Investigation of the Structure of the Modulated Doubly Ordered

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Investigation of the Structure of the Modulated Doubly Ordered Perovskite NaLaCoWO6 and Its Reversible Phase Transition with a Colossal Temperature Hysteresis Peng Zuo, Céline Darie, Claire V. Colin, and Holger Klein*

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University Grenoble Alpes and CNRS, Institute Néel, 38000 Grenoble, France ABSTRACT: Transmission electron microscopy, neutron diffraction, and synchrotron powder X-ray diffraction reveal a complex modulated structure on the doubly ordered perovskite NaLaCoWO6. Electron diffraction patterns as well as high-resolution transmission electron microscopy images clearly show a periodicity of 12ap, where ap is the cell parameter of the generic perovskite, along either the [100]p or [010]p direction. Annular bright-field scanning transmission electron microscopy of slightly tilted samples shows that there is no chemical origin for the superstructure but that it is caused by geometric rearrangements. An atomic model of the superstructure is proposed on the basis of octahedral tilt twinning. At low temperature, NaLaCoWO6 undergoes a phase transition and the superstructure disappears. The compound takes on the more usual monoclinic P21 structure below the transition. Neutron powder diffraction reveals and electron diffraction confirms an unusually large temperature hysteresis, where the transition takes place at ∼180 K on cooling and at ∼320 K on heating. This hysteresis can be attributed to the necessity of rearranging the oxygen octahedra and the thus induced energy barrier for the transition.

1. INTRODUCTION Magnetoelectric multiferroics is drawing considerable research interest not only for the variety of attractive fundamental phenomena but also for potential technological applications, such as energy efficient memory devices and multiple state memories. To overcome the shortcomings of known multiferroics, a new approach to inducing spontaneous ferroelectric polarization by a combination of two nonpolar rotation modes of the oxygen octahedra in magnetic materials was proposed. This so-called “hybrid improper ferroelectricity (HIF)”1−3 could lead to materials exhibiting high polar fields and a strong coupling with magnetism, making them promising for applications. Recently, attention has turned to the rather unexplored class of doubly ordered perovskites of general formula AA′BB′O6, which have been predicted to manifest HIF.4,5 The first compound synthesized in this class was NaLaMgWO6 in 1984, and its unit cell was determined as monoclinic in dimensions of √2ap*√2ap*2ap (where ap represents the unit cell parameters of the aristotype perovskite).6 The cations Na+ and La3+ at the A- and A′-sites, respectively, have a layered ordering, whereas the other two cations Mg2+ and W6+, at the B- and B′-sites, respectively, are ordered in the fashion of rock salt. In the framework of research for more materials displaying HIF experimentally, we have investigated NaLnCoWO6 compounds with Ln = Y, La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, and Yb.7 Synchrotron X-ray powder diffraction (SXRPD) and neutron powder diffraction (NPD) have shown that all compounds have layered Na/Ln ordering and rock salt Co/W ordering, and nine compounds (Ln = Y, Sm, © XXXX American Chemical Society

Eu, Gd, Tb, Dy, Ho, Er, and Yb) crystallize in the polar P21 space group. The structure is indeed the targeted one of a doubly ordered perovskite. The SXRPD data obtained from the compounds containing La, Pr, and Nd, however, could be refined in the centrosymmetric space group C2/m. This refinement yielded the average structure of these compounds, but electron diffraction revealed the existence of superstructures in these phases. Such superstructures have also been observed in some other doubly ordered perovskites, such as NaLaMgWO6, NaNdMgWO6, KLaMnWO6, NaCeMnWO6, NaPrMnWO6, KLaCaWO6, and NaLaCaWO6.8−13 A large variety of superstructure patterns and periodicities appeared among these compounds, for instance, commensurate stripes for NaLaMgWO68,9 or commensurate chessboard patterns for KLaMnWO611 and incommensurate stripes and chessboard patterns in NaPrMnWO6.12 Different scenarios have been proposed to explain the origin of the superstructures: compositional modulation, octahedral tilting, and ionic displacements accompanied by chemical ordering (e.g., NaNdMgWO610) or not (e.g., NaLaMgWO614). In the present work, we investigate the local structure of NaLaCoWO6 as well as its superstructure by transmission electron microscopy (TEM), scanning transmission electron microscopy (STEM), and NPD. Different from the compounds possessing superstructures that are mentioned above, NaLaCoWO6 shows a phase transition at low temperature, exhibiting an unusually large temperature hysteresis, this phase Received: April 24, 2018

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DOI: 10.1021/acs.inorgchem.8b01129 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 1. (a) C2/m refinement of NPD data collected on D2B at ILL, with a wavelength of 1.594 Å; the quality of the fit is not satisfactory and much worse than the SXRPD refinement. Extra peaks are observed in the NPD pattern; a typical 2θ region with extra peaks is illustrated in (b). The corresponding SXRPD region is shown in (c), satellite peaks can hardly be observed. reduce the number of refined parameters, the oxygen isotropic displacement parameters were constrained to be the same. Crystal structure drawings were performed with VESTA program package.20

transition and its link with the superstructure will also be discussed with TEM, SXRPD, and NPD results.15

2. EXPERIMENTAL SECTION NaLaCoWO6 was synthesized by solid-state reaction at 925 °C at ambient pressure from Na2CO3 (2% Na in excess, 99.5%, VWR), La2O3 (99.995%, Prolabo), CoCO3·xH2O (99%, Sigma-Aldrich), and WO3 (99.998%, Alfa Aesar) precursors. After washing away a small amount of a Na2WO4 impurity, X-ray powder diffraction (XRPD) confirmed that the sample was pure. For details of the synthesis, see the ref 7. For TEM, the sample was ground under ethanol in an agate mortar and dispersed on a copper grid with an amorphous carbon membrane. Electron diffraction experiments and high-resolution electron microscopy were carried out on a Philips CM300 ST TEM operated at 300 kV. In situ cooling experiments were performed in the Philips CM300 ST using a liquid nitrogen-cooled holder with a nominal minimal temperature of 100 K. The STEM experiments using a highangle annular dark-field (HAADF) and an annular bright-field (ABF) detector were carried out on a FEI Titan3 Ultimate TEM operated at 200 kV and on a FEI Themis Z operated at 200 kV. The beam convergence was 30.0 mrad, the HAADF collection angle ranged from 54 to 200 mrad, and the BF collection angle range was 11 mrad. NPD was carried out at the Institut Laue-Langevin (ILL) at Grenoble, France, on the beamlines D1B and D2B. The temperaturedependent NPD data was collected on the high-intensity two-axis powder diffractometer of the beamline D1B, from 0 to 128°, with a step size of 0.1° and a wavelength of 2.52 Å selected by a pyrolytic graphite (002) monochromator. The temperature range of 100−550 K was investigated. Other NPD experiments were performed on the D2B high-resolution two-axis diffractometer, from 0 to 160°, with a step size of 0.05° and a wavelength of 1.594 Å selected by a Ge(335) monochromator, at room temperature and 100 K, respectively.16 SXRPD was carried out at the SOLEIL Synchrotron source located at Saint-Aubin, France, on the 2-circle diffractometer of the CRISTAL beamline. The sample was measured at room temperature and 100 K controlled by a cryostream system, from 0 to 65°, with a step of 0.002° and a wavelength of 0.5818 Å. Diffraction patterns were refined by the Rietveld method implemented in FullProf Suite.17 The background in the refinement was defined by linear interpolation of selected points in the diffraction pattern, and the profile was described by the Thompson−Cox−Hastings model.18 An asymmetry correction was applied to the Finger formulation of the axial divergence.19 To

3. RESULTS 3.1. High-Temperature Phase. In a previous work,7 the structure of NaLaCoWO 6 at room temperature was determined to be monoclinic with the space group C2/m from a refinement of SXRPD data. The unit cell was given as 2ap*2ap*2ap (where ap is the unit cell parameter of the aristotype perovskite), and the oxygen octahedral tilting scheme, a0b−c0 in Glazer’s notation.21 A comparison with the structure of space group P21/m that was previously proposed in the literature22 shows that the differences stem essentially from the oxygen-atom positions. Consequently, we collected NPD data to confirm the details of the oxygen positions. The quality of the C2/m NPD pattern refinement is not totally satisfactory, as shown in Figure 1a. Especially, some extra satellite peaks appear in the refined C2/m NPD pattern (see Figure 1b), which are not observed in the corresponding SXRPD pattern (see Figure 1c). To clarify the origin of the satellite reflections observed in NPD, we performed a TEM investigation of the sample. Figure 2 shows the [001]p zone axis where the indices are given with respect to the parent perovskite. Within the precision of electron diffraction patterns, the strong reflections are on a square lattice and it is therefore impossible to distinguish between the a* and b* directions of the unit cell. In the center of the squares formed by the basic reflections of the perovskite, one can observe a doublet of reflections around the position that would be indexed with half integers in the perovskite unit cell. The same type of satellite reflections can also be observed around the main reflections of the perovskite. The lines connecting the satellites of a same reflection are parallel to one of the a* or b* axes of the perovskite. The distance of the satellites from the main reflection correspond to one-twelfth of the unit cell parameters ap* or bp* of the parent perovskite. A high-resolution transmission electron micrograph (HRTEM) of this phase in the same orientation clearly B


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doubly ordered perovskite (Figure 4a). The fast Fourier transform (FFT) of this image, shown in the insert, confirms that only the spots corresponding to the doubly ordered perovskite are obtained and no additional satellites can be observed. The ABF image (Figure 4b) that is mainly sensitive to light elements and that was recorded simultaneously doesn’t show a clear stripe contrast in the image either; however, the FFT in the insert yields the satellite reflections also observed in electron diffraction. However, when tilting the sample away from the zone axis, a stripelike contrast appears. Figure 5a shows the ABF image where the sample was tilted by approximately 2° around a ⟨110⟩ direction. Two domains of stripes can be observed with perpendicular orientations of the stripes. Tilting the sample around one of the fundamental directions a or b of the perovskite unit cell makes the stripe contrast appear only in one of the domains (Figure 5b). Tilting the sample around the same axis but in the opposite direction inverses the contrast in the stripes (Figure 5c), as can be seen from the dark contrast indicated by a red arrow that is observed in a bright stripe in Figure 5b and in a dark stripe in Figure 5c. When the sample is tilted around the other fundamental direction (b or a), the stripe contrast appears in the other domain. It should be noted that tilting the sample did not make a stripelike contrast appear in the HAADF images. 3.2. Phase Transition. During low-temperature NPD that was performed to study a potential magnetic ordering in this compound, a phase transition was observed. This transition affects in particular the two shoulders of the peak shown in Figure 1b. Figure 6 shows diffractograms in the relevant angular domain obtained on the D1B beamline at ILL during a cycle of heating from 100 to 550 K and then cooling down to 100 K again. During heating, the phase transition temperature can be estimated as 320 K, whereas on cooling, the transition temperature is close to 180 K, yielding an unusually large hysteresis of around 140 K. The same phase transition was also observed in selected area electron diffraction (SAED) (Figure 7). In the high-temperature phase image along the [001]p zone axis, the satellite reflections are clearly visible (Figure 7a), but at low temperature (∼100 K), their intensities decrease and the reflections with half integer indices appear (Figure 7b). Heating the sample back to room temperature yielded an almost complete recovery of the satellites and disappearance of the central reflections (Figure 7c). Further heating the crystal by concentrating the electron beam on the sample led to the disappearance of the half integer reflections (Figure 7d), indicating a complete reversibility of the phase transition. 3.3. Structure of the Low-Temperature Phase. A joint refinement combining the SXRPD and NPD data obtained at T = 100 K was carried out by the Rietveld method. As the average structure of the high-temperature phase possesses the C2/m symmetry, it was assumed that the low-temperature phase would belong to a subgroup. A refinement using the maximal subgroup C2, however, yielded no satisfactory fit. Taking the systematic extinctions and the theoretical predictions concerning the possible space groups for doubly ordered AA′BB′O622 into account, the space groups P21/m and P21 were concluded to be the best candidates to explain the peak positions. Since these two space groups have exactly the same extinction conditions, their discrimination relies on the peak intensities that are related to their tilting scheme of oxygen octahedra. The space group P21/m has the tilting

Figure 2. [001]p selected area electron diffraction (SAED) pattern of NaLaCoWO6 at room temperature. The indices are given in the basic perovskite unit cell.

shows a contrast modulation in the form of stripes (Figure 3). The squares of white dots correspond to the periodicity of the

Figure 3. HRTEM image taken from the high-temperature phase of NaLaCoWO6 along the zone axis [001]p; the white arrows indicate the basic directions of the perovskite cell. A contrast of dark and bright stripes is observed with a periodicity 12ap.

aristotype perovskite unit cell. The stripes are parallel to the edges of these squares, and the repeat distance is equal to 12 small squares confirming the periodicity of 12ap already deduced from the diffraction satellites. Note that such a modulation was also observed in the related compound NaLaMgWO6 before.8,9 Two sources were proposed to explain the contrast: octahedral tilt twinning and chemical compositional modulation. Since the interpretation of contrasts in HRTEM images is not straightforward, we turned to scanning transmission electron microscopy (STEM) using a high-angle annular dark-field (HAADF) and an annular bright-field (ABF) detector. When the sample is well aligned in the [001]p zone axis, the HAADF images that are mostly sensitive to heavy elements only show the periodic contrast corresponding to the C


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Figure 4. HAADF image (a) and simultaneously recorded ABF image (b) obtained in the [001] orientation of NaLaCoWO6. The inserts are the corresponding FFTs of the images. The arrows indicate the directions a and b of the parent perovskite. HAADF as well as ABF don’t show stripelike contrast. Although the FFT of the HAADF image doesn’t show evidence of any superstructure, the superstructure peaks are clearly visible in the FFT of the ABF image.

Figure 5. Investigation on the relationship between tilting the sample away from the perfect alignment and the stripe contrast in STEM ABF images: (a) tilting the sample along a diagonal ⟨110⟩ direction; (b, c) when tilting the sample along one of the fundamental directions a or b, contrast appears only in the upper domain. The contrast highlighted by a red arrow is observed in a bright stripe (b) or in a dark stripe (c), thus showing that the contrast is inversed for opposite tilting directions. The white arrows indicate the directions a and b of the parent perovskite.

D


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Figure 6. Left: NPD study (D1B at ILL, λ = 2.52 Å) on the phase transition on heating from 100 to 550 K, where the transition temperature is observed around 320 K and cooling from 550 to 100 K, where the transition temperature is observed around 180 K. Right: temperature and intensities of a satellite and the main reflection as a function of time.

Figure 7. SAED of the [001] zone axis of NaLaCoWO6 at different temperatures: (a) the high-temperature phase at room temperature, (b) after cooling the sample down to the nominal temperature 100 K, (c) after heating the sample from 100 K back to room temperature, and (d) after a further heating by condensing the beam on the sample for 5 min.

scheme a−a−c0, whereas it is a−a−c+ for P21. Considering that the tilting here involves only the oxygen octahedra, NPD is the best technique to distinguish between P21/m and P21 owing to its high sensitivity to probe oxygen positions. The refinement in the P21 space group provides a superior fit than that of P21/ m (Figure 8). Different respective weights of the NPD/SXRPD data were tested in the P21 joint refinement on the data collected at 100

K. The best global agreement was obtained with equal weights. The corresponding refinement patterns are shown in Figure 9. The Bragg factors are 6.60% (NPD) and 5.64% (SXRPD), indicating the correct space group assignment. It is worth noticing that large anisotropic strain broadening was observed in the diffraction data, which may be an indication that defects remain after the phase transition. E


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not only show a large temperature hysteresis but it is also surprising from a structural point of view. Usually, phase transitions that involve the creation or disappearance of domains take place from a higher symmetry at high temperature to a lower symmetry at lower temperature. The domains then appear at low temperature as a result of multiple possibilities of reducing the symmetry. However, in our case, structural domains of higher local symmetry transform into a lower symmetry structure at low temperature without any domains. An important question we want to answer is therefore the origin of the superstructure in NaLaCoWO6. The stripelike contrasts observed in HRTEM images are very regular with a width of the stripes that corresponds to six unit cells of the aristotype perovskite, making the periodicity 12ap. The appearance of sharp satellite reflections in the electron diffraction patterns shows that these stripes are of a long-range order so that we can speak of a superstructure of the doubly ordered perovskite. Electron and neutron diffraction show that the superstructure disappears at low temperature and that it reappears with the same sharp satellite reflections when heating above the transition temperature. The long-range order of six unit cell-wide stripes is therefore restored. But what is the origin of this superstructure? In related phases, some superstructures were concluded to be originated from (i) chemical ordering (compositional segregation on the A-site), (ii) changes in the tilting of the oxygen octahedra (ionic displacements), or (iii) a combination of both. HAADF-STEM is also frequently called Z-contrast imaging because it yields images where heavier atoms give a brighter contrast than lighter atoms. This can be very useful when looking for the arrangements of heavy atoms in a complex crystal structure or for compositional changes in a sample. The latter was the reason why we attempted to obtain HAADFSTEM images in zone axis orientation of the high-temperature phase of NaLaCoWO6. When the crystal is as close as experimentally possible to the zone axis there is no contrast corresponding to the stripes observed in HRTEM images. The corresponding FFT also doesn’t show any sign of a superstructure. We can therefore exclude chemical ordering of the heavy elements as the origin of the superstructure. ABF-STEM images also show no obvious contrast corresponding to the stripes, provided that the crystal is well aligned in the zone axis orientation. In the corresponding FFT (insert of Figure 4b), however, satellite spots equivalent to those observed in electron diffraction are obtained. Since there is no visible stripe contrast, the satellites can’t stem from intensity modulations in the image but rather from shifts of the white dots in the image. Tilting the crystal from the perfect orientation by a few degrees, however, makes the stripe contrast appear very clearly. This can be observed in Figure 5 where two domains with different orientations of the stripes are observed. When the crystal is tilted around the [110] direction of the unit cell, the contrast can be observed in both domains, whereas tilting the crystal around either the [100] or the [010] directions makes the contrast appear only in one of the domains. Interestingly, the contrast depends not only on the tilt axis but also on the tilt direction. Inverting the tilt direction also inverts the contrast of the stripes from bright to dark and vice versa. If the contrast was due to chemical modulations, a slight tilt should not affect the contrast in the images and in particular, the inversion of the tilt direction should not inverse the contrast.

Figure 8. Comparison between the NPD refinements at 100 K in space groups Pi1/m and Pi1 in a selected 2θ region (36−46°).

All refined crystallographic parameters are listed in Table 1, and the selected bond lengths, bond angles, and the derived bond valence sums of each atom are all listed in Table 2. Note that on the sodium site, a small amount of La was introduced to obtain a reasonable Biso value at this site; otherwise, the Biso is negative. The proportions of Na and La on this site were refined with the constraint of full occupancy of the site. The refined La proportion is less than 3.9%. Other tests like mixing La at the Na site together with mixing Na at the La site with a constraint of full occupancy of the Na and La sites as well as all elements in stoichiometry were also attempted. In all cases, the occupancy deviations of the Na and La sites are not larger than 4% and the fit is no better than that shown in Figure 9 considering the refinement agreement factors. The refined crystal structure is shown in Figure 10. The tilting scheme of the P21 structure adopts a−a−c+, and the unit cell has the dimensions of √2ap*√2ap*2ap. It shares the common structural features with other NaLnCoWO6 compounds that also have the P21 symmetry:7 the Na/La sites order in layers, whereas the Co/W sites order in a rock salt type; the second-order Jahn−Teller effect of W6+ is well reflected from the difference of the W−O5 and W−O6 bond lengths, the W6+ tending to move toward the Na layer. All calculated bond valence sums are very close to the expected valences, indicating the refinement was appropriate, and the space group assignment correct.

4. DISCUSSION At room temperature, NaLaCoWO6 shows a superstructure that gives a stripelike contrast in HRTEM images that is confirmed by electron diffraction. Such a superstructure has been observed in other doubly ordered perovskites. However, the case of NaLaCoWO6 is somewhat special since it shows a phase transition at low temperature. This phase transition does F


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Inorganic Chemistry

Figure 9. Joint refinement of NaLaCoWO6 combining the SXRPD and NPD data collected at 100 K in space group P21.

Table 1. Crystallographic Parameters of NaLaCoWO6 from the Joint Refinement (P21) at 100 Ka atom

Wyckoff symbol

x

y

z

B (Å2)

occupancy

Na La1 La2 Co W O1 O2 O3 O4 O5 O6

2a 2a 2a 2a 2a 2a 2a 2a 2a 2a 2a

0.231(6) 0.231(6) 0.252(1) 0.749(2) 0.7533(5) 0.53(1) 0.51(1) −0.02(1) −0.04(1) 0.823(5) 0.674(5)

0.778(6) 0.778(6) 0.728(2) 0.767(4) 0.75 0.495(9) 0.472(9) 0.050(9) 0.024(9) 0.77(1) 0.75(2)

−0.001(4) −0.001(4) 0.500(1) 0.248(1) 0.7685(2) 0.702(7) 0.282(7) 0.219(7) 0.785(7) 0.504(3) −0.013(3)

0.8(5) 0.8(5) 0.7(3) 0.4(2) 0.57(3) 1.0(1) 1.0(1) 1.0(1) 1.0(1) 1.0(1) 1.0(1)

0.961(7) 0.039(7) 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Space group P21, Z = 2. Unit cell parameters: a = 5.53091 Å, b = 5.53226 Å, c = 7.89281 Å, β = 90.22028°, and V/Z = 120.753 Å3. Discrepancy factors: (NPD) χ2 = 3.43, Rp = 14.0%, and Rwp = 13.0%, RBragg = 6.60%; (SXRPD) χ2 = 28.3, Rp = 13.3%, Rwp = 18.3%, and RBragg = 5.64%. a

12ap*2ap*2ap or 2ap*12ap*2ap. Following the procedure of a previous study on NaLaMgWO6,9 we have built three structural models. These models are based on the structures obtained from NPD refinements of the average structure either in a 2ap*2ap*2ap unit cell and the C2/m space group or in a √2ap*√2ap*2ap unit cell and the P21/m space group. Model 1 is based on the C2/m NPD refinement. Since the tilting scheme of C2/m is a0b−c0, which means the octahedra only tilt around the b-axis, the superstructure can only propagate along the b-axis to have a tilt twinning at the middle of the superstructure unit cell. As a result, the unit cell

Furthermore, the stripe contrast disappears in the lowtemperature phase; if it was due to chemical modulation, this would imply a reversible cation (dis-)ordering, which is very unlikely at these temperatures (close or below room temperature). The stripe contrast has therefore to be attributed to a different source. Since the tilting is a geometrical change in the experimental setup, geometrical aspects of the structure come to mind. One such structural effect could be an octahedral tilt twinning. According to the SAED and stripe contrast in the HRTEM images, the unit cell of the superstructure has dimensions of G


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Inorganic Chemistry

Table 2. Selected Bond Lengths, Bond Valence Sums, and Bond Angles of NaLaCoWO6 from the Joint Refinement at 100 K bond lengths (Å) Co−O1 Co−O2 Co−O3 Co−O4 Co−O5 Co−O6 Co−O average W−O1 W−O2 W−O3 W−O4 W−O5 W−O6 W−O average

bond valence sums 2.03(6) 2.15(6) 2.02(6) 2.10(6) 2.06(3) 2.11(3) 2.077(7) 1.95(6) 1.91(6) 1.86(6) 1.92(6) 2.12(3) 1.78(3) 1.923(7)

Na La1 La2 Co W O1 O2 O3 O4 O5 O6

1.0(2) 2.73(6) 2.81(5) 2.22(4) 6.3(1) 2.23(6) 2.09(6) 2.16(8) 1.90(6) 1.916(3) 2.19(4)

bond angles (deg) Co−O1−W Co−O2−W Co−O3−W Co−O4−W Co−O5−W Co−O6−W

151.7(9) 159.0(8) 162.4(10) 163.5(9) 157.9(4) 154.0(4)

its unit cell is 12ap*2ap*2ap. The main principle to build the model is the same as that of model 1, this time creating a tilt twinning at the middle of the unit cell along the a-axis. The unit cell size of model 3 is 2ap*12ap*2ap, and the tilt twinning is at the middle along the b-axis. All structures of these models are shown in Figure 11. Each model contains 240 atoms in the unit cell. By construction, they are related by symmetry, which leads to 18 (17) atomic parameters for the P21/m (C2/m) model, respectively. We did not succeed, however, in performing a Rietveld refinement of the NPD data because of the very low number of superstructure peaks observable in the NPD (three peaks). We therefore simulated NPD and synchrotron X-ray powder diffraction (SXRD) patterns of the models to compare them qualitatively to the observed data. The lattice parameters used in these simulations are from the C2/m SXRPD refinement, with the parameter corresponding to the 12ap direction multiplied by 6. All profile parameters are the same as those in the C2/m NPD or SXRD refinement. A representative 2θ range related to the superstructure in the simulated NPD and SXPD patterns is shown and compared with the corresponding observed pattern in Figure 12. The 2θ range selected in the NPD and SXRPD simulations are in the same Q-range. In the NPD simulations, the calculated pattern of model 1 shows intensity at the satellite positions, however, the main peaks cannot be explained with this model. Models 2 and 3 can well explain the positions of all observed peaks and the relative intensities in this specific region. Considering that no refinement has been done, it is impossible to distinguish between these two models. It can be noted although that both models well reproduce the satellite reflections that are characteristic of the superstructure modulation. The simulated SXRPD patterns with these three models are compared in Figure 12b; the main peaks in the observed pattern are approximately reproduced by the simulations, without any strong evidence about the superstructure, like in the NPD data. During the phase transition, the high-temperature phase in the local P21/m symmetry and periodic octahedral tilt boundaries transforms into the low-temperature phase with the space group P21 without any periodic boundaries. This transition from higher to lower symmetry involves an additional tilting of the oxygen octahedra. In the hightemperature phase, the tilting scheme is a−a−c0, whereas in the low-temperature phase, an additional tilt around the c-axis is observed (a−a−c+). Locally, one can easily imagine adding an

Figure 10. Schematic view of the crystal structure of the lowtemperature NaLaCoWO6 phase (space group P21). The spheres are Na (yellow), La (gray), Co (green), W (blue), and O (red).

of model 1 has dimensions 2ap*12ap*2ap and the tilting scheme a0b−c0. In this case, the refined average unit cell corresponds to 1/6 of the superstructure unit cell. To build the model, the y coordinates of all atoms in the refined unit cell are divided by 6, which yields the first block of representing onesixth of the structure. Then, 1/6 and 1/3 are added to the y coordinates of the first block, respectively, to build the second and the third blocks. After this step, half of the unit cell is filled. Then, the tilt twinning is applied at this antiphase boundary to build the second half of the unit cell. The model 1 is shown in Figure 11a; the octahedra at the two sides of the tilt twinning boundary are tilted in the same direction along the b-axis. Models 2 and 3 are built based on the P21/m NPD refinement. Since it is difficult to distinguish whether the propagation direction of the superstructure is along [100]p or [010]p, model 2 is made to propagate along the a-axis, and model 3, along b-axis. Both of them possess the P21/m tilting scheme a−a−c0. The unit cell of the P21/m structure has dimensions √2ap*√2ap*2ap, where the a-axis is along the [110]p direction and the b-axis is along the [11̅0]p direction. The first step in building these models is to convert the coordinate axes to be consistent with the aristotype perovskite (which coincides with the C2/m) unit cell. The new x coordinates are thus obtained by (yMP − xMP)/2 (xMP and yMP are the x and y coordinates in the P21/m unit cell, respectively), and the new y coordinates, by (yMP + xMP)/2. Since there is no difference in the c-axis, all z coordinates are kept the same. Model 2 is modulated along the a-axis so that H


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Figure 11. Structures of different models with octahedral tilt twinning to describe the structural modulations in the high-temperature phase. (a) Model based on the C2/m NPD refinement with the unit cell 2ap*12ap*2ap and the tilting scheme a0b−a0, (b) model based on the P21/m NPD refinement with the unit cell 12ap*2ap*2ap and the tilting scheme a−a−c0, and (c) model based on the P21/m NPD refinement with the unit cell 2ap*12iap*2ap and the tilting scheme a−a−c0. The spheres are Na (yellow), La (gray), Co (green), W (blue), and O (red).

Figure 12. Comparison between the simulated (a) NPD and (b) SXPD patterns of different superstructure models and the observed pattern (in red). Model 1 (in green) corresponds to the unit cell parameters 2ap*12ap*2ap and the tilting scheme a0b−a0; model 2 (in cyan) corresponds to the unit cell parameters 12ap*2ap*2ap and the tilting scheme a−a−c0; and model 3 (in blue) corresponds to the unit cell parameters 2ap*12ap*2ap and the tilting scheme a−a−c0.

temperature phase (a−a−c0, model 2 or 3) corresponds to ferroelastic tilting (FAt) domain walls (DWs); see Figure 13. Each DW involves a single tilt switch at the phase boundary,

additional tilt; however, at the domain boundaries, the situation is different. Following the classification proposed by Huang,23 the periodic tilt twinning observed in the highI


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Inorganic Chemistry

Figure 13. Periodic tilt twinning observed in the high-temperature phase (a−a−c0) corresponds to ferroelastic tilting (FAt) domain walls. In the low-temperature phase, an octahedral in-phase rotation mode (a0a0c+) has to be combined. Starting from the FAt configuration, there are two possibilities to combine the rotation mode: (i) ferroelastic tilting (FAt) between states with the same rotation and (ii) ferroelastic tilting + rotation (FAtr) DWs between states with different rotations. Finally, the polar phase P21 does not only involve the two modes of octahedron tilt but also a polar mode that couples with them. The FAt DWs considered will therefore form 90° ferroelectric DWs.

either a0a−c0 for model 2 or a−a0c0 for model 3. In the lowtemperature phase, an octahedral in-phase rotation mode (denoted a0a0c+ in Glazer notation) has to be combined. Rotations are either clockwise or anticlockwise. Starting from the FAt configuration, there are two possibilities to combine the rotation mode: (i) ferroelastic tilting (FAt) between states with the same rotation and (ii) ferroelastic tilting + rotation (FAtr) DWs between states with different rotations. FAtr DW are accompanied with a complete frustration of octahedral rotation at the walls and therefore are much less energetically favorable than the case (i), which still implies strong distortions of the octahedra at the boundary. Finally, the polar phase P21 does not only involve the two modes of octahedron tilt but also a polar mode that couples with them. The FAt DWs considered will therefore form 90° ferroelectric DWs. The mirror symmetric twin domains with respect to the twin boundary imply a ferroelectric uncharged (head-to-tail) twin boundary. The electrostatic energy cost of this type of wall is certainly less important compared to that of charged walls (head-to-head or tail-to-tail), but it is still substantial. Combining the rotation to the FAt DW has therefore a double energetic cost: elastic and electrostatic. Taking into consideration the very large number of domain walls due to the small domain size (12ap = 46 Å), this cost is certainly too large and prevents their formation. To obtain a structure without tilt domains, a reorganization of one of the domains is necessary so that the tilting scheme can be the same throughout the crystal and in addition, the c+ tilting can take place. The reorganization of the tilt domains involves certainly a relatively high energy barrier for the transformation. This could explain the large temperature hysteresis of ∼140 K that we observed.

Internal constraints from defects could be responsible for the fact that not all particles have their phase transition at the same temperature. On the other hand, the periodicity of 12ap of the modulation is very regular in the sense that it is precisely observed over large distances, as can be seen from its observation from diffraction experiments, and it is very robust since the phase transition is reversible. More detailed studies are obviously necessary, but one can imagine that this periodicity is linked to a relaxation of elastic constraints. It is worth mentioning that the two other phases in the NaLnCoWO6 series that have been synthesized at ambient pressure, NaPrCoWO6 and NaNdCoWO6, also show modulated structures. In contrast to that in NaLaCoWO6, the modulation takes place in two dimensions, leading to periodicities of 16*ap/√2 along the [110] and [11̅ 0] directions (Figure 14). No phase transition was observed for these phases down to 2 K. A detailed investigation of their structures will be published elsewhere. Hysteretic ferroelectric phase transitions were also observed in other ferroelectric systems. In several tetragonal tungsten bronze compounds (see, for instance, Zhu et al.24 and references therein), the hysteretic phase transition is associated with the complex tetragonal tungsten bronze crystal structures with different superstructures above and below Tc and the difficulty in nucleating ferroelectric domains on cooling through Tc. Thermal hysteresis was also evidenced at the incommensurate−commensurate transition point in Rb2ZnCl4, K2SeO4, Rb2ZnBr4, and K2ZnCl4 (see Hamano et al.25 and references therein). The observed thermal hysteresis is understood as defects acting as obstacles to diffusion of discommensurations that prevent the crystal from reaching J


Inorganic Chemistry

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Peng Zuo: 0000-0003-1524-3200 Claire V. Colin: 0000-0003-1332-7929 Holger Klein: 0000-0002-5787-7298 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful to the French network METSA for providing beam time on STEM and H. Okuno at CEA, Grenoble, France for the technical assistance on STEM experiments. The authors are also grateful to D. Stroppa (FEI Company) for the additional STEM experiments. We also acknowledge Institut Laue-Langevin at Grenoble, France for allocating the beam time on the beamlines D1B and D2B and the technical assistance of V. Nassif (D1B), S. Djellit (D1B), and E. Suard (D2B). We are also grateful to Synchrotron SOLEIL at Saint-Aubin, France for allocating the beam time on the beamline CRISTAL and the technical support of E. Elkaim.

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Figure 14. Superstructures observed in (a, b) NaPrCoWO6 and (c, d) NaNdCoWO6, evidenced from the HRTEM (a, c). The arrows indicate the [100] and [010] directions of the parent perovskite. The corresponding SAED patterns (b, d) are indexed in the parent perovskite unit cell. Since the parameters a and b are very similar, no distinction between them can be made in the images and diffraction patterns.

thermal equilibrium. What makes the transition unique in NaLaCoWO6 is the fact that there is no disorder involved at the transition and that the superstructure is totally deleted at the ferroelectric phase transition.

5. CONCLUSIONS In this work, we have shown that in the series of doubly ordered perovskites NaLnCoWO6, the compound NaLaCoWO6 shows an unusual behavior. At room temperature, it has a modulated structure that can be attributed to tilt twinning domains of oxygen octahedra. The modulation disappears at a phase transition at low temperature, where the local structure changes symmetry from the P21/m to the P21 space group. Because of the necessity of reorganizing the oxygen octahedra tilts during the reversible phase transition, the latter exhibits a large hysteresis of ∼140 K.

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REFERENCES

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CCDC 1841445 contains the supplementary crystallographic data for this paper. These data can be obtained free of charge via www.ccdc.cam.ac.uk/data_request/cif, or by emailing [email protected], or by contacting The Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK; fax: +44 1223 336033. K


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Investigation of the Structure of the Modulated Doubly Ordered

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