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Phase coexistence in NaTaO3 at room temperature; a high resolution neutron powder diffraction study
Solid State Sciences 43 (2015) 15e21
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Phase coexistence in NaTaO3 at room temperature; a high resolution neutron powder diffraction study Kevin S. Knight a, b, *, Brendan J. Kennedy c a
ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxon OX11 0QX, UK Department of Earth Sciences, The Natural History Museum, Cromwell Road, London SW7 5BD, UK c School of Chemistry, The University of Sydney, Sydney, New South Wales 2006, Australia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 January 2015 Received in revised form 5 March 2015 Accepted 18 March 2015 Available online 19 March 2015
Room temperature high resolution neutron powder diffraction data, measured in time-of-flight, from two independent samples of NaTaO3 shows the presence of phase coexistence of two orthorhombic structures with space groups Pbnm, and Cmcm. The failure of earlier work to recognise the extent of the hysteresis associated with the high temperature (~763 K on heating) Cmcm e Pbnm phase transition, that extends down to room temperature, and probably to 0 K, is due to data having been collected at too low a real-space resolution to characterise the diagnostic pseudocubic fundamental and superlattice reflection multiplicities. The phase fraction of the Cmcm phase increases with increasing temperature from 45 weight % at 298 K, to 74 weight % at 758 K. Throughout the whole temperature interval 298 Ke758 K, the volume per formula unit of the Cmcm phase exceeds that of the Pbnm phase by an almost constant ~0.01 Å3 suggesting the addition of pressure would supress the volume fraction of the higher temperature phase. The crystal structure of both phases, determined from data collected at 298 K, are reported, with the atomic displacement parameters of the Cmcm phase being significantly larger than those associated with the Pbnm phase, probably reflecting a high degree of thermal and static disorder. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: NaTaO3 Crystal structure Neutron diffraction Phase transitions
1. Introduction Identification of the correct unit cell metric and space group for hettotype phases of simple perovskite-structured compounds is problematic for two principal reasons. Firstly, the spontaneous strains that develop at zone-boundary phase transitions may be small [1], and hence it is necessary to collect data at the highest real-space resolution to permit analysis of the fundamental reflection multiplicities and separations. Secondly, the diagnostic superlattice reflections of the lower symmetry structures derive essentially from anion displacements [2], which in the case of oxide systems with heavy atoms in the dodecahedral and/or octahedral sites requires either sophisticated data collection strategies for Xray powder diffraction, or the use of neutron diffraction, where the scattering length of oxygen has a comparable magnitude to those of the cations. These zone-boundary phase transitions, frequently termed tilt
* Corresponding author. ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxon OX11 0QX, UK. E-mail address: [email protected] (K.S. Knight). http://dx.doi.org/10.1016/j.solidstatesciences.2015.03.016 1293-2558/© 2015 Elsevier Masson SAS. All rights reserved.
transitions in perovskite-structured phases, are a commonly observed phenomenon and occur when the crystal becomes unstable to a set of normal mode of vibrations of the aristotype phase [2]. For non-ferroelectric perovskite-structured compounds, without cation ordering of the dodecahedral and octahedral sites, these modes transform as basis vectors of either/or both the irreþ ducible representations Rþ 4 and M3 [2e5]. In the former case, successive layers of octahedra rotate in the opposite sense (equivalent to an anti-phase rotation [4]), in the latter, successive layers of octahedra rotate in the same sense (equivalent to an in-phase rotation [4]). Superlattice reflections associated with these soft mode condensations are therefore observed in the diffraction patterns of hettotype phases at the R and/or M points of the pseudocubic Brillouin zone. Based on the earlier ideas of Megaw [6], Glazer used model building methods to systematize the permitted lattice metrics and space groups of perovskite-structures that exhibit these zone-boundary phase transitions [4]. More recently, these deductions have been reinvestigated and corrected using formal group theoretical techniques [3,5]. Perovskite-structured NaTaO3 has been the subject of a number of studies, initially as a potentially ferroelectric material [7,8], as a
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model compound to study zone-boundary phase transitions [9,10], and latterly, as a photocatalyst for splitting water molecules as a clean and renewable source of hydrogen [11e14]. An early experimental determination of the dielectric constant suggested NaTaO3 was ferroelectric with a Curie temperature of 748 K [7], however subsequent investigations found no evidence for ferroelectric behaviour [8,15]. Temperature-dependent optical birefringence studies showed the presence of 3 structural phase transitions, cubic e tetragonal at 903 K, tetragonal e orthorhombic at 853 K (indicatrix parallel to the cubic <100> ie pseudocubic orientation), and orthorhombic e orthorhombic at 753 K (one principal axis parallel to cubic <100> ie rhombic orientation) [8]. These transition temperatures were later confirmed by DTA [16] and neutron powder diffraction [17,18]. The earliest report of crystallographic analysis of NaTaO3 used Xray powder diffraction techniques and reported a unit cell √2a a √2a, where a is the lattice parameter of the aristotype phase [19]. A subsequent single crystal X-ray diffraction study determined the space group as polar Pc21n, in accord with the believed ferroelectric nature of the phase at the time, and observed a doubling of the unit cell b axis (√2a 2a √2a) [20]. The ambient temperature and pressure phase was later studied by Xray powder diffraction [21] and a crystal structure was refined in the centrosymmetric space group Pcmn (an alternate setting of Space Group (S.G.) No. 62), in keeping with the experimentally determined non-ferroelectric behaviour [8,15]. This structure was subsequently refined to higher precision in the anion coordinates using medium resolution neutron powder diffraction, and the two high temperature hettotype phases were identified, and their crystal structures reported in space groups Bmmb (an alternate setting of S.G. No. 63) (803 K) and P4/mbm (S.G. No. 127) (893 K) [18]. More recently, two contemporaneous studies of the temperature dependent structural crystallography of NaTaO3 have been made with the aim of using it as a model system for studying zone boundary phase transitions in perovskite-structured phases [9,10]. Both studies utilised the advantages of neutron powder diffraction over X-ray powder diffraction but were carried out at significantly different real-space resolutions. The lower resolution investigation [10] carried out using the HB-4 diffractometer at the High Flux Isotope Reactor of the Oak Ridge National Laboratory, was in full agreement with the earlier investigation made on the D1a diffractometer at the Institut Laue-Langevin [18]. The higher resolution study carried out using the time-of-flight diffractometer HRPD on the ISIS spallation neutron source was in agreement with both studies at temperatures higher than the Pcmn e Bmmb phase transition temperature ~758 K, but not below [9]. Unfortunately no details of the discrepancy between the expected data from a perovskite structure in space group Pcmn (or any equivalent setting of S.G. No. 62) and that experimentally observed were given in the paper [9]. Further evidence for a possible inconsistency between the crystal structures derived from the medium resolution neutron diffraction studies and correct crystal structure at room temperature has been afforded by 23Na multiple-quantum magic-angle spinning (MQMAS) NMR [22]. Small discrepancies were observed between the experimentally observed MQMAS and MAS spectra and those calculated using the accepted room temperature crystal structure. In this submission we report a re-evaluation of the original HRPD data [9] and furthermore, compare them with a data set collected on a sample of identical synthesis as that used in the HB-4 study. 2. Experimental section The principal sources of the data that have been re-analysed for
this manuscript have already been described in detail [9], and we cis the methodology below. High resolution time-ofsimply pre flight (TOF) neutron powder diffraction data were collected on a sample of commercial NaTaO3 (SigmaeAldrich, 99.9þ% purity) in the TOF window 30e130 ms, at room temperature, and at 83 temperatures between 373 K and 1003 K. An additional TOF window, 100e200 ms, was also collected under ambient conditions to monitor the longer d-spacing reflections. The raw data were reduced as described previously to produce data sets in the TOF range 32e120 ms (~0.64e2.4 Å) and a single data set 102e190 ms (~2.04e3.8 Å) for profile refinement using the GSAS suite of programs. The intrinsic resolution of the instrument is to first order independent of Q (4psin(q)/l), with Dd/d ¼ 4 104. An instrument parameter file for the GSAS lineshape 4 which is suitable for use with the hkl-dependent line broadening functions of Stephens [23] was derived by fitting data collected on the NIST standard silicon powder SRM640b (data collected ~6 weeks after the NaTaO3 experiment). For comparison purposes, a second sample of NaTaO3 was also measured at room temperature in the short (30e130 ms) TOF window. This sample, synthesised in the Chemistry Department, Sydney University, was prepared in an identical manner to that described in the high-temperature crystallographic study that used the medium resolution neutron powder diffractometer HB-4 [10]. 3. Results and discussion 3.1. Crystallographic background The results of the group theoretical analysis of the permitted space groups for simple perovskite-structured compounds [4] reduces structural characterisation to a two-step process [24]. Firstly, the tilt class is identified by the presence of diagnostic superlattice reflections on the surface of the pseudocubic Brillouin zone. These can be summarised as follows: superlattice reflections at the R point alone e antiephase tilting; superlattice reflections at the M point alone e in-phase tilting; the presence of R and M point superlattice reflections e both anti-phase and in-phase tilting (Note in the case of both tilt systems being present, then superlattice reflections at the X point of the pseudocubic Brillouin zone are also observed [25]). The second step of the process requires determination of the pseudocubic lattice metric from an investigation of the multiplicities of the fundamental pseudocubic Bragg reflections, and it is in this process that high direct space resolution is a prerequisite. Taking the previously accepted sequence of phase transitions in NaTaO3 for granted [18], and using space group settings of the two lowest temperature phases as Pbnm (S.G. No. 62), and Cmcm (S.G. No. 63), we expect to observe superlattice reflections at the R, M, and X points of the pseudocubic Brillouin zone from group theoretical arguments [4] (Pbnm: aacþ; Cmcm: a0bcþ in Glazer notation [3]). The pseudocubic metric (subscript p) is related to the crystallographic unit cells by the matrix ½ ½ 0/½ ½ 0/0 0 ½ for space group Pbnm (ap ¼ bp s cp, ap ¼ bp ¼ 90 gp s 90 ), and ½ 0 0/0 ½ 0/0 0 ½ for space group Cmcm (ap s bp s cp, ap ¼ bp ¼ gp ¼ 90 ). The pseudocubic fundamental reflection 111 would therefore be expected to be a singlet in Cmcm (index 2 2 2 in the true orthorhombic unit cell) but a doublet in Pbnm due to the monoclinic subcell metric (indices 0 2 2, 2 0 2 in the true orthorhombic unit cell). 3.2. Analysis of room temperature data The data collected at room temperature from both HRPD and HB-4 only indicate superlattice reflections on the surface of the pseudocubic Brillouin zone (R, M, X points) and hence the
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permitted space groups are either Cmcm, Pbnm (Pnma), P 1 1 21/m (P21/m), or P42/nmc [4]. In order, the Glazer notation and pseudocubic subcells are: a0bcþ, ap s bp s cp, ap ¼ bp ¼ gp ¼ 90 ; aacþ, ap ¼ bp s cp, ap ¼ bp ¼ 90 gp s 90 ; abcþ, ap s bp s cp, ap ¼ bp ¼ 90 gp s 90 ; aþaþc, ap ¼ bp s cp ap ¼ bp ¼ gp ¼ 90 . Fig. 1 illustrates a diagnostic part of the time-of-flight diffraction pattern of NaTaO3 (SigmaeAldrich) collected at room temperature, and containing one fundamental reflection at ~2.25 Å, and two superlattice reflections at ~2.35 Å (R point) and ~2.46 Å (M point). The splitting of the pseudocubic fundamental 111 reflection at d ~2.25 Å into a partially resolved triplet is inconsistent with any of the four space groups outlined above, and clearly illustrates that the accepted space group and crystal structure of NaTaO3 at room temperature being orthorhombic, space group Pbnm [10,18,21] is incorrect. The observation that the splitting of the fundamental and superlattice reflections are inconsistent with a single phase exhibiting both in-phase, and anti-phase tilting [4] requires careful re-evaluation of the diffraction data, in-line with the known behaviour at temperatures greater than 758 K. The accepted phase transition Cmcm e Pbnm is required to be first order [4] which is most easily appreciated by noting the anti-phase tilt has to discontinuously change from pseudocubic [110] to [010]. As phase coexistence is an expected consequence of first order phase transitions, the simplest explanation of the triplet of reflections observed at ~2.25 Å at room temperature is the coexistence of a Pbnm phase, which contributes two reflections to the multiplet, with a Cmcm phase, which contributes a single reflection. Fig. 2 illustrates the same region of the diffraction pattern using data collected from a sample synthesised at Sydney University. Again a triplet is observed, although the relative intensities are clearly different to that seen in Fig. 1. We return to this difference in the Conclusions section of this paper. Superimposed on this plot are calculated normalised peak profiles for a Bragg peak at 2.5 Å based on the resolution functions of HRPD, full black line, D1a (l ¼ 1.911 Å [18]) dashed line, and HB4 (l ¼ 1.5 Å [10]) dot-dash line. The full widths at half maximum intensity of the two reactor-based diffractometer profiles exceeds that of the individual
Fig. 1. A diagnostic part of the time-of-flight neutron powder diffraction pattern of commercially produced (SigmaeAldrich) NaTaO3. Reflections are indexed on the pseudocubic subcell and show the 111 fundamental reflection (marked F) and two superlattice reflections at the R, and M points of the pseudocubic Brilluoin zone. The splitting of the 111 reflection into a triplet proves that at room temperature, the material is polyphasic, and not a single phase, space group Pbnm, as previously described. Tick marks indicating the Bragg reflections from the Pbnm phase (lower), and the Cmcm phase (upper) are shown below the data.
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Fig. 2. The fundamental pseudocubic reflection 111 as measured (circles) using high resolution time-of-flight neutron powder diffraction (HRPD) from the sample of NaTaO3 synthesised at the Department of Chemistry, Sydney University. Superimposed are the resolution functions of HRPD (full line), D1a (dashed line) and HB4 (dot-dash line). The full widths at half maximum intensity of D1a and HB4 exceed the width of the triplet indicating why the phase coexistence had not been identified in previous studies.
experimental Bragg peaks by a factor of ~4, and hence it is clear that these instruments, that were employed in the earlier studies, have insufficient direct space resolution to observe the subtle line splitting that occurs between the two phases in the room temperature diffraction pattern of NaTaO3. 3.3. Crystal structure and refinement A model for the structural state of NaTaO3 at room temperature was generated from the ambient temperature crystal structure in space group Pbnm derived from fitting the HB4 data [10] with a crystal structure in space group Cmcm derived from fitting the HRPD data [9]. Room temperature unit cell parameters for the Cmcm phase were determined by extrapolation from the high temperature results published earlier [9]. The room temperature data collected on the commercial sample was of a significantly higher statistical quality than that collected for the sample synthesised at Sydney University, and hence detailed Rietveld analysis was only carried out for data from the commercial sample. The impurity phase Na2Ta4O11 [9,26] that was observed in these data was added as a third phase in the Rietveld refinement. Considering that the intrinsic diffraction patterns of both perovskite-structured phases are in themselves strongly pseudosymmetric, and furthermore, the general problem of distinguishing the correct space group in compounds where there is an ambiguity between space groups Pbnm, and Cmcm, it is hardly surprising that a stable refinement was initially difficult to achieve. Attempts to link atomic displacement parameters between the three chemically distinct elements of the two perovskite-structured phases were unsuccessful, as was any attempt to relate the lineshape parameters to simplify the fitting procedure. Fixing the structural models and allowing free refinement of the unit cells and lineshape using the Lebail method were also ineffective; however these results strongly suggested that both phases exhibited a degree of hkl-dependent line broadening. Successful refinement of the model against the data was only achieved by fixing the lineshape parameters of the two perovskite-structured phases at instrumental resolution, and then allowing the Stephens broadening parameters [23] to fit the peak profile correctly. Although they introduced a large number of
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additional variables to the least squares procedure, the anions were refined fully anisotropically which improved the fit to the data in a statistically significant manner. Fig. 3 illustrates the final fit to the room temperature data, and the refined structural parameters for the perovskite phases are listed in Table 1. For comparison of the phase with Cmcm space group, we report structural parameters derived from fitting data collected in the centre of its stability field (778 K). We believe any mis-fitting that remains could be due to diffuse scattering from stacking faulting, which has previously been observed in NaNbO3 in phase P [27], and for which the refinement software is not capable of handling. Alternatively, and perhaps more plausibly, it could be related to some other form of microstructural defect arising at the interfaces between the presumably quasi-epitaxially related crystallites of the two different crystal structures. Bond lengths within the two phases, and calculated bond valence parameters for the cations [28] are reported in Tables 2 and 3; the crystal structures are shown in Fig. 4. Bond lengths and bond valencies for both cations in both structures have acceptable values, and the atomic displacement parameters for atoms in the Pbnm-structured phase are sensible. The polyhedral volumes in the Pbnm phase show evidence for ~37% free volume, significantly larger than that found in the coexisting Cmcm phase, ~9%. The volume per formula unit for the Cmcm phase is ~0.01 Å3 greater than that of the Pbnm phase, and this excess volume persists up to the phase transition temperature as shown in Fig. 5. This suggests that the application of pressure at the transition temperature may reduce the degree of hysteresis that has been observed. Consideration of Table 1 indicates the most significant difference between the Cmcm structure within its phase field, with that 460 K below the nominal phase boundary, lies with the magnitude of the atomic displacement parameters of the octahedral unit. At room temperature these are on average a factor of 2e3 greater than those determined at 778 K and presumably represent significant static disorder rather than normal thermal displacements, which are probably represented by the equivalent parameters from the Pbnm-structured phase. However, in the absence of an atomic resolution study of the microstructure of the interfacial defects
between the two phases, and a more detailed high temperature crystallographic study of the phase coexistence region, we cannot be certain that the atomic displacement parameters of the Pbnm phase are entirely representative of thermal motion. The marked difference in the atomic displacement parameters of the equivalent atoms in the coexisting phases explains the failure of the refinement procedure when these parameters were constrained to be equal, recalling that since neutrons are point scatters, they are sensitive to atomic displacement. Analysis of the two crystal structures in terms of the magnitudes of the symmetry-adapted basis vectors of the aristotype phase [5,29,30] shows that those associated with the octahedral tilts have almost identical ampliþ tudes: Rþ 4 ,Cmcm: 0.230 Å Pbnm: 0.245 Å, and M3 ,Cmcm: 0.283 Å Pbnm: 0.266 Å. The sequence of phase transitions in NaTaO3 ðPbnm/Cmcm/P4=mbm/Pm3mÞ, in comparison with those exhibited by SrZrO3 (and most other SrBIVO3 compounds) ðPbnm/Imma/I4=mcm/Pm3mÞ, has been discussed in the most recent review of mode decomposition techniques for analysing hettotype structures of higher symmetry phases [5]. In the former sequence, the first transition occurs when the vector associated with the Rþ 4 mode changes direction, whilst in the latter sequence, the vector associated with the Mþ 3 distortion vanishes at the phase transition temperature. The similarity of the order parameter amplitudes in the coexisting phases of NaTaO3 is possible evidence for the free energy being close to isotropic with respect to the direction of the Rþ 4 distortion. Whilst this observation provides a basis for the phase coexistence, it does not, however, give an explanation for the large degree of hysteresis observed at the Cmcm e Pbnm phase transition in NaTaO3, which is probably a result of kinetic hindering. A detailed crystallographic analysis of the HRPD data within the observed coexistence range is unfortunately not possible, as most data were collected with short data collection times for a parametric study of the structural phase transitions, and not for full structure refinement. However it was possible to follow the evolution of the phase fractions of the two perovskite-structured components by free, unconstrained refinement. In this analysis, the presence of the impurity phase Na2Ta4O11, rather than a nuisance, should permit confidence in the final results if it occurs as a constant weight fraction irrespective of the nature of the NaTaO3
Fig. 3. The final Rietveld fit to the SigmaeAldrich NaTaO3 sample. Observed data, dots, calculated pattern, full line. The difference pattern, observed e calculated is shown below the reflection tick markers which are in the order Na2Ta4O11 (top), NaTaO3 Cmcm (middle), and NaTaO3 Pbnm (bottom).
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Table 1 Crystallographic parameters for the coexisting two phases of NaTaO3 at room temperature and the Cmcm phase at 778 K. Structural parameters Lattice Parameters/Å
a b c
Unit cell volume/Å3 Na1
x y z 100uiso/Å2 x y z 100uiso/Å2 x y z 100uiso/Å2 x y z 100u11/Å2 100u22/Å2 100u33/Å2 100u12/Å2 100ueq/Å2 x y z 100u11/Å2 100u22/Å2 100u33/Å2 100u12/Å2 100u13/Å2 100u23/Å2/ 100ueq/Å2 x y z 100u11/Å2 100u22/Å2 100u33/Å2 100u23/Å2 100ueq/Å2
Na2
Ta
O1
O2
O3
Pbnm
Cmcm
Cmcm (778 K)
5.47832(3) 5.52269(4) 7.79159(5) 235.735(2) 0.0041(3) 0.5177(4) 0.25 1.66(4)
7.77927(8) 7.7815(2) 7.7899(1) 471.559(8) 0.0 0.011(3) 0.25 7.0(4) 0.0 0.490(3) 0.25 6.4(3) 0.25 0.25 0.0 5.72(8) 0.2861(6) 0.2518(11) 0.25 3.4(2) 11.6(8) 6.3(4) 0.1(6) 7.1(9) 0.2866(6) 0.0 0.0 2.2(2) 11.0(6) 12.0(7) 0.0 0.0 0.3(4) 8(1.0) 0.0 0.2139(8) 0.0228(8) 0.3(2) 15.5(9) 7.2(5) 3.3(4) 8(1)
7.83216(3) 7.8463(1) 7.8526(1) 482.573(3) 0.0 0.004(2) 0.25 4.9(2) 0.0 0.493(2) 0.25 4.1(2) 0.25 0.25 0.0 1.33(2) 0.2725(3) 0.2513(7) 0.25 3.0(2) 5.2(3) 1.9(1) 0.8(2) 3.4(4) 0.2775(4) 0.0 0.0 3.0(2) 0.6(1) 6.7(3) 0.0 0.0 0.3(2) 3.4(4) 0.0 0.2256(4) 0.0213(4) 1.35(8) 4.4(2) 2.9(2) 0.6(1) 2.9(3)
0.0 0.0 0.0 0.48(2) 0.0628(2) 0.0092(2) 0.25 0.78(5) 1.12(6) 0.51(6) 0.14(5) 0.8(1) 0.2152(1) 0.2836(1) 0.0316(1) 0.95(3) 0.82(3) 1.47(4) 0.44(4) 0.13(3) 0.21(3) 1.08(6)
Pbnm. Na, O1: 4c x, y, 1/4; Ta: 4a 0, 0, 0; O2 8d x, y, z. Cmcm. Na1/2: 4c 0, y, 1/4; Ta: 8d 1/4, 1/4, 0; O1: 8g x, y, 1/4; O2: 8e x, 0, 0; O3: 8f 0, y, z. Ambient temperature refinement: Rp ¼ 0.047, Rwp ¼ 0.058, c2 ¼ 8.0 for 81 variables.
Table 2 Selected bond lengths and bond valence sums for the cations in NaTaO3 with space group Pbnm at room temperature. Cation Na
Bond Valence Sum/v.u. NaO8 Polyhedral Volume/Å3 Ta
Bond Valence Sum/v.u. TaO6 Octahedral Volume/Å3
Anion i
O1 O1ii O2 (2) O2i (2) O2ii (2)
O1 (2) O2 (2) O2iii (2)
Table 3 Selected bond lengths and bond valence sums for the cations in NaTaO3 with space group Cmcm at room temperature.
Bond length/Å
Cation
Anion
Bond length/Å
2.639(3) 2.422(2) 2.430(3) 2.723(2) 2.732(1) 0.99 27.01(2) 1.9787(2) 1.9757(7) 1.9807(7) 5.12 10.324(1)
Na1
O1 (2) O1i (2) O2 (4) O3 (2) O3i (2)
2.91(2) 2.61(2) 2.962(4) 2.37(2) 2.75(2) 1.08 50.3(3) 2.90(2) 2.63(2) 2.560(3) 2.78(2) 0.98 39.2(3) 1.9677(6) 1.9661(7) 1.973(1) 5.26 10.16(4)
O1i: x, 1 þ y, z; O1i: x, 1 þ y, z; O1ii: 1/2 þ x, 1/2 þ y, z; O2i: 1/2 x, 1/2 þ y, z; O2ii: x, 1 y, 1/2 þ z; O2iii: x, y, z.
phase(s). Fig. 6 illustrates the weight fraction of the components of the sample from 298 K to 828 K i.e. from the coexistence region through the Cmcm phase field. The transition temperature is
Bond Valence Sum/v.u. NaO12 Polyhedral Volume/Å3 Na2
Bond Valence Sum/v.u. NaO10 Polyhedral Volume/Å3 Ta
Bond Valence Sum/v.u. TaO6 Octahedral Volume/Å3
O1 (2) O1ii (2) O2i (4) O3 (2)
O1 (2) O2 (2) O2 (2)
O1i: 1/2 x, 1/2 þ y, z; O1ii: 1/2 x, 1/2 þ y, z; O2i: 1/2 x, 1/2 þ y, z; O3i: x, y, 1/ 2 þ z.
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Fig. 6. The temperature variation of the weight fractions of the three phases present in the SigmaeAldrich NaTaO3 sample. The weight fraction of the Pbnm phase increases with decreasing temperature from the phase transition temperature (indicated by the vertical dashed line). The full black line shows an empirical fit to these data (described in the text) that suggests only 57% transformation will occur at liquid helium temperatures (4.2 K).
designated by the vertical dashed line. It can be seen that the weight fraction of Na2Ta4O11 is indeed constant at ~6 wt.% over the whole temperature interval, and that the weight fraction of the Cmcm phase increases monotonically with temperature towards the phase transition temperature. Fitting the weight fraction of the Pbnm phase to a simple expression of the form a(1 T/Tc)b (r2 ¼ 0.98866, a ¼ 0.5722(4), Tc ¼ 766(2) K, b ¼ 0.191(6)) suggests the weight fraction at 0 K is of the order of 57%, with hysteresis therefore extending over a temperature range of 758 K. 4. Conclusions Fig. 4. The crystal structures of NaTaO3 at room temperature. Space group Pbnm top, space group Cmcm bottom. Both diagrams indicate the anisotropic atomic displacement parameters at 50% probability. The magnitude of the atomic displacement parameters in the Cmcm phase most probably represents the high degree of structural disorder in this phase which is 460 K below its nominal phase stability temperature.
Fig. 5. The temperature dependence of the excess volume per formula unit of the Cmcm phase with respect to the Pbnm phase. The application of pressure at, and below the phase transition temperature, would be expected to reduce the phase fraction of the Cmcm phase.
Room temperature, high resolution, time-of-flight neutron powder diffraction data measured from two polycrystalline samples of NaTaO3, presumably synthesised under different conditions, show the presence of phase coexistence of two crystallographic phases in space groups Pbnm, and Cmcm. This result contradicts the current belief that the ambient temperature crystal structure of NaTaO3 crystallises in the space group Pbnm that has been deduced from medium resolution X-ray and neutron powder diffraction [10,18,19]. Single crystal structural analysis, carried out at room temperature using a Weissenberg camera on a crystal grown at 1523 K (i.e. cooled from the cubic phase field), only determined a single phase in the polar space group Pc21n [20]. However, the direct space resolution of the Weissenberg camera would be insufficient to separate the multiple twinning of the two phases if a similar degree of hysteresis was found to exist in single crystal specimens. It is probable that current laboratory CCD area detectors and software which allows interrogation of reciprocal space using reconstruction methods would make identifying the twinning much easier, but it would remain a challenging problem [31]. To solve this structural problem by single crystal methods would probably require the low beam divergence offered by synchrotron to extract the required detail in the diffraction pattern [31]. The phase coexistence represents an extreme case of hysteretical behaviour that has occurred when NaTaO3 is cooled from the temperature of synthesis through the first order phase transition at ~758 K. The differences observed between the commercially produced material and that synthesised at Sydney University is simply
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related to the weight fractions of the two phases, which are different in the two samples. The most probable physical difference between the two materials that could produce this effect is the cooling rate through the Cmcm e Pbnm phase transition. Further work is currently being undertaken to investigate the nature of the kinetics that affect/hinder this phase transition. The nature of the microstructure and interfacial defects of the coexisting phases of NaTaO3 would make a timely electron microscopy study. Acknowledgements KSK is grateful to the technicians of the ISIS Sample Environment Group for support during the original high temperature investigation and to Dr David Allan (Diamond Light Source) for his views on the single crystal experiment. Prof. Manuel Perez-Mato (Universidad del Pais Vasco) is thanked for discussions of the likely cause of the phase coexistence. KSK would like to acknowledge the many years of friendship and fruitful collaboration he had had with the late Nick (Charles Nicholas Wright) Darlington (1945e2013), especially during the original experiments carried out on NaTaO3. The work at the University of Sydney was supported by the Australian Research Council. References [1] M.A. Carpenter, E.K.H. Salje, A. Graeme-Barber, Eur. J. Mineral. 10 (1998) 621e691.
[2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31]
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R.A. Cowley, Phys. Rev. 134 (1964) A981eA997. A.M. Glazer, Acta Crystallogr. B28 (1972) 3384e3392. C.J. Howard, H.T. Stokes, Acta Crystallogr. B54 (1998) 782e789. J.M. Perez-Mato, D. Orobengoa, M.I. Aroyo, Acta Crystallogr. A66 (2010) 558e590. H.D. Megaw, Ferroelectricity in Crystals, Methuen, London, 1957. B.T. Matthias, Phys. Rev. 75 (1949) 1771. L.E. Cross, Philos. Mag. A 1 (1956) 76e92. C.N.W. Darlington, K.S. Knight, Acta Crystallogr. B55 (1999) 24e30. B.J. Kennedy, A.K. Prodjosantoso, C.J. Howard, J. Phys. Condens. Matter 11 (1999) 6319e6327. W. Lin, C. Cheng, C. Hu, H. Teng, Appl. Phys. Lett. 89 (2006) 211904. H. Kato, A. Kudo, Chem. Phys. Lett. 295 (1998) 487e492. H. Kato, A. Kudo, J. Phys. Chem. B 105 (2001) 4285e4292. B. Modak, K. Srinivasu, S.K. Ghosh, Phys. Chem. Chem. Phys. 16 (2014) 17116e17124. H. Iwasaki, T. Ikeda, J. Phys. Soc. Jpn. 18 (1963) 157e163. jcik, Ferroelectrics 99 (1989) 105e113. A. Aleksandrowicz, K. Wo I.G. Ismailzade, Kristallografiya 7 (1962) 718e723. M. Ahtee, C.N.W. Darlington, Acta Crystallogr. B36 (1980) 1007e1014. P. Vousden, Acta Crystallogr. 4 (1951) 373e376. H.F. Kay, J.L. Miles, Acta Crystallogr. 10 (1957) 213e218. M. Ahtee, L. Unonius, Acta Crystallogr. A33 (1977) 150e154. s, R. Gautier, C.J. Pickard, R.I. Walton, Phys. Chem. S.E. Ashbrook, L. Le Polle Chem. Phys. 8 (2006) 3423e3431. P.W. Stephens, J. Appl. Crystallogr. 32 (1999) 281e289. A.M. Glazer, Acta Crystallogr. A31 (1975) 756e762. C.N.W. Darlington, Phys. Stat. Sol. b 76 (1976) 231e239. T. Ercit, F. Hawthorne, P. Cerny, Bull. Mineral. 108 (1985) 541e542. C.N.W. Darlington, Ferroelectrics 3 (1971) 9e15. I.D. Brown, D. Altermatt, Acta Crystallogr. B41 (1985) 244e247. K.S. Knight, Can. Mineral. 47 (2009) 381e400. K.S. Knight, Can. Mineral. 49 (2011) 793e808. D.R. Allan, Personal communication.
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Phase coexistence in NaTaO3 at room temperature; a high resolution neutron powder diffraction study Kevin S. Knight a, b, *, Brendan J. Kennedy c a
ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxon OX11 0QX, UK Department of Earth Sciences, The Natural History Museum, Cromwell Road, London SW7 5BD, UK c School of Chemistry, The University of Sydney, Sydney, New South Wales 2006, Australia b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 January 2015 Received in revised form 5 March 2015 Accepted 18 March 2015 Available online 19 March 2015
Room temperature high resolution neutron powder diffraction data, measured in time-of-flight, from two independent samples of NaTaO3 shows the presence of phase coexistence of two orthorhombic structures with space groups Pbnm, and Cmcm. The failure of earlier work to recognise the extent of the hysteresis associated with the high temperature (~763 K on heating) Cmcm e Pbnm phase transition, that extends down to room temperature, and probably to 0 K, is due to data having been collected at too low a real-space resolution to characterise the diagnostic pseudocubic fundamental and superlattice reflection multiplicities. The phase fraction of the Cmcm phase increases with increasing temperature from 45 weight % at 298 K, to 74 weight % at 758 K. Throughout the whole temperature interval 298 Ke758 K, the volume per formula unit of the Cmcm phase exceeds that of the Pbnm phase by an almost constant ~0.01 Å3 suggesting the addition of pressure would supress the volume fraction of the higher temperature phase. The crystal structure of both phases, determined from data collected at 298 K, are reported, with the atomic displacement parameters of the Cmcm phase being significantly larger than those associated with the Pbnm phase, probably reflecting a high degree of thermal and static disorder. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: NaTaO3 Crystal structure Neutron diffraction Phase transitions
1. Introduction Identification of the correct unit cell metric and space group for hettotype phases of simple perovskite-structured compounds is problematic for two principal reasons. Firstly, the spontaneous strains that develop at zone-boundary phase transitions may be small [1], and hence it is necessary to collect data at the highest real-space resolution to permit analysis of the fundamental reflection multiplicities and separations. Secondly, the diagnostic superlattice reflections of the lower symmetry structures derive essentially from anion displacements [2], which in the case of oxide systems with heavy atoms in the dodecahedral and/or octahedral sites requires either sophisticated data collection strategies for Xray powder diffraction, or the use of neutron diffraction, where the scattering length of oxygen has a comparable magnitude to those of the cations. These zone-boundary phase transitions, frequently termed tilt
* Corresponding author. ISIS Facility, STFC Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxon OX11 0QX, UK. E-mail address: [email protected] (K.S. Knight). http://dx.doi.org/10.1016/j.solidstatesciences.2015.03.016 1293-2558/© 2015 Elsevier Masson SAS. All rights reserved.
transitions in perovskite-structured phases, are a commonly observed phenomenon and occur when the crystal becomes unstable to a set of normal mode of vibrations of the aristotype phase [2]. For non-ferroelectric perovskite-structured compounds, without cation ordering of the dodecahedral and octahedral sites, these modes transform as basis vectors of either/or both the irreþ ducible representations Rþ 4 and M3 [2e5]. In the former case, successive layers of octahedra rotate in the opposite sense (equivalent to an anti-phase rotation [4]), in the latter, successive layers of octahedra rotate in the same sense (equivalent to an in-phase rotation [4]). Superlattice reflections associated with these soft mode condensations are therefore observed in the diffraction patterns of hettotype phases at the R and/or M points of the pseudocubic Brillouin zone. Based on the earlier ideas of Megaw [6], Glazer used model building methods to systematize the permitted lattice metrics and space groups of perovskite-structures that exhibit these zone-boundary phase transitions [4]. More recently, these deductions have been reinvestigated and corrected using formal group theoretical techniques [3,5]. Perovskite-structured NaTaO3 has been the subject of a number of studies, initially as a potentially ferroelectric material [7,8], as a
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model compound to study zone-boundary phase transitions [9,10], and latterly, as a photocatalyst for splitting water molecules as a clean and renewable source of hydrogen [11e14]. An early experimental determination of the dielectric constant suggested NaTaO3 was ferroelectric with a Curie temperature of 748 K [7], however subsequent investigations found no evidence for ferroelectric behaviour [8,15]. Temperature-dependent optical birefringence studies showed the presence of 3 structural phase transitions, cubic e tetragonal at 903 K, tetragonal e orthorhombic at 853 K (indicatrix parallel to the cubic <100> ie pseudocubic orientation), and orthorhombic e orthorhombic at 753 K (one principal axis parallel to cubic <100> ie rhombic orientation) [8]. These transition temperatures were later confirmed by DTA [16] and neutron powder diffraction [17,18]. The earliest report of crystallographic analysis of NaTaO3 used Xray powder diffraction techniques and reported a unit cell √2a a √2a, where a is the lattice parameter of the aristotype phase [19]. A subsequent single crystal X-ray diffraction study determined the space group as polar Pc21n, in accord with the believed ferroelectric nature of the phase at the time, and observed a doubling of the unit cell b axis (√2a 2a √2a) [20]. The ambient temperature and pressure phase was later studied by Xray powder diffraction [21] and a crystal structure was refined in the centrosymmetric space group Pcmn (an alternate setting of Space Group (S.G.) No. 62), in keeping with the experimentally determined non-ferroelectric behaviour [8,15]. This structure was subsequently refined to higher precision in the anion coordinates using medium resolution neutron powder diffraction, and the two high temperature hettotype phases were identified, and their crystal structures reported in space groups Bmmb (an alternate setting of S.G. No. 63) (803 K) and P4/mbm (S.G. No. 127) (893 K) [18]. More recently, two contemporaneous studies of the temperature dependent structural crystallography of NaTaO3 have been made with the aim of using it as a model system for studying zone boundary phase transitions in perovskite-structured phases [9,10]. Both studies utilised the advantages of neutron powder diffraction over X-ray powder diffraction but were carried out at significantly different real-space resolutions. The lower resolution investigation [10] carried out using the HB-4 diffractometer at the High Flux Isotope Reactor of the Oak Ridge National Laboratory, was in full agreement with the earlier investigation made on the D1a diffractometer at the Institut Laue-Langevin [18]. The higher resolution study carried out using the time-of-flight diffractometer HRPD on the ISIS spallation neutron source was in agreement with both studies at temperatures higher than the Pcmn e Bmmb phase transition temperature ~758 K, but not below [9]. Unfortunately no details of the discrepancy between the expected data from a perovskite structure in space group Pcmn (or any equivalent setting of S.G. No. 62) and that experimentally observed were given in the paper [9]. Further evidence for a possible inconsistency between the crystal structures derived from the medium resolution neutron diffraction studies and correct crystal structure at room temperature has been afforded by 23Na multiple-quantum magic-angle spinning (MQMAS) NMR [22]. Small discrepancies were observed between the experimentally observed MQMAS and MAS spectra and those calculated using the accepted room temperature crystal structure. In this submission we report a re-evaluation of the original HRPD data [9] and furthermore, compare them with a data set collected on a sample of identical synthesis as that used in the HB-4 study. 2. Experimental section The principal sources of the data that have been re-analysed for
this manuscript have already been described in detail [9], and we cis the methodology below. High resolution time-ofsimply pre flight (TOF) neutron powder diffraction data were collected on a sample of commercial NaTaO3 (SigmaeAldrich, 99.9þ% purity) in the TOF window 30e130 ms, at room temperature, and at 83 temperatures between 373 K and 1003 K. An additional TOF window, 100e200 ms, was also collected under ambient conditions to monitor the longer d-spacing reflections. The raw data were reduced as described previously to produce data sets in the TOF range 32e120 ms (~0.64e2.4 Å) and a single data set 102e190 ms (~2.04e3.8 Å) for profile refinement using the GSAS suite of programs. The intrinsic resolution of the instrument is to first order independent of Q (4psin(q)/l), with Dd/d ¼ 4 104. An instrument parameter file for the GSAS lineshape 4 which is suitable for use with the hkl-dependent line broadening functions of Stephens [23] was derived by fitting data collected on the NIST standard silicon powder SRM640b (data collected ~6 weeks after the NaTaO3 experiment). For comparison purposes, a second sample of NaTaO3 was also measured at room temperature in the short (30e130 ms) TOF window. This sample, synthesised in the Chemistry Department, Sydney University, was prepared in an identical manner to that described in the high-temperature crystallographic study that used the medium resolution neutron powder diffractometer HB-4 [10]. 3. Results and discussion 3.1. Crystallographic background The results of the group theoretical analysis of the permitted space groups for simple perovskite-structured compounds [4] reduces structural characterisation to a two-step process [24]. Firstly, the tilt class is identified by the presence of diagnostic superlattice reflections on the surface of the pseudocubic Brillouin zone. These can be summarised as follows: superlattice reflections at the R point alone e antiephase tilting; superlattice reflections at the M point alone e in-phase tilting; the presence of R and M point superlattice reflections e both anti-phase and in-phase tilting (Note in the case of both tilt systems being present, then superlattice reflections at the X point of the pseudocubic Brillouin zone are also observed [25]). The second step of the process requires determination of the pseudocubic lattice metric from an investigation of the multiplicities of the fundamental pseudocubic Bragg reflections, and it is in this process that high direct space resolution is a prerequisite. Taking the previously accepted sequence of phase transitions in NaTaO3 for granted [18], and using space group settings of the two lowest temperature phases as Pbnm (S.G. No. 62), and Cmcm (S.G. No. 63), we expect to observe superlattice reflections at the R, M, and X points of the pseudocubic Brillouin zone from group theoretical arguments [4] (Pbnm: aacþ; Cmcm: a0bcþ in Glazer notation [3]). The pseudocubic metric (subscript p) is related to the crystallographic unit cells by the matrix ½ ½ 0/½ ½ 0/0 0 ½ for space group Pbnm (ap ¼ bp s cp, ap ¼ bp ¼ 90 gp s 90 ), and ½ 0 0/0 ½ 0/0 0 ½ for space group Cmcm (ap s bp s cp, ap ¼ bp ¼ gp ¼ 90 ). The pseudocubic fundamental reflection 111 would therefore be expected to be a singlet in Cmcm (index 2 2 2 in the true orthorhombic unit cell) but a doublet in Pbnm due to the monoclinic subcell metric (indices 0 2 2, 2 0 2 in the true orthorhombic unit cell). 3.2. Analysis of room temperature data The data collected at room temperature from both HRPD and HB-4 only indicate superlattice reflections on the surface of the pseudocubic Brillouin zone (R, M, X points) and hence the
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permitted space groups are either Cmcm, Pbnm (Pnma), P 1 1 21/m (P21/m), or P42/nmc [4]. In order, the Glazer notation and pseudocubic subcells are: a0bcþ, ap s bp s cp, ap ¼ bp ¼ gp ¼ 90 ; aacþ, ap ¼ bp s cp, ap ¼ bp ¼ 90 gp s 90 ; abcþ, ap s bp s cp, ap ¼ bp ¼ 90 gp s 90 ; aþaþc, ap ¼ bp s cp ap ¼ bp ¼ gp ¼ 90 . Fig. 1 illustrates a diagnostic part of the time-of-flight diffraction pattern of NaTaO3 (SigmaeAldrich) collected at room temperature, and containing one fundamental reflection at ~2.25 Å, and two superlattice reflections at ~2.35 Å (R point) and ~2.46 Å (M point). The splitting of the pseudocubic fundamental 111 reflection at d ~2.25 Å into a partially resolved triplet is inconsistent with any of the four space groups outlined above, and clearly illustrates that the accepted space group and crystal structure of NaTaO3 at room temperature being orthorhombic, space group Pbnm [10,18,21] is incorrect. The observation that the splitting of the fundamental and superlattice reflections are inconsistent with a single phase exhibiting both in-phase, and anti-phase tilting [4] requires careful re-evaluation of the diffraction data, in-line with the known behaviour at temperatures greater than 758 K. The accepted phase transition Cmcm e Pbnm is required to be first order [4] which is most easily appreciated by noting the anti-phase tilt has to discontinuously change from pseudocubic [110] to [010]. As phase coexistence is an expected consequence of first order phase transitions, the simplest explanation of the triplet of reflections observed at ~2.25 Å at room temperature is the coexistence of a Pbnm phase, which contributes two reflections to the multiplet, with a Cmcm phase, which contributes a single reflection. Fig. 2 illustrates the same region of the diffraction pattern using data collected from a sample synthesised at Sydney University. Again a triplet is observed, although the relative intensities are clearly different to that seen in Fig. 1. We return to this difference in the Conclusions section of this paper. Superimposed on this plot are calculated normalised peak profiles for a Bragg peak at 2.5 Å based on the resolution functions of HRPD, full black line, D1a (l ¼ 1.911 Å [18]) dashed line, and HB4 (l ¼ 1.5 Å [10]) dot-dash line. The full widths at half maximum intensity of the two reactor-based diffractometer profiles exceeds that of the individual
Fig. 1. A diagnostic part of the time-of-flight neutron powder diffraction pattern of commercially produced (SigmaeAldrich) NaTaO3. Reflections are indexed on the pseudocubic subcell and show the 111 fundamental reflection (marked F) and two superlattice reflections at the R, and M points of the pseudocubic Brilluoin zone. The splitting of the 111 reflection into a triplet proves that at room temperature, the material is polyphasic, and not a single phase, space group Pbnm, as previously described. Tick marks indicating the Bragg reflections from the Pbnm phase (lower), and the Cmcm phase (upper) are shown below the data.
17
Fig. 2. The fundamental pseudocubic reflection 111 as measured (circles) using high resolution time-of-flight neutron powder diffraction (HRPD) from the sample of NaTaO3 synthesised at the Department of Chemistry, Sydney University. Superimposed are the resolution functions of HRPD (full line), D1a (dashed line) and HB4 (dot-dash line). The full widths at half maximum intensity of D1a and HB4 exceed the width of the triplet indicating why the phase coexistence had not been identified in previous studies.
experimental Bragg peaks by a factor of ~4, and hence it is clear that these instruments, that were employed in the earlier studies, have insufficient direct space resolution to observe the subtle line splitting that occurs between the two phases in the room temperature diffraction pattern of NaTaO3. 3.3. Crystal structure and refinement A model for the structural state of NaTaO3 at room temperature was generated from the ambient temperature crystal structure in space group Pbnm derived from fitting the HB4 data [10] with a crystal structure in space group Cmcm derived from fitting the HRPD data [9]. Room temperature unit cell parameters for the Cmcm phase were determined by extrapolation from the high temperature results published earlier [9]. The room temperature data collected on the commercial sample was of a significantly higher statistical quality than that collected for the sample synthesised at Sydney University, and hence detailed Rietveld analysis was only carried out for data from the commercial sample. The impurity phase Na2Ta4O11 [9,26] that was observed in these data was added as a third phase in the Rietveld refinement. Considering that the intrinsic diffraction patterns of both perovskite-structured phases are in themselves strongly pseudosymmetric, and furthermore, the general problem of distinguishing the correct space group in compounds where there is an ambiguity between space groups Pbnm, and Cmcm, it is hardly surprising that a stable refinement was initially difficult to achieve. Attempts to link atomic displacement parameters between the three chemically distinct elements of the two perovskite-structured phases were unsuccessful, as was any attempt to relate the lineshape parameters to simplify the fitting procedure. Fixing the structural models and allowing free refinement of the unit cells and lineshape using the Lebail method were also ineffective; however these results strongly suggested that both phases exhibited a degree of hkl-dependent line broadening. Successful refinement of the model against the data was only achieved by fixing the lineshape parameters of the two perovskite-structured phases at instrumental resolution, and then allowing the Stephens broadening parameters [23] to fit the peak profile correctly. Although they introduced a large number of
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additional variables to the least squares procedure, the anions were refined fully anisotropically which improved the fit to the data in a statistically significant manner. Fig. 3 illustrates the final fit to the room temperature data, and the refined structural parameters for the perovskite phases are listed in Table 1. For comparison of the phase with Cmcm space group, we report structural parameters derived from fitting data collected in the centre of its stability field (778 K). We believe any mis-fitting that remains could be due to diffuse scattering from stacking faulting, which has previously been observed in NaNbO3 in phase P [27], and for which the refinement software is not capable of handling. Alternatively, and perhaps more plausibly, it could be related to some other form of microstructural defect arising at the interfaces between the presumably quasi-epitaxially related crystallites of the two different crystal structures. Bond lengths within the two phases, and calculated bond valence parameters for the cations [28] are reported in Tables 2 and 3; the crystal structures are shown in Fig. 4. Bond lengths and bond valencies for both cations in both structures have acceptable values, and the atomic displacement parameters for atoms in the Pbnm-structured phase are sensible. The polyhedral volumes in the Pbnm phase show evidence for ~37% free volume, significantly larger than that found in the coexisting Cmcm phase, ~9%. The volume per formula unit for the Cmcm phase is ~0.01 Å3 greater than that of the Pbnm phase, and this excess volume persists up to the phase transition temperature as shown in Fig. 5. This suggests that the application of pressure at the transition temperature may reduce the degree of hysteresis that has been observed. Consideration of Table 1 indicates the most significant difference between the Cmcm structure within its phase field, with that 460 K below the nominal phase boundary, lies with the magnitude of the atomic displacement parameters of the octahedral unit. At room temperature these are on average a factor of 2e3 greater than those determined at 778 K and presumably represent significant static disorder rather than normal thermal displacements, which are probably represented by the equivalent parameters from the Pbnm-structured phase. However, in the absence of an atomic resolution study of the microstructure of the interfacial defects
between the two phases, and a more detailed high temperature crystallographic study of the phase coexistence region, we cannot be certain that the atomic displacement parameters of the Pbnm phase are entirely representative of thermal motion. The marked difference in the atomic displacement parameters of the equivalent atoms in the coexisting phases explains the failure of the refinement procedure when these parameters were constrained to be equal, recalling that since neutrons are point scatters, they are sensitive to atomic displacement. Analysis of the two crystal structures in terms of the magnitudes of the symmetry-adapted basis vectors of the aristotype phase [5,29,30] shows that those associated with the octahedral tilts have almost identical ampliþ tudes: Rþ 4 ,Cmcm: 0.230 Å Pbnm: 0.245 Å, and M3 ,Cmcm: 0.283 Å Pbnm: 0.266 Å. The sequence of phase transitions in NaTaO3 ðPbnm/Cmcm/P4=mbm/Pm3mÞ, in comparison with those exhibited by SrZrO3 (and most other SrBIVO3 compounds) ðPbnm/Imma/I4=mcm/Pm3mÞ, has been discussed in the most recent review of mode decomposition techniques for analysing hettotype structures of higher symmetry phases [5]. In the former sequence, the first transition occurs when the vector associated with the Rþ 4 mode changes direction, whilst in the latter sequence, the vector associated with the Mþ 3 distortion vanishes at the phase transition temperature. The similarity of the order parameter amplitudes in the coexisting phases of NaTaO3 is possible evidence for the free energy being close to isotropic with respect to the direction of the Rþ 4 distortion. Whilst this observation provides a basis for the phase coexistence, it does not, however, give an explanation for the large degree of hysteresis observed at the Cmcm e Pbnm phase transition in NaTaO3, which is probably a result of kinetic hindering. A detailed crystallographic analysis of the HRPD data within the observed coexistence range is unfortunately not possible, as most data were collected with short data collection times for a parametric study of the structural phase transitions, and not for full structure refinement. However it was possible to follow the evolution of the phase fractions of the two perovskite-structured components by free, unconstrained refinement. In this analysis, the presence of the impurity phase Na2Ta4O11, rather than a nuisance, should permit confidence in the final results if it occurs as a constant weight fraction irrespective of the nature of the NaTaO3
Fig. 3. The final Rietveld fit to the SigmaeAldrich NaTaO3 sample. Observed data, dots, calculated pattern, full line. The difference pattern, observed e calculated is shown below the reflection tick markers which are in the order Na2Ta4O11 (top), NaTaO3 Cmcm (middle), and NaTaO3 Pbnm (bottom).
K.S. Knight, B.J. Kennedy / Solid State Sciences 43 (2015) 15e21
19
Table 1 Crystallographic parameters for the coexisting two phases of NaTaO3 at room temperature and the Cmcm phase at 778 K. Structural parameters Lattice Parameters/Å
a b c
Unit cell volume/Å3 Na1
x y z 100uiso/Å2 x y z 100uiso/Å2 x y z 100uiso/Å2 x y z 100u11/Å2 100u22/Å2 100u33/Å2 100u12/Å2 100ueq/Å2 x y z 100u11/Å2 100u22/Å2 100u33/Å2 100u12/Å2 100u13/Å2 100u23/Å2/ 100ueq/Å2 x y z 100u11/Å2 100u22/Å2 100u33/Å2 100u23/Å2 100ueq/Å2
Na2
Ta
O1
O2
O3
Pbnm
Cmcm
Cmcm (778 K)
5.47832(3) 5.52269(4) 7.79159(5) 235.735(2) 0.0041(3) 0.5177(4) 0.25 1.66(4)
7.77927(8) 7.7815(2) 7.7899(1) 471.559(8) 0.0 0.011(3) 0.25 7.0(4) 0.0 0.490(3) 0.25 6.4(3) 0.25 0.25 0.0 5.72(8) 0.2861(6) 0.2518(11) 0.25 3.4(2) 11.6(8) 6.3(4) 0.1(6) 7.1(9) 0.2866(6) 0.0 0.0 2.2(2) 11.0(6) 12.0(7) 0.0 0.0 0.3(4) 8(1.0) 0.0 0.2139(8) 0.0228(8) 0.3(2) 15.5(9) 7.2(5) 3.3(4) 8(1)
7.83216(3) 7.8463(1) 7.8526(1) 482.573(3) 0.0 0.004(2) 0.25 4.9(2) 0.0 0.493(2) 0.25 4.1(2) 0.25 0.25 0.0 1.33(2) 0.2725(3) 0.2513(7) 0.25 3.0(2) 5.2(3) 1.9(1) 0.8(2) 3.4(4) 0.2775(4) 0.0 0.0 3.0(2) 0.6(1) 6.7(3) 0.0 0.0 0.3(2) 3.4(4) 0.0 0.2256(4) 0.0213(4) 1.35(8) 4.4(2) 2.9(2) 0.6(1) 2.9(3)
0.0 0.0 0.0 0.48(2) 0.0628(2) 0.0092(2) 0.25 0.78(5) 1.12(6) 0.51(6) 0.14(5) 0.8(1) 0.2152(1) 0.2836(1) 0.0316(1) 0.95(3) 0.82(3) 1.47(4) 0.44(4) 0.13(3) 0.21(3) 1.08(6)
Pbnm. Na, O1: 4c x, y, 1/4; Ta: 4a 0, 0, 0; O2 8d x, y, z. Cmcm. Na1/2: 4c 0, y, 1/4; Ta: 8d 1/4, 1/4, 0; O1: 8g x, y, 1/4; O2: 8e x, 0, 0; O3: 8f 0, y, z. Ambient temperature refinement: Rp ¼ 0.047, Rwp ¼ 0.058, c2 ¼ 8.0 for 81 variables.
Table 2 Selected bond lengths and bond valence sums for the cations in NaTaO3 with space group Pbnm at room temperature. Cation Na
Bond Valence Sum/v.u. NaO8 Polyhedral Volume/Å3 Ta
Bond Valence Sum/v.u. TaO6 Octahedral Volume/Å3
Anion i
O1 O1ii O2 (2) O2i (2) O2ii (2)
O1 (2) O2 (2) O2iii (2)
Table 3 Selected bond lengths and bond valence sums for the cations in NaTaO3 with space group Cmcm at room temperature.
Bond length/Å
Cation
Anion
Bond length/Å
2.639(3) 2.422(2) 2.430(3) 2.723(2) 2.732(1) 0.99 27.01(2) 1.9787(2) 1.9757(7) 1.9807(7) 5.12 10.324(1)
Na1
O1 (2) O1i (2) O2 (4) O3 (2) O3i (2)
2.91(2) 2.61(2) 2.962(4) 2.37(2) 2.75(2) 1.08 50.3(3) 2.90(2) 2.63(2) 2.560(3) 2.78(2) 0.98 39.2(3) 1.9677(6) 1.9661(7) 1.973(1) 5.26 10.16(4)
O1i: x, 1 þ y, z; O1i: x, 1 þ y, z; O1ii: 1/2 þ x, 1/2 þ y, z; O2i: 1/2 x, 1/2 þ y, z; O2ii: x, 1 y, 1/2 þ z; O2iii: x, y, z.
phase(s). Fig. 6 illustrates the weight fraction of the components of the sample from 298 K to 828 K i.e. from the coexistence region through the Cmcm phase field. The transition temperature is
Bond Valence Sum/v.u. NaO12 Polyhedral Volume/Å3 Na2
Bond Valence Sum/v.u. NaO10 Polyhedral Volume/Å3 Ta
Bond Valence Sum/v.u. TaO6 Octahedral Volume/Å3
O1 (2) O1ii (2) O2i (4) O3 (2)
O1 (2) O2 (2) O2 (2)
O1i: 1/2 x, 1/2 þ y, z; O1ii: 1/2 x, 1/2 þ y, z; O2i: 1/2 x, 1/2 þ y, z; O3i: x, y, 1/ 2 þ z.
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Fig. 6. The temperature variation of the weight fractions of the three phases present in the SigmaeAldrich NaTaO3 sample. The weight fraction of the Pbnm phase increases with decreasing temperature from the phase transition temperature (indicated by the vertical dashed line). The full black line shows an empirical fit to these data (described in the text) that suggests only 57% transformation will occur at liquid helium temperatures (4.2 K).
designated by the vertical dashed line. It can be seen that the weight fraction of Na2Ta4O11 is indeed constant at ~6 wt.% over the whole temperature interval, and that the weight fraction of the Cmcm phase increases monotonically with temperature towards the phase transition temperature. Fitting the weight fraction of the Pbnm phase to a simple expression of the form a(1 T/Tc)b (r2 ¼ 0.98866, a ¼ 0.5722(4), Tc ¼ 766(2) K, b ¼ 0.191(6)) suggests the weight fraction at 0 K is of the order of 57%, with hysteresis therefore extending over a temperature range of 758 K. 4. Conclusions Fig. 4. The crystal structures of NaTaO3 at room temperature. Space group Pbnm top, space group Cmcm bottom. Both diagrams indicate the anisotropic atomic displacement parameters at 50% probability. The magnitude of the atomic displacement parameters in the Cmcm phase most probably represents the high degree of structural disorder in this phase which is 460 K below its nominal phase stability temperature.
Fig. 5. The temperature dependence of the excess volume per formula unit of the Cmcm phase with respect to the Pbnm phase. The application of pressure at, and below the phase transition temperature, would be expected to reduce the phase fraction of the Cmcm phase.
Room temperature, high resolution, time-of-flight neutron powder diffraction data measured from two polycrystalline samples of NaTaO3, presumably synthesised under different conditions, show the presence of phase coexistence of two crystallographic phases in space groups Pbnm, and Cmcm. This result contradicts the current belief that the ambient temperature crystal structure of NaTaO3 crystallises in the space group Pbnm that has been deduced from medium resolution X-ray and neutron powder diffraction [10,18,19]. Single crystal structural analysis, carried out at room temperature using a Weissenberg camera on a crystal grown at 1523 K (i.e. cooled from the cubic phase field), only determined a single phase in the polar space group Pc21n [20]. However, the direct space resolution of the Weissenberg camera would be insufficient to separate the multiple twinning of the two phases if a similar degree of hysteresis was found to exist in single crystal specimens. It is probable that current laboratory CCD area detectors and software which allows interrogation of reciprocal space using reconstruction methods would make identifying the twinning much easier, but it would remain a challenging problem [31]. To solve this structural problem by single crystal methods would probably require the low beam divergence offered by synchrotron to extract the required detail in the diffraction pattern [31]. The phase coexistence represents an extreme case of hysteretical behaviour that has occurred when NaTaO3 is cooled from the temperature of synthesis through the first order phase transition at ~758 K. The differences observed between the commercially produced material and that synthesised at Sydney University is simply
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related to the weight fractions of the two phases, which are different in the two samples. The most probable physical difference between the two materials that could produce this effect is the cooling rate through the Cmcm e Pbnm phase transition. Further work is currently being undertaken to investigate the nature of the kinetics that affect/hinder this phase transition. The nature of the microstructure and interfacial defects of the coexisting phases of NaTaO3 would make a timely electron microscopy study. Acknowledgements KSK is grateful to the technicians of the ISIS Sample Environment Group for support during the original high temperature investigation and to Dr David Allan (Diamond Light Source) for his views on the single crystal experiment. Prof. Manuel Perez-Mato (Universidad del Pais Vasco) is thanked for discussions of the likely cause of the phase coexistence. KSK would like to acknowledge the many years of friendship and fruitful collaboration he had had with the late Nick (Charles Nicholas Wright) Darlington (1945e2013), especially during the original experiments carried out on NaTaO3. The work at the University of Sydney was supported by the Australian Research Council. References [1] M.A. Carpenter, E.K.H. Salje, A. Graeme-Barber, Eur. J. Mineral. 10 (1998) 621e691.
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