Supporting information
Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270107050640/sq3101sup1.cif | |
Structure factor file (CIF format) https://doi.org/10.1107/S0108270107050640/sq3101Isup2.hkl |
Single crystals of PZN-8%PT were grown in a PbO flux using a ratio of 35% PZN-8%PT to 65% flux. Powders were placed in a platinum crucible and held at 1473 K for 2 h. The sample was cooled at approximately 1 K h-1 down to 1173 K and then at 50 K h-1 down to room temperature. Crystals were extracted using a hot HNO3 solution, lightly crushed and passed through a 143 µm sieve. Approximately 2 cm3 of the coarse powder was loaded into a thin-walled aluminium can for data collection on the HRPD diffractometer (resolution Δd/d ≈ 4 × 10-4) at the ISIS facility, Rutherford Appleton Laboratory, Didcot, UK. The sample was cooled in a liquid helium cryostat to 4 K. After equilibrating at this temperature, diffraction data were recorded from 30 to 120 ms for 90 min.
Rietveld analyses used the program GSAS (Larson & Von Dreele, 1994). Only the data from the high-resolution backscattering bank were used in the refinement. Typically, lattice parameters, atom coordinates (Zn/Nb/Ti, O), isotropic displacement parameters, scale, four polynomial background parameters and two isotropic peak profile parameters were refined. The anisotropic peak-broadening model of Stephens (1999) was necessary to obtain acceptable fits in any space group. Further details of the refinement are given in the following section.
As the crystal structures in the PZN-PT system are pseudo-cubic, it is not possible to use single-peak or even peak deconvolution techniques to assess their symmetry. Instead, the structure of PZN-8%PT was assessed through a long series of Rietveld refinements. A group theoretical analysis by Forrester et al. (2001) has given the potential space groups and their relationships in the absence of octahedral tilting, as reproduced in Fig. 1. Space groups resulting from coupling of octahedral tilting with the ferroelectric distortion have been determined by Stokes et al. (2002), but were not considered here as no superlattice peaks due to octahedral tilting were detected. Within Fig. 1, only P1 has not been proposed as the space group of the MPB phase(s) in PZN-PT. The refinements were therefore conducted in all the space groups in the diagram except P1 and the parent cubic structure, Pm3m. Each of the refinements was given equal opportunity to fit, refining the same set of parameters in as many sensible ways as possible from numerous starting positions. The refined lattice parameters, atomic coordinates and isotropic displacement parameters are available in the supplementary materials.
In examining the output of the Rietveld refinements, the usual statistical measures were found to be not sensitive enough to discriminate between some closely competing models. Instead, certain diagnostic peaks (reflections) were found to discriminate well between the models when consulted in sufficient detail. In particular, the 200 peak is so oddly shaped that it was found that particular attention to the peak-shape parameters was required in order to obtain a fit to that part of the pattern. This and the other diagnostic peaks from each of the refinements are shown in Fig. 2. It is probably no accident that the most useful diagnostic peaks (200, 220 and 222) occur when the scattering vector is perpendicular to the three principal directions in the Devonshire expansion of the free energy of a ferroelectric (Devonshire, 1949, 1951). The refinement results are now discussed in turn, beginning with the simplest and ending with the most probable solution.
R3m (Fig. 2a). The phase diagram of Kuwata et al. (1981) suggests that the rhombohedral ferroelectric phase extends beyond 8%PT at cryogenic temperatures. Combined with our observations of a rhombohedral ground state in PZN and PZN-4.5%PT (Kisi et al., 2005; Forrester et al., 2006), this was the logical starting point. Although superficially the fit of the overall pattern to R3m looks good (e.g. on the same scale as Fig. 3), there are areas of significant misfit that could not be corrected. This is most easily observable in the 200 and 222 peaks, but is present in all of the diffraction peaks to some degree. The 200 peak in Fig. 2(a) clearly has a second peak on the low-d side, and therefore a two-phase refinement was the logical progression.
R3m+P4mm c > a (Fig. 2b). In the older literature, this two-phase mixture was the accepted state of samples in the MPB region of PZT ceramics. It is also a logical structure in PZN-8%PT (i.e. at the MPB) between the R region at <8%PT and the T region at >9%PT, according to older literature (e.g. Kuwata et al., 1981). The Rietveld refinement is again superficially reasonable on the scale of Fig. 3 (73%R3m + 27%P4mm). The lattice parameters and peak-width parameters can be manipulated to make the 200 peak fit very well. However, the lattice parameters of the R and T phases cannot be fitted to both the h00 and hhh peaks concurrently. If the 200 peak is forced to fit, then hhh moves outside the low-d side of the experimental peak envelope. The fit shown in Fig. 2(b) is the `average' fit obtained by free refinement of the lattice parameters. The fit is worse than for the single-phase rhombohedral model. The only way to model the 200 peak correctly and force the calculated 222 position to lie within the observed {222} envelope was to set the a and c lattice parameters of the T phase such that c < a, which became the next model.
R3m+P4mm c < a (Fig. 2c). Although a tetragonal ferroelectric with a > c is a physically unreasonable structure, as an exercise in data analysis this refinement converged to a much improved fit compared with the previous two. The refined phase proportions are 72%R3m + 28%P4mm. Although the fit has greatly improved, there is a slight misfit in the very top of the 200 peak and at the high-d side of the 220 peak, which could not be corrected with additional parameters or damped refinements. Analysis of the possible phases (Fig. 1) indicates that a pseudo-tetragonal phase with c < a would be orthorhombic in space group Amm2.
R3m+Amm2 (Fig. 2d). The fit to the 200 and 222 peaks here is nearly identical to the previous fit, as are the refined phase proportions (84%R3m + 16%Amm2) if corrected for cell doubling in the orthorhombic structure. The 220 peak is improved by the additional degrees of freedom given in the orthorhombic space group. Nonetheless, the misfits at the 200 and 222 peaks remain. Although they may seem minor, in this system where little separates the correct from the incorrect this solution must be rejected.
When fully orthorhombic or monoclinic solutions were initially attempted, satisfactory fits could not be obtained. In general, agreement was worse than for R3m+P4mm with a < c (Fig. 2b). Later trials revealed that this was due to a too-conservative application of the anisotropic broadening correction (Stephens, 1999), comprising just two or three of the available anisotropic broadening parameters (six for orthorhombic and nine for monoclinic). Once the full broadening parameter set was released, coupled with the structural parameters, quite reasonable and potentially convincing fits were obtained in the three space groups, Amm2, Pm and Cm, associated with the polarization rotation theory and prior synchrotron studies (Noheda et al., 2001; Vanderbilt & Cohen, 2001).
Amm2 (Fig. 2e). The fit in Amm2 is of the same overall quality as the fit in the R3m+Amm2 model but with many fewer parameters. Improved agreement is observed for the 200 and 222 peaks. However, the 220 peak does not fit well.
Pm (Fig. 2f). The refinements here produced inferior agreement with the data, which is easily visible in the 220 and 222 peaks.
Cm (Fig. 2g). The figure clearly shows that the space group Cm produces a superior fit compared with any of the other options. For completeness, two-phase refinements were attempted using Cm+R3m and Cm+P4mm, with no further improvement over the single-phase Cm refinement shown in Fig. 2(g).
From the foregoing, it was concluded that the space group of PZN-8%PT at 4 K is Cm. The Rietveld refinement using that space group is shown in full in Fig. 3 and the structure is illustrated in Fig. 4.
Data collection: ISIS in-house software; cell refinement: Please complete; data reduction: ISIS in-house software; program(s) used to solve structure: Please complete; program(s) used to refine structure: GSAS (Larson & Von Dreele, 1994); molecular graphics: Atoms (Dowty, 2005); software used to prepare material for publication: enCIFer (Allen et al., 2004).
Pb(Zn0.3066Nb0.6133Ti0.08)O3 | V = 133.00 (1) Å3 |
Mr = 336.06 | Z = 2 |
Monoclinic, Cm | Neutron radiation |
Hall symbol: C -2y | T = 4 K |
a = 5.7461 (2) Å | Particle morphology: powder |
b = 5.7278 (2) Å | pale yellow |
c = 4.0409 (3) Å | ?, ? × ? × ? mm |
β = 90.155 (3)° | Specimen preparation: Prepared at 1473 K and 0 kPa, cooled at 1 K min−1 |
Powder 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 |
Least-squares matrix: full | Excluded region(s): no excluded regions |
Rp = 0.091 | Profile function: TOF Profile function number 4 with 21 terms Profile coefficients for exponential pseudovoigt convolution (Von Dreele, 1990) (unpublished) Microstrain broadening by Stephens (1999) #1 (alp ) = 0.1335 #2 (bet-0) = 0.028942 #3 (bet-1) = 0.006569 #4 (sig-1) = 75.0 #5 (sig-2) = 1.0 #6 (gam-2) = 0.00 #7 (g2ec ) = 0.00 #8 (gsf ) = 0.00 #9 (rstr ) = 0.000 #10(rsta ) = 0.000 #11(rsca ) = 0.000 #12(eta ) = 0.3000 #13(S400 ) = 1.4E+01 #14(S040 ) = 1.6E+01 #15(S004 ) = 1.6E+02 #16(S220 ) = 1.7E+01 #17(S202 ) = -1.7E+01 #18(S022 ) = -3.1E+01 #19(S301 ) = 1.2E+01 #20(S103 ) = -3.0E+01 #21(S121 ) = 0.0E+00 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rwp = 0.111 | 34 parameters |
Rexp = 0.087 | 0 restraints |
R(F2) = 0.15716 | (Δ/σ)max = 0.43 |
χ2 = 1.638 | Background function: GSAS background function number 4 with four terms. Power series in Q**2n/n! 1: 0.162824 2: 7.647420E-04 3: 4.876620E-06 4: -3.356860E-07 |
? data points |
Pb(Zn0.3066Nb0.6133Ti0.08)O3 | β = 90.155 (3)° |
Mr = 336.06 | V = 133.00 (1) Å3 |
Monoclinic, Cm | Z = 2 |
a = 5.7461 (2) Å | Neutron radiation |
b = 5.7278 (2) Å | T = 4 K |
c = 4.0409 (3) Å | ?, ? × ? × ? mm |
Powder diffractometer | Scan method: time of flight |
Specimen mounting: 11mm Al slab can | 2θfixed = 168.33 |
Data collection mode: transmission | Distance from specimen to detector: 1000 mm |
Rp = 0.091 | ? data points |
Rwp = 0.111 | 34 parameters |
Rexp = 0.087 | 0 restraints |
R(F2) = 0.15716 | (Δ/σ)max = 0.43 |
χ2 = 1.638 |
Experimental. resolution Δd/d ≈4x10-4 Diffraction patterns recorded from 30000 to 120000µs |
Refinement. Resolution Δd/d ≈4x10-4 Diffraction patterns recorded from 30000 to 120000µs |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Pb1 | 0.0 | 0.0 | 0.0 | 0.0450 (9)* | |
Zn1 | 0.4688 (9) | 0.0 | 0.4787 (9) | 0.0240 (9)* | 0.30666 |
Nb1 | 0.4688 (9) | 0.0 | 0.4787 (9) | 0.0240 (9)* | 0.61333 |
Ti1 | 0.4688 (9) | 0.0 | 0.4787 (9) | 0.0240 (9)* | 0.08 |
O1 | 0.4235 (12) | 0.0 | 0.009 (4) | 0.00835* | |
O2 | 0.240 (2) | 0.2453 (13) | 0.478 (3) | 0.02563* |
Pb1—Zn1i | 3.616 (2) | O2—Pb1iv | 2.888 (11) |
Zn1—Pb1ii | 3.616 (2) | Pb1—O1ix | 2.900 (8) |
Zn1—O2 | 1.921 (8) | Pb1—O1viii | 2.900 (8) |
Zn1—O2iii | 1.921 (8) | O1—Pb1vi | 2.900 (8) |
O2—Zn1 | 1.921 (8) | O1—Pb1xi | 2.900 (8) |
Zn1—O1 | 1.915 (16) | Pb1—O2xiii | 2.992 (7) |
O1—Zn1 | 1.915 (16) | Pb1—O2xiv | 2.992 (7) |
Zn1—O1iv | 2.159 (16) | O2—Pb1xv | 2.992 (7) |
O1—Zn1v | 2.159 (16) | Pb1—Zn1 | 3.312 (5) |
Zn1—O2vi | 2.138 (8) | Pb1—Zn1v | 3.426 (2) |
Zn1—O2vii | 2.138 (8) | Zn1—Pb1iv | 3.426 (2) |
O2—Zn1viii | 2.138 (8) | Zn1—Pb1vi | 3.463 (2) |
Pb1—O1 | 2.434 (7) | Zn1—Pb1xi | 3.463 (2) |
Pb1—O2 | 2.755 (11) | Pb1—Zn1ix | 3.463 (2) |
Pb1—O2iii | 2.755 (11) | Pb1—Zn1viii | 3.463 (2) |
Pb1—O2ix | 2.84 (1) | Pb1—Zn1xiii | 3.557 (2) |
Pb1—O2x | 2.84 (1) | Pb1—Zn1xvi | 3.557 (2) |
O2—Pb1xi | 2.84 (1) | Zn1—Pb1xvii | 3.557 (2) |
Pb1—O2v | 2.888 (11) | Zn1—Pb1xv | 3.557 (2) |
Pb1—O2xii | 2.888 (11) | ||
O1—Zn1—O1iv | 165.3 (4) | O2iii—Zn1—O2vii | 176.6 (5) |
O1—Zn1—O2 | 84.7 (4) | O2—Zn1—O2vii | 90.02 (3) |
O1—Zn1—O2iii | 84.7 (4) | O2iii—Zn1—O2vi | 90.02 (3) |
O1—Zn1—O2vi | 95.1 (3) | O2vi—Zn1—O2vii | 87.0 (3) |
O1—Zn1—O2vii | 95.1 (3) | Pb1—O1—Zn1v | 96.2 (5) |
O1iv—Zn1—O2 | 85.5 (3) | Pb1—O1—Zn1 | 98.5 (5) |
O1iv—Zn1—O2iii | 85.5 (3) | Pb1—O1—Zn1 | 98.5 (5) |
O1iv—Zn1—O2vi | 96.5 (4) | Zn1v—O1—Zn1 | 165.3 (4) |
O1iv—Zn1—O2vii | 96.5 (4) | Zn1—O1—Nb1v | 165.3 (4) |
O2—Zn1—O2iii | 93.8 (4) | Zn1—O2—Zn1viii | 176.6 (5) |
O2—Zn1—O2vi | 176.6 (5) | Zn1viii—O2—Nb1iv | 176.6 (5) |
Symmetry codes: (i) x−1, y, z; (ii) x+1, y, z; (iii) x, −y, z; (iv) x, y, z+1; (v) x, y, z−1; (vi) x+1/2, y−1/2, z; (vii) x+1/2, −y+1/2, z; (viii) x−1/2, y+1/2, z; (ix) x−1/2, y−1/2, z; (x) x−1/2, −y+1/2, z; (xi) x+1/2, y+1/2, z; (xii) x, −y, z−1; (xiii) x−1/2, y−1/2, z−1; (xiv) x−1/2, −y+1/2, z−1; (xv) x+1/2, y+1/2, z+1; (xvi) x−1/2, y+1/2, z−1; (xvii) x+1/2, y−1/2, z+1. |
Experimental details
Crystal data | |
Chemical formula | Pb(Zn0.3066Nb0.6133Ti0.08)O3 |
Mr | 336.06 |
Crystal system, space group | Monoclinic, Cm |
Temperature (K) | 4 |
a, b, c (Å) | 5.7461 (2), 5.7278 (2), 4.0409 (3) |
β (°) | 90.155 (3) |
V (Å3) | 133.00 (1) |
Z | 2 |
Radiation type | Neutron |
µ (mm−1) | ? |
Specimen shape, size (mm) | ?, ? × ? × ? |
Data collection | |
Diffractometer | Powder diffractometer |
Specimen mounting | 11mm Al slab can |
Data collection mode | Transmission |
Scan method | Time of flight |
Absorption correction | ? GSAS absorption/surface roughness correction: function number 0 No correction is applied. |
Tmin, Tmax | 1.000, 1.000 |
2θ values (°) | 2θfixed = 168.33 |
Distance from specimen to detector (mm) | 1000 |
Refinement | |
R factors and goodness of fit | Rp = 0.091, Rwp = 0.111, Rexp = 0.087, R(F2) = 0.15716, χ2 = 1.638 |
No. of data points | ? |
No. of parameters | 34 |
(Δ/σ)max | 0.43 |
Computer programs: ISIS in-house software, Please complete, GSAS (Larson & Von Dreele, 1994), Atoms (Dowty, 2005), enCIFer (Allen et al., 2004).
The crystal structure of the perovskite relaxor ferroelectric Pb(Zn1/3Nb2/3)O3 (lead zinc niobate or PZN) and its alloys with PbTiO3 (PZN-PT) is of interest due to the outstanding piezoelectric properties of these compounds (e.g. Park & Shrout, 1997). PZN-PT is a solid solution with multiple occupancy of the perovskite B site by Zn, Nb and Ti. The crystal structure–property relationship in PZN-PT is poorly understood, due to extreme pseudosymmetry and the unavailability of single-domain single crystals. One feature that is certain and which adds to the mystique is that the maximum piezoelectric response is along [001] of the parent cubic phase, whereas the spontaneous polarization is along [111] of the ferroelectrically distorted crystals over a wide composition range. The region where the highest piezoelectric properties have been measured is at the morphotropic phase boundary (MPB) PZN-8%PT. This is the composition range where the rhombohedral PZN structure (R3m) meets the tetragonal PbTiO3 structure (P4mm).
The structure of PZN-8%PT and of MPB phases in general has been widely debated. The systems PbZrO3–PbTiO3 (PZT) and Pb(Mn1/3Nb2/3)O3–PbTiO3 (PMN-PT) are considered analogue systems. Previous work on PZN-PT has relied on synchrotron X-ray (Noheda et al., 2001; 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 X-ray powder diffraction (Ohwada et al., 2001; Noheda et al., 2002; La-Orauttapong et al., 2002). These experimental studies have focused on the lattice symmetry. The pseudo-cubic nature of the structure has made the determination of the true symmetry extremely difficult, even with three-axis diffractometers (Noheda et al., 2002).
Many papers have implicated structural phase transitions in the piezoelectric response of these materials. Originally, an electric-field induced phase transition from rhombohedral (R3m) to tetragonal (P4mm) was proposed (Park & Shrout, 1997; Paik et al., 1999; Durbin et al., 1999). In recent years, many variations have been proposed in the region of the MPB in both PZN-PT and PZT. A monoclinic phase (Cm) rather than the traditional R3m+P4mm coexistence at the MPB in PZT was first observed by Noheda et al. (1999) and a new phase diagram was proposed which incorporates this phase (Noheda et al., 2000). This monoclinic phase was explained as a bridging structure between R3m and P4mm, as there is no symmetry axis, just a mirror plane. This mirror plane is the only symmetry element common to R3m and P4mm. The MPB in both PZN-PT and PZT has since been studied by many groups. One suggestion is that this region is in fact orthorhombic in space group Amm2 (La-Orauttapong et al., 2002). Many other phases or combinations of phases have been proposed at the MPBs. These include but are not restricted to R3c+Cm (Frantti et al., 2003), Pm (Bertram et al., 2003), Cm+Cc (Ranjan et al., 2005) and Cc (Woodward et al., 2005). These studies have included analogue systems PZT and PMN-PT, studies of poled PZN-PT crystals (e.g. Marssi & Dammak, 2007) and studies of PZN-PT with applied electric fields (e.g. Viehland et al., 2001). Results for PZN-PT materials have been postulated from a consideration of lattice symmetry only; no ion coordinates have been published other than for PZN (Kisi et al., 2006). Given that the spontaneous and induced polarizations depend on ion coordinates and not lattice symmetry, there is an urgent need for the ground state of PZN-8%PT to be known.
Structural variations between the possible structures are largely due to differences in the O ion coordinates, giving a strong motivation for the use of neutron diffraction. The presence of ferroelectric domains makes the refinement of ion coordinates from standard single-crystal data very difficult. Consequently, this paper presents the crystal structure determination and refinement for Pb(Zn0.3066Nb0.6133Ti0.08)O3 (PZN-8%PT) using very high resolution neutron powder diffraction. We find that the ground state of PZN-8%PT is monoclinic in space group Cm. The principal direction of the spontaneous polarization is close to [100]M = [110]C.