PbZn_1/3Nb_2/3O₃ at 4.2 and 295 K

The structure of the relaxor ferroelectric lead zinc niobium trioxide, Pb(Zn_1/3Nb_2/3)O₃, known as PZN, was determined at 4.2 and 295 K from very high resolution neutron powder diffraction data. The material is known for its extraordinary piezoelectric properties which are closely linked to the structure. Pseudo-cubic lattice parameters have led to considerable controversy over the symmetry of the structure, which was found to be rhombohedral in the space group R3m at both temperatures. Atomic coordinates have been determined for the first time. They show that, whereas the deviation of the rhombohedral angle from 90° approaches zero at 295 K, the atomic coordinates do not approach typical cubic positions and hence the polarization remains high.

Comment

Recently, the crystal structures of the perovskite relaxor ferroelectric Pb(Zn_1/3Nb_2/3)O₃ (lead zinc niobate or PZN) and its alloys with PbTiO₃ (PZN-xPT) have been widely debated in relation to the exceptional piezoelectric properties of these materials (e.g. Park & Shrout, 1997). A curious aspect of the crystal structure–property relationship in these materials is that the maximum piezoelectric response is along [001], whereas the spontaneous polarization is along [111] of the nominally rhombohedral crystals. Single-domain single crystals are not available and so previous work has relied on synchrotron X-ray (Noheda et al., 2001; Noheda, Cox & Shirane, 2002; Cox et al., 2001) and neutron diffraction (Ohwada et al., 2001) reciprocal-space scans around a limited number of reflections from polydomain single crystals, and on X-ray powder diffraction (Ohwada et al., 2001; Noheda, Zhong et al., 2002; La-Orauttapong et al., 2002). All of the previous experimental studies have dealt only with the lattice symmetry, due to a focus of the work on the polarization rotation hypothesis for the large piezoelectric response (Fu & Cohen, 2000). The materials are pseudo-cubic, making the determination of the true symmetry extremely difficult, even with three-axis diffractometers (Noheda, Zhong et al., 2002). Park & Shrout (1997) first suggested that an electric field-induced phase transition occurred during piezoelectric cycling of PZN-8%PT and that this facilitates the large piezoelectric response. This was rapidly supported by X-ray diffraction studies (Paik et al., 1999; Durbin et al., 1999). The observed symmetry was pseudo-tetra­gonal. However, Durbin et al. (1999) noted that the true symmetry was more likely to be monoclinic. Noheda et al. (2001) also concluded that a field-induced transition was responsible and proposed that the monoclinic space group is Pm. The same or a very similar mechanism has been proposed for all PZN-xPT crystals in the range 0 < x < 9%.

The counterpoint has come from Kisi et al. (2003) who argued, on group theoretical and physical property grounds, that the large response is more likely to be founded on the very soft elastic constants of the materials than on the lattice symmetry. The observed monoclinic symmetry under an electric field directed along [001] is exactly as expected for the conventional piezoelectric distortion of a rhombohedral crystal. However, this does not constitute a phase transition, nor does it explain the large piezoelectric response. An understanding of the connection between the crystal structure and the piezoelectric properties can only be derived from measured ion coordinates. These can then be used to compute the electric polarization by methods such as that given by Darlington et al. (1994).

This paper reports the full crystal structure of the end member, PZN, for the first time. The use of very high resolution neutron diffraction ensures both that the O-ion positions are reliably determined in the presence of far heavier elements such as Pb, and that the problem of pseudo-symmetry is minimized. Data at both 4.2 and 295 K were used to enhance the discrimination between different structural models. Visual inspection of the 111, 200 and 222 reflections in the high-resolution neutron diffraction patterns supported the conventional rhombohedral symmetry. The 111 and 222 reflections are split approximately in the ratio 3:1 and 200 remains unsplit. This aspect has been discussed by Kisi et al. (2005) in relation to reports of a cubic `X-phase' in this system. Rietveld refinements were initially conducted using the 4.2 K data, due to the larger rhombohedral distortion at this temperature. Refinements in the space group R3m, illustrated in Fig. 1(a), gave reasonable agreement. The major misfit is due to slightly anisotropic reflection widths, in which 200 is broader than 111 by ≃ 0.2 times the full width at half-maximum. Geometrically, it is possible for a monoclinic distortion both to split the 111 reflection (β > 90°) and to broaden 200 (a ≠ b ≠ c) if a, b and c are sufficiently similar. Given that monoclinic phases have been reported in this material, refinements were attempted in all of the monoclinic space groups recently proposed [Cm, Cc (Ic) and Pm], with unsatisfactory results. No improvement in the agreement was observed even when a considerable number of extra parameters were added to the refinement. The best fit, shown in Fig. 1(b), used the monoclinic structure in Cm (Frantti et al., 2003). Octa­hedral rotation in combination with ferroelectric cation displacements was ruled out by the absence of R-point (e.g. R3c) or M-point (e.g. Cc) superlattice reflections. This was confirmed by Rietveld refinement, which converged to unrotated octa­hedral positions regardless of the initial conditions. A two-phase mixture of rhombohedral (R3m) and tetra­gonal (P4mm) structures was also tested for completeness. The final refinements were undertaken in R3m using the anisotropic broadening model of Stephens (1999), as implemented in GSAS (Larson & Von Dreele, 1986), to model the effect of inter­domain strains due to the microscopic ferroelectric domain structure within the crystallites. Only one additional parameter, S400, was required. The final fit is illustrated in Fig. 1(c). A projection of the structure at 4.2 K perpendicular to the polar axis, [111], is illustrated in Fig. 2(a) and an equivalent view of the undistorted cubic structure is shown in Fig. 2(b). The Pb atoms are aligned, illustrating the large relative displacement of the Zn/Nb and O ions.

Structure refinements using the 295 K data were undertaken using the 4.2 K structure as a starting point. The refined structure at 295 K is the same as that at 4.2 K, with slightly reduced rhombohedral distortion and cation displacements. The departure of the rhombohedral angle from 90° diminishes with increasing temperature as the transition to cubic at approximately 400 K is approached. However, the atom coordinates remain relatively unchanged. Similar behaviour has been observed as phase transitions are approached in some other ferroelectrics, such as BaTiO₃ (Darlington et al., 1994). This is somewhat contrary to the widely held notion that the ferroelectric distortion controls the crystal structure at all levels, i.e. that the lattice distortion should always scale with the ion positions and electric polarization. PZN has an extremely small distortion from cubic and yet has a large polarization, in contrast with, say, PbTiO₃, which has a large spontaneous strain but considerably smaller polarization. These observations indicate that, in ferroelectric materials, the relationship between the lattice parameters and atomic coordinates (and hence electric polarization) is more complex than in the non-ferroelectric perovskites.

Figure 1 Results of Rietveld refinements using the 4.2 K data in the range 1–2.4 Å for models in (a) space group R3m without anisotropic broadening correction, (b) space group Cm and (c) space group R3m with the anisotropic broadening parameter S400 refined. Data are given as +, the calculated profile as a solid line and the difference profile as a solid line below. Vertical markers above the difference profile indicate the calculated Bragg reflection positions. Data in the range 2–2.4 Å are plotted according to the right-hand scale. Insets show details of the fit to the important 400 and 222 reflections.

Figure 2 Views of (a) the 4.2 K structure and (b) the undistorted cubic structure, both projected perpendicular to the polar axis, [111].

Experimental

The flux growth method of Mulvihill et al. (1996) was used to grow single crystals of composition Pb(Zn_1/3Nb_2/3)O₃. Crystals in the size range 0.5–15 mm were extracted from the flux in a hot HNO₃ solution. The chemical composition of the crystals and their homogeneity were verified using scanning electron microscopy-based energy dispersive spectroscopy (EDS) analysis. Using an agate pestle and mortar, crystals were lightly crushed to a size that passed through a coarse sieve (143 µm), so as to avoid strain and particle-size broadening. Good powder averaging was obtained using approximately 2 ml of powder sample.

Neutron powder diffraction patterns were recorded in transmission on the HRPD diffractometer (resolution Δd/d ≃ 4 × 10⁻⁴) at the ISIS facility, Rutherford Appleton Laboratory, England. Samples were held in a thin-walled aluminium can within a liquid helium cryostat. Diffraction patterns were recorded from 30 to 130 ms at room temperature and at 4.2 K for 20 and 90 min, respectively.

PZN at 4.2 K

Crystal data

• PbZn_1/3Nb_2/3O₃

• M_r = 337.40

• Trigonal, R 3m

• a = 4.06048 (6) Å

• α = 89.8693 (4)°

• V = 66.95 (1) ų

• Z = 1

• D_x = 8.367 Mg m⁻³

• Time-of-flight neutron radiation

• λ = 0.65–2.45 Å

• T = 4.2 K

• Specimen shape: powder

• Specimen prepared at 101.3 kPa

• Specimen prepared by cooling from 1473 to 1173 K at 1 K min⁻¹ and at 50 K min⁻¹ thereafter

• Particle morphology: <143 μm particles, pale yellow

Data collection

• HRPD beamline, ISIS, Didcot

• Specimen mounting: 11 mm aluminium slab can

• Scan method: time-of-flight

Refinement

• R_p = 0.062

• R_wp = 0.074

• R_exp = 0.040

• S = 2.48

• Wavelength of incident radiation: 0.65–2.45 Å

• Excluded region(s): none

• Profile function: pseudo-Voight convoluted with double exponential incorportating the anisotropic microstrain broadening model of Stephens (1999)

• 34 parameters

• (Δ/σ)_max = 0.01

• Preferred orientation correction: none

PZN at 295 K

Crystal data

• PbZn_1/3Nb_2/3O₃

• M_r = 338.93

• Trigonal, R 3m

• a = 4.06240 (8) Å

• α = 89.8693 (4)°

• V = 67.04 (1) ų

• Z = 1

• D_x = 8.396 Mg m⁻³

• Time-of-flight neutron radiation

• λ = 0.65–2.45 Å

• T = 295 K

• Specimen shape: powder

• Specimen prepared at 101.3 kPa

• Specimen prepared at 101.3 kPa

• Specimen prepared by cooling from 1473 to 1173 K at 1 K min⁻¹ and at 50 K min⁻¹ thereafter

• Particle morphology: <143 μm particles, pale yellow

Data collection

• HRPD beamline, ISIS, Didcot

• Specimen mounting: 11 mm aluminium slab can

• Specimen mounted in transmission mode

• Scan method: time-of-flight

Refinement

• R_p = 0.075

• R_wp = 0.088

• R_exp = 0.080

• S = 1.49

• Wavelength of incident radiation: 0.65–2.45 Å

• Excluded region(s): none

• Profile function: pseudo-Voight convoluted with double exponential incorportating the anisotropic microstrain broadening model of Stephens (1999)

• 37 parameters

• (Δ/σ)_max = 0.03

• Preferred orientation correction: none

Rietveld analyses used the program GSAS (Larson & Von Dreele, 1986). Data from the small crystal sample recorded by both the high-resolution backscattering bank and the high-intensity 90° detector bank were used simultaneously. Typically, lattice parameters, atom coordinates (Zn/Nb, O), isotropic displacement parameters (Zn/Nb), anisotropic displacement parameters (Pb, O), scale, eight polynomial background parameters and two peak profile parameters were used. The 4.2 K data were used to refine the Zn/Nb ratio of the B cation site and this ratio was held constant during refinements based on the 295 K data. In addition, the anisotropic peak-broadening model of Stephens (1999) was applied.

For both compounds, data collection: ISIS software (local programs); program(s) used to refine structure: GSAS (Larson & Von Dreele, 1986); molecular graphics: CaRine Crystallography (Bondias & Monceau, 2005) and GRAPHER (Golden Software, 2005); software used to prepare material for publication: GSAS.

Supporting information

S1. Comment

Recently, the crystal structures of the perovskite relaxor ferroelectric Pb(Zn_1/3Nb_2/3)O₃ (lead zinc niobate or PZN) and its alloys with PbTiO₃ (PZN-xPT) have been widely debated in relation to the exceptional piezoelectric properties of these materials (e.g. Park & Shrout, 1997). A curious aspect of the crystal structure–property relationship in these materials is that the maximum piezoelectric response is along [001], whereas the spontaneous polarization is along [111] of the nominally rhombohedral crystals. Single-domain single crystals are not available and so previous work has relied on synchrotron X-ray (Noheda et al., 2001; Noheda, Cox & Shirane, 2002; Cox et al., 2001) and neutron diffraction (Ohwada et al., 2001) reciprocal-space scans around a limited number of reflections from poly domain single crystals, and on X-ray powder diffraction (Ohwada et al., 2001; Noheda, Zhong et al., 2002; La-Orauttapong et al., 2002). All of the previous experimental studies have dealt only with the lattice symmetry, due to a focus of the work on the polarization rotation hypothesis for the large piezoelectric response (Fu & Cohen, 2000). The materials are pseudo-cubic, making the determination of the true symmetry extremely difficult, even with three-axis diffractometers (Noheda, Zhong et al., 2002). Park & Shrout (1997) first suggested that an electric field-induced phase transition occurred during piezoelectric cycling of PZN-8%PT and that this facilitates the large piezoelectric response. This was rapidly supported by X-ray diffraction studies (Paik et al., 1999; Durbin et al., 1999). The observed symmetry was pseudo-tetragonal. However, Durbin et al. (1999) noted that the true symmetry was more likely to be monoclinic. Noheda et al. (2001) also concluded that a field-induced transition was responsible and proposed that the monoclinic space group is Pm. The same or a very similar mechanism has been proposed for all PZN-xPT crystals in the range 0 < x < 9%.

The counterpoint has come from Kisi et al. (2003) who argued, on group theoretical and physical property grounds, that the large response is more likely to be founded on the very soft elastic constants of the materials than on the lattice symmetry. The observed monoclinic symmetry under an electric field directed along [001] is exactly as expected for the conventional piezoelectric distortion of a rhombohedral crystal. However, this does not constitute a phase transition, nor does it explain the large piezoelectric response. An understanding of the connection between the crystal structure and the piezoelectric properties can only be derived from measured ion coordinates. These can then be used to compute the electric polarization by methods such as that given by Darlington et al. (1994).

This paper reports the full crystal structure of the end member, PZN, for the first time. The use of very high resolution neutron diffraction ensures both that the O ion positions are reliably determined in the presence of far heavier elements such as Pb, and that the problem of pseudo-symmetry is minimized. Data at both 4.2 K and 295 K were used to enhance the discrimination between different structural models. Visual inspection of the 111, 200 and 222 reflections in the high-resolution neutron diffraction patterns supported the conventional rhombohedral symmetry. The 111 and 222 reflections are split approximately in the ratio 3:1 and 200 remains un-split. This aspect has been discussed by Kisi et al. (2005) in relation to reports of a cubic `X-phase' in this system. Rietveld refinements were initially conducted using the 4.2 K data, due to the larger rhombohedral distortion at this temperature. Refinements in space group R3m, illustrated in Fig. 1(a), gave reasonable agreement. The major misfit is due to slightly anisotropic reflection widths, in which 200 is broader than 111 by ≈ 0.2 times the full width at half-maximum. Geometrically, it is possible for a monoclinic distortion both to split the 111 reflection (β > 90°) and to broaden 200 (a ≠ b ≠ c) if a, b and c are sufficiently similar. Given that monoclinic phases have been reported in this material, refinements were attempted in all of the monoclinic space groups recently proposed [Cm, Cc (Ic) and Pm], with unsatisfactory results. No improvement in the agreement was observed even when a considerable number of extra parameters were added to the refinement. The best fit, shown in Fig. 1(b), used the monoclinic structure in Cm (Frantti et al., 2003). Octahedral rotation in combination with ferroelectric cation displacements was ruled out by the absence of R-point (e.g. R3c) or M-point (e.g. Cc) superlattice reflections. This was confirmed by Rietveld refinement, which converged to un-rotated octahedral positions regardless of the initial conditions. A two-phase mixture of rhombohedral (R3m) and tetragonal (P4 mm) structures was also tested for completeness. The final refinements were undertaken in R3m using the anisotropic broadening model of Stephens (1999), as implemented in GSAS (Larson & Von Dreele, 1986), to model the effect of interdomain strains due to the microscopic ferroelectric domain structure within the crystallites. Only one additional parameter, S400, was required. The final fit is illustrated in Fig. 1(c). A projection of the structure at 4.2 K perpendicular to the polar axis, [111], is illustrated in Fig. 2(a) and an equivalent view of the undistorted cubic structure is shown in Fig. 2(b). The Pb atoms are aligned, illustrating the large relative displacement of the Zn/Nb and O ions.

Structure refinements using the 295 K data were undertaken using the 4.2 K structure as a starting point. The refined structure at 295 K is the same as that at 4.2 K, with slightly reduced rhombohedral distortion and cation displacements. The departure of the rhombohedral angle from 90° diminishes with increasing temperature as the transition to cubic at approximately 400 K is approached. However, the atom coordinates remain relatively unchanged. Similar behaviour has been observed as phase transitions are approached in some other ferroelectrics, such as BaTiO₃ (Darlington et al., 1994). This is somewhat contrary to the widely held notion that the ferroelectric distortion controls the crystal structure at all levels, i.e. that the lattice distortion should always scale with the ion positions and electric polarization. PZN has an extremely small distortion from cubic and yet has a large polarization, in contrast with, say, PbTiO₃, which has a large spontaneous strain but considerably smaller polarization. These observations indicate that, in ferroelectric materials, the relationship between the lattice parameters and atom coordinates (and hence electric polarization) is more complex than in the non-ferroelectric perovskites.

S2. Experimental

The flux growth method of Mulvihill et al. (1996) was used to grow single crystals of composition Pb(Zn_1/3Nb_2/3)O₃. Crystals in the size range 0.5–15 mm were extracted from the flux in a hot HNO₃ solution. The chemical composition of the crystals and their homogeneity were verified using scanning electron microscopy-based EDS [Please give in full] analysis. Using an agate pestle and mortar, crystals were lightly crushed to a size that passed through a coarse sieve (143 µm), so as to avoid strain and particle-size broadening. Good powder averaging was obtained using ≈ 2 ml of powder sample.

Neutron powder diffraction patterns were recorded in transmission on the HRPD diffractometer (resolution Δd/d ≈ 4 × 10⁻⁴) at the ISIS facility, Rutherford Appleton Laboratory, UK. Samples were held in a thin-walled aluminium can within a liquid helium cryostat. Diffraction patterns were recorded from 30 to 130 ms at room temperature and at 4.2 K for 20 min and 90 min, respectively.

S3. Refinement

Rietveld analyses used the program GSAS (Larson & Von Dreele, 1986). Data from the small crystal sample recorded by both the high-resolution backscattering bank and the high-intensity 90° detector bank were used simultaneously. Typically, lattice parameters, atom coordinates (Zn/Nb, O), isotropic displacement parameters (Zn/Nb), anisotropic displacement parameters (Pb, O), scale, eight polynomial background parameters and two peak profile parameters were used. The 4.2 K data were used to refine the Zn/Nb ratio of the B cation site and this ratio was held constant during refinements based on the 295 K data. In addition, the anisotropic peak-broadening model of Stephens (1999) was applied.

Computing details

For both compounds, program(s) used to refine structure: GSAS.

Figures

Fig. 1. Results of Rietveld refinements using the 4.2 K data in the range 1–2.4 Å for models in (a) space group R3m without anisotropic broadening correction, (b) space group Cm and (c) space group R3m with the anisotropic broadening parameter S400 refined. Data are given as +, the calculated profile as a solid line and the difference profile as a solid line below. Vertical markers above the difference profile indicate the calculated Bragg reflection positions. Data in the range 2–2.4 Å are plotted according to the right-hand scale. Insets show details of the fit to the important 400 and 222 reflections.

Fig. 2. Views of (a) the 4.2 K structure and (b) the undistorted cubic structure, both projected perpendicular to the polar axis [111].

(PZN4K) lead zinc niobium trioxide

Crystal data

Nb0.61O3PbZn0.39	Dx = 8.367 Mg m^−3
Mr = 337.40	Time-of-flight neutron radiation
Trigonal, R3m	T = 4 K
a = 4.06048 (6) Å	Particle morphology: <143 µm particles
c = 4.06048 Å	pale yellow
V = 66.95 (1) Å^3	?, ? × ? × ? mm
Z = 1

Data collection

HRPD, ISIS, Didcot diffractometer	Scan method: time of flight
Radiation source: ISIS, Spallation	2θfixed = 168.33
Specimen mounting: 11mm Al slab can	Distance from specimen to detector: 1000 mm
Data collection mode: transmission

Refinement

Least-squares matrix: full	Excluded region(s): no excluded regions
Rp = 0.062	34 parameters
Rwp = 0.074	0 restraints
Rexp = ?	Weighting scheme based on measured s.u.'s
R(F^2) = 0.06901	(Δ/σ)max = 0.01
χ^2 = 6.150	Background function: GSAS Background function number 1 with 12 terms. Shifted Chebyshev function of 1st kind 1: 0.439789 2: 2.990220E-03 3: 4.821580E-02 4: 1.914300E-02 5: 3.191740E-02 6: 3.362380E-02 7: 1.183440E-02 8: 7.640780E-03 9: 1.057330E-0210: 2.050820E-0211: -4.850290E-0312: 1.058700E-02
? data points

Special details

Experimental. resolution Δd/d ≈4x10_-4 Diffraction patterns recorded from 30 to 130 ms

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pb1	0.5	0.5	0.5	0.04227
Zn1	0.0258 (3)	0.0258 (3)	0.0258 (3)	0.0142 (3)*	0.389
Nb1	0.0258 (3)	0.0258 (3)	0.0258 (3)	0.0142 (3)*	0.611
O1	0.5438 (5)	0.0547 (4)	0.0547 (4)	0.02313

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb1	0.0423 (5)	0.0423 (5)	0.0423 (5)	−0.0146 (5)	−0.0146 (5)	−0.0146 (5)
O1	0.0239 (8)	0.0227 (5)	0.0227 (5)	0.0004 (6)	0.0004 (6)	−0.0045 (8)

Geometric parameters (Å, º)

Pb1—Nb1	3.343 (2)	Pb1—O1^i	2.8907 (3)
Pb1—Nb1^i	3.4572 (6)	Nb1—O1^iii	1.964 (2)
Pb1—Nb1^ii	3.5787 (7)	Nb1—O1	2.110 (3)
Pb1—O1	2.565 (2)
O1—Pb1—O1^iv	66.28 (7)	O1—Nb1—O1^iv	83.3 (1)
O1^iii—Nb1—O1	170.6 (2)	Pb1—O1—Nb1	90.73 (7)
O1^iii—Nb1—O1^v	96.5 (1)	Pb1—O1—Nb1^vi	98.7 (1)
O1^iii—Nb1—O1^iv	89.70 (2)	Nb1—O1—Nb1^vi	170.6 (2)

Symmetry codes: (i) x, y, z+1; (ii) x, y+1, z+1; (iii) x−1, y, z; (iv) z, x, y; (v) z, x−1, y; (vi) x+1, y, z.

(295K)

Crystal data

Nb0.61O3PbZn0.39	Z = 1
Mr = 338.93	Dx = 8.396 Mg m^−3
Trigonal, R3m	Time-of-flight neutron radiation, λ = 0.65-2.45 Å
a = 4.06240 (8) Å	T = 295 K
c = 4.0624 Å	pale yellow
V = 67.04 (1) Å^3	?, ? × ? × ? mm

Data collection

HRPD beamline, ISIS, Didcot diffractometer

Refinement

Least-squares matrix: full	? data points
Rp = 0.075	37 parameters
Rwp = 0.088	0 restraints
Rexp = ?	(Δ/σ)max = 0.03
R(F^2) = 0.08346	Background function: GSAS Background function number 1 with 12 terms. Shifted Chebyshev function of 1st kind 1: 0.236557 2: 9.505910E-03 3: 2.018040E-02 4: 6.956430E-03 5: 8.509230E-03 6: 1.341600E-02 7: 3.919290E-03 8: 2.020580E-03 9: 5.622050E-0410: 8.049800E-0311: -3.196390E-0312: 3.955620E-03; GSAS Background function number 4 with 4 terms. Power series in Q**2n/n! 1: 0.441369 2: -1.651550E-03 3: 4.525360E-05 4: 2.316550E-05
χ^2 = 2.220

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq	Occ. (<1)
Pb1	0.5	0.5	0.5	0.0494
Zn1	0.0216 (5)	0.0216 (5)	0.0216 (5)	0.0167 (5)*	0.39
Nb1	0.0216 (5)	0.0216 (5)	0.0216 (5)	0.0167 (5)*	0.61
O1	0.5377 (7)	0.0469 (6)	0.0469 (6)	0.0269

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Pb1	0.0495 (8)	0.0495 (8)	0.0495 (8)	−0.012 (1)	−0.012 (1)	−0.012 (1)
O1	0.023 (1)	0.0288 (7)	0.0288 (7)	−0.0013 (9)	−0.0013 (9)	−0.005 (1)

Geometric parameters (Å, º)

Pb1—Nb1	3.362 (3)	Pb1—O1^i	2.8868 (4)
Pb1—Nb1^i	3.466 (1)	Nb1—O1^iii	1.977 (4)
Pb1—Nb1^ii	3.574 (1)	Nb1—O1	2.094 (4)
Pb1—O1	2.614 (3)
O1—Pb1—O1^iv	65.3 (1)	O1—Nb1—O1^iv	84.6 (2)
O1^iii—Nb1—O1	172.5 (3)	Pb1—O1—Nb1	90.5 (1)
O1^iii—Nb1—O1^v	95.3 (2)	Pb1—O1—Nb1^vi	97.1 (2)
O1^iii—Nb1—O1^iv	89.80 (2)	Nb1—O1—Nb1^vi	172.5 (3)

Symmetry codes: (i) x, y, z+1; (ii) x, y+1, z+1; (iii) x−1, y, z; (iv) z, x, y; (v) z, x−1, y; (vi) x+1, y, z.