supplementary materials


Acta Cryst. (2013). E69, i19    [ doi:10.1107/S1600536813005497 ]

Redetermination of Nd2Ti2O7: a non-centrosymmetric structure with perovskite-type slabs

N. Ishizawa, K. Ninomiya, T. Sakakura and J. Wang

Abstract top

Single crystals of dineodymium(III) dititanium(IV) heptaoxide, Nd2Ti2O7, were synthesized by the flux method and found to belong to the family of compounds with perovskite-type structural motifs. The asymmetric unit contains four Nd, four Ti and 14 O-atom sites. The perovskite-type slabs are stacked parallel to (010) with a thickness corresponding to four corner-sharing TiO6 octahedra. The Nd and Ti ions are displaced from the geometrical centres of respective coordination polyhedra so that the net polarization occurs along the c axis. The investigated crystals were all twinned and have a halved monoclinic unit cell in comparison with the first structure determination of this compound [Scheunemann & Müller-Buschbaum (1975). J. Inorg. Nucl. Chem. 37, 2261-2263].

Comment top

The structure of Nd2Ti2O7 contains perovskite-type slabs consisting of TiO6 octahedra and Nd ions (Fig. 1 and Fig. 2(a)). The slabs are stacked along b with interconnecting Nd—O bonds. The thickness of the slabs corresponds to four corner-sharing TiO6 octahedra. The TiO6 octahedra have two tilt systems about c and b* which are closely related to the displacements of Nd atoms. The mode of the Nd atom displacements along b* is schematically illustrated by arrows in Fig. 2(a) with respect to the dashed lines drawn parallel to a. The Nd and Ti ions are displaced from the geometrical centres of respective coordination polyhedra so that a net polarization occurs in the crystal. The magnitude of the spontaneous polarization was estimated to be approximately 18 µC cm-2 along the polar c axis assuming formal charges for constituent atoms.

Scheunemann & Müller-Buschbaum (1975) (hereafter abbreviated as SMB) have previously determined the structure of Nd2Ti2O7 based on single-crystal X-ray diffraction data and reported monoclinic symmetry and space group P21 with unit-cell dimensions a = 7.677 Å, b = 26.013 Å, c = 5.465 Å, and γ = 98.4° (the original cell setting in P1211 has been converted to the current setting in P1121 with the c axis unique). The unit cell of the SMB structure (Fig. 2(b)) is doubled along b compared with that of the present study. The SMB structure contains two kinds of perovskite-type slabs with octahedra coloured in green and orange, respectively. The green-coloured slab is essentially the same as that in the present study, which can be understood in terms of the octahedral tilt about b* and the mode of the Nd atom displacements along b* as indicated by arrows. In contrast, the orange-coloured slab in the SMB structure has very small octahedral tilts about b* in combination with negligible Nd atom displacements along b*. The existence of different types of slabs stacked alternately along b justifies the doubled unit cell in the SMB structure. The presence of two modifications (Fig. 2(a) and (b)) at room temperature, having different unit cells with the same space group, leaves room for further investigations on the crystal chemistry of Nd2Ti2O7.

Harvey et al. (2005) (hereafter abbreviated as HWLSR) studied a Nd2(Zr1-xTix)2O7 solid solution and reported a monoclinic modification for the end member Nd2Ti2O7 based on neutron powder data and analyzed by the Rietveld method. The HWLSR structure is plotted in Fig. 2(c). The monoclinic unit cell of the HWLSR structure has similar dimensions to that of SMB. Although no reference is given in their paper to the initial structure model for the Rietveld refinement, it appears possible that the starting SMB model, if used, could easily converge to the HWLSR structure because the symmetry is the same and the parameter shifts are rather small. It is important, however, that the SMB and HWLSR structures are different in that the latter consists of essentially the same green-type slabs. The simulated powder diffraction diagrams of the SMB and HWLSR structures are shown in Fig. 3, indicating a differenece in intensities of reflections at low angles with k = odd. The structure-checking program PLATON (Spek, 2009) actually found additional twofold screw symmetries lying at the boundary of the slabs in the HWLSR structure with atom shifts less than 0.22 Å, hence suggesting a halved monoclinic unit cell as shown in Fig. 2(a).

Diffraction data in the present study were taken using a conventional sealed X-ray tube. Within the limitations of the experiment, we could not find any superstructure reflections that would double the unit cell volume. It should be noted that twinning of the investigated crystal does emerge as extra reflections with h = odd (Fig. 4), and that the reciprocal pattern of the components can be indexed on basis of doubled monoclinic unit cells like those of HWLSR or SMB. However, it is not difficult to distinguish the twinning because the extra extinction condition appears for reflections with h = even and k = odd (Fig. 4). A trial integration was carried out for the present crystal, assuming a doubled monoclinic cell similar like that of SMB or HWLSR, but the mode of Nd atom displacements in the doubled cell was essentially the same as those in Fig. 2(c), and no structure similar to Fig. 2(b) was obtained.

As a conclusion, the HWLSR structure model is supposedly the same as the present one. On the other hand, it seems difficult to discard the possibility of two monoclinic modifications for Nd2Ti2O7 at room temperature as far as the SMB structure exists.

Related literature top

For previous determinations of Nd2Ti2O7, see: Scheunemann & Müller-Buschbaum (1975); Harvey et al. (2005). For related compounds, see: Gasperin (1975); Ishizawa et al. (1980); Schmalle et al. (1993). For the extinction method, see: Becker & Coppens (1974).

Experimental top

Crystals were grown by the flux method using Nd2O3 (Wako Co., 99.9%) and TiO2 (Wako, 99%) as starting materials, and Na2MoO4.2H2O as the flux. A preliminary heat treatment at 1273 K for 12 h was applied to Nd2O3 before weighing. A 15 g mixture containing a 20 mol% solute corresponding to the Nd2Ti2O7 composition was put in a platinum crucible. The platinum crucible was then placed in an alumina crucible with alumina powder and heated in an electric furnace under air atmosphere. The sample was kept at 1373 K for 10 h, and then cooled to 1173 K at the rate of 5 K h-1, with subsequent furnace-cooling by turning off the power. Purple and transparent crystals with approximate dimensions of 200 × 300 × 50 µm3 were obtained after washing the flux component with warm water. Neither the flux component nor other impurities were detected beyond the limit of detection using energy dispersive spectroscopic analysis with a JED-2300 instrument (Jeol Ltd.).

Refinement top

The charge-flipping structure solution program SUPERFLIP (Palatinus & Chapuis, 2007) indicated that the present Nd2Ti2O7 crystals are isostructural with the monoclinic modifications of La2Ti2O7 (Gasperin, 1975) and Ca2Nb2O7 (Ishizawa et al., 1980). Further refinements were thus carried out using the atom positions of monoclinic Ca2Nb2O7 as starting parameters. All the crystals showed twinning where one twin component (m2) is obtained by rotating the other (m1) by 180° about b*. The orientation relationships of the two twin components are illustrated in Fig. 4. The twin scheme is essentially the same as that described for La2Ti2O7 (Schmalle et al., 1993). Since the monoclinic lattice is metrically the sublattice of the pseudo-orthorhombic one in reciprocal space (Fig. 4), all the reflections of the twin components with h = even are almost perfectly overlapped whereas those with h = odd are not overlapped at all. The integration of peak intensities were carried out separately for the lattices of the m1 and m2 components, and an absorption correction was processed by TWINABS (Bruker, 2008). In addition to the above, crystals undergo twinning by merohedry where the spontaneous polarization vectors of the ferroelectric domains are aligned oppositely along c. The refinement was thus carried out assuming four twin components, m1, m2 and their inverted ones, resulting in roughly similar volume fractions of 23 (3)%, 28 (2)%, 22 (1)% and 27 (1) %, respectively. The lowest angle reflections, 010 and its equivalents at θ =1.58°, were removed from the refinement because their intensities were seriously affected by the beamstop. Anisotropic and isotropic atomic displacement parameters were used for the two types of metal and the O atoms, respectively.

Computing details top

Data collection: APEX2 (Bruker, 2008); cell refinement: SAINT (Bruker, 2008); data reduction: SAINT (Bruker, 2008); program(s) used to solve structure: SUPERFLIP (Palatinus & Chapuis, 2007); program(s) used to refine structure: JANA2006 (Petříček et al., 2006); molecular graphics: ATOMS (Dowty, 2006) and DIAMOND (Brandenburg & Putz, 2005); software used to prepare material for publication: PLATON (Spek, 2009) and publCIF (Westrip, 2010).

Figures top
[Figure 1] Fig. 1. View of a part of the Nd2Ti2O7 structure with displacement ellipsoids drawn at the 95% probability level. Symmetry codes are given in the geometric parameters Table.
[Figure 2] Fig. 2. Comparison of the Nd2Ti2O7 structures, (a) present study, (b) Scheunemann & Müller-Buschbaum (1975), (c) Harvey et al. (2005). Unit cells and atomic parameters are shifted for comparison. Two kinds of perovskite-type slabs are illustrated using green- and orange-coloured TiO6 octahedra, respectively. The small black arrows indicate the displacements of Nd atoms (red spheres) along b* with respect to the dashed lines drawn parallel to a.
[Figure 3] Fig. 3. Powder diffraction diagrams of Nd2Ti2O7 calculated from the atomic coordinates given by Scheunemann & Müller-Buschbaum (1975) (top) and Harvey et al. (2005) (bottom). Indices are given for several peaks which characterise the difference between the two structures.
[Figure 4] Fig. 4. Schematic representation of the hk0 reciprocal section of Nd2Ti2O7. The monoclinic twin components, m1 and m2, are represented by black and red colour, respectively. The doubled monoclinic unit cell, S, determined by Scheunemann & Müller-Buschbaum (1975), and Harvey et al. (2005) is given in green colour. The c* axes of all modifications are perpendicular to the paper.
Dineodymium(III) dititanium(IV) heptaoxide top
Crystal data top
Nd2Ti2O7F(000) = 880
Mr = 496.2Dx = 6.110 Mg m3
Monoclinic, P1121Mo Kα radiation, λ = 0.71069 Å
Hall symbol: P 2zcCell parameters from 12720 reflections
a = 7.6747 (1) Åθ = 3.2–40.2°
b = 13.0025 (2) ŵ = 21.77 mm1
c = 5.4640 (1) ÅT = 293 K
β = 90°Block, purple
V = 539.24 (2) Å30.11 × 0.08 × 0.07 mm
Z = 4
Data collection top
Bruker APEXII CCD
diffractometer
6200 reflections with I > 3σ(I)
Radiation source: X-ray tubeRint = 0.049
φ and ω scansθmax = 40.3°, θmin = 1.6°
Absorption correction: multi-scan
(TWINABS; Bruker, 2008)
h = 1313
Tmin = 0.134, Tmax = 0.206k = 2323
25187 measured reflectionsl = 99
6608 independent reflections
Refinement top
Refinement on FWeighting scheme based on measured s.u.'s w = 1/(σ2(F) + 0.0001F2)
R[F2 > 2σ(F2)] = 0.024(Δ/σ)max = 0.016
wR(F2) = 0.027Δρmax = 2.44 e Å3
S = 1.37Δρmin = 1.57 e Å3
6608 reflectionsExtinction correction: B-C type 1 Gaussian isotropic (Becker & Coppens, 1974)
133 parametersExtinction coefficient: 349 (12)
0 restraintsAbsolute structure: Flack (1983), 3019 Friedel pairs
1 constraintFlack parameter: 0.220 (12)
Crystal data top
Nd2Ti2O7V = 539.24 (2) Å3
Mr = 496.2Z = 4
Monoclinic, P1121Mo Kα radiation
a = 7.6747 (1) ŵ = 21.77 mm1
b = 13.0025 (2) ÅT = 293 K
c = 5.4640 (1) Å0.11 × 0.08 × 0.07 mm
β = 90°
Data collection top
Bruker APEXII CCD
diffractometer
6608 independent reflections
Absorption correction: multi-scan
(TWINABS; Bruker, 2008)
6200 reflections with I > 3σ(I)
Tmin = 0.134, Tmax = 0.206Rint = 0.049
25187 measured reflectionsθmax = 40.3°
Refinement top
R[F2 > 2σ(F2)] = 0.0240 restraints
wR(F2) = 0.027Δρmax = 2.44 e Å3
S = 1.37Δρmin = 1.57 e Å3
6608 reflectionsAbsolute structure: Flack (1983), 3019 Friedel pairs
133 parametersFlack parameter: 0.220 (12)
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
Nd10.22817 (5)0.906931 (15)0.75507 (4)0.00599 (5)
Nd20.14522 (4)0.574954 (15)0.34489 (4)0.00563 (5)
Nd30.71953 (5)0.881350 (15)0.74678 (4)0.00533 (5)
Nd40.64866 (4)0.612953 (17)0.28408 (4)0.00796 (5)
Ti10.47020 (19)0.87935 (5)0.25800 (16)0.00463 (15)
Ti20.41480 (19)0.67491 (5)0.78904 (13)0.00476 (16)
Ti30.96662 (19)0.88160 (5)0.25934 (16)0.00437 (15)
Ti40.92426 (19)0.67911 (5)0.78238 (14)0.00521 (16)
O10.5306 (4)0.9810 (2)0.5246 (6)0.0050 (6)*
O20.5001 (5)0.7695 (3)0.4494 (7)0.0081 (6)*
O30.4073 (5)0.5586 (2)0.5773 (6)0.0064 (5)*
O40.2248 (6)0.8923 (2)0.3081 (6)0.0099 (5)*
O50.1746 (6)0.6954 (2)0.6923 (6)0.0072 (5)*
O60.4338 (5)0.8188 (2)0.9387 (6)0.0044 (5)*
O70.3756 (5)0.6078 (3)0.0680 (7)0.0114 (7)*
O80.9591 (5)0.9796 (3)0.5265 (6)0.0079 (6)*
O90.8867 (5)0.7715 (3)0.4553 (7)0.0073 (6)*
O100.8731 (5)0.5702 (2)0.5633 (6)0.0065 (5)*
O110.7275 (6)0.9089 (2)0.1730 (6)0.0062 (5)*
O120.6740 (6)0.6933 (2)0.8421 (6)0.0084 (5)*
O130.9747 (5)0.8155 (2)0.9432 (6)0.0072 (6)*
O140.9226 (5)0.5940 (2)0.0518 (6)0.0063 (6)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
Nd10.00488 (8)0.00601 (7)0.00701 (8)0.00062 (9)0.00008 (13)0.00075 (7)
Nd20.00502 (8)0.00630 (7)0.00558 (8)0.00087 (10)0.00014 (11)0.00051 (6)
Nd30.00446 (8)0.00581 (7)0.00580 (8)0.00100 (9)0.00004 (12)0.00079 (6)
Nd40.00543 (9)0.01077 (8)0.00800 (9)0.00231 (10)0.00042 (12)0.00119 (6)
Ti10.0050 (3)0.0047 (2)0.0043 (2)0.0010 (4)0.0009 (7)0.0001 (2)
Ti20.0042 (3)0.0046 (2)0.0052 (3)0.0002 (3)0.0013 (6)0.00020 (18)
Ti30.0041 (3)0.0049 (2)0.0044 (2)0.0014 (3)0.0011 (7)0.0000 (2)
Ti40.0055 (3)0.0045 (2)0.0056 (3)0.0003 (4)0.0013 (7)0.0005 (2)
Geometric parameters (Å, º) top
Nd1—O12.691 (3)Nd4—O92.710 (3)
Nd1—O1i2.631 (3)Nd4—O102.426 (4)
Nd1—O42.450 (3)Nd4—O12vi2.627 (3)
Nd1—O52.742 (3)Nd4—O142.499 (4)
Nd1—O62.312 (4)Ti1—O11.975 (3)
Nd1—O8ii2.701 (4)Ti1—O1vii2.220 (3)
Nd1—O8i2.659 (4)Ti1—O21.812 (4)
Nd1—O11i2.411 (3)Ti1—O41.935 (5)
Nd1—O13ii2.360 (4)Ti1—O6vi1.917 (3)
Nd2—O32.415 (4)Ti1—O112.010 (4)
Nd2—O52.450 (3)Ti2—O22.269 (4)
Nd2—O72.318 (4)Ti2—O31.898 (3)
Nd2—O10ii2.398 (4)Ti2—O51.973 (4)
Nd2—O10iii2.423 (3)Ti2—O62.028 (3)
Nd2—O14ii2.381 (4)Ti2—O7v1.760 (4)
Nd2—O14iv2.457 (3)Ti2—O121.989 (5)
Nd3—O12.410 (3)Ti3—O4viii1.984 (5)
Nd3—O22.621 (3)Ti3—O81.944 (4)
Nd3—O4i2.931 (3)Ti3—O8ix2.213 (3)
Nd3—O62.458 (4)Ti3—O91.820 (4)
Nd3—O82.401 (3)Ti3—O111.977 (4)
Nd3—O92.601 (4)Ti3—O13vi1.935 (3)
Nd3—O11v2.355 (3)Ti4—O5viii1.964 (4)
Nd3—O122.474 (3)Ti4—O92.196 (4)
Nd3—O132.494 (4)Ti4—O101.851 (3)
Nd4—O22.636 (4)Ti4—O121.984 (5)
Nd4—O32.472 (4)Ti4—O131.965 (3)
Nd4—O3iii2.481 (3)Ti4—O14v1.841 (3)
Nd4—O72.398 (4)
O1—Ti1—O1vii84.56 (13)O4viii—Ti3—O888.84 (15)
O1—Ti1—O293.27 (15)O4viii—Ti3—O8ix83.46 (13)
O1—Ti1—O488.45 (14)O4viii—Ti3—O9101.10 (15)
O1—Ti1—O6vi162.01 (13)O4viii—Ti3—O11164.50 (12)
O1—Ti1—O1185.18 (13)O4viii—Ti3—O13vi93.06 (16)
O1vii—Ti1—O2172.96 (16)O8—Ti3—O8ix85.77 (14)
O1vii—Ti1—O483.65 (13)O8—Ti3—O991.99 (16)
O1vii—Ti1—O6vi78.18 (12)O8—Ti3—O1186.75 (14)
O1vii—Ti1—O1180.38 (13)O8—Ti3—O13vi165.40 (14)
O2—Ti1—O4103.01 (15)O8ix—Ti3—O9174.89 (17)
O2—Ti1—O6vi103.26 (15)O8ix—Ti3—O1181.40 (13)
O2—Ti1—O1192.78 (15)O8ix—Ti3—O13vi80.08 (13)
O4—Ti1—O6vi94.59 (16)O9—Ti3—O1193.89 (15)
O4—Ti1—O11163.29 (13)O9—Ti3—O13vi101.82 (15)
O6vi—Ti1—O1186.97 (15)O11—Ti3—O13vi87.61 (16)
O2—Ti2—O384.58 (13)O5viii—Ti4—O986.72 (14)
O2—Ti2—O584.71 (13)O5viii—Ti4—O1090.78 (16)
O2—Ti2—O681.60 (13)O5viii—Ti4—O12167.53 (13)
O2—Ti2—O7v172.61 (17)O5viii—Ti4—O1387.47 (15)
O2—Ti2—O1281.44 (14)O5viii—Ti4—O14v100.64 (16)
O3—Ti2—O591.46 (16)O9—Ti4—O1082.06 (14)
O3—Ti2—O6166.09 (13)O9—Ti4—O1282.86 (14)
O3—Ti2—O7v98.63 (15)O9—Ti4—O1383.96 (14)
O3—Ti2—O1295.54 (16)O9—Ti4—O14v171.88 (16)
O5—Ti2—O685.68 (14)O10—Ti4—O1294.53 (16)
O5—Ti2—O7v101.79 (17)O10—Ti4—O13165.99 (15)
O5—Ti2—O12163.81 (12)O10—Ti4—O14v94.32 (14)
O6—Ti2—O7v95.28 (15)O12—Ti4—O1384.64 (15)
O6—Ti2—O1284.04 (14)O12—Ti4—O14v90.22 (16)
O7v—Ti2—O1291.59 (17)O13—Ti4—O14v99.66 (14)
Symmetry codes: (i) x+1, y+2, z+1/2; (ii) x1, y, z; (iii) x+1, y+1, z1/2; (iv) x+1, y+1, z+1/2; (v) x, y, z+1; (vi) x, y, z1; (vii) x+1, y+2, z1/2; (viii) x+1, y, z; (ix) x+2, y+2, z1/2.
Acknowledgements top

This work was supported by JSPS KAKENHI grant No. 22360272.

references
References top

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