data collection: CAD4-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 LuMnO3. The top panel shows a view along the basal plane. Lu is represented by shaded spheres, and the MnO5 clusters are represented by trigonal bipyramids. This panel highlights the two-dimensional nature of the structure. The lower panel depicts a view along the c axis of two layers to show the stacking of the bipyramids.
	Fig. 2. Perspective ORTEPII (Johnson, 1976) drawing of all inequivalent atoms. All atoms are represented by atomic displacement ellipsoids drawn to encompass 50% of the electron density.

Lutetium Manganese Oxide

Crystal data

LuMnO3	Unit cell parameters (Duisenberg, 1992. J. Appl. Cryst. 25, 92-96) 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 yield extra symmetry elements (Spek, 1988. J. Appl. Cryst. 21, 578-579; Le Page 1987. J. Appl. Cryst. 20, 264-269; Le Page, Y. 1988. J. Appl. Cryst. 21, 983-984), but they are not compatible with the structure.
Mr = 277.90	Dx = 7.719 Mg m^−3
Hexagonal, P63cm	Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 6c -2	Cell parameters from 22 reflections
a = 6.038 (1) Å	θ = 28.0–28.8°
c = 11.361 (1) Å	µ = 46.03 mm^−1
V = 358.70 (9) Å^3	T = 293 K
Z = 6	Platelet, black
F(000) = 720	0.12 × 0.10 × 0.004 mm

Data collection

Enraf Nonius CAD-4F diffractometer	610 reflections with F > 4σ(F)
Radiation source: fine focus sealed Philips Mo tube	Rint = 0.094
Perpendicular mounted graphite monochromator	θmax = 40.0°, θmin = 3.6°
ω/2θ scans	h = −10→9
Absorption correction: analytical (Meulenaer & Tompa, 1965)	k = 0→10
Tmin = 0.084, Tmax = 0.759	l = −20→20
4711 measured reflections	3 standard reflections every 180 min
833 independent reflections	intensity decay: no decay, variation 2.8%

Refinement

Refinement on F^2	0 constraints
Least-squares matrix: full	w = 1/[σ^2(Fo^2) + (0.0293P)^2] where P = (Fo^2 + 2Fc^2)/3
R[F^2 > 2σ(F^2)] = 0.027	(Δ/σ)max < 0.001
wR(F^2) = 0.065	Δρmax = 2.0 (4) e Å^−3
S = 1.05	Δρmin = −5.6 (4) e Å^−3
833 reflections	Extinction correction: SHELXL97 (Sheldrick, 1997), Fc^*=kFc[1+0.001xFc^2λ^3/sin(2θ)]^-1/4
32 parameters	Extinction coefficient: 0.0024 (2)
1 restraint

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
Lu1	0.00000	0.00000	0.27394 (6)	0.00438 (12)
Lu2	−0.66667	−0.33333	0.23038 (2)	0.00460 (1)
Mn	−0.3355 (10)	−0.3355 (10)	−0.00077 (13)	0.0048 (5)
O1	−0.3070 (18)	−0.3070 (18)	0.1642 (6)	0.0053 (16)
O2	−0.3614 (17)	−0.3614 (17)	−0.1638 (6)	0.0068 (16)
O3	0.00000	0.00000	−0.0285 (12)	0.0034 (19)
O4	−0.66667	−0.33333	0.0190 (9)	0.0077 (19)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Lu1	0.0044 (2)	0.0044 (2)	0.0043 (2)	0.0022 (1)	0.0000	0.0000
Lu2	0.0041 (1)	0.0041 (1)	0.0056 (2)	0.0021 (1)	0.0000	0.0000
Mn	0.0053 (14)	0.0053 (6)	0.0023 (3)	0.0016 (7)	−0.0005	−0.0005 (3)
O1	0.007 (3)	0.007 (3)	0.004 (2)	0.005 (3)	0.0015 (17)	0.0015 (17)
O2	0.006 (3)	0.006 (3)	0.007 (2)	0.002 (3)	−0.0018 (17)	−0.0018 (17)
O3	0.004 (2)	0.004 (2)	0.002 (5)	0.0019 (12)	0.0000	0.0000
O4	0.009 (3)	0.009 (3)	0.005 (4)	0.0045 (14)	0.0000	0.0000

Geometric parameters (Å, º)

Lu1—O1	2.234 (9)	Lu2—O2^vii	2.277 (12)
Lu1—O2^i	2.294 (10)	Lu2—O1^viii	2.227 (15)
Lu1—O3^i	2.244 (14)	Lu2—O2^ix	2.277 (9)
Lu1—O3	3.436 (14)	Lu2—O1^x	2.227 (11)
Lu1—O1^ii	2.234 (12)	Lu2—O2^v	2.277 (10)
Lu1—O2^iii	2.294 (9)	Mn—O1	1.882 (7)
Lu1—O1^iv	2.234 (11)	Mn—O2	1.859 (7)
Lu1—O2^v	2.294 (12)	Mn—O3	2.050 (6)
Lu2—O1	2.227 (12)	Mn—O4	2.019 (7)
Lu2—O4	2.401 (10)	Mn—O4^xi	2.019 (6)
Lu2—O4^vi	3.279 (10)
O1—Lu1—O2^i	77.1 (4)	O1^viii—Lu2—O2^v	76.8 (4)
O1—Lu1—O3^i	123.9 (2)	O1^x—Lu2—O2^ix	77.6 (4)
O1—Lu1—O1^ii	91.9 (4)	O2^ix—Lu2—O2^v	94.7 (3)
O1—Lu1—O2^iii	164.0 (3)	O1^x—Lu2—O2^v	167.8 (3)
O1—Lu1—O1^iv	91.9 (4)	O1—Mn—O2	179.6 (6)
O1—Lu1—O2^v	77.1 (4)	O1—Mn—O3	93.6 (5)
O2^i—Lu1—O3^i	72.04 (18)	O1—Mn—O4	86.2 (5)
O1^ii—Lu1—O2^i	77.1 (5)	O1—Mn—O4^xi	86.2 (5)
O2^i—Lu1—O2^iii	110.9 (4)	O2—Mn—O3	86.0 (5)
O1^iv—Lu1—O2^i	164.0 (3)	O2—Mn—O4	94.0 (5)
O2^i—Lu1—O2^v	110.9 (4)	O2—Mn—O4^xi	94.0 (5)
O1^ii—Lu1—O3^i	123.9 (2)	O3—Mn—O4	120.2 (3)
O2^iii—Lu1—O3^i	72.04 (18)	O3—Mn—O4^xi	120.2 (3)
O1^iv—Lu1—O3^i	123.9 (2)	O4—Mn—O4^xi	119.4 (3)
O2^v—Lu1—O3^i	72.04 (19)	Lu1—O1—Lu2	104.2 (4)
O1^ii—Lu1—O2^iii	77.1 (4)	Lu1—O1—Mn	129.2 (5)
O1^ii—Lu1—O1^iv	91.9 (5)	Lu1—O1—Lu2^xi	104.2 (4)
O1^ii—Lu1—O2^v	164.0 (3)	Lu2—O1—Mn	106.8 (5)
O1^iv—Lu1—O2^iii	77.1 (4)	Lu2—O1—Lu2^xi	103.0 (4)
O2^iii—Lu1—O2^v	110.9 (4)	Lu2^xi—O1—Mn	106.8 (4)
O1^iv—Lu1—O2^v	77.1 (5)	Lu1^xii—O2—Mn	103.1 (4)
O1—Lu2—O4	70.3 (2)	Lu2^xii—O2—Mn	123.9 (5)
O1—Lu2—O2^vii	167.8 (3)	Lu2^xiii—O2—Mn	123.9 (6)
O1—Lu2—O1^viii	109.2 (4)	Lu1^xii—O2—Lu2^xii	100.8 (4)
O1—Lu2—O2^ix	76.8 (3)	Lu1^xii—O2—Lu2^xiii	100.8 (3)
O1—Lu2—O1^x	109.2 (5)	Lu2^xii—O2—Lu2^xiii	99.9 (3)
O1—Lu2—O2^v	77.6 (4)	Lu1^xii—O3—Mn	98.8 (4)
O2^vii—Lu2—O4	121.9 (2)	Mn—O3—Mn^ii	117.7 (3)
O1^viii—Lu2—O4	70.3 (2)	Mn—O3—Mn^iv	117.7 (3)
O2^ix—Lu2—O4	121.87 (19)	Lu1^xii—O3—Mn^ii	98.8 (4)
O1^x—Lu2—O4	70.27 (19)	Lu1^xii—O3—Mn^iv	98.8 (4)
O2^v—Lu2—O4	121.9 (2)	Mn^ii—O3—Mn^iv	117.7 (4)
O1^viii—Lu2—O2^vii	77.6 (4)	Lu2—O4—Mn	96.4 (3)
O2^vii—Lu2—O2^ix	94.7 (3)	Lu2—O4—Mn^viii	96.4 (3)
O1^x—Lu2—O2^vii	76.8 (4)	Lu2—O4—Mn^x	96.4 (3)
O2^vii—Lu2—O2^v	94.7 (3)	Mn—O4—Mn^viii	118.8 (3)
O1^viii—Lu2—O2^ix	167.8 (3)	Mn—O4—Mn^x	118.8 (3)
O1^viii—Lu2—O1^x	109.2 (5)	Mn^viii—O4—Mn^x	118.8 (3)

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